├── .gitattributes ├── PBMR_Topology_Syllabus.pdf ├── PBMR_Algorithms_Syllabus.pdf ├── PBMR_Statistics_Syllabus.pdf ├── PBMR_GraphTheory_Syllabus.pdf ├── PBMR_LinearAlgebra_Syllabus.pdf ├── PBMR_MatrixAlgebra_Syllabus.pdf ├── PBMR_MeasureTheory_Syllabus.pdf ├── PBMR_Optimization_Syllabus.pdf ├── PBMR_RealAnalysis_Syllabus.pdf ├── PBMR_ProofTechniques_Syllabus.pdf ├── PBMR_BayesianStatistics_Syllabus.pdf ├── PBMR_LargeSampleTheory_Syllabus.pdf ├── source ├── figures │ ├── dependency_tree.png │ ├── proofbasedmathreadings_logo_square.gif │ └── proofbasedmathreadings_logo_square.png ├── render.sh ├── PBMR_NumericalLinearAlgebra_Syllabus.qmd ├── PBMR_MatrixAlgebra_Syllabus.qmd ├── PBMR_GraphTheory_Syllabus.qmd ├── PBMR_Optimization_Syllabus.qmd ├── PBMR_MeasureTheory_Syllabus.qmd ├── PBMR_ProofTechniques_Syllabus.qmd ├── PBMR_Algorithms_Syllabus.qmd ├── PBMR_MeasureTheoreticProbability_Syllabus.qmd ├── PBMR_LargeSampleTheory_Syllabus.qmd ├── PBMR_Topology_Syllabus.qmd ├── PBMR_BayesianStatistics_Syllabus.qmd ├── PBMR_RealAnalysis_Syllabus.qmd ├── PBMR_LinearAlgebra_Syllabus.qmd └── PBMR_Statistics_Syllabus.qmd ├── PBMR_NumericalLinearAlgebra_Syllabus.pdf ├── PBMR_MeasureTheoreticProbability_Syllabus.pdf ├── LICENSE ├── .github └── workflows │ └── build.yaml ├── README.md └── .gitignore /.gitattributes: -------------------------------------------------------------------------------- 1 | *.sh linguist-vendored -------------------------------------------------------------------------------- /PBMR_Topology_Syllabus.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/zekiakyol/proof-based-math-readings/HEAD/PBMR_Topology_Syllabus.pdf -------------------------------------------------------------------------------- /PBMR_Algorithms_Syllabus.pdf: -------------------------------------------------------------------------------- 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-------------------------------------------------------------------------------- https://raw.githubusercontent.com/zekiakyol/proof-based-math-readings/HEAD/source/figures/proofbasedmathreadings_logo_square.png -------------------------------------------------------------------------------- /source/render.sh: -------------------------------------------------------------------------------- 1 | #!/bin/bash 2 | 3 | MAGENTA=$(tput setaf 5) 4 | RESET=$(tput sgr0) 5 | 6 | printf "Please list the Quarto files you want to render. Type 'all' to render all Quarto files.\n Examples: \n\t ${MAGENTA}filename1.qmd \n\t filename1.qmd filename2.qmd \n\t all\n${RESET}" 7 | read quartofiles 8 | 9 | if [ "$quartofiles" == "all" ]; then 10 | quarto render *.qmd --to pdf 11 | else 12 | quarto render $quartofiles --to pdf 13 | fi 14 | 15 | mv *.pdf .. -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2023-2026 Zeki Akyol 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining 6 | a copy of this software and associated documentation files (the 7 | "Software"), to deal in the Software without restriction, including 8 | without limitation the rights to use, copy, modify, merge, publish, 9 | distribute, sublicense, and/or sell copies of the Software, and to 10 | permit persons to whom the Software is furnished to do so, subject to 11 | the following conditions: 12 | 13 | The above copyright notice and this permission notice shall be 14 | included in all copies or substantial portions of the Software. 15 | 16 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 17 | EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF 18 | MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 19 | NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE 20 | LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION 21 | OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION 22 | WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. -------------------------------------------------------------------------------- /.github/workflows/build.yaml: -------------------------------------------------------------------------------- 1 | name: Render Quarto files to PDF 2 | 3 | on: 4 | push: 5 | branches: main 6 | pull_request: 7 | branches: main 8 | 9 | jobs: 10 | build: 11 | runs-on: ubuntu-latest 12 | env: 13 | GITHUB_PAT: ${{ secrets.GITHUB_TOKEN }} 14 | steps: 15 | - name: Checkout repository 16 | uses: actions/checkout@v4 17 | 18 | - name: Setup pandoc 19 | uses: r-lib/actions/setup-pandoc@v2 20 | 21 | - name: Setup R 22 | uses: r-lib/actions/setup-r@v2 23 | with: 24 | r-version: '4.5.2' 25 | 26 | - name: Install R Dependencies 27 | uses: r-lib/actions/setup-r-dependencies@v2 28 | with: 29 | packages: 30 | any::rmarkdown 31 | any::tibble 32 | 33 | - name: Setup Quarto and TinyTeX 34 | uses: quarto-dev/quarto-actions/setup@v2 35 | with: 36 | version: 1.8.26 37 | tinytex: true 38 | 39 | - name: TEST Render Quarto files to PDF 40 | run: | 41 | printf "Listing all Quarto (.qmd) files:" 42 | find . -name "*.qmd" 43 | printf "" 44 | for file in $(find . -name "*.qmd"); do 45 | printf "Rendering $file to PDF" 46 | quarto render "$file" --to pdf || exit 1 47 | done 48 | 49 | - name: Install Poppler tools 50 | run: | 51 | sudo apt-get update 52 | sudo apt-get install -y poppler-utils 53 | 54 | - name: TEST PDF pages 55 | run: | 56 | for file in $(find . -type f -name "*.pdf"); do 57 | echo "Checking $file..." 58 | pages=$(pdfinfo "$file" | grep Pages | awk '{print $2}') 59 | if [ "$pages" -ne 3 ]; then 60 | echo "$file does not have exactly 3 pages! It has $pages pages." 61 | exit 1 62 | fi 63 | done 64 | echo "All PDF files have exactly 3 pages." -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | ## Proof-Based Math Readings 2 | 3 | - **Proof-Based Math Readings** is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 4 | - Please use the [:page_facing_up: Application Google Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 5 | 6 | 7 | 8 | 9 | 10 |
11 | 12 | ## Syllabuses 13 | 14 | :scroll: Syllabus | :closed_book: Book | :hourglass: Time 15 | :-- | :--: | :--: 16 | [Algorithms](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_Algorithms_Syllabus.pdf) | Introduction to Algorithms
- T. Cormen, C. Leiserson, R. Rivest, C. Stein (4th Edition, 2022) | 12 Weeks 17 | [Graph Theory](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_GraphTheory_Syllabus.pdf) | A First Course in Graph Theory
- Gary Chartrand, Ping Zhang (2012) | 12 Weeks 18 | [Optimization](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_Optimization_Syllabus.pdf) | A First Course in Optimization Theory
- Rangarajan K. Sundaram (1996) | 12 Weeks 19 | [Measure Theoretic Probability](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_MeasureTheoreticProbability_Syllabus.pdf) | A First Look at Rigorous Probability Theory
- Jeffrey S. Rosenthal (2nd Edition, 2025) | 12 Weeks 20 | [Bayesian Statistics](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_BayesianStatistics_Syllabus.pdf) | Bayesian Econometrics
- Gary Koop (2003) | 12 Weeks 21 | [Large Sample Theory](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_LargeSampleTheory_Syllabus.pdf) | Elements of Large-Sample Theory
- Erich L. Lehmann (1999) | 12 Weeks 22 | [Statistics](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_Statistics_Syllabus.pdf) | Statistical Inference
- George Casella, Roger Berger (2nd Edition, 2024) | 12 Weeks 23 | [Numerical Linear Algebra](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_NumericalLinearAlgebra_Syllabus.pdf) | Numerical Linear Algebra
- Lloyd N. Trefethen, David Bau III (2022)| 12 Weeks 24 | [Matrix Algebra](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_MatrixAlgebra_Syllabus.pdf) | Matrix Algebra
- Karim M. Abadir, Jan R. Magnus (2005) | 12 Weeks 25 | [Linear Algebra](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_LinearAlgebra_Syllabus.pdf) | Linear Algebra Done Right
- Sheldon Axler (4th Edition, 2025) | 12 Weeks 26 | [Measure Theory](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_MeasureTheory_Syllabus.pdf) | Measure, Integration & Real Analysis
- Sheldon Axler (2025) | 12 Weeks 27 | [Topology](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_Topology_Syllabus.pdf) | Topology
- James Munkres (2nd Edition, 2014) | 12 Weeks 28 | [Real Analysis](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_RealAnalysis_Syllabus.pdf) | Basic Analysis I
- Jiri Lebl (Version 6.2, 2025) | 12 Weeks 29 | [Proof Techniques](https://github.com/zekiakyol/proof-based-math-readings/blob/main/PBMR_ProofTechniques_Syllabus.pdf) | Book of Proof
- Richard Hammack (3.4 Edition, 2025) | 12 Weeks 30 | 31 | ## Dependency Tree 32 | 33 | 34 | 35 | 36 | 37 |
38 | 39 | ## Licenses 40 | 41 | - Figures are licensed under Creative Commons [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0). 42 | - Codes are licensed under [MIT License](https://github.com/zekiakyol/proof-based-math-readings/blob/main/LICENSE). 43 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | .DS_Store 2 | .Rhistory 3 | 4 | # TeX 5 | 6 | ## Core latex/pdflatex auxiliary files: 7 | *.aux 8 | *.lof 9 | *.log 10 | *.lot 11 | *.fls 12 | *.out 13 | *.toc 14 | *.fmt 15 | *.fot 16 | *.cb 17 | *.cb2 18 | .*.lb 19 | 20 | ## Intermediate documents: 21 | *.dvi 22 | *.xdv 23 | *-converted-to.* 24 | # these rules might exclude image files for figures etc. 25 | # *.ps 26 | # *.eps 27 | # *.pdf 28 | 29 | ## Generated if empty string is given at "Please type another file name for output:" 30 | .pdf 31 | 32 | ## Bibliography auxiliary files (bibtex/biblatex/biber): 33 | *.bbl 34 | *.bbl-SAVE-ERROR 35 | *.bcf 36 | *.bcf-SAVE-ERROR 37 | *.blg 38 | *-blx.aux 39 | *-blx.bib 40 | *.run.xml 41 | 42 | ## Build tool auxiliary files: 43 | *.fdb_latexmk 44 | *.synctex 45 | *.synctex(busy) 46 | *.synctex.gz 47 | *.synctex.gz(busy) 48 | *.pdfsync 49 | *.rubbercache 50 | rubber.cache 51 | 52 | ## Build tool directories for auxiliary files 53 | # latexrun 54 | latex.out/ 55 | 56 | ## Auxiliary and intermediate files from other packages: 57 | # algorithms 58 | *.alg 59 | *.loa 60 | 61 | # achemso 62 | acs-*.bib 63 | 64 | # amsthm 65 | *.thm 66 | 67 | # attachfile2 68 | *.atfi 69 | 70 | # beamer 71 | *.nav 72 | *.pre 73 | *.snm 74 | *.vrb 75 | 76 | # changes 77 | *.soc 78 | *.loc 79 | 80 | # comment 81 | *.cut 82 | 83 | # cprotect 84 | *.cpt 85 | 86 | # elsarticle (documentclass of Elsevier journals) 87 | *.spl 88 | 89 | # endnotes 90 | *.ent 91 | 92 | # fixme 93 | *.lox 94 | 95 | # feynmf/feynmp 96 | *.mf 97 | *.mp 98 | *.t[1-9] 99 | *.t[1-9][0-9] 100 | *.tfm 101 | 102 | #(r)(e)ledmac/(r)(e)ledpar 103 | *.end 104 | *.?end 105 | *.[1-9] 106 | *.[1-9][0-9] 107 | *.[1-9][0-9][0-9] 108 | *.[1-9]R 109 | *.[1-9][0-9]R 110 | *.[1-9][0-9][0-9]R 111 | *.eledsec[1-9] 112 | *.eledsec[1-9]R 113 | *.eledsec[1-9][0-9] 114 | *.eledsec[1-9][0-9]R 115 | *.eledsec[1-9][0-9][0-9] 116 | *.eledsec[1-9][0-9][0-9]R 117 | 118 | # glossaries 119 | *.acn 120 | *.acr 121 | *.glg 122 | *.glg-abr 123 | *.glo 124 | *.glo-abr 125 | *.gls 126 | *.gls-abr 127 | *.glsdefs 128 | *.lzo 129 | *.lzs 130 | *.slg 131 | *.slo 132 | *.sls 133 | 134 | # uncomment this for glossaries-extra (will ignore makeindex's style files!) 