└── README.md /README.md: -------------------------------------------------------------------------------- 1 | # How to learn Mathematics from the ground up 2 | A guide to the intrepid adventurer 3 | 4 | 5 | ## Description 6 | 7 | Imagine the following scenario, you are a middle age engineer that studied applied mathematics in the context of a certain field of engineering and would like to remember everything again, or better to learn everything again from the ground up! With your knowledge of having done the path once, and experience to know what is a good book, what would be the best path to revisit everything again, or to structure the best a path to a friends children or a family member life journey? This will be a journey from the most basics mathematics, all the way to pure mathematics, a real adventure along 50 books :-D
8 | 9 | 10 | ## Important and free resource 11 | 12 | One of the most valuable resources in math from kinder garden to college math.
13 | 14 | * Khan Academy
15 | https://www.khanacademy.org/ 16 | 17 | 18 | ## Motivational books on Mathematics 19 | 20 | 1. **Video - The Map of Mathematics**
21 | [https://www.youtube.com/watch?v=OmJ-4B-mS-Y](https://www.youtube.com/watch?v=OmJ-4B-mS-Y) 22 | 23 | 2. **The Math Book - Big Ideas Simply Explained**
24 | by DK 25 | 26 | 3. **The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth**
27 | by Paul Hoffman 28 | 29 | 4. **Logicomix: An epic search for truth**
30 | by Apostolos Doxiadis, Christos Papadimitriou 31 | 32 | 33 | ## First years in math 34 | 35 | This is a series that focus on giving you a problem solving mentality, with this book series the intent is to teach you how you to solve problems with mathematics as a tool. The solution books have worked out problems, so you can rely on them for self study.
36 | 37 | 1. **The Art of Problem Solving: Prealgebra**
38 | by Richard Rusczyk, David Patrick, Ravi Boppana
39 | Text: 608 pages. Solutions: 224 pages. 40 | 41 | 2. **The Art of Problem Solving: Introduction to Algebra, 2nd Ed**
42 | by Richard Rusczyk
43 | Text: 656 pages. Solutions: 312 pages. 44 | 45 | 3. **The Art of Problem Solving: Introduction to Counting & Probability, 2nd Ed**
46 | by David Patrick
47 | Text: 256 pages. Solutions: 120 pages. 48 | 49 | 4. **The Art of Problem Solving: Introduction to Geometry, 2nd Ed**
50 | by Richard Rusczyk
51 | Text: 557 pages. Solutions: 226 pages. 52 | 53 | 5. **The Art of Problem Solving: Introduction to Number Theory**
54 | by Mathew Crawford
55 | Text: 336 pages. Solutions: 144 pages. 56 | 57 | 58 | ## Intermediate years in math 59 | 60 | 1. **The Art of Problem Solving: Intermediate Algebra**
61 | by Richard Rusczyk and Mathew Crawford
62 | Text: 720 pages. Solutions: 336 pages. 63 | 64 | 2. **The Art of Problem Solving: Intermediate Counting & Probability**
65 | by David Patrick
66 | Text: 400 pages. Solutions: 208 pages. 67 | 68 | 69 | ## Pre-Calculus 70 | 71 | At this point you have three good options see what adjusts better to you.
72 | 73 | 1. **The Art of Problem Solving: Precalculus, 2nd Ed**
74 | by Richard Rusczyk
75 | Text: 528 pages. Solutions: 272 pages. 76 | 77 | 2. **Precalculus: Mathematics for Calculus 7th ed**
78 | by James Stewart, Lothar Redlin, Saleem Watson 79 | 80 | 3. **Precalculus**
81 | by Jay Abramson
82 | [https://openstax.org/details/books/precalculus](https://openstax.org/details/books/precalculus) 83 | 84 | 85 | # University or college mathematics 86 | 87 | 88 | ## Linear Algebra 89 | 90 | You will learn Linear Algebra with examples in code (Python and Matlab) without calculus.
91 | 92 | 1. **Linear Algebra: Theory, Intuition, Code**
93 | by Mike X Cohen 94 | 95 | 96 | ## Calculus and friends 97 | 98 | This is a book to motivate you to go further in the most beautiful way!
99 | 100 | 1. **Calculus Made Easy**
101 | by Silvanus P. Thompson, Martin Gardner 102 | 103 | Then to my knowledge there are 3 similar good paths that you can follow, but with increasing depth in mathematics and Calculus.
