├── .gitignore ├── CS598-Topics-in-Graph-Algorithms ├── Figures │ ├── SSSP-dummy-source.pdf │ ├── SSSP-dummy-source.pdf_tex │ ├── SSSP-dummy-source.svg │ ├── SSSP-fix-dag.pdf │ ├── SSSP-fix-dag.pdf_tex │ ├── SSSP-fix-dag.svg │ ├── SSSP-hop.pdf │ ├── SSSP-hop.pdf_tex │ ├── SSSP-hop.svg │ ├── algo-tree-embedding-recursive-tree-construction.pdf │ ├── algo-tree-embedding-recursive-tree-construction.pdf_tex │ ├── algo-tree-embedding-recursive-tree-construction.svg │ ├── boundary-and-partition-well-linked-cut-tree.pdf │ ├── boundary-and-partition-well-linked-cut-tree.pdf_tex │ ├── boundary-and-partition-well-linked-cut-tree.svg │ ├── constant-degree-blow-up.pdf │ ├── constant-degree-blow-up.pdf_tex │ ├── constant-degree-blow-up.svg │ ├── cover.png │ ├── cut-matching-linear-projection.pdf │ ├── cut-matching-linear-projection.pdf_tex │ ├── cut-matching-linear-projection.svg │ ├── cut-tree.pdf │ ├── cut-tree.pdf_tex │ ├── cut-tree.svg │ ├── expander-cut-tree-star.pdf │ ├── expander-cut-tree-star.pdf_tex │ ├── expander-cut-tree-star.svg │ ├── expansion-matching.pdf │ ├── expansion-matching.pdf_tex │ ├── expansion-matching.svg │ ├── grid-cut-tree.pdf │ ├── grid-cut-tree.pdf_tex │ ├── grid-cut-tree.svg │ ├── grid-well-linked.pdf │ ├── grid-well-linked.pdf_tex │ ├── grid-well-linked.svg │ ├── hierarchical-expander-decomposition-characterization.pdf │ ├── hierarchical-expander-decomposition-characterization.pdf_tex │ ├── hierarchical-expander-decomposition-characterization.svg │ ├── highway.pdf │ ├── highway.pdf_tex │ ├── highway.svg │ ├── isolating-cut-bipartition-cut.pdf │ ├── isolating-cut-bipartition-cut.pdf_tex │ ├── isolating-cut-bipartition-cut.svg │ ├── isolating-cut-unique-disjoint.pdf │ ├── isolating-cut-unique-disjoint.pdf_tex │ ├── isolating-cut-unique-disjoint.svg │ ├── label.pdf │ ├── label.pdf_tex │ ├── label.svg │ ├── multi-cut-random-partition-probability-proof-case.pdf │ ├── multi-cut-random-partition-probability-proof-case.pdf_tex │ ├── multi-cut-random-partition-probability-proof-case.svg │ ├── multi-cut-random-partition-probability-proof.pdf │ ├── multi-cut-random-partition-probability-proof.pdf_tex │ ├── multi-cut-random-partition-probability-proof.svg │ ├── negative-weight-edge-splitting.pdf │ ├── negative-weight-edge-splitting.pdf_tex │ ├── negative-weight-edge-splitting.svg │ ├── partition.pdf │ ├── partition.pdf_tex │ ├── partition.svg │ ├── residual-graph.pdf │ ├── residual-graph.pdf_tex │ ├── residual-graph.svg │ ├── respect.pdf │ ├── respect.pdf_tex │ ├── respect.svg │ ├── tree-decomposition-cycle.pdf │ ├── tree-decomposition-cycle.pdf_tex │ ├── tree-decomposition-cycle.svg │ ├── tree-decomposition-tree.pdf │ ├── tree-decomposition-tree.pdf_tex │ ├── tree-decomposition-tree.svg │ ├── tree-decomposition.pdf │ ├── tree-decomposition.pdf_tex │ └── tree-decomposition.svg ├── GraphAlgo.bbl ├── GraphAlgo.pdf ├── GraphAlgo.synctex.gz ├── GraphAlgo.tex ├── Lectures │ ├── lec_1.tex │ ├── lec_10.tex │ ├── lec_11.tex │ ├── lec_12.tex │ ├── lec_13.tex │ ├── lec_14.tex │ ├── lec_15.tex │ ├── lec_16.tex │ ├── lec_17.tex │ ├── lec_18.tex │ ├── lec_19.tex │ ├── lec_2.tex │ ├── lec_20.tex │ ├── lec_21.tex │ ├── lec_22.tex │ ├── lec_23.tex │ ├── lec_24.tex │ ├── lec_3.tex │ ├── lec_4.tex │ ├── lec_5.tex │ ├── lec_6.tex │ ├── lec_7.tex │ ├── lec_8.tex │ └── lec_9.tex ├── appendix.tex ├── indent.log └── reference.bib ├── EECS544-Analysis-of-Social-Networks ├── Figures │ ├── action-function-eg.pdf │ ├── action-function-eg.pdf_tex │ ├── action-function-eg.svg │ ├── bipartite-graph-generalization.pdf │ ├── bipartite-graph-generalization.pdf_tex │ ├── bipartite-graph-generalization.svg │ ├── branching-processes.pdf │ ├── branching-processes.pdf_tex │ ├── branching-processes.svg │ ├── cover.png │ ├── katz-centrality.pdf │ ├── katz-centrality.pdf_tex │ ├── katz-centrality.svg │ ├── monte-carlo-estimator-1.pdf │ ├── monte-carlo-estimator-1.pdf_tex │ ├── monte-carlo-estimator-1.svg │ ├── monte-carlo-estimator-2 copy.pdf_tex │ ├── monte-carlo-estimator-2.pdf │ ├── monte-carlo-estimator-2.pdf_tex │ ├── monte-carlo-estimator-2.svg │ ├── monte-carlo-estimator-3 copy.pdf_tex │ ├── monte-carlo-estimator-3.pdf │ ├── monte-carlo-estimator-3.pdf_tex │ ├── monte-carlo-estimator-3.svg │ ├── monte-carlo-estimator-4.pdf │ ├── monte-carlo-estimator-4.pdf_tex │ ├── monte-carlo-estimator-4.svg │ ├── ne-football.pdf │ ├── ne-football.pdf_tex │ ├── ne-football.svg │ ├── ne-intersection.pdf │ ├── ne-intersection.pdf_tex │ ├── ne-intersection.svg │ ├── ne-market-entering.pdf │ ├── ne-market-entering.pdf_tex │ ├── ne-market-entering.svg │ ├── ne-matching-pennies.pdf │ ├── ne-matching-pennies.pdf_tex │ ├── ne-matching-pennies.svg │ ├── ne-social-welfare.pdf │ ├── ne-social-welfare.pdf_tex │ ├── ne-social-welfare.svg │ ├── pareto-optimal.pdf │ ├── pareto-optimal.pdf_tex │ ├── pareto-optimal.svg │ ├── personalized-pagerank.pdf │ ├── personalized-pagerank.pdf_tex │ ├── personalized-pagerank.svg │ ├── probability-simplex.pdf │ ├── probability-simplex.pdf_tex │ ├── probability-simplex.svg │ ├── random-graph-cn.pdf │ ├── random-graph-cn.pdf_tex │ ├── random-graph-cn.svg │ ├── random-graph-logn.pdf │ ├── random-graph-logn.pdf_tex │ ├── random-graph-logn.svg │ ├── random-graph-n^c.pdf │ ├── random-graph-n^c.pdf_tex │ ├── random-graph-n^c.svg │ ├── random-walker.pdf │ ├── random-walker.pdf_tex │ ├── random-walker.svg │ ├── rmk:lec11-1.pdf │ ├── rmk:lec11-1.pdf_tex │ ├── rmk:lec11-1.svg │ ├── satisfaction-eg-1.pdf │ ├── satisfaction-eg-1.pdf_tex │ ├── satisfaction-eg-1.svg │ ├── satisfaction-eg-2.pdf │ ├── satisfaction-eg-2.pdf_tex │ ├── satisfaction-eg-2.svg │ ├── satisfaction-eg-3.pdf │ ├── satisfaction-eg-3.pdf_tex │ ├── satisfaction-eg-3.svg │ ├── sub-critical-regime.pdf │ ├── sub-critical-regime.pdf_tex │ ├── sub-critical-regime.svg │ ├── super-critical-regime.pdf │ ├── super-critical-regime.pdf_tex │ ├── super-critical-regime.svg │ ├── triadic-closure.pdf │ ├── triadic-closure.pdf_tex │ ├── triadic-closure.svg │ ├── two-component-graph.pdf │ ├── two-component-graph.pdf_tex │ ├── two-component-graph.svg │ ├── utility-c.pdf │ ├── utility-c.pdf_tex │ └── utility-c.svg ├── Lectures │ ├── lec_1.tex │ ├── lec_10.tex │ ├── lec_11.tex │ ├── lec_12.tex │ ├── lec_13.tex │ ├── lec_14.tex │ ├── lec_15.tex │ ├── lec_16.tex │ ├── lec_17.tex │ ├── lec_18.tex │ ├── lec_19.tex │ ├── lec_2.tex │ ├── lec_20.tex │ ├── lec_21.tex │ ├── lec_22.tex │ ├── lec_23.tex │ ├── lec_24.tex │ ├── lec_25.tex │ ├── lec_3.tex │ ├── lec_4.tex │ ├── lec_5.tex │ ├── lec_6.tex │ ├── lec_7.tex │ ├── lec_8.tex │ └── lec_9.tex ├── SocNetAnalysis.bbl ├── SocNetAnalysis.pdf ├── SocNetAnalysis.synctex.gz ├── SocNetAnalysis.tex ├── appendix.tex └── reference.bib ├── EECS598-001-Approximation-Algorithms-and-Hardness-of-Approximation ├── AppxAlgo.bbl ├── AppxAlgo.pdf ├── AppxAlgo.synctex.gz ├── AppxAlgo.tex ├── Figures │ ├── 3-coloring-threshold.pdf │ ├── 3-coloring-threshold.pdf_tex │ ├── 3-coloring-threshold.svg │ ├── 3-coloring.pdf │ ├── 3-coloring.pdf_tex │ ├── 3-coloring.svg │ ├── bipoint-rounding-II.pdf │ ├── bipoint-rounding-II.pdf_tex │ ├── bipoint-rounding-II.svg │ ├── bipoint-rounding-III.pdf │ ├── bipoint-rounding-III.pdf_tex │ ├── bipoint-rounding-III.svg │ ├── bipoint-rounding.pdf │ ├── bipoint-rounding.pdf_tex │ ├── bipoint-rounding.svg │ ├── cover.png │ ├── facility-location.pdf │ ├── facility-location.pdf_tex │ ├── facility-location.svg │ ├── fbv-line-segment.pdf │ ├── fbv-line-segment.pdf_tex │ ├── fbv-line-segment.svg │ ├── fbv-minimality.pdf │ ├── fbv-minimality.pdf_tex │ ├── fbv-minimality.svg │ ├── fbv-path.pdf │ ├── fbv-path.pdf_tex │ ├── fbv-path.svg │ ├── gw-ratio.pdf │ ├── gw-ratio.pdf_tex │ ├── gw-ratio.svg │ ├── indirected-connected.pdf │ ├── indirected-connected.pdf_tex │ ├── indirected-connected.svg │ ├── label-cover.pdf │ ├── label-cover.pdf_tex │ ├── label-cover.svg │ ├── lec13-1.pdf │ ├── lec13-1.pdf_tex │ ├── lec13-1.svg │ ├── max-k-coverage.pdf │ ├── max-k-coverage.pdf_tex │ ├── max-k-coverage.svg │ ├── memos-critique.pdf │ ├── mkc-compare-to-3lin.pdf │ ├── mkc-compare-to-3lin.pdf_tex │ ├── mkc-compare-to-3lin.svg │ ├── set-system-bip.pdf │ ├── set-system-bip.pdf_tex │ ├── set-system-bip.svg │ ├── unique-game.pdf │ ├── unique-game.pdf_tex │ └── unique-game.svg ├── Lectures │ ├── lec_1.tex │ ├── lec_10.tex │ ├── lec_11.tex │ ├── lec_12.tex │ ├── lec_13.tex │ ├── lec_14.tex │ ├── lec_15.tex │ ├── lec_16.tex │ ├── lec_17.tex │ ├── lec_18.tex │ ├── lec_19.tex │ ├── lec_2.tex │ ├── lec_20.tex │ ├── lec_21.tex │ ├── lec_22.tex │ ├── lec_23.tex │ ├── lec_24.tex │ ├── lec_25.tex │ ├── lec_26.tex │ ├── lec_3.tex │ ├── lec_4.tex │ ├── lec_5.tex │ ├── lec_6.tex │ ├── lec_7.tex │ ├── lec_8.tex │ └── lec_9.tex ├── appendix.tex └── reference.bib ├── MATH561-Linear-Programming ├── Figures │ ├── 1-norm.pdf │ ├── 1-norm.pdf_tex │ ├── 1-norm.svg │ ├── column-geometry.pdf │ ├── column-geometry.pdf_tex │ ├── column-geometry.svg │ ├── cones-join.pdf │ ├── cones-join.pdf_tex │ ├── cones-join.svg │ ├── convex-function.pdf │ ├── convex-function.pdf_tex │ ├── convex-function.svg │ ├── convex-piecewise-linear-function.pdf │ ├── convex-piecewise-linear-function.pdf_tex │ ├── convex-piecewise-linear-function.svg │ ├── convex-set.pdf │ ├── convex-set.pdf_tex │ ├── convex-set.svg │ ├── cover.png │ ├── cutting-planes-tighter-bound.pdf │ ├── cutting-planes-tighter-bound.pdf_tex │ ├── cutting-planes-tighter-bound.svg │ ├── extreme-ray.pdf │ ├── extreme-ray.pdf_tex │ ├── extreme-ray.svg │ ├── farkas-lemma-extended.pdf │ ├── farkas-lemma-extended.pdf_tex │ ├── farkas-lemma-extended.svg │ ├── farkas-lemma.pdf │ ├── farkas-lemma.pdf_tex │ ├── farkas-lemma.svg │ ├── feasible-direction.pdf │ ├── feasible-direction.pdf_tex │ ├── feasible-direction.svg │ ├── integer-programming-branch-and-bound.pdf │ ├── integer-programming-branch-and-bound.pdf_tex │ ├── integer-programming-branch-and-bound.svg │ ├── integer-programming-cutting-plane.pdf │ ├── integer-programming-cutting-plane.pdf_tex │ ├── integer-programming-cutting-plane.svg │ ├── integer-programming-eg1.2.pdf │ ├── integer-programming-eg1.2.pdf_tex │ ├── integer-programming-eg1.2.svg │ ├── integer-programming-eg1.3.pdf │ ├── integer-programming-eg1.3.pdf_tex │ ├── integer-programming-eg1.3.svg │ ├── integer-programming-eg1.4.pdf │ ├── integer-programming-eg1.4.pdf_tex │ ├── integer-programming-eg1.4.svg │ ├── integer-programming-eg1.pdf │ ├── integer-programming-eg1.pdf_tex │ ├── integer-programming-eg1.svg │ ├── integer-programming-eg2.pdf │ ├── integer-programming-eg2.pdf_tex │ ├── integer-programming-eg2.svg │ ├── integer-programming-pitfall.pdf │ ├── integer-programming-pitfall.pdf_tex │ ├── integer-programming-pitfall.svg │ ├── lagrangian-maximizer.pdf │ ├── lagrangian-maximizer.pdf_tex │ ├── lagrangian-maximizer.svg │ ├── local-analysis-dual.pdf │ ├── local-analysis-dual.pdf_tex │ ├── local-analysis-dual.svg │ ├── local-analysis.pdf │ ├── local-analysis.pdf_tex │ ├── local-analysis.svg │ ├── maximizer-lemma-triangle-inequality.pdf │ ├── maximizer-lemma-triangle-inequality.pdf_tex │ ├── maximizer-lemma-triangle-inequality.svg │ ├── opt-cones.pdf │ ├── opt-cones.pdf_tex │ ├── opt-cones.svg │ ├── pivot-swap.pdf │ ├── pivot-swap.pdf_tex │ ├── pivot-swap.svg │ ├── plateau.pdf │ ├── plateau.pdf_tex │ ├── plateau.svg │ ├── ray.pdf │ ├── ray.pdf_tex │ ├── ray.svg │ ├── representation-theorem.pdf │ ├── representation-theorem.pdf_tex │ ├── representation-theorem.svg │ ├── simplex.pdf │ ├── simplex.pdf_tex │ ├── simplex.svg │ ├── simplicial-cones.pdf │ ├── simplicial-cones.pdf_tex │ ├── simplicial-cones.svg │ ├── strong-weak-constraint.pdf │ ├── strong-weak-constraint.pdf_tex │ ├── strong-weak-constraint.svg │ ├── subgradient-theorem.pdf │ ├── subgradient-theorem.pdf_tex │ └── subgradient-theorem.svg ├── Lectures │ ├── lec_1.tex │ ├── lec_10.tex │ ├── lec_11.tex │ ├── lec_12.tex │ ├── lec_13.tex │ ├── lec_14.tex │ ├── lec_15.tex │ ├── lec_16.tex │ ├── lec_17.tex │ ├── lec_18.tex │ ├── lec_19.tex │ ├── lec_2.tex │ ├── lec_20.tex │ ├── lec_21.tex │ ├── lec_22.tex │ ├── lec_23.tex │ ├── lec_24.tex │ ├── lec_3.tex │ ├── lec_4.tex │ ├── lec_5.tex │ ├── lec_6.tex │ ├── lec_7.tex │ ├── lec_8.tex │ └── lec_9.tex ├── LinProg.bbl ├── LinProg.pdf ├── LinProg.synctex.gz ├── LinProg.tex └── reference.bib ├── MATH592-Introduction-to-Algebraic-Topology ├── AlgTop.bbl ├── AlgTop.pdf ├── AlgTop.synctex.gz ├── AlgTop.tex ├── Figures │ ├── 3-torus.pdf │ ├── 3-torus.pdf_tex │ ├── 3-torus.svg │ ├── ans:ex-1:lec-40.pdf │ ├── ans:ex-1:lec-40.pdf_tex │ ├── ans:ex-1:lec-40.svg │ ├── ans:ex-3:lec-40.pdf │ ├── ans:ex-3:lec-40.pdf_tex │ ├── ans:ex-3:lec-40.svg │ ├── c2-lec21.pdf │ ├── c2-lec21.pdf_tex │ ├── c2-lec21.svg │ ├── cellular-boundary-map.pdf │ ├── cellular-boundary-map.pdf_tex │ ├── cellular-boundary-map.svg │ ├── col:lec14:1.pdf │ ├── col:lec14:1.pdf_tex │ ├── col:lec14:1.svg │ ├── computing-local-homology-idea.pdf │ ├── computing-local-homology-idea.pdf_tex │ ├── computing-local-homology-idea.svg │ ├── connecting-homomorphism-relative-homology-rn.pdf │ ├── connecting-homomorphism-relative-homology-rn.pdf_tex │ ├── connecting-homomorphism-relative-homology-rn.svg │ ├── cover.png │ ├── def:covering-space.pdf │ ├── def:covering-space.pdf_tex │ ├── def:covering-space.svg │ ├── def:fundamental-group-elements.pdf │ ├── def:fundamental-group-elements.pdf_tex │ ├── def:fundamental-group-elements.svg │ ├── def:fundamental-group-inverses.pdf │ ├── def:fundamental-group-inverses.pdf_tex │ ├── def:fundamental-group-inverses.svg │ ├── def:fundamental-group.pdf │ ├── def:fundamental-group.pdf_tex │ ├── def:fundamental-group.svg │ ├── def:homotopy-equivalence.pdf │ ├── def:homotopy-equivalence.pdf_tex │ ├── def:homotopy-equivalence.svg │ ├── def:homotopy-of-paths.pdf │ ├── def:homotopy-of-paths.pdf_tex │ ├── def:homotopy-of-paths.svg │ ├── def:homotopy.pdf │ ├── def:homotopy.pdf_tex │ ├── def:homotopy.svg │ ├── def:local-degree.pdf │ ├── def:local-degree.pdf_tex │ ├── def:local-degree.svg │ ├── def:path-composition.pdf │ ├── def:path-composition.pdf_tex │ ├── def:path-composition.svg │ ├── def:relative-homology-1.pdf │ ├── def:relative-homology-1.pdf_tex │ ├── def:relative-homology-1.svg │ ├── def:relative-homology-2.pdf │ ├── def:relative-homology-2.pdf_tex │ ├── def:relative-homology-2.svg │ ├── def:simplex.pdf │ ├── def:simplex.pdf_tex │ ├── def:simplex.svg │ ├── def:standard-simplex.pdf │ ├── def:standard-simplex.pdf_tex │ ├── def:standard-simplex.svg │ ├── def:subsimplex.pdf │ ├── def:subsimplex.pdf_tex │ ├── def:subsimplex.svg │ ├── eg-2:seifert-van-kampen-theorem.pdf │ ├── eg-2:seifert-van-kampen-theorem.pdf_tex │ ├── eg-2:seifert-van-kampen-theorem.svg │ ├── eg:barycentric-subdivision.pdf │ ├── eg:barycentric-subdivision.pdf_tex │ ├── eg:barycentric-subdivision.svg │ ├── eg:cellular-homology-calc-torus.pdf │ ├── eg:cellular-homology-calc-torus.pdf_tex │ ├── eg:cellular-homology-calc-torus.svg │ ├── eg:closed-disk-eq-point.pdf │ ├── eg:closed-disk-eq-point.pdf_tex │ ├── eg:closed-disk-eq-point.svg │ ├── eg:constructing-sphere-1.pdf │ ├── eg:constructing-sphere-1.pdf_tex │ ├── eg:constructing-sphere-1.svg │ ├── eg:constructing-sphere-2-gluing-instr.pdf │ ├── eg:constructing-sphere-2-gluing-instr.pdf_tex │ ├── eg:constructing-sphere-2-gluing-instr.svg │ ├── eg:constructing-sphere-2.pdf │ ├── eg:constructing-sphere-2.pdf_tex │ ├── eg:constructing-sphere-2.svg │ ├── eg:constructing-torus-gluing-instr.pdf │ ├── eg:constructing-torus-gluing-instr.pdf_tex │ ├── eg:constructing-torus-gluing-instr.svg │ ├── eg:constructing-torus-simplicial.pdf │ ├── eg:constructing-torus-simplicial.pdf_tex │ ├── eg:constructing-torus-simplicial.svg │ ├── eg:constructing-torus.pdf │ ├── eg:constructing-torus.pdf_tex │ ├── eg:constructing-torus.svg │ ├── eg:cylinder-mobiusband.pdf │ ├── eg:cylinder-mobiusband.pdf_tex │ ├── eg:cylinder-mobiusband.svg │ ├── eg:degree-m-map-disks-computation.pdf │ ├── eg:degree-m-map-disks-computation.pdf_tex │ ├── eg:degree-m-map-disks-computation.svg │ ├── eg:degree-m-map-disks.pdf │ ├── eg:degree-m-map-disks.pdf_tex │ ├── eg:degree-m-map-disks.svg │ ├── eg:excision-1.pdf │ ├── eg:excision-1.pdf_tex │ ├── eg:excision-1.svg │ ├── eg:homology-rp2.pdf │ ├── eg:homology-rp2.pdf_tex │ ├── eg:homology-rp2.svg │ ├── eg:homotopy.pdf │ ├── eg:homotopy.pdf_tex │ ├── eg:homotopy.svg │ ├── eg:lec14:1.pdf │ ├── eg:lec14:1.pdf_tex │ ├── eg:lec14:1.svg │ ├── eg:lec14:2.pdf │ ├── eg:lec14:2.pdf_tex │ ├── eg:lec14:2.svg │ ├── eg:lec17:n-sheeted-cover.pdf │ ├── eg:lec17:n-sheeted-cover.pdf_tex │ ├── eg:lec17:n-sheeted-cover.svg │ ├── eg:lec17:regular.pdf │ ├── eg:lec17:regular.pdf_tex │ ├── eg:lec17:regular.svg │ ├── eg:lec31-degree-n.pdf │ ├── eg:lec31-degree-n.pdf_tex │ ├── eg:lec31-degree-n.svg │ ├── eg:lec31:cw-complex-torus.pdf │ ├── eg:lec31:cw-complex-torus.pdf_tex │ ├── eg:lec31:cw-complex-torus.svg │ ├── eg:more-careful-torus-cellular.pdf │ ├── eg:more-careful-torus-cellular.pdf_tex │ ├── eg:more-careful-torus-cellular.svg │ ├── eg:path-connected.pdf │ ├── eg:path-connected.pdf_tex │ ├── eg:path-connected.svg │ ├── eg:punched-circle.pdf │ ├── eg:punched-circle.pdf_tex │ ├── eg:punched-circle.svg │ ├── eg:quotient-cw-complex-sphere.pdf │ ├── eg:quotient-cw-complex-sphere.pdf_tex │ ├── eg:quotient-cw-complex-sphere.svg │ ├── eg:quotient-cw-complex-torus.pdf │ ├── eg:quotient-cw-complex-torus.pdf_tex │ ├── eg:quotient-cw-complex-torus.svg │ ├── eg:real-projective-space-degree.pdf │ ├── eg:real-projective-space-degree.pdf_tex │ ├── eg:real-projective-space-degree.svg │ ├── eg:rel-homotopy.pdf │ ├── eg:rel-homotopy.pdf_tex │ ├── eg:rel-homotopy.svg │ ├── eg:seifert-van-kampen-theorem.pdf │ ├── eg:seifert-van-kampen-theorem.pdf_tex │ ├── eg:seifert-van-kampen-theorem.svg │ ├── eg:star-shaped.pdf │ ├── eg:star-shaped.pdf_tex │ ├── eg:star-shaped.svg │ ├── ex:cw-complex-gluing.pdf │ ├── ex:cw-complex-gluing.pdf_tex │ ├── ex:cw-complex-gluing.svg │ ├── higher-homotopy-group-dim2.pdf │ ├── higher-homotopy-group-dim2.pdf_tex │ ├── higher-homotopy-group-dim2.svg │ ├── lec-41-2.pdf │ ├── lec-41-2.pdf_tex │ ├── lec-41-2.svg │ ├── lec-41-3.pdf │ ├── lec-41-3.pdf_tex │ ├── lec-41-3.svg │ ├── lec11-eg2:torus-ver2.pdf │ ├── lec11-eg2:torus-ver2.pdf_tex │ ├── lec11-eg2:torus-ver2.svg │ ├── lec11-eg2:torus.pdf │ ├── lec11-eg2:torus.pdf_tex │ ├── lec11-eg2:torus.svg │ ├── lec11-eg:2-sphere.pdf │ ├── lec11-eg:2-sphere.pdf_tex │ ├── lec11-eg:2-sphere.svg │ ├── lec11:eg-3:1.pdf │ ├── lec11:eg-3:1.pdf_tex │ ├── lec11:eg-3:1.svg │ ├── lec11:eg-3:2.pdf │ ├── lec11:eg-3:2.pdf_tex │ ├── lec11:eg-3:2.svg │ ├── lec11:eg-3:3.pdf │ ├── lec11:eg-3:3.pdf_tex │ ├── lec11:eg-3:3.svg │ ├── lec11:ex.pdf │ ├── lec11:ex.pdf_tex │ ├── lec11:ex.svg │ ├── lec12-eg.pdf │ ├── lec12-eg.pdf_tex │ ├── lec12-eg.svg │ ├── lec21-3-torus.pdf │ ├── lec21-3-torus.pdf_tex │ ├── lec21-3-torus.svg │ ├── lec21-demo-of-homology-group.pdf │ ├── lec21-demo-of-homology-group.pdf_tex │ ├── lec21-demo-of-homology-group.svg │ ├── lec21-torus.pdf │ ├── lec21-torus.pdf_tex │ ├── lec21-torus.svg │ ├── les-on-relative-spheres.pdf │ ├── les-on-relative-spheres.pdf_tex │ ├── les-on-relative-spheres.svg │ ├── note:chain-as-a-map.pdf │ ├── note:chain-as-a-map.pdf_tex │ ├── note:chain-as-a-map.svg │ ├── pf:col:lec14-2.pdf │ ├── pf:col:lec14-2.pdf_tex │ ├── pf:col:lec14-2.svg │ ├── pf:col:lec14-3.pdf │ ├── pf:col:lec14-3.pdf_tex │ ├── pf:col:lec14-3.svg │ ├── pf:col:lec14-4.pdf │ ├── pf:col:lec14-4.pdf_tex │ ├── pf:col:lec14-4.svg │ ├── pf:col:lec14-5.pdf │ ├── pf:col:lec14-5.pdf_tex │ ├── pf:col:lec14-5.svg │ ├── pf:col:lec14-6.pdf │ ├── pf:col:lec14-6.pdf_tex │ ├── pf:col:lec14-6.svg │ ├── pf:col:lec14-7.pdf │ ├── pf:col:lec14-7.pdf_tex │ ├── pf:col:lec14-7.svg │ ├── pf:col:lec14-8.pdf │ ├── pf:col:lec14-8.pdf_tex │ ├── pf:col:lec14-8.svg │ ├── pf:col:lec14-9.pdf │ ├── pf:col:lec14-9.pdf_tex │ ├── pf:col:lec14-9.svg │ ├── pf:col:lec14.pdf │ ├── pf:col:lec14.pdf_tex │ ├── pf:col:lec14.svg │ ├── pf:excision.pdf │ ├── pf:excision.pdf_tex │ ├── pf:excision.svg │ ├── pf:functoriality-is-homotopy-invariant-2.pdf │ ├── pf:functoriality-is-homotopy-invariant-2.pdf_tex │ ├── pf:functoriality-is-homotopy-invariant-2.svg │ ├── pf:functoriality-is-homotopy-invariant.pdf │ ├── pf:functoriality-is-homotopy-invariant.pdf_tex │ ├── pf:functoriality-is-homotopy-invariant.svg │ ├── pf:lec12-1.pdf │ ├── pf:lec12-1.pdf_tex │ ├── pf:lec12-1.svg │ ├── pf:lec12-2.pdf │ ├── pf:lec12-2.pdf_tex │ ├── pf:lec12-2.svg │ ├── pf:lec16:prop:1.pdf │ ├── pf:lec16:prop:1.pdf_tex │ ├── pf:lec16:prop:1.svg │ ├── pf:lma:lec8-1.pdf │ ├── pf:lma:lec8-1.pdf_tex │ ├── pf:lma:lec8-1.svg │ ├── pf:lma:lec8-2.pdf │ ├── pf:lma:lec8-2.pdf_tex │ ├── pf:lma:lec8-2.svg │ ├── pf:lma:lec8-3.pdf │ ├── pf:lma:lec8-3.pdf_tex │ ├── pf:lma:lec8-3.svg │ ├── pf:lma:lec8-4.pdf │ ├── pf:lma:lec8-4.pdf_tex │ ├── pf:lma:lec8-4.svg │ ├── pf:lma:lec9-2.pdf │ ├── pf:lma:lec9-2.pdf_tex │ ├── pf:lma:lec9-2.svg │ ├── pf:lma:lec9-3.pdf │ ├── pf:lma:lec9-3.pdf_tex │ ├── pf:lma:lec9-3.svg │ ├── pf:lma:lec9-4.pdf │ ├── pf:lma:lec9-4.pdf_tex │ ├── pf:lma:lec9-4.svg │ ├── pf:lma:lec9.pdf │ ├── pf:lma:lec9.pdf_tex │ ├── pf:lma:lec9.svg │ ├── pf:prop:lec17-1.pdf │ ├── pf:prop:lec17-1.pdf_tex │ ├── pf:prop:lec17-1.svg │ ├── pf:prop:lec17-2.pdf │ ├── pf:prop:lec17-2.pdf_tex │ ├── pf:prop:lec17-2.svg │ ├── pf:prop:lifting-criterion-2.pdf │ ├── pf:prop:lifting-criterion-2.pdf_tex │ ├── pf:prop:lifting-criterion-2.svg │ ├── pf:prop:lifting-criterion.pdf │ ├── pf:prop:lifting-criterion.pdf_tex │ ├── pf:prop:lifting-criterion.svg │ ├── pf:seifert-van-kampen-thm-1.pdf │ ├── pf:seifert-van-kampen-thm-1.pdf_tex │ ├── pf:seifert-van-kampen-thm-1.svg │ ├── pf:seifert-van-kampen-thm-2.pdf │ ├── pf:seifert-van-kampen-thm-2.pdf_tex │ ├── pf:seifert-van-kampen-thm-2.svg │ ├── pf:seifert-van-kampen-thm-3.pdf │ ├── pf:seifert-van-kampen-thm-3.pdf_tex │ ├── pf:seifert-van-kampen-thm-3.svg │ ├── pf:thm:seifert-van-kampen-theorem-on-groupoid-2.pdf │ ├── pf:thm:seifert-van-kampen-theorem-on-groupoid-2.pdf_tex │ ├── pf:thm:seifert-van-kampen-theorem-on-groupoid-2.svg │ ├── pf:thm:seifert-van-kampen-theorem-on-groupoid-3.pdf │ ├── pf:thm:seifert-van-kampen-theorem-on-groupoid-3.pdf_tex │ ├── pf:thm:seifert-van-kampen-theorem-on-groupoid-3.svg │ ├── pf:thm:seifert-van-kampen-theorem-on-groupoid-4.pdf │ ├── pf:thm:seifert-van-kampen-theorem-on-groupoid-4.pdf_tex │ ├── pf:thm:seifert-van-kampen-theorem-on-groupoid-4.svg │ ├── pf:thm:seifert-van-kampen-theorem-on-groupoid.pdf │ ├── pf:thm:seifert-van-kampen-theorem-on-groupoid.pdf_tex │ ├── pf:thm:seifert-van-kampen-theorem-on-groupoid.svg │ ├── pf:torus-fundamental-group.pdf │ ├── pf:torus-fundamental-group.pdf_tex │ ├── pf:torus-fundamental-group.svg │ ├── reflection-about-equator.pdf │ ├── reflection-about-equator.pdf_tex │ ├── reflection-about-equator.svg │ ├── rmk:lec17:1.pdf │ ├── rmk:lec17:1.pdf_tex │ ├── rmk:lec17:1.svg │ ├── rmk:simplicial-complex.pdf │ ├── rmk:simplicial-complex.pdf_tex │ ├── rmk:simplicial-complex.svg │ ├── simplicial-homology-venn-diagram.pdf │ ├── simplicial-homology-venn-diagram.pdf_tex │ └── simplicial-homology-venn-diagram.svg ├── Lectures │ ├── lec_1.tex │ ├── lec_10.tex │ ├── lec_11.tex │ ├── lec_12.tex │ ├── lec_13.tex │ ├── lec_14.tex │ ├── lec_15.tex │ ├── lec_16.tex │ ├── lec_17.tex │ ├── lec_18.tex │ ├── lec_19.tex │ ├── lec_2.tex │ ├── lec_20.tex │ ├── lec_21.tex │ ├── lec_22.tex │ ├── lec_23.tex │ ├── lec_24.tex │ ├── lec_25.tex │ ├── lec_26.tex │ ├── lec_27.tex │ ├── lec_28.tex │ ├── lec_29.tex │ ├── lec_3.tex │ ├── lec_30.tex │ ├── lec_31.tex │ ├── lec_32.tex │ ├── lec_33.tex │ ├── lec_34.tex │ ├── lec_35.tex │ ├── lec_36.tex │ ├── lec_37.tex │ ├── lec_38.tex │ ├── lec_39.tex │ ├── lec_4.tex │ ├── lec_40.tex │ ├── lec_41.tex │ ├── lec_5.tex │ ├── lec_6.tex │ ├── lec_7.tex │ ├── lec_8.tex │ └── lec_9.tex ├── appendix.tex └── reference.bib ├── MATH595-Stochastic-Processes-on-Graphs ├── Figures │ ├── cover.png │ ├── ctbp-ancestor.pdf │ ├── ctbp-ancestor.pdf_tex │ ├── ctbp-ancestor.svg │ ├── ctbp-typical-vertex.pdf │ ├── ctbp-typical-vertex.pdf_tex │ ├── ctbp-typical-vertex.svg │ ├── ctbp.pdf │ ├── ctbp.pdf_tex │ ├── ctbp.svg │ ├── erdős-rényi-1-neighborhood.pdf │ ├── erdős-rényi-1-neighborhood.pdf_tex │ ├── erdős-rényi-1-neighborhood.svg │ ├── first-passage-percolation.pdf │ ├── first-passage-percolation.pdf_tex │ ├── first-passage-percolation.svg │ ├── hopfield-network.pdf │ ├── hopfield-network.pdf_tex │ ├── hopfield-network.svg │ ├── mean-of-component-size.pdf │ ├── mean-of-component-size.pdf_tex │ ├── mean-of-component-size.svg │ ├── subgraph-count-1.pdf │ ├── subgraph-count-1.pdf_tex │ ├── subgraph-count-1.svg │ ├── subgraph-count-2.pdf │ ├── subgraph-count-2.pdf_tex │ ├── subgraph-count-2.svg │ ├── torus-first-passage-percolation.pdf │ ├── torus-first-passage-percolation.pdf_tex │ └── torus-first-passage-percolation.svg ├── GraphStocPro.bbl ├── GraphStocPro.pdf ├── GraphStocPro.synctex.gz ├── GraphStocPro.tex ├── Lectures │ ├── lec_1.tex │ ├── lec_10.tex │ ├── lec_11.tex │ ├── lec_12.tex │ ├── lec_13.tex │ ├── lec_14.tex │ ├── lec_15.tex │ ├── lec_16.tex │ ├── lec_17.tex │ ├── lec_18.tex │ ├── lec_19.tex │ ├── lec_2.tex │ ├── lec_20.tex │ ├── lec_21.tex │ ├── lec_22.tex │ ├── lec_23.tex │ ├── lec_24.tex │ ├── lec_25.tex │ ├── lec_26.tex │ ├── lec_27.tex │ ├── lec_28.tex │ ├── lec_3.tex │ ├── lec_4.tex │ ├── lec_5.tex │ ├── lec_6.tex │ ├── lec_7.tex │ ├── lec_8.tex │ └── lec_9.tex ├── appendix.tex ├── indent.log └── reference.bib ├── MATH597-Analysis-II ├── Figures │ ├── thm:caratheodory-extension-1a.pdf │ ├── thm:caratheodory-extension-1a.pdf_tex │ ├── thm:caratheodory-extension-1a.svg │ ├── thm:hahn-decomposition.pdf │ ├── thm:hahn-decomposition.pdf_tex │ └── thm:hahn-decomposition.svg ├── Lectures │ ├── lec_1.tex │ ├── lec_10.tex │ ├── lec_11.tex │ ├── lec_12.tex │ ├── lec_13.tex │ ├── lec_14.tex │ ├── lec_15.tex │ ├── lec_16.tex │ ├── lec_17.tex │ ├── lec_18.tex │ ├── lec_19.tex │ ├── lec_2.tex │ ├── lec_20.tex │ ├── lec_21.tex │ ├── lec_22.tex │ ├── lec_23.tex │ ├── lec_24.tex │ ├── lec_25.tex │ ├── lec_26.tex │ ├── lec_27.tex │ ├── lec_28.tex │ ├── lec_29.tex │ ├── lec_3.tex │ ├── lec_30.tex │ ├── lec_31.tex │ ├── lec_32.tex │ ├── lec_33.tex │ ├── lec_34.tex │ ├── lec_35.tex │ ├── lec_36.tex │ ├── lec_37.tex │ ├── lec_38.tex │ ├── lec_39.tex │ ├── lec_4.tex │ ├── lec_40.tex │ ├── lec_5.tex │ ├── lec_6.tex │ ├── lec_7.tex │ ├── lec_8.tex │ └── lec_9.tex ├── ReAnalysis.bbl ├── ReAnalysis.pdf ├── ReAnalysis.synctex.gz ├── ReAnalysis.tex ├── appendix.tex └── reference.bib ├── MATH602-Real-Analysis-II ├── Figures │ ├── orthogonality-principle.pdf │ ├── orthogonality-principle.pdf_tex │ ├── orthogonality-principle.svg │ ├── separation-of-a-point-from-convex-set.pdf │ ├── separation-of-a-point-from-convex-set.pdf_tex │ └── separation-of-a-point-from-convex-set.svg ├── Lectures │ ├── lec_1.tex │ ├── lec_10.tex │ ├── lec_11.tex │ ├── lec_12.tex │ ├── lec_13.tex │ ├── lec_14.tex │ ├── lec_15.tex │ ├── lec_16.tex │ ├── lec_17.tex │ ├── lec_18.tex │ ├── lec_19.tex │ ├── lec_2.tex │ ├── lec_20.tex │ ├── lec_21.tex │ ├── lec_22.tex │ ├── lec_23.tex │ ├── lec_24.tex │ ├── lec_25.tex │ ├── lec_26.tex │ ├── lec_27.tex │ ├── lec_28.tex │ ├── lec_3.tex │ ├── lec_4.tex │ ├── lec_5.tex │ ├── lec_6.tex │ ├── lec_7.tex │ ├── lec_8.tex │ └── lec_9.tex ├── ReAnalysis-II.bbl ├── ReAnalysis-II.pdf ├── ReAnalysis-II.synctex.gz ├── ReAnalysis-II.tex ├── appendix.tex └── reference.bib ├── MATH635-Riemannian-Geometry ├── Figures │ ├── 2nd-variation.pdf │ ├── 2nd-variation.pdf_tex │ ├── 2nd-variation.svg │ ├── circle-exponential-map.pdf │ ├── circle-exponential-map.pdf_tex │ ├── circle-exponential-map.svg │ ├── conjugate-point.pdf │ ├── conjugate-point.pdf_tex │ ├── conjugate-point.svg │ ├── construct-geodesic-killing-field.pdf │ ├── construct-geodesic-killing-field.pdf_tex │ ├── construct-geodesic-killing-field.svg │ ├── construct-geodesic-zero.pdf │ ├── construct-geodesic-zero.pdf_tex │ ├── construct-geodesic-zero.svg │ ├── construct-geodesic.pdf │ ├── construct-geodesic.pdf_tex │ ├── construct-geodesic.svg │ ├── coordinate-chart.pdf │ ├── coordinate-chart.pdf_tex │ ├── coordinate-chart.svg │ ├── coordinate-transition.pdf │ ├── coordinate-transition.pdf_tex │ ├── coordinate-transition.svg │ ├── cover.png │ ├── curve-self-intersect-and-corner.pdf │ ├── curve-self-intersect-and-corner.pdf_tex │ ├── curve-self-intersect-and-corner.svg │ ├── cylinder-circle-bundle.pdf │ ├── cylinder-circle-bundle.pdf_tex │ ├── cylinder-circle-bundle.svg │ ├── cylinder-circle-section.pdf │ ├── cylinder-circle-section.pdf_tex │ ├── cylinder-circle-section.svg │ ├── cylinder-geodesic-minimizing.pdf │ ├── cylinder-geodesic-minimizing.pdf_tex │ ├── cylinder-geodesic-minimizing.svg │ ├── differential.pdf │ ├── differential.pdf_tex │ ├── differential.svg │ ├── directional-derivative.pdf │ ├── directional-derivative.pdf_tex │ ├── directional-derivative.svg │ ├── gr.pdf │ ├── gr.pdf_tex │ ├── gr.svg │ ├── grassmannian-transition.pdf │ ├── grassmannian-transition.pdf_tex │ ├── grassmannian-transition.svg │ ├── hopf-rinow-theorem.pdf │ ├── hopf-rinow-theorem.pdf_tex │ ├── hopf-rinow-theorem.svg │ ├── hopf-rinow-uniqueness.pdf │ ├── hopf-rinow-uniqueness.pdf_tex │ ├── hopf-rinow-uniqueness.svg │ ├── ligo.pdf │ ├── ligo.pdf_tex │ ├── ligo.svg │ ├── local-flow.pdf │ ├── local-flow.pdf_tex │ ├── local-flow.svg │ ├── maps-between-manifolds.pdf │ ├── maps-between-manifolds.pdf_tex │ ├── maps-between-manifolds.svg │ ├── morse-function-circles.pdf │ ├── morse-function-circles.pdf_tex │ ├── morse-function-circles.svg │ ├── morse-function-torus.pdf │ ├── morse-function-torus.pdf_tex │ ├── morse-function-torus.svg │ ├── motivation-bundle-field.pdf │ ├── motivation-bundle-field.pdf_tex │ ├── motivation-bundle-field.svg │ ├── non-differentiable.pdf │ ├── non-differentiable.pdf_tex │ ├── non-differentiable.svg │ ├── non-embedding.pdf │ ├── non-embedding.pdf_tex │ ├── non-embedding.svg │ ├── non-immersion.pdf │ ├── non-immersion.pdf_tex │ ├── non-immersion.svg │ ├── non-increasing-function.pdf │ ├── non-increasing-function.pdf_tex │ ├── non-increasing-function.svg │ ├── parallel-transport.pdf │ ├── parallel-transport.pdf_tex │ ├── parallel-transport.svg │ ├── riemannian-curvature-geometric-significant.pdf │ ├── riemannian-curvature-geometric-significant.pdf_tex │ ├── riemannian-curvature-geometric-significant.svg │ ├── space-form.pdf │ ├── space-form.pdf_tex │ ├── space-form.svg │ ├── sphere-order.pdf │ ├── sphere-order.pdf_tex │ ├── sphere-order.svg │ ├── stereographic-projection.pdf │ ├── stereographic-projection.pdf_tex │ ├── stereographic-projection.svg │ ├── submanifold-2nd-fundamental-form.pdf │ ├── submanifold-2nd-fundamental-form.pdf_tex │ ├── submanifold-2nd-fundamental-form.svg │ ├── tangent-space.pdf │ ├── tangent-space.pdf_tex │ ├── tangent-space.svg │ ├── tilted-torus.pdf │ ├── tilted-torus.pdf_tex │ ├── tilted-torus.svg │ ├── vector-bundle.pdf │ ├── vector-bundle.pdf_tex │ └── vector-bundle.svg ├── Lectures │ ├── lec_1.tex │ ├── lec_10.tex │ ├── lec_11.tex │ ├── lec_12.tex │ ├── lec_13.tex │ ├── lec_14.tex │ ├── lec_15.tex │ ├── lec_16.tex │ ├── lec_17.tex │ ├── lec_18.tex │ ├── lec_19.tex │ ├── lec_2.tex │ ├── lec_20.tex │ ├── lec_21.tex │ ├── lec_22.tex │ ├── lec_23.tex │ ├── lec_24.tex │ ├── lec_25.tex │ ├── lec_26.tex │ ├── lec_27.tex │ ├── lec_28.tex │ ├── lec_3.tex │ ├── lec_4.tex │ ├── lec_5.tex │ ├── lec_6.tex │ ├── lec_7.tex │ ├── lec_8.tex │ └── lec_9.tex ├── RiemGeo.bbl ├── RiemGeo.pdf ├── RiemGeo.synctex.gz ├── RiemGeo.tex ├── appendix.tex └── reference.bib ├── MATH681-Mathematical-Logic ├── Figures │ ├── cell.pdf │ ├── cell.pdf_tex │ ├── cell.svg │ ├── cover.png │ ├── disjoint-union-finite-graphs.pdf │ ├── disjoint-union-finite-graphs.pdf_tex │ ├── disjoint-union-finite-graphs.svg │ ├── linear-order-ap.pdf │ ├── linear-order-ap.pdf_tex │ ├── linear-order-ap.svg │ ├── random-graph-qe.pdf │ ├── random-graph-qe.pdf_tex │ ├── random-graph-qe.svg │ ├── random-graph-theory.pdf │ ├── random-graph-theory.pdf_tex │ ├── random-graph-theory.svg │ ├── square-free.pdf │ ├── square-free.pdf_tex │ └── square-free.svg ├── Lectures │ ├── lec_1.tex │ ├── lec_10.tex │ ├── lec_11.tex │ ├── lec_12.tex │ ├── lec_13.tex │ ├── lec_14.tex │ ├── lec_15.tex │ ├── lec_16.tex │ ├── lec_17.tex │ ├── lec_18.tex │ ├── lec_19.tex │ ├── lec_2.tex │ ├── lec_20.tex │ ├── lec_21.tex │ ├── lec_22.tex │ ├── lec_23.tex │ ├── lec_24.tex │ ├── lec_25.tex │ ├── lec_26.tex │ ├── lec_27.tex │ ├── lec_28.tex │ ├── lec_3.tex │ ├── lec_4.tex │ ├── lec_5.tex │ ├── lec_6.tex │ ├── lec_7.tex │ ├── lec_8.tex │ └── lec_9.tex ├── Logic.pdf ├── Logic.synctex.gz ├── Logic.tex ├── appendix.tex └── reference.bib ├── README.md ├── STAT575-Large-Sample-Theory ├── Figures │ └── cover.png ├── LargeSample.bbl ├── LargeSample.pdf ├── LargeSample.synctex.gz ├── LargeSample.tex ├── Lectures │ ├── lec_1.tex │ ├── lec_10.tex │ ├── lec_11.tex │ ├── lec_12.tex │ ├── lec_13.tex │ ├── lec_14.tex │ ├── lec_15.tex │ ├── lec_16.tex │ ├── lec_17.tex │ ├── lec_18.tex │ ├── lec_19.tex │ ├── lec_2.tex │ ├── lec_20.tex │ ├── lec_21.tex │ ├── lec_22.tex │ ├── lec_23.tex │ ├── lec_24.tex │ ├── lec_25.tex │ ├── lec_26.tex │ ├── lec_27.tex │ ├── lec_28.tex │ ├── lec_3.tex │ ├── lec_4.tex │ ├── lec_5.tex │ ├── lec_6.tex │ ├── lec_7.tex │ ├── lec_8.tex │ └── lec_9.tex ├── appendix.tex └── reference.bib ├── STAT576-Empirical-Process-Theory ├── EmpProcess.bbl ├── EmpProcess.pdf ├── EmpProcess.synctex.gz ├── EmpProcess.tex ├── Figures │ ├── chaining.pdf │ ├── chaining.pdf_tex │ ├── chaining.svg │ ├── cover.png │ ├── margin-plot.pdf │ ├── margin-plot.pdf_tex │ ├── margin-plot.svg │ ├── mode-estimation-growth.pdf │ ├── mode-estimation-growth.pdf_tex │ ├── mode-estimation-growth.svg │ ├── obtuse-angle-lemma.pdf │ ├── obtuse-angle-lemma.pdf_tex │ ├── obtuse-angle-lemma.svg │ ├── star-estimator.pdf │ ├── star-estimator.pdf_tex │ ├── star-estimator.svg │ ├── star-shape.pdf │ ├── star-shape.pdf_tex │ └── star-shape.svg ├── Lectures │ ├── lec_1.tex │ ├── lec_10.tex │ ├── lec_11.tex │ ├── lec_12.tex │ ├── lec_13.tex │ ├── lec_14.tex │ ├── lec_15.tex │ ├── lec_16.tex │ ├── lec_17.tex │ ├── lec_18.tex │ ├── lec_19.tex │ ├── lec_2.tex │ ├── lec_20.tex │ ├── lec_21.tex │ ├── lec_22.tex │ ├── lec_23.tex │ ├── lec_24.tex │ ├── lec_25.tex │ ├── lec_26.tex │ ├── lec_27.tex │ ├── lec_28.tex │ ├── lec_29.tex │ ├── lec_3.tex │ ├── lec_30.tex │ ├── lec_31.tex │ ├── lec_4.tex │ ├── lec_5.tex │ ├── lec_6.tex │ ├── lec_7.tex │ ├── lec_8.tex │ └── lec_9.tex ├── appendix.tex └── reference.bib └── preview.png /.gitignore: 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-------------------------------------------------------------------------------- /CS598-Topics-in-Graph-Algorithms/GraphAlgo.tex: -------------------------------------------------------------------------------- 1 | \documentclass[a4paper]{report} 2 | \input{~/Developer/LaTeX-Template/Note/header.tex} 3 | \author{Pingbang Hu} 4 | \title{CS598\\Topics in Graph Algorithms} 5 | 6 | \usepackage[stable]{footmisc} 7 | 8 | \thispagestyle{empty} 9 | \addbibresource{reference.bib} 10 | 11 | \DeclareMathOperator{\OPT}{\textsf{OPT}} 12 | 13 | \begin{document} 14 | 15 | \maketitle 16 | 17 | \begin{abstract} 18 | This is an advanced graduate-level graph algorithm course taught by \href{https://chekuri.cs.illinois.edu/}{Chandra Chekuri} at University of Illinois Urbana-Champaign. This exploratory seminar-style course will cover selection of topics in graph algorithms with an emphasis on recent developments on fast algorithms for a variety of problems such as shortest paths, flows, cuts, and matchings. Structural results and connections to past ideas and results will also be discussed. More information can be found on the \href{https://courses.grainger.illinois.edu/cs598csc/fa2024/}{course website}. 19 | 20 | \vfill 21 | \begin{center} 22 | \includegraphics[width=.8\linewidth]{Figures/cover.png} 23 | \end{center} 24 | \vfill 25 | This course is taken in Fall 2024, and the date on the cover page is the last updated time. 26 | \end{abstract} 27 | 28 | \tableofcontents 29 | 30 | \lec{1}{24} 31 | 32 | \newpage 33 | %─────Appendix──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 34 | \appendix 35 | \appendixpage{} 36 | 37 | \input{appendix.tex} 38 | 39 | \newpage 40 | %─────Reference────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 41 | \pagestyle{plain} 42 | \printbibliography{} 43 | 44 | \end{document} -------------------------------------------------------------------------------- /CS598-Topics-in-Graph-Algorithms/Lectures/lec_14.tex: -------------------------------------------------------------------------------- 1 | \lecture{14}{10 Oct.\ 11:00}{Real Negative Weights Shortest Path Continued} 2 | Next, we need to deal with the so-called \emph{betweenness reduction}. 3 | 4 | \todo[inline]{I'm being lazy. 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It will be recreated by 7 | % biber as required. 8 | % 9 | \begingroup 10 | \makeatletter 11 | \@ifundefined{ver@biblatex.sty} 12 | {\@latex@error 13 | {Missing 'biblatex' package} 14 | {The bibliography requires the 'biblatex' package.} 15 | \aftergroup\endinput} 16 | {} 17 | \endgroup 18 | 19 | 20 | \refsection{0} 21 | \datalist[entry]{anyt/global//global/global/global} 22 | \entry{easley2010networks}{book}{}{} 23 | \name{author}{2}{}{% 24 | {{hash=fe694fafd2b1b454369282e8dff07f92}{% 25 | family={Easley}, 26 | familyi={E\bibinitperiod}, 27 | given={D.}, 28 | giveni={D\bibinitperiod}}}% 29 | {{hash=3a07403d0e72923a2c8f6519d0e8b233}{% 30 | family={Kleinberg}, 31 | familyi={K\bibinitperiod}, 32 | given={J.}, 33 | giveni={J\bibinitperiod}}}% 34 | } 35 | \list{publisher}{1}{% 36 | {Cambridge University Press}% 37 | } 38 | \strng{namehash}{ee11f34fe9eafcdda6beea4371846505} 39 | \strng{fullhash}{1fa4ee4ecfc317c3eca648267b8f4c8f} 40 | \strng{fullhashraw}{1fa4ee4ecfc317c3eca648267b8f4c8f} 41 | \strng{bibnamehash}{1fa4ee4ecfc317c3eca648267b8f4c8f} 42 | \strng{authorbibnamehash}{1fa4ee4ecfc317c3eca648267b8f4c8f} 43 | \strng{authornamehash}{ee11f34fe9eafcdda6beea4371846505} 44 | \strng{authorfullhash}{1fa4ee4ecfc317c3eca648267b8f4c8f} 45 | \strng{authorfullhashraw}{1fa4ee4ecfc317c3eca648267b8f4c8f} 46 | \field{labelalpha}{EK10} 47 | \field{sortinit}{E} 48 | \field{sortinithash}{8da8a182d344d5b9047633dfc0cc9131} 49 | \field{labelnamesource}{author} 50 | \field{labeltitlesource}{title} 51 | \field{isbn}{9781139490306} 52 | \field{title}{Networks, Crowds, and Markets: Reasoning about a Highly Connected World} 53 | \field{year}{2010} 54 | \verb{urlraw} 55 | \verb https://books.google.com/books?id=atfCl2agdi8C 56 | \endverb 57 | \verb{url} 58 | \verb https://books.google.com/books?id=atfCl2agdi8C 59 | \endverb 60 | \endentry 61 | \enddatalist 62 | \endrefsection 63 | \endinput 64 | 65 | -------------------------------------------------------------------------------- /EECS544-Analysis-of-Social-Networks/SocNetAnalysis.