135 | # *.ist 136 | 137 | # gnuplot 138 | *.gnuplot 139 | *.table 140 | 141 | # gnuplottex 142 | *-gnuplottex-* 143 | 144 | # gregoriotex 145 | *.gaux 146 | *.glog 147 | *.gtex 148 | 149 | # htlatex 150 | *.4ct 151 | *.4tc 152 | *.idv 153 | *.lg 154 | *.trc 155 | *.xref 156 | 157 | # hypdoc 158 | *.hd 159 | 160 | # hyperref 161 | *.brf 162 | 163 | # knitr 164 | *-concordance.tex 165 | # TODO Uncomment the next line if you use knitr and want to ignore its generated tikz files 166 | # *.tikz 167 | *-tikzDictionary 168 | 169 | # latexindent will create succesive backup files by default 170 | #*.bak* 171 | 172 | # listings 173 | *.lol 174 | 175 | # luatexja-ruby 176 | *.ltjruby 177 | 178 | # makeidx 179 | *.idx 180 | *.ilg 181 | *.ind 182 | 183 | # minitoc 184 | *.maf 185 | *.mlf 186 | *.mlt 187 | *.mtc[0-9]* 188 | *.slf[0-9]* 189 | *.slt[0-9]* 190 | *.stc[0-9]* 191 | 192 | # minted 193 | _minted* 194 | *.data.minted 195 | *.pyg 196 | 197 | # morewrites 198 | *.mw 199 | 200 | # newpax 201 | *.newpax 202 | 203 | # nomencl 204 | *.nlg 205 | *.nlo 206 | *.nls 207 | 208 | # pax 209 | *.pax 210 | 211 | # pdfpcnotes 212 | *.pdfpc 213 | 214 | # sagetex 215 | *.sagetex.sage 216 | *.sagetex.py 217 | *.sagetex.scmd 218 | 219 | # scrwfile 220 | *.wrt 221 | 222 | # spelling 223 | *.spell.bad 224 | *.spell.txt 225 | 226 | # svg 227 | svg-inkscape/ 228 | 229 | # sympy 230 | *.sout 231 | *.sympy 232 | sympy-plots-for-*.tex/ 233 | 234 | # pdfcomment 235 | *.upa 236 | *.upb 237 | 238 | # pythontex 239 | *.pytxcode 240 | pythontex-files-*/ 241 | 242 | # tcolorbox 243 | *.listing 244 | 245 | # thmtools 246 | *.loe 247 | 248 | # TikZ & PGF 249 | *.dpth 250 | *.md5 251 | *.auxlock 252 | 253 | # titletoc 254 | *.ptc 255 | 256 | # todonotes 257 | *.tdo 258 | 259 | # vhistory 260 | *.hst 261 | *.ver 262 | 263 | # easy-todo 264 | *.lod 265 | 266 | # xcolor 267 | *.xcp 268 | 269 | # xmpincl 270 | *.xmpi 271 | 272 | # xindy 273 | *.xdy 274 | 275 | # xypic precompiled matrices and outlines 276 | *.xyc 277 | *.xyd 278 | 279 | # endfloat 280 | *.ttt 281 | *.fff 282 | 283 | # Latexian 284 | TSWLatexianTemp* 285 | 286 | ## Editors: 287 | # WinEdt 288 | *.bak 289 | *.sav 290 | 291 | # latexindent.pl 292 | *.bak[0-9]* 293 | 294 | # Texpad 295 | .texpadtmp 296 | 297 | # LyX 298 | *.lyx~ 299 | 300 | # Kile 301 | *.backup 302 | 303 | # gummi 304 | .*.swp 305 | 306 | # KBibTeX 307 | *~[0-9]* 308 | 309 | # TeXnicCenter 310 | *.tps 311 | 312 | # auto folder when using emacs and auctex 313 | ./auto/* 314 | *.el 315 | 316 | # expex forward references with \gathertags 317 | *-tags.tex 318 | 319 | # standalone packages 320 | *.sta 321 | 322 | # Makeindex log files 323 | *.lpz 324 | 325 | # xwatermark package 326 | *.xwm 327 | 328 | # REVTeX puts footnotes in the bibliography by default, unless the nofootinbib 329 | # option is specified. Footnotes are the stored in a file with suffix Notes.bib. 330 | # Uncomment the next line to have this generated file ignored. 331 | #*Notes.bib -------------------------------------------------------------------------------- /source/PBMR_NumericalLinearAlgebra_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Numerical Linear Algebra**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=2cm 24 | - left=2cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Numerical Linear Algebra*. 71 | 72 | # Prerequisites and Format 73 | 74 | - Proof Techniques resources below. 75 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 76 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 77 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 78 | 79 | # Resources 80 | 81 | ## Main Book 82 | 83 | **Numerical Linear Algebra - Lloyd N. Trefethen, David Bau III (1997 or 2022)** is our main book because it is well-written and well-structured. 84 | 85 | \begin{itemize} 86 | \item[\faBook] Numerical Linear Algebra - Lloyd N. Trefethen, David Bau III (1997 or 2022) 87 | \item[\faBook] \href{http://math.ucdavis.edu/~saito/courses/229A/typos.pdf}{Numerical Linear Algebra - Lloyd N. Trefethen, David Bau III (1997 or 2022, Errata)} 88 | \item[\faBook] \href{https://github.com/leeyngdo/Numerical-Linear-Algebra}{Numerical Linear Algebra - Lloyd N. Trefethen, David Bau III (1997 or 2022, Solutions by Youngdo Lee)} 89 | \end{itemize} 90 | 91 | ## Supplementary 92 | 93 | ### Proof Techniques 94 | 95 | \begin{itemize} 96 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 97 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum)} 98 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn)} 99 | \end{itemize} 100 | 101 | \newpage 102 | 103 | # Reading Schedule 104 | 105 | - **NLA** is the abrevviation of **Numerical Linear Algebra - Lloyd N. Trefethen, David Bau III (1997 or 2022)**. 106 | 107 | ::: {.callout-tip icon=false} 108 | ## **\faBook NLA \hfill Week 01-02 \faCalendar* ** 109 | 110 | \begin{itemize} 111 | \item[] Part I: Fundamentals 112 | \end{itemize} 113 | ::: 114 | 115 | ::: {.callout-tip icon=false} 116 | ## **\faBook NLA \hfill Week 03-04 \faCalendar* ** 117 | 118 | \begin{itemize} 119 | \item[] Part II: QR Factorization and Least Squares 120 | \end{itemize} 121 | ::: 122 | 123 | ::: {.callout-tip icon=false} 124 | ## **\faBook NLA \hfill Week 05-06 \faCalendar* ** 125 | 126 | \begin{itemize} 127 | \item[] Part III: Conditioning and Stability 128 | \end{itemize} 129 | ::: 130 | 131 | ::: {.callout-tip icon=false} 132 | ## **\faBook NLA \hfill Week 07-08 \faCalendar* ** 133 | 134 | \begin{itemize} 135 | \item[] Part IV: Systems of Equations 136 | \end{itemize} 137 | ::: 138 | 139 | ::: {.callout-tip icon=false} 140 | ## **\faBook NLA \hfill Week 09-10 \faCalendar* ** 141 | 142 | \begin{itemize} 143 | \item[] Part V: Eigenvalues 144 | \end{itemize} 145 | ::: 146 | 147 | ::: {.callout-tip icon=false} 148 | ## **\faBook NLA \hfill Week 11-12 \faCalendar* ** 149 | 150 | \begin{itemize} 151 | \item[] Part VI: Iterative Methods 152 | \end{itemize} 153 | ::: 154 | 155 | # Further Readings (Optional) 156 | 157 | ::: {.callout-note appearance="minimal"} 158 | \begin{itemize} 159 | \item[\faBook] Matrix Computations - Gene H. Golub, Charles F. Van Loan (4th Edition, 2013) 160 | \item[\faBook] \href{https://www.cs.cornell.edu/cv/cvl_home/books/}{Matrix Computations - Gene H. Golub, Charles F. Van Loan (4th Edition, 2013, Errata and M-files)} 161 | \end{itemize} 162 | ::: 163 | -------------------------------------------------------------------------------- /source/PBMR_MatrixAlgebra_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Matrix Algebra**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=2cm 24 | - left=2cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Matrix Algebra*. 71 | 72 | # Prerequisites and Format 73 | 74 | - Proof Techniques resources below and [\faYoutube Linear Algebra - Gilbert Strang (2005)](https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8). 75 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 76 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 77 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 78 | 79 | # Resources 80 | 81 | ## Main Book 82 | 83 | **Matrix Algebra - Karim M. Abadir, Jan R. Magnus (2005)** is our main book because it is well-written and well-structured. It also provides detailed solutions for the exercises. 84 | 85 | \begin{itemize} 86 | \item[\faBook] Matrix Algebra - Karim M. Abadir, Jan R. Magnus (2005) 87 | \item[\faBook] \href{https://github.com/zekiakyol/compact-erratas/blob/main/MatrixAlgebra_KarimAbadirJanMagnus_Errata.pdf}{Matrix Algebra - Karim M. Abadir, Jan R. Magnus (2005, Errata)} 88 | \end{itemize} 89 | 90 | ## Supplementary 91 | 92 | ### Matrix Algebra 93 | 94 | \begin{itemize} 95 | \item[\faScroll] \href{https://www.sciencedirect.com/science/article/pii/S0304407624002070}{A Gentle Introduction to Matrix Calculus - Jan R. Magnus (2024)} 96 | \item[\faBook] \href{https://www2.imm.dtu.dk/pubdb/edoc/imm3274.pdf}{The Matrix Cookbook - Kaare Brandt Petersen, Michael Syskind Pedersen (2012)} 97 | \item[\faBook] \href{https://media.pearsoncmg.com/ph/bp/bridgepages/bp_greene_bridgepage/Econometric_Analysis_8/Greene_Appendices.pdf}{Econometric Theory - William H. Greene (Appendix A, 8th Edition, 2020)} 98 | \item[\faCalculator] \href{https://www.matrixcalculus.org}{matrixcalculus.org} 99 | \end{itemize} 100 | 101 | ### Proof Techniques 102 | 103 | \begin{itemize} 104 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 105 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum)} 106 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn)} 107 | \end{itemize} 108 | 109 | \newpage 110 | 111 | # Reading Schedule 112 | 113 | - **MA** is the abbreviation of **Matrix Algebra - Karim M. Abadir, Jan R. Magnus (2005)**. 114 | 115 | ::: {.callout-tip icon=false} 116 | ## **\faBook MA \hfill Week 01 \faCalendar* ** 117 | 118 | \begin{itemize} 119 | \item[] Appendix A: Some mathematical tools 120 | \item[] Appendix B: Notation 121 | \item[] Chapter 1: Vectors 122 | \item[] Chapter 2: Matrices 123 | \end{itemize} 124 | ::: 125 | 126 | ::: {.callout-tip icon=false} 127 | ## **\faBook MA \hfill Week 02 \faCalendar* ** 128 | 129 | \begin{itemize} 130 | \item[] Chapter 3: Vector spaces 131 | \item[] Chapter 4: Rank, inverse, and determinant 132 | \end{itemize} 133 | ::: 134 | 135 | ::: {.callout-tip icon=false} 136 | ## **\faBook MA \hfill Week 03-04 \faCalendar* ** 137 | 138 | \begin{itemize} 139 | \item[] Chapter 5: Partitioned matrices 140 | \item[] Chapter 6: Systems of equations 141 | \end{itemize} 142 | ::: 143 | 144 | ::: {.callout-tip icon=false} 145 | ## **\faBook MA \hfill Week 05-06 \faCalendar* ** 146 | 147 | \begin{itemize} 148 | \item[] Chapter 7: Eigenvalues, eigenvectors, and factorizations 149 | \item[] Chapter 8: Positive (semi)definite and idempotent matrices 150 | \item[] Chapter 9: Matrix functions 151 | \end{itemize} 152 | ::: 153 | 154 | ::: {.callout-tip icon=false} 155 | ## **\faBook MA \hfill Week 07-08-09 \faCalendar* ** 156 | 157 | \begin{itemize} 158 | \item[] Chapter 10: Kronecker product, vec-operator, and Moore-Penrose inverse 159 | \item[] Chapter 11: Patterned matrices: commutation- and duplication matrix 160 | \end{itemize} 161 | ::: 162 | 163 | ::: {.callout-tip icon=false} 164 | ## **\faBook MA \hfill Week 10-11-12 \faCalendar* ** 165 | 166 | \begin{itemize} 167 | \item[] Chapter 12: Matrix inequalities 168 | \item[] Chapter 13: Matrix calculus 169 | \end{itemize} 170 | ::: 171 | 172 | # Further Readings (Optional) 173 | 174 | ::: {.callout-note appearance="minimal"} 175 | \begin{itemize} 176 | \item[\faBook] Matrix Differential Calculus with Applications in Statistics and Econometrics - Jan R. Magnus, Heinz Neudecker (3rd Edition, 2019) 177 | \end{itemize} 178 | ::: 179 | -------------------------------------------------------------------------------- /source/PBMR_GraphTheory_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Graph Theory**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=2cm 24 | - left=2cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Graph Theory*. 71 | 72 | # Prerequisites and Format 73 | 74 | - Proof Techniques resources below. 75 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 76 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 77 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 78 | 79 | # Resources 80 | 81 | ## Main Book and Main Book's Playlist 82 | 83 | **A First Course in Graph Theory - Gary Chartrand, Ping Zhang (2012)** is our main book because it is well-written and well-structured. 84 | 85 | Mikhail Lavrov's playlist is our playlist because the narrative is great. 