104 | 105 | 106 | **First path**
107 | 108 | 109 | 2. **Engineering Mathematics, 5th Ed**
110 | by Prof Anthony Croft, Dr Robert Davison, et al. 111 | 112 | 113 | **Second path**
114 | 115 | 116 | 3. **Modern Engineering Mathematics, 6th Ed**
117 | by Glyn James, Phil Dyke 118 | 119 | 4. **Advanced Modern Engineering Mathematics, 5th Ed**
120 | by Glyn James, David Burley, Dick Clements, et al. 121 | 122 | 123 | **Third path**
124 | 125 | 126 | 5. **Mathematical Methods for Physics and Engineering: A Comprehensive Guide 3rd Ed**
127 | by K. F. Riley 128 | 129 | 6. **Student Solution Manual 1st Ed for Mathematical Methods for Physics and Engineering 3th Ed**
130 | by K. F. Riley 131 | 132 | 133 | ## Fourier Series and Transforms 134 | 135 | 1. **Fourier Analysis: An Introduction**
136 | by Elias M. Stein and Rami Shakarchi 137 | 138 | 2. **Fast Fourier Transform and Its Applications 2th Ed**
139 | by E. Brigham 140 | 141 | 142 | ## Probability and Statistics 143 | 144 | Then you need to learn about Probability and Statistics the following are two nice books with a companion book with the solutions.
145 | 146 | 1. **Probability: For the Enthusiastic Beginner**
147 | by David J. Morin 148 | 149 | 2. **Introduction to Probability, Statistics, and Random Processes**
150 | by Hossein Pishro-Nik
151 | [http://www.probabilitycourse.com/preface.php](http://www.probabilitycourse.com/preface.php) 152 | 153 | 3. **Student's Solutions Guide for Introduction to Probability, Statistics, and Random Processes**
154 | by Hossein Pishro-Nik
155 | [http://www.probabilitycourse.com/preface.php](http://www.probabilitycourse.com/preface.php) 156 | 157 | 4. **All of Statistics: A Concise Course in Statistical Inference**
158 | by Larry Wasserman 159 | 160 | 161 | ## Optimization 162 | 163 | Then you will need to learn about Optimization, two good books, the first with code in Julia.
164 | 165 | 1. **Algorithms for Optimization**
166 | by Mykel J. Kochenderfer, Tim A. Wheeler
167 | Note: See the book PDF site link on the authors page.
168 | [https://mykel.kochenderfer.com/textbooks/](https://mykel.kochenderfer.com/textbooks/) 169 | 170 | 2. **Convex Optimization**
171 | by Boyd, Vandenberghe
172 | [https://web.stanford.edu/~boyd/cvxbook/](https://web.stanford.edu/~boyd/cvxbook/) 173 | 174 | 175 | ## Discrete Mathematics 176 | 177 | 1. **Discrete Mathematics with Applications 5th Ed**
178 | by Susanna S. Epp 179 | 180 | 181 | ## Numerical Analysis and Computational Mathematics 182 | 183 | 1. **Numerical Methods for Engineers 8th Ed**
184 | by Steven Chapra, Raymond Canale 185 | 186 | 2. **Numerical Recipes 3rd Edition: The Art of Scientific Computing**
187 | by William H. Press 188 | 189 | 3. **Numerical Methods in Physics with Python**
190 | by Alex Gezerlis 191 | 192 | 4. **Computational Physics: Problem Solving with Python 3rd Ed**
193 | by Rubin H. Landau, Manuel J Páez, Cristian C. Bordeianu 194 | 195 | 5. **Applied Computational Physics**
196 | by Joseph F. Boudreau, Eric S. Swanson 197 | 198 | 6. **Hans Petter Langtangen - Various writings**
199 | [http://hplgit.github.io/](http://hplgit.github.io/) 200 | 201 | 7. **Hans Petter Langtangen - Last versions**
202 | [https://library.oapen.org/discover?rpp=10&etal=0&query=Langtangen%2C+Hans+Petter&scope=&group_by=none&page=1](https://library.oapen.org/discover?rpp=10&etal=0&query=Langtangen%2C+Hans+Petter&scope=&group_by=none&page=1) 203 | 204 | 205 | ## Information Theory 206 | 207 | 1. **A Mind at Play: How Claude Shannon Invented the Information Age**
208 | by Jimmy Soni, Rob Goodman
209 | 210 | 2. **Information Theory, Inference and Learning Algorithms**
211 | by David J. C. MacKay
212 | Note: In the author site you have de **book** and the **video lectures**.
213 | [http://www.inference.org.uk/mackay/itila/](http://www.inference.org.uk/mackay/itila/) 214 | 215 | 216 | ## Error Correction Codes 217 | 218 | 1. **Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications**
219 | by Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
220 | Note: Book on open access.