86 | 87 | \begin{itemize} 88 | \item[\faBook] A First Course in Graph Theory - Gary Chartrand, Ping Zhang (2012) 89 | \item[\faYoutube] \href{https://facultyweb.kennesaw.edu/mlavrov/courses/3322-spring-2021.php}{A First Course in Graph Theory - Gary Chartrand, Ping Zhang (2012, Playlist by Mikhail Lavrov)} 90 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH}{A First Course in Graph Theory - Gary Chartrand, Ping Zhang (2012, Playlist by Wrath of Math)} 91 | \item[\faBook] \href{https://web.evanchen.cc/notes/SJSU179.pdf}{A First Course in Graph Theory - Gary Chartrand, Ping Zhang (2012, Notes by Evan Chen)} 92 | \end{itemize} 93 | 94 | ## Supplementary 95 | 96 | ### Graph Theory 97 | 98 | \begin{itemize} 99 | \item[\faYoutube] \href{https://www.youtube.com/watch?v=LFKZLXVO-Dg}{Introduction to Graph Theory: A Computer Science Perspective - Reducible (2020)} 100 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVqjIisMyo_9h78itHVS2hZzkthxFHoT7}{Graph Theory - Don Sheehy (2020)} 101 | \item[\faMouse] \href{https://d3gt.com/index.html}{D3 Graph Theory (Interactive)} 102 | \item[\faMouse] \href{https://graphonline.ru/en/}{Graph Online (Interactive)} 103 | \end{itemize} 104 | 105 | ### Proof Techniques 106 | 107 | \begin{itemize} 108 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 109 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum)} 110 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn)} 111 | \end{itemize} 112 | 113 | \newpage 114 | 115 | # Reading Schedule 116 | 117 | **FCGT** is the abrevviation of **A First Course in Graph Theory - Gary Chartrand, Ping Zhang (2012)**. 118 | 119 | ::: {.callout-tip icon=false} 120 | ## **\faBook FCGT \hfill Week 01 \faCalendar* ** 121 | 122 | \begin{itemize} 123 | \item[] Appendix 1: Sets and Logic 124 | \item[] Appendix 2: Equivalence Relations and Functions 125 | \item[] Appendix 3: Methods of Proof 126 | \end{itemize} 127 | ::: 128 | 129 | ::: {.callout-tip icon=false} 130 | ## **\faBook FCGT \hfill Week 02 \faCalendar* ** 131 | 132 | \begin{itemize} 133 | \item[] Chapter 1: Introduction 134 | \end{itemize} 135 | ::: 136 | 137 | ::: {.callout-tip icon=false} 138 | ## **\faBook FCGT \hfill Week 03-04 \faCalendar* ** 139 | 140 | \begin{itemize} 141 | \item[] Chapter 2: Degrees 142 | \item[] Chapter 3: Isomorphic Graphs 143 | \end{itemize} 144 | ::: 145 | 146 | ::: {.callout-tip icon=false} 147 | ## **\faBook FCGT \hfill Week 05-06 \faCalendar* ** 148 | 149 | \begin{itemize} 150 | \item[] Chapter 4: Trees 151 | \item[] Chapter 5: Connectivity 152 | \end{itemize} 153 | ::: 154 | 155 | ::: {.callout-tip icon=false} 156 | ## **\faBook FCGT \hfill Week 07-08 \faCalendar* ** 157 | 158 | \begin{itemize} 159 | \item[] Chapter 6: Traversability 160 | \item[] Chapter 7: Digraphs 161 | \end{itemize} 162 | ::: 163 | 164 | ::: {.callout-tip icon=false} 165 | ## **\faBook FCGT \hfill Week 09-10 \faCalendar* ** 166 | 167 | \begin{itemize} 168 | \item[] Chapter 8: Matchings and Factorization 169 | \item[] Chapter 9: Planarity 170 | \end{itemize} 171 | ::: 172 | 173 | ::: {.callout-tip icon=false} 174 | ## **\faBook FCGT \hfill Week 11-12 \faCalendar* ** 175 | 176 | \begin{itemize} 177 | \item[] Chapter 10: Coloring Graphs 178 | \end{itemize} 179 | ::: 180 | 181 | # Further Readings (Optional) 182 | 183 | ::: {.callout-note appearance="minimal"} 184 | \begin{itemize} 185 | \item[\faBook] Graphs and Digraphs - G. Chartrand, H. Jordon, V. Vatter, P. Zhang (7th Edition, 2024) 186 | \end{itemize} 187 | ::: 188 | -------------------------------------------------------------------------------- /source/PBMR_Optimization_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Optimization**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=2cm 24 | - left=2cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Optimization*. 71 | 72 | # Prerequisites and Format 73 | 74 | - Proof Techniques resources below. 75 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 76 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 77 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 78 | 79 | # Resources 80 | 81 | ## Main Book and Main Book's Playlist 82 | 83 | **A First Course in Optimization Theory - Rangarajan K. Sundaram (1996)** is our main book because it is well-written and well-structured. 84 | 85 | \begin{itemize} 86 | \item[\faBook] A First Course in Optimization Theory - Rangarajan K. Sundaram (1996) 87 | \item[\faBook] \href{https://github.com/frrad/optimization-368}{A First Course in Optimization Theory - Rangarajan K. Sundaram (1996, Solutions by Frederick Robinson)} 88 | \item[\faBook] A First Course in Optimization Theory - Rangarajan K. Sundaram (1996, Solutions by Paolo Pin) 89 | \end{itemize} 90 | 91 | ## Supplementary 92 | 93 | ### Optimization 94 | 95 | \begin{itemize} 96 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLcjqUUQt__ZE6wp_c4-FcRdmzBvx8VN7O}{Foundations for Optimization - Mark Walker (2020)} 97 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLcjqUUQt__ZE0ZSTNRyBIgLJ5obPHdmxC}{Optimization - Mark Walker (2020)} 98 | \end{itemize} 99 | 100 | ### Proof Techniques 101 | 102 | \begin{itemize} 103 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 104 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum)} 105 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn)} 106 | \end{itemize} 107 | 108 | ### Real Analysis 109 | 110 | \begin{itemize} 111 | \item[\faBook] \href{https://www.jirka.org/ra}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025)} 112 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025, Playlist by Casey Rodriguez)} 113 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP613ULTyHAqz04niYf722x7S}{Introduction To Metric Spaces - Paige Bright (2023)} 114 | \end{itemize} 115 | 116 | \newpage 117 | 118 | # Reading Schedule 119 | 120 | **AFCOT** is the abbreviation of **A First Course in Optimization Theory - Rangarajan K. Sundaram (1996)**. 121 | 122 | ::: {.callout-tip icon=false} 123 | ## **\faBook AFCOT \hfill Week 01-02 \faCalendar* ** 124 | 125 | \begin{itemize} 126 | \item[] Appendix A: Set Theory and Logic: An Introduction 127 | \item[] Appendix B: The Real Line 128 | \item[] Appendix C: Structures on Vector Spaces 129 | \item[] Chapter 1: Mathematical Preliminaries 130 | \end{itemize} 131 | ::: 132 | 133 | ::: {.callout-tip icon=false} 134 | ## **\faBook AFCOT \hfill Week 03-04 \faCalendar* ** 135 | 136 | \begin{itemize} 137 | \item[] Chapter 2: Optimization in $\mathbb{R}^n$ 138 | \end{itemize} 139 | ::: 140 | 141 | ::: {.callout-tip icon=false} 142 | ## **\faBook AFCOT \hfill Week 05-06 \faCalendar* ** 143 | 144 | \begin{itemize} 145 | \item[] Chapter 3: Existence of Solutions: The Weierstrass Theorem 146 | \item[] Chapter 4: Unconstrained Optima 147 | \end{itemize} 148 | ::: 149 | 150 | ::: {.callout-tip icon=false} 151 | ## **\faBook AFCOT \hfill Week 07-08-09 \faCalendar* ** 152 | 153 | \begin{itemize} 154 | \item[] Chapter 5: Equality Constraints and the Theorem of Lagrange 155 | \item[] Chapter 6: Inequality Constraints and the Theorem of Kuhn and Tucker 156 | \end{itemize} 157 | ::: 158 | 159 | ::: {.callout-tip icon=false} 160 | ## **\faBook AFCOT \hfill Week 10-11-12 \faCalendar* ** 161 | 162 | \begin{itemize} 163 | \item[] Chapter 7: Convex Structures in Optimization Theory 164 | \item[] Chapter 8: Quasi-Convexity and Optimization 165 | \end{itemize} 166 | ::: 167 | 168 | # Further Readings (Optional) 169 | 170 | ::: {.callout-note appearance="minimal"} 171 | \begin{itemize} 172 | \item[\faBook] Optimization by Vector Space Methods - David G. Luenberger (1997) 173 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLmI22X7juoWVgfWKyuQM0ZdiwghWXOOHY}{Optimization by Vector Space Methods - David G. Luenberger (1997, Playlist by Peter Galbacs)} 174 | \end{itemize} 175 | ::: 176 | -------------------------------------------------------------------------------- /source/PBMR_MeasureTheory_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Measure Theory**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=2cm 24 | - left=2cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Measure Theory*. 71 | 72 | # Prerequisites and Format 73 | 74 | - Proof Techniques, Real Analysis, and Topology resources below. 75 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 76 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 77 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 78 | 79 | # Resources [All are open-access] 80 | 81 | ## Main Book and Main Book's Playlist 82 | 83 | **Measure, Integration & Real Analysis - Sheldon Axler (2025, Errata-free version)** is our main book for this session because it is well-written, well-structured, and open-access. 84 | 85 | \begin{itemize} 86 | \item[\faBook] \href{https://measure.axler.net/MIRA.pdf}{Measure, Integration \& Real Analysis - Sheldon Axler (2025, Errata-free version)} 87 | \item[\faYoutube] Measure, Integration \& Real Analysis - Sheldon Axler (202X, Playlist) $\rightarrow$ will be added after the 2nd edition. 88 | \end{itemize} 89 | 90 | ## Supplementary 91 | 92 | ### Measure Theory 93 | 94 | \begin{itemize} 95 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLBh2i93oe2qvMVqAzsX1Kuv6-4fjazZ8j}{Measure Theory - The Bright Side of Mathematics (2025)} 96 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLyqSpQzTE6M_DZRQxHUafLgeLxZxMpVGS}{Measure Theory - Indrava Roy (2020)} 97 | \item[\faYoutube] \href{https://www.youtube.com/watch?v=LDNDTOVnKJk}{A horizontal integral?! Introduction to Lebesgue Integration - vcubingx (2020)} 98 | \item[\faYoutube] \href{https://www.open.ac.uk/library/digital-archive/module/xcri:M331/program}{The Lebesgue Integral - BBC (1975)} 99 | \end{itemize} 100 | 101 | ### Proof Techniques 102 | 103 | \begin{itemize} 104 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 105 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum)} 106 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn)} 107 | \end{itemize} 108 | 109 | ### Real Analysis 110 | 111 | \begin{itemize} 112 | \item[\faBook] \href{https://measure.axler.net/SupplementMIRA.pdf}{Measure, Integration \& Real Analysis - Sheldon Axler (2025, Supplement)} 113 | \item[\faBook] \href{https://www.jirka.org/ra}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025)} 114 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025, Playlist by Casey Rodriguez)} 115 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP613ULTyHAqz04niYf722x7S}{Introduction To Metric Spaces - Paige Bright (2023)} 116 | \end{itemize} 117 | 118 | \newpage 119 | 120 | # Reading Schedule 121 | 122 | - **MIRA** is the abbreviation of **Measure, Integration & Real Analysis - Sheldon Axler (2025)**. 123 | 124 | ::: {.callout-tip icon=false} 125 | ## **\faBook MIRA, Chapter 1: Riemann Integration \hfill Week 01 \faCalendar* ** 126 | 127 | \begin{itemize} 128 | \item[] \textbf{1A} Review: Riemann Integral 129 | \item[] \textbf{1B} Riemann Integral Is Not Good Enough 130 | \end{itemize} 131 | ::: 132 | 133 | ::: {.callout-tip icon=false} 134 | ## **\faBook MIRA, Chapter 2: Measures \hfill Week 02-03-04-05 \faCalendar* ** 135 | 136 | \begin{itemize} 137 | \item[] \textbf{2A} Outer Measure on $\mathbf{R}$ 138 | \item[] \textbf{2B} Measurable Spaces and Functions 139 | \item[] \textbf{2C} Measures and Their Properties 140 | \item[] \textbf{2D} Lebesgue Measure 141 | \item[] \textbf{2E} Convergence of Measurable Functions 142 | \end{itemize} 143 | ::: 144 | 145 | ::: {.callout-tip icon=false} 146 | ## **\faBook MIRA, Chapter 3: Integration \hfill Week 06-07-08 \faCalendar* ** 147 | 148 | \begin{itemize} 149 | \item[] \textbf{3A} Integration with Respect to a Measure 150 | \item[] \textbf{3B} Limits of Integrals \& Integrals of Limits 151 | \end{itemize} 152 | ::: 153 | 154 | ::: {.callout-tip icon=false} 155 | ## **\faBook MIRA, Chapter 4: Differentiation \hfill Week 09 \faCalendar* ** 156 | 157 | \begin{itemize} 158 | \item[] \textbf{4A} Hardy–Littlewood Maximal Function 159 | \item[] \textbf{4B} Derivatives of Integrals 160 | \end{itemize} 161 | ::: 162 | 163 | ::: {.callout-tip icon=false} 164 | ## **\faBook MIRA, Chapter 5: Product Measures \hfill Week 10-11-12 \faCalendar* ** 165 | 166 | \begin{itemize} 167 | \item[] \textbf{5A} Products of Measure Spaces 168 | \item[] \textbf{5B} Iterated Integrals 169 | \item[] \textbf{5C} Lebesgue Integration on $\mathbf{R}^n$ 170 | \end{itemize} 171 | ::: 172 | 173 | # Further Readings (Optional) 174 | 175 | ::: {.callout-note appearance="minimal"} 176 | \begin{itemize} 177 | \item[] Our Measure Theoretic Probability syllabus at \href{https://github.com/zekiakyol/proof-based-math-readings}{\faGithub github.com/zekiakyol/proof-based-math-readings} 178 | \end{itemize} 179 | ::: 180 | -------------------------------------------------------------------------------- /source/PBMR_ProofTechniques_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Proof Techniques**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=2cm 24 | - left=2cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Proof Techniques*. 71 | 72 | # Prerequisites and Format 73 | 74 | - Calculus resources below. 75 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 76 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 77 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 78 | 79 | # Resources [All are open-access] 80 | 81 | ## Main Book and Main Book's Playlist 82 | 83 | **Book of Proof - Richard Hammack (3.4 Edition, 2025)** is our main book because it is a well-written and well-structured pedagogical masterpiece. It is also open-access and provides detailed solutions for odd-numbered exercises at the end of the book. 84 | 85 | Jeremy Teitelbaum's playlist on Book of Proof is our main playlist because his narrative is great. 86 | 87 | \begin{itemize} 88 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 89 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum, Chapters 1-12)} 90 | \end{itemize} 91 | 92 | ## Supplementary 93 | 94 | ### Proof Techniques 95 | 96 | Because our main playlist does not cover Chapters 13-14, we cover these chapters from Michael Penn's playlist. 97 | 98 | \begin{itemize} 99 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn, Chapters 1-14)} 100 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLpcwHaLYiaEUk-DVrPHjPpGmwL04WMbNQ}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Valerie Hower, Chapters 1-12)} 101 | \item[\faBook] \href{https://summit.plymouth.edu/bitstream/handle/20.500.12774/381/psu-oer-024.pdf?sequence=1&isAllowed=y}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Workbook by Justin Wright)} 102 | \item[\faScroll] \href{https://danaernst.com/IBL-IntroToProof/IntroToProof.pdf#page=140}{Appendix A: Elements of Style for Proofs - Dana C. Ernst (2025)} 103 | \end{itemize} 104 | 105 | ### Calculus 106 | 107 | \begin{itemize} 108 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr}{Essence of Calculus - 3Blue1Brown (2023)} 109 | \item[\faBook\faYoutube] \href{https://ocw.mit.edu/courses/18-01-single-variable-calculus-fall-2006}{Single Variable Calculus - David Jerison (2006)} 110 | \item[\faBook\faYoutube] \href{https://ocw.mit.edu/courses/18-02-multivariable-calculus-fall-2007}{Multivariable Calculus - Denis Auroux (2007)} 111 | \item[\faCalculator] \href{https://www.geogebra.org/m/f08hfjvx}{Sequences and Series Calculator - Geogebra} 112 | \item[\faCalculator] \href{https://www.geogebra.org/graphing}{Function Graph - Geogebra} 113 | \end{itemize} 114 | 115 | \newpage 116 | 117 | # Reading Schedule 118 | 119 | 1) Read the chapter and watch the matching playlist. 120 | 2) Solve the odd-numbered exercises and check their solutions at the end of the book. 121 | 3) Solve the even-numbered exercises and check their solutions using our unofficial solutions manual. 122 | 4) If stuck, ask questions in Discord. 123 | 124 | ::: {.callout-tip icon=false} 125 | ## **\faBook Book of Proof \hfill Week 01 \faCalendar* ** 126 | 127 | \begin{itemize} 128 | \item[] Chapter 1: Sets 129 | \item[] Chapter 2: Logic 130 | \item[] Chapter 3: Counting 131 | \end{itemize} 132 | ::: 133 | 134 | ::: {.callout-tip icon=false} 135 | ## **\faBook Book of Proof \hfill Week 02-03 \faCalendar* ** 136 | 137 | \begin{itemize} 138 | \item[] Chapter 4: Direct Proof 139 | \item[] Chapter 5: Contrapositive Proof 140 | \item[] Chapter 6: Proof by Contradiction 141 | \end{itemize} 142 | ::: 143 | 144 | ::: {.callout-tip icon=false} 145 | ## **\faBook Book of Proof \hfill Week 04-05 \faCalendar* ** 146 | 147 | \begin{itemize} 148 | \item[] Chapter 7: Proving Non-Conditional Statements 149 | \item[] Chapter 8: Proofs Involving Sets 150 | \item[] Chapter 9: Disproof 151 | \end{itemize} 152 | ::: 153 | 154 | ::: {.callout-tip icon=false} 155 | ## **\faBook Book of Proof \hfill Week 06 \faCalendar* ** 156 | 157 | \begin{itemize} 158 | \item[] Chapter 10: Mathematical Induction 159 | \end{itemize} 160 | ::: 161 | 162 | ::: {.callout-tip icon=false} 163 | ## **\faBook Book of Proof \hfill Week 07-08 \faCalendar* ** 164 | 165 | \begin{itemize} 166 | \item[] Chapter 11: Relations 167 | \item[] Chapter 12: Functions 168 | \end{itemize} 169 | ::: 170 | 171 | ::: {.callout-tip icon=false} 172 | ## **\faBook Book of Proof \hfill Week 09-10 \faCalendar* ** 173 | 174 | \begin{itemize} 175 | \item[] Chapter 14: Cardinality of Sets \hfill (This chapter requires a solid understanding of Chapter 12) 176 | \end{itemize} 177 | ::: 178 | 179 | ::: {.callout-tip icon=false} 180 | ## **\faBook Book of Proof \hfill Week 11-12 \faCalendar* ** 181 | 182 | \begin{itemize} 183 | \item[] Chapter 13: Proofs in Calculus \hfill (This chapter is denser than the previous ones) 184 | \end{itemize} 185 | ::: 186 | 187 | # Further Readings (Optional) 188 | 189 | ::: {.callout-note appearance="minimal"} 190 | \begin{itemize} 191 | \item[\faBook] Mathematical Proofs - G. Chartrand, A. Polimeni, P. Zhang (\textbf{Chapter 0-14}, 4th Edition, 2018) \href{https://media.pearsoncmg.com/cmg/pmmg_mml_shared/Chartrand_4e}{\faDesktop} 192 | \end{itemize} 193 | ::: 194 | -------------------------------------------------------------------------------- /source/PBMR_Algorithms_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Algorithms**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=1.5cm 24 | - left=1.5cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Algorithms*. 71 | 72 | # Prerequisites and Format 73 | 74 | - Supplementary Python and one of the Algorithms resources below. 75 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 76 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 77 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 78 | 79 | # Resources 80 | 81 | ## Main Book and Main Book's Playlist 82 | 83 | **Introduction to Algorithms - T. Cormen, C. Leiserson, R. Rivest, C. Stein (4th Edition, 2022)** is our main book for this session because it is well-written and well-structured. 84 | 85 | \begin{itemize} 86 | \item[\faBook] Introduction to Algorithms - T. Cormen, C. Leiserson, R. Rivest, C. Stein (4th Edition, 2022) 87 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY}{Introduction to Algorithms - T. Cormen, C. Leiserson, R. Rivest, C. Stein (4th Edition, 2022, Playlist)} 88 | \item[\faBook] \href{https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/11599/e4-bugs.html}{Introduction to Algorithms - T. Cormen, C. Leiserson, R. Rivest, C. Stein (4th Edition, 2022, Errata)} 89 | \item[\faBook] \href{https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/11599/selected-solutions.pdf}{Introduction to Algorithms - T. Cormen, C. Leiserson, R. Rivest, C. Stein (4th Edition, 2022, Selected Solutions)} 90 | \item[\faBook] \href{https://sites.math.rutgers.edu/~ajl213/CLRS/CLRS.html}{Introduction to Algorithms - T. Cormen, C. Leiserson, R. Rivest, C. Stein (3rd Edition, 2009, Solutions by M. Bodnar, A. Lohr)} 91 | \end{itemize} 92 | 93 | ## Supplementary 94 | 95 | ### Python 96 | 97 | \begin{itemize} 98 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP62A-ynp6v6-LGBCzeH3VAQB}{Introduction to CS and Programming using Python - Ana Bell (2022)} 99 | \end{itemize} 100 | 101 | ### Algorithms 102 | 103 | \begin{itemize} 104 | \item[\faBook] Grokking Algorithms - Aditya Bhargava (2nd Edition, 2024) $\qquad\qquad \rightarrow$ Easier to read 105 | \item[\faBook] \href{https://www.adit.io/errata.html}{Grokking Algorithms - Aditya Bhargava (2nd Edition, 2024, Errata)} 106 | \item[\faBook] Data Structures and Algorithms in Python - M. T. Goodrich, R. Tamassia, M. H. Goldwasser (2013) 107 | \item[\faBook] \href{https://runestone.academy/ns/books/published/pythonds3/index.html}{Problem Solving with Algorithms and Data Structures using Python - B. Miller, D. Ranum, R. Yasinovskyy (3rd Edition, 2023)} 108 | \item[\faYoutube] \href{https://www.youtube.com/@gjenkinsedu/featured}{Problem Solving with Algorithms and Data Structures using Python - B. Miller, D. Ranum, R. Yasinovskyy (3rd Edition, 2023, Playlist by Gerry Jenkins)} 109 | \item[\faMouse] \href{https://leetcode.com/problemset/}{leetcode.com} 110 | \end{itemize} 111 | 112 | ### Proof Techniques 113 | 114 | \begin{itemize} 115 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 116 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum)} 117 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn)} 118 | \end{itemize} 119 | 120 | \newpage 121 | 122 | # Reading Schedule 123 | 124 | - **CLRS** is the abbreviation of **Introduction to Algorithms - T. Cormen, C. Leiserson, R. Rivest, C. Stein (4th Edition, 2022)**. 125 | 126 | ::: {.callout-tip icon=false} 127 | ## **\faBook CLRS \hfill Week 01 \faCalendar* ** 128 | 129 | \begin{itemize} 130 | \item[] Appendix A: Summations 131 | \item[] Appendix B: Sets, Etc. 132 | \item[] Appendix C: Counting and Probability 133 | \item[] Appendix D: Matrices 134 | \end{itemize} 135 | ::: 136 | 137 | ::: {.callout-tip icon=false} 138 | ## **\faBook CLRS \hfill Week 02-03 \faCalendar* ** 139 | 140 | \begin{itemize} 141 | \item[] Chapter 1: The Role of Algorithms in Computing 142 | \item[] Chapter 2: Getting Started 143 | \item[] Chapter 3: Characterizing Running Times 144 | \end{itemize} 145 | ::: 146 | 147 | ::: {.callout-tip icon=false} 148 | ## **\faBook CLRS \hfill Week 04-05 \faCalendar* ** 149 | 150 | \begin{itemize} 151 | \item[] Chapter 4: Divide-and-Conquer 152 | \item[] Chapter 5: Probabilistic Analysis and Randomized Algorithms 153 | \end{itemize} 154 | ::: 155 | 156 | ::: {.callout-tip icon=false} 157 | ## **\faBook CLRS \hfill Week 06-07 \faCalendar* ** 158 | 159 | \begin{itemize} 160 | \item[] Chapter 6: Heapsort 161 | \item[] Chapter 7: Quicksort 162 | \item[] Chapter 8: Sorting in Linear Time 163 | \item[] Chapter 9: Medians and Order Statistics 164 | \end{itemize} 165 | ::: 166 | 167 | ::: {.callout-tip icon=false} 168 | ## **\faBook CLRS \hfill Week 08-09-10 \faCalendar* ** 169 | 170 | \begin{itemize} 171 | \item[] Chapter 10: Elementary Data Structures 172 | \item[] Chapter 11: Hash Tables 173 | \item[] Chapter 12: Binary Search Trees 174 | \item[] Chapter 13: Red-Black Trees 175 | \end{itemize} 176 | ::: 177 | 178 | ::: {.callout-tip icon=false} 179 | ## **\faBook CLRS \hfill Week 11-12 \faCalendar* ** 180 | 181 | \begin{itemize} 182 | \item[] Chapter 14: Dynamic Programming 183 | \item[] Chapter 15: Greedy Algorithms 184 | \end{itemize} 185 | ::: 186 | -------------------------------------------------------------------------------- /source/PBMR_MeasureTheoreticProbability_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Measure Theoretic Probability**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=2cm 24 | - left=2cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Measure Theoretic Probability*. 