221 | [https://www.springer.com/gp/book/9783319511023](https://www.springer.com/gp/book/9783319511023) 222 | 223 | 2. **Error Correction Coding: Mathematical Methods and Algorithms 2nd Ed**
224 | by Todd K. Moon 225 | 226 | 227 | ## Problems with answers 228 | 229 | 1. **Schaum's 3,000 Solved Problems in Calculus**
230 | by Elliott Mendelson 231 | 232 | 2. **Schaum's Outline of Calculus, 6th Ed**
233 | by Frank Ayres, Elliott Mendelson 234 | 235 | 3. **Schaum's Outline of Advanced Calculus, 3rd Ed**
236 | by Robert Wrede, Murray Spiegel 237 | 238 | 4. **Schaum's Outline of Advanced Mathematics for Engineers and Scientists**
239 | by Murray Spiegel 240 | 241 | 5. **Schaum's Outline of Probability and Statistics, 4th Ed**
242 | by John Schiller, R. Alu Srinivasan, Murray Spiegel 243 | 244 | 6. **Schaum's Outline of Discrete Mathematics, 3rd Ed**
245 | by Seymour Lipschutz, Marc Lipson 246 | 247 | 7. **Schaum's Outline of Complex Variables, 2th Ed**
248 | by Murray Spiegel, Seymour Lipschutz, John Schiller, Dennis Spellman 249 | 250 | 8. **Schaum's Outline of Differential Equations, 4th Ed**
251 | by Richard Bronson, Gabriel B. Costa 252 | 253 | 8. **Schaum's Outline of Partial Differential Equations**
254 | by Paul DuChateau, D. Zachmann 255 | 256 | 10. **Vector Analysis, 2nd Ed**
257 | by Murray Spiegel, Seymour Lipschutz, Dennis Spellman 258 | 259 | 11. **Schaums Outline of Tensor Calculus**
260 | by David Kay 261 | 262 | 263 | ## Very good synthesis of all around Mathematics 264 | 265 | 1. **The Princeton Companion to Mathematics**
266 | by Timothy Gowers, June Barrow-Green, Imre Leader 267 | 268 | 2. **The Princeton Companion to Applied Mathematics**
269 | by Nicholas J. Higham, Mark R. Dennis, Paul Glendinning, Paul A. Martin, Fadil Santosa, Jared Tanner 270 | 271 | 272 | # To go further into Pure Mathematics 273 | 274 | This book section specific recommendation come from the wonderful video about learning pure mathematics, see the video and the video description for more details.
275 | 276 | * Aleph 0 - How to learn pure mathematics on your own: a complete self-study guide
277 | [https://www.youtube.com/watch?v=fo-alw2q-BU](https://www.youtube.com/watch?v=fo-alw2q-BU) 278 | 279 | 280 | ## Real Analysis 281 | 282 | 1. **Calculus, 4th Ed**
283 | by Michael Spivak, Michael Spivak 284 | 285 | 2. **Combined Answer Book For Calculus Third and Fourth Editions, 1th Ed**
286 | by Michael Spivak 287 | 288 | 3. **Understanding Analysis**
289 | by Stephen Abbott. 290 | 291 | 292 | ## Linear Algebra 293 | 294 | 2. **Linear Algebra Done Right**
295 | by Sheldon Axler 296 | 297 | 298 | And for the problems.
299 | 300 | 301 | 3. **Linear Algebra**
302 | by Insel, Freidberg, and Spence 303 | 304 | 305 | ## Topology 306 | 307 | 1. **Topology through Inquiry**
308 | by Su and Starbird 309 | 310 | 311 | ## Differential Equations 312 | 313 | 1. **Differential Equations with Boundary Value Problems**
314 | by Zill and Cullen 315 | 316 | 317 | ## Complex Analysis 318 | 319 | 1. **A Friendly Approach to Complex Analysis**
320 | by Sara Maad and Amol Sasane 321 | 322 | 2. **Visual Complex Analysis**
323 | by Tristan Needham 324 | 325 | 326 | ## Abstract Algebra 327 | 328 | 1. **Contemporary Abstract Algebra**
329 | by Gallian 330 | 331 | 332 | ## Differential Geometry 333 | 334 | 1. **A Geometric Approach to Differential Forms**
335 | by David Bachman 336 | 337 | 2. **Introduction to Manifolds**
338 | by Loring Tu 339 | 340 | 341 | # The great men and women behind mathematics 342 | 343 | 1. **Men of Mathematics**
344 | by E.T. Bell 345 | 346 | 347 | # All my other guides 348 | 349 | * The links to all my guides are in:
350 | **Guides on Linux - Programming - Embedded - Electronics - Aeronautics**
351 | [https://github.com/joaocarvalhoopen/Guides_Linux-Programming-Electronics-Aeronautics](https://github.com/joaocarvalhoopen/Guides_Linux-Programming-Electronics-Aeronautics) 352 | 353 | 354 | # Have fun! 355 | 356 | Best regards,
357 | João Nuno Carvalho 358 | --------------------------------------------------------------------------------