71 | 72 | # Prerequisites and Format 73 | 74 | - Proof Techniques and Real Analysis resources below. 75 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 76 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 77 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 78 | 79 | # Resources 80 | 81 | ## Main Book and Main Book's Playlist 82 | 83 | **A First Look at Rigorous Probability Theory - Jeffrey S. Rosenthal (2nd Edition, 2006 or 2025)** is our main book for this session because it is well-written and well-structured. 84 | 85 | Jem Corcoran's playlist is our main playlist because her narrative is great. 86 | 87 | \begin{itemize} 88 | \item[\faBook] A First Look at Rigorous Probability Theory - Jeffrey S. Rosenthal (2nd Edition, 2006 or 2025) 89 | \item[\faBook] \href{http://probability.ca/jeff/ftpdir/errata2.pdf}{A First Look at Rigorous Probability Theory - Jeffrey S. Rosenthal (2nd Edition, 2006 or 2025, Errata)} 90 | \item[\faBook] \href{http://probability.ca/jeff/ftpdir/grprobsol.pdf}{A First Look at Rigorous Probability Theory - Jeffrey S. Rosenthal (2nd Edition, 2006 or 2025, Solutions)} 91 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLLyj1Zd4UWrO6VtBSiQLsNlo9QBm30nxC}{A First Look at Rigorous Probability Theory - Jeffrey S. Rosenthal (2nd Edition, 2006 or 2025, Playlist by J. Corcoran)} 92 | \end{itemize} 93 | 94 | ## Supplementary 95 | 96 | ### Measure Theoretic Probability 97 | 98 | \begin{itemize} 99 | \item[\faBook] \href{https://services.math.duke.edu/~rtd/PTE/PTE5_011119.pdf}{Probability: Theory and Examples - Rick Durrett (5th Edition, 2019)} 100 | \item[\faBook] \href{https://hoillee.wordpress.com/wp-content/uploads/2021/09/durrett-5e-solutions.pdf}{Probability: Theory and Examples - Rick Durrett (5th Edition, 2019, Solutions by Hoil Lee, Wonjun Seo)} 101 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLQHzlagV3jqLPA6Jy-Lia-NAniMZ3kw08}{Probability: Theory and Examples - Rick Durrett (5th Edition, 2019, Solutions by Luke Andrejek)} 102 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLEAYkSg4uSQ2jWy81M94YUJKFejoR7dal}{Measure Theoretic Probability I - Supriyo Bhar (2021)} 103 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLyqSpQzTE6M_FbA7OwN2jI2Ime2yb5REk}{Probability Foundations - Krishna Jagannathan (2020)} 104 | \end{itemize} 105 | 106 | ### Proof Techniques 107 | 108 | \begin{itemize} 109 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 110 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum)} 111 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn)} 112 | \end{itemize} 113 | 114 | ### Real Analysis 115 | 116 | \begin{itemize} 117 | \item[\faBook] \href{https://www.jirka.org/ra}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025)} 118 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025, Playlist by Casey Rodriguez)} 119 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP613ULTyHAqz04niYf722x7S}{Introduction To Metric Spaces - Paige Bright (2023)} 120 | \end{itemize} 121 | 122 | \newpage 123 | 124 | # Reading Schedule 125 | 126 | **RPT** is the abbreviation of **A First Look at Rigorous Probability Theory - Jeffrey S. Rosenthal (2nd Edition, 2006 or 2020)**. 127 | 128 | ::: {.callout-tip icon=false} 129 | ## **\faBook RPT \hfill Week 01-02 \faCalendar* ** 130 | 131 | \begin{itemize} 132 | \item[] Appendix A: Mathematical Background 133 | \item[] Chapter 1: The need for measure theory 134 | \item[] Chapter 2: Probability triples 135 | \end{itemize} 136 | ::: 137 | 138 | ::: {.callout-tip icon=false} 139 | ## **\faBook RPT \hfill Week 03-04 \faCalendar* ** 140 | 141 | \begin{itemize} 142 | \item[] Chapter 3: Further probabilistic foundations 143 | \item[] Chapter 4: Expected values 144 | \end{itemize} 145 | ::: 146 | 147 | ::: {.callout-tip icon=false} 148 | ## **\faBook RPT \hfill Week 05-06 \faCalendar* ** 149 | 150 | \begin{itemize} 151 | \item[] Chapter 5: Inequality and convergence 152 | \item[] Chapter 6: Distributions of random variables 153 | \end{itemize} 154 | ::: 155 | 156 | ::: {.callout-tip icon=false} 157 | ## **\faBook RPT \hfill Week 07-08 \faCalendar* ** 158 | 159 | \begin{itemize} 160 | \item[] Chapter 9: More probability theorems 161 | \item[] Chapter 10: Weak convergence 162 | \end{itemize} 163 | ::: 164 | 165 | ::: {.callout-tip icon=false} 166 | ## **\faBook RPT \hfill Week 09-10 \faCalendar* ** 167 | 168 | \begin{itemize} 169 | \item[] Chapter 11: Characteristic functions 170 | \end{itemize} 171 | ::: 172 | 173 | ::: {.callout-tip icon=false} 174 | ## **\faBook RPT \hfill Week 11-12 \faCalendar* ** 175 | 176 | \begin{itemize} 177 | \item[] Chapter 12: Decomposition of probability laws 178 | \item[] Chapter 13: Conditional probability and expectation 179 | \end{itemize} 180 | ::: 181 | 182 | # Further Readings (Optional) 183 | 184 | ::: {.callout-note appearance="minimal"} 185 | \begin{itemize} 186 | \item[] Our Measure Theory syllabus at \href{https://github.com/zekiakyol/proof-based-math-readings}{\faGithub github.com/zekiakyol/proof-based-math-readings} 187 | \end{itemize} 188 | ::: 189 | -------------------------------------------------------------------------------- /source/PBMR_LargeSampleTheory_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Large Sample Theory**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=2cm 24 | - left=2cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Large Sample Theory*. 71 | 72 | # Prerequisites and Format 73 | 74 | - Proof Techniques and Real Analysis resources below. 75 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 76 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 77 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 78 | 79 | # Resources 80 | 81 | ## Main Book and Main Book's Playlist 82 | 83 | **Elements of Large-Sample Theory - Erich L. Lehmann (1999)** is our main book for this session because it is well-written and well-structured. 84 | 85 | Jingyi Jessica Li's playlist is our main playlist because her narrative is great. 86 | 87 | \begin{itemize} 88 | \item[\faBook] Elements of Large-Sample Theory - Erich L. Lehmann (1999) $\mspace{18mu} \rightarrow$ Easier but doesn't contain solutions 89 | \item[\faBook] \href{https://github.com/zekiakyol/compact-erratas/blob/main/ElementsOfLargeSampleTheory_ErichLehmann_Errata.pdf}{Elements of Large-Sample Theory - Erich L. Lehmann (1999, Errata)} 90 | \item[\faBook] A Course in Large Sample Theory - Thomas S. Ferguson (2002) $\rightarrow$ Harder but contains solutions 91 | \item[\faBook] \href{https://www.math.ucla.edu/~tom/LST/Errata.pdf}{A Course in Large Sample Theory - Thomas S. Ferguson (2002, Errata)} 92 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLAYxx7zX5F1NKukTVwMADi1D5dbufWJkz}{A Course in Large Sample Theory - Thomas S. Ferguson (2002, Playlist by Jingyi Jessica Li)} 93 | \item[\faBook] \href{https://jsb-lab.org/stats-203-large-sample-theory}{A Course in Large Sample Theory - Thomas S. Ferguson (2002, Notes by Jingyi Jessica Li)} 94 | \end{itemize} 95 | 96 | ## Supplementary 97 | 98 | ### Large-Sample Theory 99 | 100 | \begin{itemize} 101 | \item[\faBook] \href{https://sites.psu.edu/drh20/david-hunters-home-page/asymptotics-notes}{Notes for a Graduate-Level Course in Asymptotics for Statisticians - David R. Hunter (2025)} 102 | \item[\faScroll] \href{https://www.jstor.org/stable/25652246}{Understanding Convergence Concepts: A Visual-Minded and Graphical Simulation-Based Approach - P. Micheaux, B. Liquet (2009)} 103 | \end{itemize} 104 | 105 | ### Proof Techniques 106 | 107 | \begin{itemize} 108 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 109 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum)} 110 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn)} 111 | \end{itemize} 112 | 113 | ### Real Analysis 114 | 115 | \begin{itemize} 116 | \item[\faBook] \href{https://www.jirka.org/ra}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025)} 117 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025, Playlist by Casey Rodriguez)} 118 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP613ULTyHAqz04niYf722x7S}{Introduction To Metric Spaces - Paige Bright (2023)} 119 | \end{itemize} 120 | 121 | \newpage 122 | 123 | # Reading Schedule 124 | 125 | - **ELST** is the abbreviation of **Elements of Large-Sample Theory - Erich L. Lehmann (1999)**. 126 | 127 | ::: {.callout-tip icon=false} 128 | ## **\faBook ELST, Chapter 1: Mathematical Background \hfill Week 01-02 \faCalendar* ** 129 | 130 | \begin{itemize} 131 | \item[] \textbf{1.1} The concept of limit 132 | \item[] \textbf{1.2} Embedding sequences 133 | \item[] \textbf{1.3} Infinite series 134 | \item[] \textbf{1.4} Order relations and rates of convergence 135 | \item[] \textbf{1.5} Continuity 136 | \item[] \textbf{1.6} Distributions 137 | \end{itemize} 138 | ::: 139 | 140 | ::: {.callout-tip icon=false} 141 | ## **\faBook ELST, Chapter 2: Convergence in Probability and in Law \hfill Week 03-04-05-06 \faCalendar* ** 142 | 143 | \begin{itemize} 144 | \item[] \textbf{2.1} Convergence in probability 145 | \item[] \textbf{2.2} Applications 146 | \item[] \textbf{2.3} Convergence in law 147 | \item[] \textbf{2.4} The central limit theorem 148 | \item[] \textbf{2.5} Taylor's theorem and the delta method 149 | \item[] \textbf{2.6} Uniform convergence 150 | \item[] \textbf{2.7} The CLT for independent non-identical random variables 151 | \item[] \textbf{2.8} Central limit theorem for dependent variables 152 | \end{itemize} 153 | ::: 154 | 155 | ::: {.callout-tip icon=false} 156 | ## **\faBook ELST, Chapter 3: Performance of Statistical Tests \hfill Week 07-08-09 \faCalendar* ** 157 | 158 | \begin{itemize} 159 | \item[] \textbf{3.1} Critical values 160 | \item[] \textbf{3.2} Comparing two treatments 161 | \item[] \textbf{3.3} Power and sample size 162 | \item[] \textbf{3.4} Comparison of tests: Relative efficiency 163 | \item[] \textbf{3.5} Robustness 164 | \end{itemize} 165 | ::: 166 | 167 | ::: {.callout-tip icon=false} 168 | ## **\faBook ELST, Chapter 4: Estimation \hfill Week 10-11-12 \faCalendar* ** 169 | 170 | \begin{itemize} 171 | \item[] \textbf{4.1} Confidence intervals 172 | \item[] \textbf{4.2} Accuracy of point estimators 173 | \item[] \textbf{4.3} Comparing estimators 174 | \item[] \textbf{4.4} Sampling from a finite population 175 | \end{itemize} 176 | ::: 177 | 178 | # Further Readings (Optional) 179 | 180 | ::: {.callout-note appearance="minimal"} 181 | \begin{itemize} 182 | \item[\faBook] Asymptotic Theory for Econometricians - Halbert White (Revised Edition, 2000) 183 | \end{itemize} 184 | ::: 185 | -------------------------------------------------------------------------------- /source/PBMR_Topology_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Topology**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=2cm 24 | - left=2cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Topology*. 71 | 72 | # Prerequisites and Format 73 | 74 | - Proof Techniques and Real Analysis resources below. 75 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 76 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 77 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 78 | 79 | # Resources 80 | 81 | ## Main Book and Main Book's Playlist 82 | 83 | **Topology - James Munkres (2nd Edition, 2014)** is our main book for this session because it is well-written, well-structured, and has plenty of intuitive figures. 84 | 85 | \begin{itemize} 86 | \item[\faBook] Topology - James Munkres (2nd Edition, 2014) 87 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLLq_gUfXAnkl8bjQh-hGQ9u24xZP9x0dx}{Topology - James Munkres (2nd Edition, 2014, Playlist by Bruno Zimmermann, Video 1-15)} 88 | \item[\faBook] \href{https://math-study.net/topology}{Topology - James Munkres (2nd Edition, 2014, Solutions for Chapter 1-2 by Dan Whitman)} 89 | \item[\faBook] \href{https://solverer.com/library/james_munkres/topology_classic_version}{Topology - James Munkres (2nd Edition, 2014, Solutions for Chapter 1-2 by solverer)} 90 | \item[\faBook] \href{https://positron0802.wordpress.com/topology-munkres}{Topology - James Munkres (2nd Edition, 2014, Solutions for Chapter 2-3 by positron0802)} 91 | \item[\faBook] \href{https://dbfin.com/topology/munkres/}{Topology - James Munkres (2nd Edition, 2014, Solutions for Chapter 1-2-3-4 by dbFin)} 92 | \end{itemize} 93 | 94 | ## Supplementary 95 | 96 | ### Topology 97 | 98 | \begin{itemize} 99 | \item[\faBook] Schaum's Outline of General Topology - Seymour Lipschutz (2011) $\rightarrow$ Beginner friendly and contains solutions 100 | \item[\faBook] \href{https://www.topologywithouttears.net}{Topology Without Tears - Sidney A. Morris (2024)} $\mspace{112mu} \rightarrow$ Beginner friendly and open-access 101 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLfKcn7LuYa_Kr3_aWePrYufu7MMYWYM5-}{General Topology - Bernard Badzioch (2020)} 102 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PL9ERqa15B9_v10p-Agp4yq-90tRYoEUv6}{Intuitive Topology - Troy Kling (2021)} 103 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLd8NbPjkXPliJunBhtDNMuFsnZPeHpm-0}{Topology - Marius Furter (2022)} 104 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1y0GB1oYh0HZ8UTIyMJN03J}{Topology - Michael Penn (2025)} 105 | \end{itemize} 106 | 107 | ### Proof Techniques 108 | 109 | \begin{itemize} 110 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 111 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum)} 112 | \end{itemize} 113 | 114 | ### Real Analysis 115 | 116 | \begin{itemize} 117 | \item[\faBook] \href{https://www.jirka.org/ra}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025)} 118 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025, Playlist by Casey Rodriguez)} 119 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP613ULTyHAqz04niYf722x7S}{Introduction To Metric Spaces - Paige Bright (2023)} 120 | \end{itemize} 121 | 122 | \newpage 123 | 124 | # Reading Schedule 125 | 126 | **TM** is the abbreviation of **Topology - James Munkres (2nd Edition, 2014)**. 127 | 128 | ::: {.callout-tip icon=false} 129 | ## **\faBook TM, Chapter 1: Set Theory and Logic \hfill Week 01 \faCalendar* ** 130 | 131 | \begin{itemize}\setlength\itemsep{-0.1cm} 132 | \item[] \textbf{1} Fundamental Concepts 133 | \item[] \textbf{2} Functions 134 | \item[] \textbf{3} Relations 135 | \item[] \textbf{4} The Integers and the Real Numbers 136 | \item[] \textbf{5} Cartesian Products 137 | \item[] \textbf{6} Finite Sets 138 | \item[] \textbf{7} Countable and Uncountable Sets 139 | \item[] \textbf{8} The Principle of Recursive Definition 140 | \item[] \textbf{9} Infinite Sets and the Axiom of Choice 141 | \item[] \textbf{10} Well-Ordered Sets 142 | \item[] \textbf{11} The Maximum Principle 143 | \end{itemize} 144 | ::: 145 | 146 | ::: {.callout-tip icon=false} 147 | ## **\faBook TM, Chapter 2: Topological Spaces and Continuous Functions \hfill Week 02-03-04-05-06-07 \faCalendar* ** 148 | 149 | \begin{itemize}\setlength\itemsep{-0.1cm} 150 | \item[] \textbf{12} Topological Spaces 151 | \item[] \textbf{13} Basis for a Topology 152 | \item[] \textbf{14} The Order Topology 153 | \item[] \textbf{15} The Product Topology on $X \times Y$ 154 | \item[] \textbf{16} The Subspace Topology 155 | \item[] \textbf{17} Closed Sets and Limit Points 156 | \item[] \textbf{18} Continuous Functions 157 | \item[] \textbf{19} The Product Topology 158 | \item[] \textbf{20} The Metric Topology 159 | \item[] \textbf{21} The Metric Topology (continued) 160 | \end{itemize} 161 | ::: 162 | 163 | ::: {.callout-tip icon=false} 164 | ## **\faBook TM, Chapter 3: Connectedness and Compactness \hfill Week 08-09-10-11-12 \faCalendar* ** 165 | 166 | \begin{itemize}\setlength\itemsep{-0.1cm} 167 | \item[] \textbf{23} Connected Spaces 168 | \item[] \textbf{24} Connected Subspaces of the Real Line 169 | \item[] \textbf{25} Components and Local Connectedness 170 | \item[] \textbf{26} Compact Spaces 171 | \item[] \textbf{27} Compact Subspaces of the Real Line 172 | \item[] \textbf{28} Limit Point Compactness 173 | \item[] \textbf{29} Local Compactness 174 | \end{itemize} 175 | ::: 176 | 177 | # Further Readings (Optional) 178 | 179 | ::: {.callout-note appearance="minimal"} 180 | \begin{itemize} 181 | \item[] Our Measure Theory and Measure Theoretic Probability syllabuses at \href{https://github.com/zekiakyol/proof-based-math-readings}{\faGithub github.com/zekiakyol/proof-based-math-readings} 182 | \end{itemize} 183 | ::: 184 | -------------------------------------------------------------------------------- /source/PBMR_BayesianStatistics_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Bayesian Statistics**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=1.6cm 24 | - left=1.6cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Bayesian Statistics*. 71 | 72 | # Prerequisites and Format 73 | 74 | - Proof Techniques and Statistics resources below. 75 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 76 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 77 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 78 | 79 | # Resources 80 | 81 | ## Main Book and Main Book's Playlist 82 | 83 | **Bayesian Econometrics - Gary Koop (2003)** is our main book for this session because it is well-written and well-structured. 84 | 85 | Gary Koop's playlist is our main playlist because his narrative is great. 86 | 87 | \begin{itemize} 88 | \item[\faBook] Bayesian Econometrics - Gary Koop (2003) 89 | \item[\faBook] \href{https://www.wiley.com/legacy/wileychi/koopbayesian/supp/corrections.pdf}{Bayesian Econometrics - Gary Koop (2003, Errata)} 90 | \item[\faYoutube] \href{https://strath-my.sharepoint.com/:f:/g/personal/ping_wu_strath_ac_uk/EgGn4azLQjtBhZJ7Sx3MAwMBxccM-CnOgleiOIN22gCq4Q?e=XEKe5u}{Bayesian Econometrics - Gary Koop (2003, Playlist)} 91 | \end{itemize} 92 | 93 | ## Supplementary 94 | 95 | ### Bayesian Statistics 96 | 97 | \begin{itemize} 98 | \item[\faBook] \href{https://www.bayesrulesbook.com}{Bayes Rules! - Alicia A. Johnson, Miles Q. Ott, Mine Dogucu (2021)} 99 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdiokWB9gEpm}{Bayesian Statistics: A Comprehensive Course - Ben Lambert (2014)} 100 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLwJRxp3blEvZ8AKMXOy0fc0cqT61GsKCG}{A Student's Guide to Bayesian Statistics - Ben Lambert (2020)} 101 | \item[\faBook] \href{https://sites.stat.columbia.edu/gelman/book/}{Bayesian Data Analysis - A. Gelman, J. Carlin, H. Stern, D. Dunson, A. Vehtari, D. Rubin (3rd Ed., 2025)} 102 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLBqnAso5Dy7O0IVoVn2b-WtetXQk5CDk6}{Bayesian Data Analysis - A. Gelman, J. Carlin, H. Stern, D. Dunson, A. Vehtari, D. Rubin (3rd Ed., 2025, Playlist)} 103 | \item[\faScroll] \href{https://www.jstor.org/stable/2685208}{Explaining the Gibbs Sampler - George Casella, Edward I. George (1992)} 104 | \item[\faScroll] \href{https://www.jstor.org/stable/2684568}{Understanding the Metropolis-Hastings Algorithm - Siddhartha Chib, Edward Greenberg (1995)} 105 | \end{itemize} 106 | 107 | ### Proof Techniques 108 | 109 | \begin{itemize} 110 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 111 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum)} 112 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn)} 113 | \end{itemize} 114 | 115 | ### Statistics 116 | 117 | \begin{itemize} 118 | \item[\faBook] \href{https://ocw.mit.edu/courses/res-6-012-introduction-to-probability-spring-2018/d973b10c2587781f86ca4f2aff49098f_MITRES_6_012S18_Textbook.pdf}{Introduction to Probability - Dimitri Bertsekas, John Tsitsiklis (2nd Edition, 2008, Summary Material)} 119 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP60hI9ATjSFgLZpbNJ7myAg6}{Introduction to Probability - Dimitri Bertsekas, John Tsitsiklis (2nd Edition, 2008, Playlist)} 120 | \item[\faBook] \href{http://athenasc.com/probbook.html}{Introduction to Probability - Dimitri Bertsekas, John Tsitsiklis (2nd Edition, 2008, Solutions \& Errata)} 121 | \end{itemize} 122 | 123 | \newpage 124 | 125 | # Reading Schedule 126 | 127 | - **BE** is the abbreviation of **Bayesian Econometrics - Gary Koop (2003)**. 128 | 129 | ::: {.callout-tip icon=false} 130 | ## **\faBook BE \hfill Week 01 \faCalendar* ** 131 | 132 | \begin{itemize} 133 | \item[] \textbf{Appendix A} Introduction to Matrix Algebra 134 | \item[] \textbf{Appendix B} Introduction to Probability and Statistics 135 | \item[] \textbf{1} An Overview of Bayesian Econometrics 136 | \end{itemize} 137 | ::: 138 | 139 | ::: {.callout-tip icon=false} 140 | ## **\faBook BE \hfill Week 02 \faCalendar* ** 141 | 142 | \begin{itemize} 143 | \item[] \textbf{2} The Normal Linear Regression Model with Natural Conjugate Prior and a Single Explanatory Variable 144 | \end{itemize} 145 | ::: 146 | 147 | ::: {.callout-tip icon=false} 148 | ## **\faBook BE \hfill Week 03-04 \faCalendar* ** 149 | 150 | \begin{itemize} 151 | \item[] \textbf{3} The Normal Linear Regression Model with Natural Conjugate Prior and Many Explanatory Variables 152 | \end{itemize} 153 | ::: 154 | 155 | ::: {.callout-tip icon=false} 156 | ## **\faBook BE \hfill Week 05-06 \faCalendar* ** 157 | 158 | \begin{itemize} 159 | \item[] \textbf{4} The Normal Linear Regression Model with Other Priors 160 | \end{itemize} 161 | ::: 162 | 163 | ::: {.callout-tip icon=false} 164 | ## **\faBook BE \hfill Week 07-08 \faCalendar* ** 165 | 166 | \begin{itemize} 167 | \item[] \textbf{5} The Nonlinear Regression Model 168 | \end{itemize} 169 | ::: 170 | 171 | ::: {.callout-tip icon=false} 172 | ## **\faBook BE \hfill Week 09-10 \faCalendar* ** 173 | 174 | \begin{itemize} 175 | \item[] \textbf{6} The Linear Regression Model with General Error Covariance Matrix 176 | \end{itemize} 177 | ::: 178 | 179 | ::: {.callout-tip icon=false} 180 | ## **\faBook BE \hfill Week 11-12 \faCalendar* ** 181 | 182 | \begin{itemize} 183 | \item[] \textbf{7} The Linear Regression Model with Panel Data 184 | \end{itemize} 185 | ::: 186 | 187 | # Further Readings (Optional) 188 | 189 | ::: {.callout-note appearance="minimal"} 190 | \begin{itemize} 191 | \item[\faBook] Bayesian Econometric Methods - Joshua Chan, Gary Koop, Dale Poirier, Justin Tobias (2nd Edition, 2019) 192 | \item[\faBook] \href{https://web.ics.purdue.edu/~jltobias/second_edition/errata.pdf}{Bayesian Econometric Methods - Joshua Chan, Gary Koop, Dale Poirier, Justin Tobias (2nd Edition, 2019, Errata)} 193 | \end{itemize} 194 | ::: 195 | -------------------------------------------------------------------------------- /source/PBMR_RealAnalysis_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Real Analysis**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=2cm 24 | - left=2cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Real Analysis*. 71 | 72 | # Prerequisites and Format 73 | 74 | - Proof Techniques resources below. 75 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 76 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 77 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 78 | 79 | # Resources [All are open-access] 80 | 81 | ## Main Book and Main Book's Playlist 82 | 83 | **Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025)** is our main book for this session because it is well-written, well-structured, and open-access. 84 | 85 | Casey Rodriguez's playlist is our main playlist because his narrative is great. 86 | 87 | \begin{itemize} 88 | \item[\faBook] \href{https://www.jirka.org/ra}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025)} 89 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025, Playlist by Casey Rodriguez)} 90 | \item[\faBook] \href{https://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/resources/mit18_100af20_lec_full2/}{Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025, Notes by Casey Rodriguez)} 91 | \end{itemize} 92 | 93 | ## Supplementary 94 | 95 | ### Real Analysis 96 | 97 | \begin{itemize} 98 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLztBpqftvzxWo4HxUYV58ENhxHV32Wxli}{Real Analysis - Wrath of Math (2025)} $\quad \rightarrow$ Start with this playlist if you find the main book challenging 99 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PL22w63XsKjqxqaF-Q7MSyeSG1W1_xaQoS}{Real Analysis - Michael Penn (2021)} 100 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLysi2xmniDSzz6xT7IzOifpoexeKccThh}{Understanding Analysis - Stephen Abbott (2nd Edition, 2016, Playlist by Marc Renault)} 101 | \item[\faBook] \href{https://uli.rocks/abbott}{Understanding Analysis - Stephen Abbott (2nd Edition, 2016, Solutions by Ulisse Mini, Jesse Liby)} 102 | \end{itemize} 103 | 104 | ### Calculus 105 | 106 | \begin{itemize} 107 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr}{Essence of Calculus - 3Blue1Brown (2023)} 108 | \item[\faBook\faYoutube] \href{https://ocw.mit.edu/courses/18-01-single-variable-calculus-fall-2006}{Single Variable Calculus - David Jerison (2006)} and \href{https://ocw.mit.edu/courses/18-02-multivariable-calculus-fall-2007}{Multivariable Calculus - Denis Auroux (2007)} 109 | \item[\faCalculator] \href{https://www.geogebra.org/m/f08hfjvx}{Sequences and Series Calculator - Geogebra} 110 | \item[\faCalculator] \href{https://www.geogebra.org/graphing}{Function Graph - Geogebra} 111 | \end{itemize} 112 | 113 | ### Proof Techniques 114 | 115 | \begin{itemize} 116 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 117 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum, Chapters 1-12)} 118 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn, Chapters 1-14)} 119 | \end{itemize} 120 | 121 | \newpage 122 | 123 | # Reading Schedule 124 | 125 | - **BAI** is the abbreviation of Basic Analysis I: Introduction to Real Analysis - Jiri Lebl (Version 6.2, 2025). 126 | 127 | ::: {.callout-tip icon=false} 128 | ## **\faBook BAI, Chapter 0: Introduction \hfill Week 01 \faCalendar* ** 129 | 130 | \begin{itemize}\setlength\itemsep{-0.2cm} 131 | \item[] List of Notation (Page 309-312) 132 | \item[] \textbf{0.1} About this book 133 | \item[] \textbf{0.2} About analysis 134 | \item[] \textbf{0.3} Basic set theory 135 | \end{itemize} 136 | ::: 137 | 138 | ::: {.callout-tip icon=false} 139 | ## **\faBook BAI, Chapter 1: Real Numbers \hfill Week 02 \faCalendar* ** 140 | 141 | \begin{itemize}\setlength\itemsep{-0.2cm} 142 | \item[] \textbf{1.1} Basic properties 143 | \item[] \textbf{1.2} The set of real numbers 144 | \item[] \textbf{1.3} Absolute value and bounded functions 145 | \item[] \textbf{1.4} Intervals and the size of $\mathbb{R}$ 146 | \end{itemize} 147 | ::: 148 | 149 | ::: {.callout-tip icon=false} 150 | ## **\faBook BAI, Chapter 2: Sequence and Series \hfill Week 03-04-05 \faCalendar* ** 151 | 152 | \begin{itemize}\setlength\itemsep{-0.2cm} 153 | \item[] \textbf{2.1} Sequences and limits 154 | \item[] \textbf{2.2} Facts about limits of sequences 155 | \item[] \textbf{2.3} Limit superior, limit inferior, and Bolzano-Weierstrass 156 | \item[] \textbf{2.4} Cauchy sequences 157 | \item[] \textbf{2.5} Series 158 | \end{itemize} 159 | ::: 160 | 161 | ::: {.callout-tip icon=false} 162 | ## **\faBook BAI, Chapter 3: Continuous Functions \hfill Week 06-07-08 \faCalendar* ** 163 | 164 | \begin{itemize}\setlength\itemsep{-0.2cm} 165 | \item[] \textbf{3.1} Limits of functions 166 | \item[] \textbf{3.2} Continuous functions 167 | \item[] \textbf{3.3} Extreme and intermediate value theorems 168 | \item[] \textbf{3.4} Uniform continuity 169 | \end{itemize} 170 | ::: 171 | 172 | ::: {.callout-tip icon=false} 173 | ## **\faBook BAI, Chapter 4: The Derivative \hfill Week 09-10 \faCalendar* ** 174 | 175 | \begin{itemize}\setlength\itemsep{-0.2cm} 176 | \item[] \textbf{4.1} The derivative 177 | \item[] \textbf{4.2} Mean value theorem 178 | \item[] \textbf{4.3} Taylor's theorem 179 | \end{itemize} 180 | ::: 181 | 182 | ::: {.callout-tip icon=false} 183 | ## **\faBook BAI, Chapter 5: The Riemann Integral \hfill Week 11-12 \faCalendar* ** 184 | 185 | \begin{itemize}\setlength\itemsep{-0.2cm} 186 | \item[] \textbf{5.1} The Riemann integral 187 | \item[] \textbf{5.2} Properties of the integral 188 | \item[] \textbf{5.3} Fundamental theorem of calculus 189 | \end{itemize} 190 | ::: 191 | 192 | # Further Readings (Optional) 193 | 194 | ::: {.callout-note appearance="minimal"} 195 | \begin{itemize} 196 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUl4u3cNGP613ULTyHAqz04niYf722x7S}{Introduction To Metric Spaces - Paige Bright (2023)} 197 | \end{itemize} 198 | ::: 199 | -------------------------------------------------------------------------------- /source/PBMR_LinearAlgebra_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Linear Algebra**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=2cm 24 | - left=2cm 25 | - top=2cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Linear Algebra*. 71 | - This session is dedicated to Sheldon Axler's lovely cat, [\faCat Moon](https://x.com/AxlerLinear/status/1691162877888204800), who passed away in August 2023. 72 | 73 | # Prerequisites and Format 74 | 75 | - Proof Techniques resources below and [\faYoutube Linear Algebra - Gilbert Strang (2005)](https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8). 76 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 77 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 78 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 79 | 80 | # Resources [All are open-access] 81 | 82 | ## Main Book and Main Book's Playlist 83 | 84 | **Linear Algebra Done Right - Sheldon Axler (4th Edition, 2025, Errata-free version)** is our main book for this session because it is well-written, well-structured, and open-access. 85 | 86 | Robert Won's playlist is our main playlist because his narrative is great. 87 | 88 | \begin{itemize} 89 | \item[\faBook] \href{https://linear.axler.net/LADR4e.pdf}{Linear Algebra Done Right - Sheldon Axler (4th Edition, 2025, Errata-free version)} 90 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLoxJTbDttvt7ny0WEJHWw6-0Sjx7EImIQ}{Linear Algebra Done Right - Sheldon Axler (4th Edition, 2025, Playlist by Robert Won)} 91 | \item[\faYoutube] \href{https://linear.axler.net/LADRvideos4e.html}{Linear Algebra Done Right - Sheldon Axler (4th Edition, 2025, Playlist by Sheldon Axler)} 92 | \item[\faBook] \href{https://blogs.gwu.edu/robertwon/2024/02/02/linear-algebra-done-right-course/}{Linear Algebra Done Right - Sheldon Axler (4th Edition, 2025, Notes by Robert Won)} 93 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLUOF6EOFxCQ2BY71kLBGleN0c9aKke3Vd}{Linear Algebra Done Right - Sheldon Axler (4th Edition, 2025, Solutions by MathwithoutCommentary)} 94 | \item[\faBook] \href{https://github.com/motivationss/Linear_Algebra_Done_Right_4th_ManualSolution}{Linear Algebra Done Right - Sheldon Axler (4th Edition, 2025, Solutions by Oliver Li)} 95 | \item[\faBook] \href{https://github.com/nehc0/Linear-Algebra-Done-Right-4th-Solutions}{Linear Algebra Done Right - Sheldon Axler (4th Edition, 2025, Solutions by nehc0)} 96 | \item[\faBook] \href{https://linearalgebras.com}{Linear Algebra Done Right - Sheldon Axler (3rd Edition, 2015, Solutions by linearalgebras)} 97 | \item[\faBook] \href{https://github.com/jubnoske08/linear_algebra}{Linear Algebra Done Right - Sheldon Axler (3rd Edition, 2015, Solutions by jubnoske08)} 98 | \item[\faBook] \href{https://solverer.com/library/sheldon_axler/linear_algebra_done_right?utm_source=reddit&utm_medium=link}{Linear Algebra Done Right - Sheldon Axler (3rd Edition, 2015, Solutions by Solverer)} 99 | \end{itemize} 100 | 101 | ## Supplementary 102 | 103 | ### Linear Algebra 104 | 105 | \begin{itemize} 106 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab}{Essence of Linear Algebra - 3Blue1Brown (2023)} 107 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLflMyS1QOtxwiN5oOuyY4W_8fZlTTnRcF}{Linear Algebra Done Right - Sheldon Axler (3rd Edition, 2015, Playlist by Jason Morton)} 108 | \item[\faScroll] \href{https://www.axler.net/DwD.pdf}{Down with Determinants! - Sheldon Axler (1994)} 109 | \end{itemize} 110 | 111 | ### Proof Techniques 112 | 113 | \begin{itemize} 114 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 115 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum)} 116 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn)} 117 | \end{itemize} 118 | 119 | \newpage 120 | 121 | # Reading Schedule 122 | 123 | - **LADR** is the abbreviation of **Linear Algebra Done Right - Sheldon Axler (4th Edition, 2025)**. 124 | 125 | ::: {.callout-tip icon=false} 126 | ## **\faBook LADR, Chapter 1: Vector Spaces \hfill Week 01 \faCalendar* ** 127 | 128 | \begin{itemize}\setlength\itemsep{-0.2cm} 129 | \item[] \textbf{1A} $\mathbf{R}^n$ and $\mathbf{C}^n$ 130 | \item[] \textbf{1B} Definition of Vector Space 131 | \item[] \textbf{1C} Subspaces 132 | \end{itemize} 133 | ::: 134 | 135 | ::: {.callout-tip icon=false} 136 | ## **\faBook LADR, Chapter 2: Finite-Dimensional Vector Spaces \hfill Week 02-03 \faCalendar* ** 137 | 138 | \begin{itemize}\setlength\itemsep{-0.2cm} 139 | \item[] \textbf{2A} Span and Linear Independence 140 | \item[] \textbf{2B} Bases 141 | \item[] \textbf{2C} Dimension 142 | \end{itemize} 143 | ::: 144 | 145 | ::: {.callout-tip icon=false} 146 | ## **\faBook LADR, Chapter 3: Linear Maps \hfill Week 04-05-06 \faCalendar* ** 147 | 148 | \begin{itemize}\setlength\itemsep{-0.2cm} 149 | \item[] \textbf{3A} Vector Space of Linear Maps 150 | \item[] \textbf{3B} Null Spaces and Ranges 151 | \item[] \textbf{3C} Matrices 152 | \item[] \textbf{3D} Invertibility and Isomorphisms 153 | \end{itemize} 154 | ::: 155 | 156 | ::: {.callout-tip icon=false} 157 | ## **\faBook LADR, Chapter 5: Eigenvalues and Eigenvectors \hfill Week 07-08 \faCalendar* ** 158 | 159 | \begin{itemize}\setlength\itemsep{-0.2cm} 160 | \item[] \textbf{5A} Invariant Subspaces 161 | \item[] \textbf{5B} The Minimal Polynomial 162 | \item[] \textbf{5C} Upper-Triangular Matrices 163 | \item[] \textbf{5D} Diagonalizable Operators 164 | \end{itemize} 165 | ::: 166 | 167 | ::: {.callout-tip icon=false} 168 | ## **\faBook LADR, Chapter 6: Inner Product Spaces \hfill Week 09-10 \faCalendar* ** 169 | 170 | \begin{itemize}\setlength\itemsep{-0.2cm} 171 | \item[] \textbf{6A} Inner Products and Norms 172 | \item[] \textbf{6B} Orthonormal Bases 173 | \item[] \textbf{6C} Orthogonal Complements and Minimization Problems 174 | \end{itemize} 175 | ::: 176 | 177 | ::: {.callout-tip icon=false} 178 | ## **\faBook LADR, Chapter 7: Operators on Inner Product Spaces \hfill Week 11-12 \faCalendar* ** 179 | 180 | \begin{itemize}\setlength\itemsep{-0.2cm} 181 | \item[] \textbf{7A} Self-Adjoint and Normal Operators 182 | \item[] \textbf{7B} Spectral Theorem 183 | \item[] \textbf{7C} Positive Operators 184 | \item[] \textbf{7D} Isometries, Unitary Operators, and Matrix Factorization 185 | \item[] \textbf{7E} Singular Value Decomposition 186 | \end{itemize} 187 | ::: 188 | 189 | # Further Readings (Optional) 190 | 191 | ::: {.callout-note appearance="minimal"} 192 | \begin{itemize} 193 | \item[\faBook] Matrix Analysis - Roger A. Horn, Charles R. Johnson (2nd Edition, 2013) 194 | \end{itemize} 195 | ::: 196 | -------------------------------------------------------------------------------- /source/PBMR_Statistics_Syllabus.qmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "**Proof-Based Math Readings \n Session: Statistics**" 3 | date: now 4 | date-format: "[Version:] DD MMMM YYYY, hh:mm A" 5 | author: "[**Zeki Akyol**](https://zekiakyol.com) \n Department of Economics \n University of California, Santa Cruz \n [Click here for the most recent version](https://github.com/zekiakyol/proof-based-math-readings)" 6 | thanks: "[zekiakyol.com](https://zekiakyol.com)" 7 | pdf-engine: pdflatex 8 | fig-dpi: 300 9 | df-print: tibble 10 | highlight-style: tango 11 | knitr: 12 | opts_chunk: 13 | collapse: true 14 | message: false 15 | fig.align: center 16 | comment: "#>" 17 | format: 18 | pdf: 19 | documentclass: article 20 | papersize: letter 21 | fontsize: 10pt 22 | geometry: 23 | - right=2cm 24 | - left=2cm 25 | - top=1.5cm 26 | - bottom=2cm 27 | toc: true 28 | toc-depth: 3 29 | toccolor: blue 30 | number-sections: true 31 | colorlinks: true 32 | urlcolor: magenta 33 | citecolor: blue 34 | execute: 35 | echo: true 36 | warning: false 37 | include-in-header: 38 | text: | 39 | \usepackage{sectsty} 40 | \allsectionsfont{\color{blue}} 41 | \setcounter{section}{-1} 42 | \usepackage{microtype} 43 | \DisableLigatures{encoding = *, family = *} 44 | \usepackage[fixed]{fontawesome5} 45 | \usepackage{float, amsmath, amssymb, amsfonts, bm, mathtools, mathastext} 46 | \usepackage[dvipsnames]{xcolor} 47 | \usepackage{enumitem} 48 | \setlist[itemize]{itemsep=0cm} 49 | \usepackage{hyperref} 50 | \hypersetup{pdfpagemode=UseNone} 51 | editor: source 52 | --- 53 | 54 | ```{r} 55 | #| echo: false 56 | library(knitr) 57 | ``` 58 | 59 | ```{r} 60 | #| echo: false 61 | #| out-width: 35% 62 | knitr::include_graphics("figures/proofbasedmathreadings_logo_square.png") 63 | ``` 64 | 65 | \newpage 66 | 67 | # Motivation 68 | 69 | - *Proof-Based Math Readings* is a free, independent online reading group where we study the mathematics required for economics master’s and PhD programs through an intuitive approach. Active since May 2023. 70 | - This session of the reading group is on *Statistics*. 71 | 72 | # Prerequisites and Format 73 | 74 | - [Introduction to Probability - Dimitri Bertsekas, John Tsitsiklis (2nd Edition, 2008, Summary Material)](https://ocw.mit.edu/courses/res-6-012-introduction-to-probability-spring-2018/d973b10c2587781f86ca4f2aff49098f_MITRES_6_012S18_Textbook.pdf) 75 | - [Introduction to Probability - Dimitri Bertsekas, John Tsitsiklis (2nd Edition, 2008, Playlist)](https://www.youtube.com/playlist?list=PLUl4u3cNGP60hI9ATjSFgLZpbNJ7myAg6) 76 | - [Introduction to Probability - Dimitri Bertsekas, John Tsitsiklis (2nd Edition, 2008, Solutions \& Errata)](http://athenasc.com/probbook.html) 77 | - Please use the [\faLink Application Form](https://docs.google.com/forms/d/e/1FAIpQLSf3OxwYuAwiDXMVTCQ_x3FTtKnHmRRkl_SXlpdfqTDty06PxQ/viewform) to join our reading group; you will receive a response within a week. 78 | - This session takes 12 weeks. We do not have face-to-face/online meetings due to the size of the group. 79 | - Members read the main book and discuss the topics/exercises in the Proof-Based Math Readings Discord \faDiscord. 80 | 81 | # Resources 82 | 83 | ## Main Book and Main Book's Playlist 84 | 85 | **Statistical Inference - George Casella, Roger Berger (2nd Edition, 2001 or 2024)** is our main book because it is well-written and well-structured. 86 | 87 | \begin{itemize} 88 | \item[\faBook] Statistical Inference - George Casella, Roger Berger (2nd Edition, 2001 or 2024) 89 | \item[\faBook] \href{https://archived.stat.ufl.edu/casella/class/errata7.pdf}{Statistical Inference - George Casella, Roger Berger (2nd Edition, 2001, Errata)} 90 | \item[\faBook] \href{https://www.ams.sunysb.edu/~zhu/ams570/Solutions-Casella-Berger.pdf}{Statistical Inference - George Casella, Roger Berger (2nd Edition, 2001 or 2024, Solutions)} 91 | \item[\faYoutube] \href{https://onedrive.live.com/?redeem=aHR0cHM6Ly8xZHJ2Lm1zL2YvYy84ZjBhMjRjODgwYTdjZDRiL0Vrdk5wNERJSkFvZ2dJOXdBQUFBQUFBQjlNRm9LdGNXc1VGUHBmcnUyaktxMmc%5FZT1HdFZsQWE&id=8F0A24C880A7CD4B%21112&cid=8F0A24C880A7CD4B}{Statistical Inference - George Casella, Roger Berger (2nd Edition, 2001 or 2024, Playlist for Chapter 1-5 by Stephen Carden)} 92 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLbRMhDVUMngeD_vOeveVE-3b7wu_AZph9}{Statistical Inference - George Casella, Roger Berger (2nd Edition, 2001 or 2024, Playlist for Chapter 5-9 by Somesh Kumar)} 93 | \end{itemize} 94 | 95 | ## Supplementary 96 | 97 | ### Probability and Statistics 98 | 99 | \begin{itemize} 100 | \item[\faBook] \href{https://drive.google.com/file/d/1VmkAAGOYCTORq1wxSQqy255qLJjTNvBI/edit}{Introduction to Probability - Joseph K. Blitzstein, Jessiza Hwang (2nd Edition, 2019)} 101 | \item[\faBook] \href{https://stat110.hsites.harvard.edu/strategic-practice-problems}{Introduction to Probability - Joseph K. Blitzstein, Jessiza Hwang (2nd Edition, 2019, Selected Solutions)} 102 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PL2SOU6wwxB0uwwH80KTQ6ht66KWxbzTIo}{Introduction to Probability - Joseph K. Blitzstein, Jessiza Hwang (2nd Edition, 2019, Playlist)} 103 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLAYxx7zX5F1PIvRju27s4CRAwhSGoxhVg}{Introduction to Mathematical Statistics - Jingyi Jessica Li (2022)} 104 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLLyj1Zd4UWrPZH-fknPLak0tlUpUISBZR}{Mathematical Statistics - Jem N. Corcoran (2024)} 105 | \item[\faBook] \href{https://statproofbook.github.io}{The Book of Statistical Proofs - Joram Soch (2024)} 106 | \item[\faYoutube] \href{https://ledaliang.github.io/journalclub/index.html#}{Statistical Ideas that Changed the World - Robert Tibshirani (2024, Interview Series)} 107 | \item[\faScroll] \href{https://arxiv.org/pdf/0804.2996}{The Epic Story of Maximum Likelihood Stephen - M. Stigler (2008)} 108 | \end{itemize} 109 | 110 | ### Proof Techniques 111 | 112 | \begin{itemize} 113 | \item[\faBook] \href{https://richardhammack.github.io/BookOfProof/}{Book of Proof - Richard Hammack (3.4 Edition, 2025)} 114 | \item[\faYoutube] \href{https://www.youtube.com/@jeremy9959/playlists?view=50&sort=dd&shelf_id=5}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Jeremy Teitelbaum)} 115 | \item[\faYoutube] \href{https://www.youtube.com/playlist?list=PLVMgvCDIRy1x00m7Oo9XzEkDDACeEK_m-}{Book of Proof - Richard Hammack (3.4 Edition, 2025, Playlist by Michael Penn)} 116 | \end{itemize} 117 | 118 | \newpage 119 | 120 | # Reading Schedule 121 | 122 | **SI** is the abbreviation of Statistical Inference - George Casella, Roger Berger (2nd Edition, 2001 or 2024). 123 | 124 | ::: {.callout-tip icon=false} 125 | ## **\faBook SI, Chapter 1: Probability Theory \hfill Week 01 \faCalendar* ** 126 | 127 | \begin{itemize}\setlength\itemsep{-0.22cm} 128 | \item[] \textbf{1.1} Set Theory 129 | \item[] \textbf{1.2} Probability Theory 130 | \item[] \textbf{1.3} Conditional Probability and Independence 131 | \item[] \textbf{1.4} Random Variables 132 | \item[] \textbf{1.5} Distribution Functions 133 | \item[] \textbf{1.6} Density and Mass Functions 134 | \end{itemize} 135 | ::: 136 | 137 | ::: {.callout-tip icon=false} 138 | ## **\faBook SI, Chapter 2: Transformations and Expectations \hfill Week 02 \faCalendar* ** 139 | 140 | \begin{itemize}\setlength\itemsep{-0.22cm} 141 | \item[] \textbf{2.1} Distributions of a Random Variable 142 | \item[] \textbf{2.2} Expected Values 143 | \item[] \textbf{2.3} Moments and Moment Generating Functions 144 | \end{itemize} 145 | ::: 146 | 147 | ::: {.callout-tip icon=false} 148 | ## **\faBook SI, Chapter 3: Common Families of Distributions \hfill Week 03-04 \faCalendar* ** 149 | 150 | \begin{itemize}\setlength\itemsep{-0.22cm} 151 | \item[] \textbf{3.1} Introduction 152 | \item[] \textbf{3.2} Discrete Distributions 153 | \item[] \textbf{3.3} Continuous Distributions 154 | \item[] \textbf{3.4} Exponential Families 155 | \item[] \textbf{3.5} Location and Scale Families 156 | \item[] \textbf{3.6} Inequality and Identities 157 | \end{itemize} 158 | ::: 159 | 160 | ::: {.callout-tip icon=false} 161 | ## **\faBook SI, Chapter 4: Multiple Random Variables \hfill Week 05-06 \faCalendar* ** 162 | 163 | \begin{itemize}\setlength\itemsep{-0.22cm} 164 | \item[] \textbf{4.1} Joint and Marginal Distributions 165 | \item[] \textbf{4.2} Conditional Distributions and Independence 166 | \item[] \textbf{4.3} Bivariate Transformations 167 | \item[] \textbf{4.4} Hierarchical Models and Mixture Distributions 168 | \item[] \textbf{4.5} Covariance and Correlation 169 | \item[] \textbf{4.6} Multivariate Distributions 170 | \item[] \textbf{4.7} Inequalities 171 | \end{itemize} 172 | ::: 173 | 174 | ::: {.callout-tip icon=false} 175 | ## **\faBook SI, Chapter 5: Properties of a Random Sample \hfill Week 07-08 \faCalendar* ** 176 | 177 | \begin{itemize}\setlength\itemsep{-0.22cm} 178 | \item[] \textbf{5.1} Basic Concepts of Random Samples 179 | \item[] \textbf{5.2} Sums of Random Variables from a Random Sample 180 | \item[] \textbf{5.3} Sampling from the Normal Distribution 181 | \item[] \textbf{5.4} Order Statistics 182 | \item[] \textbf{5.5} Convergence Concepts 183 | \item[] \textbf{5.6} Generating a Random Sample 184 | \end{itemize} 185 | ::: 186 | 187 | ::: {.callout-tip icon=false} 188 | ## **\faBook SI, Chapter 7: Point Estimation \hfill Week 09-10 \faCalendar* ** 189 | 190 | \begin{itemize}\setlength\itemsep{-0.22cm} 191 | \item[] \textbf{7.1} Introduction 192 | \item[] \textbf{7.2} Methods of Finding Estimators 193 | \item[] \textbf{7.3} Methods of Evaluating Estimators 194 | \end{itemize} 195 | ::: 196 | 197 | ::: {.callout-tip icon=false} 198 | ## **\faBook SI, Chapter 8: Hypothesis Testing \hfill Week 11-12 \faCalendar* ** 199 | 200 | \begin{itemize}\setlength\itemsep{-0.22cm} 201 | \item[] \textbf{8.1} Introduction 202 | \item[] \textbf{8.2} Methods of Finding Tests 203 | \item[] \textbf{8.3} Methods of Evaluating Tests 204 | \end{itemize} 205 | ::: 206 | --------------------------------------------------------------------------------