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/EECS544-Analysis-of-Social-Networks/SocNetAnalysis.pdf -------------------------------------------------------------------------------- /EECS544-Analysis-of-Social-Networks/SocNetAnalysis.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/EECS544-Analysis-of-Social-Networks/SocNetAnalysis.synctex.gz -------------------------------------------------------------------------------- /EECS544-Analysis-of-Social-Networks/SocNetAnalysis.tex: -------------------------------------------------------------------------------- 1 | \documentclass[a4paper]{report} 2 | \input{~/Developer/LaTeX-Template/Note/header.tex} 3 | \author{Pingbang Hu} 4 | \title{EECS544\\Analysis of Societal Networks} 5 | 6 | \thispagestyle{empty} 7 | \addbibresource{reference.bib} 8 | 9 | \newcommand{\Head}{\mathrm{H}} 10 | \newcommand{\Tail}{\mathrm{T}} 11 | 12 | \DeclareMathOperator{\nnz}{nnz} 13 | \DeclareMathOperator{\BR}{BR} 14 | 15 | \begin{document} 16 | 17 | \maketitle 18 | 19 | \begin{abstract} 20 | This is a graduate-level course about social network analysis taught by \href{https://subramanian.engin.umich.edu/}{Vijay G Subramanian} at University of Michigan, covering topics across graph partitioning algorithms, community detection algorithms, stochastic process and Markov chain, Monte Carlo algorithm, random graph theory and game theory with auctions and matching market. Additionally, we'll use Easley, D. and Kleinberg, J.~\cite{easley2010networks} as our main reference. 21 | 22 | \vfill 23 | \begin{center} 24 | \includegraphics[width=.8\linewidth]{Figures/cover.png} 25 | \end{center} 26 | \vfill 27 | This course is taken in Fall 2021, and the date on the cover page is the last updated time. 28 | \end{abstract} 29 | 30 | \tableofcontents 31 | 32 | %─────Lectures─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 33 | \newpage 34 | 35 | \lec{1}{25} 36 | 37 | \newpage 38 | %─────Appendix──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 39 | \appendix 40 | \appendixpage{} 41 | 42 | \input{appendix.tex} 43 | 44 | \newpage 45 | %─────Reference────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 46 | \pagestyle{plain} 47 | \printbibliography{} 48 | 49 | \end{document} -------------------------------------------------------------------------------- /EECS544-Analysis-of-Social-Networks/appendix.tex: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/EECS544-Analysis-of-Social-Networks/appendix.tex -------------------------------------------------------------------------------- /EECS544-Analysis-of-Social-Networks/reference.bib: -------------------------------------------------------------------------------- 1 | @book{easley2010networks, 2 | title = {Networks, Crowds, and Markets: Reasoning about a Highly Connected World}, 3 | author = {Easley, D. and Kleinberg, J.}, 4 | isbn = {9781139490306}, 5 | url = {https://books.google.com/books?id=atfCl2agdi8C}, 6 | year = {2010}, 7 | publisher = {Cambridge University Press} 8 | } 9 | 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different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | 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a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | 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with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | 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'representation-theorem.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | 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13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | 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%% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | 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It will be recreated by 7 | % biber as required. 8 | % 9 | \begingroup 10 | \makeatletter 11 | \@ifundefined{ver@biblatex.sty} 12 | {\@latex@error 13 | {Missing 'biblatex' package} 14 | {The bibliography requires the 'biblatex' package.} 15 | \aftergroup\endinput} 16 | {} 17 | \endgroup 18 | 19 | 20 | \refsection{0} 21 | \datalist[entry]{anyt/global//global/global} 22 | \entry{Linear-Opt}{book}{} 23 | \name{author}{1}{}{% 24 | {{hash=2778d00b63611810839f7e97a581468a}{% 25 | family={Lee}, 26 | familyi={L\bibinitperiod}, 27 | given={Jon}, 28 | giveni={J\bibinitperiod}}}% 29 | } 30 | \list{publisher}{1}{% 31 | {Reex Press}% 32 | } 33 | \strng{namehash}{2778d00b63611810839f7e97a581468a} 34 | \strng{fullhash}{2778d00b63611810839f7e97a581468a} 35 | \strng{bibnamehash}{2778d00b63611810839f7e97a581468a} 36 | \strng{authorbibnamehash}{2778d00b63611810839f7e97a581468a} 37 | \strng{authornamehash}{2778d00b63611810839f7e97a581468a} 38 | \strng{authorfullhash}{2778d00b63611810839f7e97a581468a} 39 | \field{labelalpha}{Lee22} 40 | \field{sortinit}{L} 41 | \field{sortinithash}{7c47d417cecb1f4bd38d1825c427a61a} 42 | \field{labelnamesource}{author} 43 | \field{labeltitlesource}{title} 44 | \field{title}{A First Course in Linear Optimization”} 45 | \field{year}{2022} 46 | \verb{urlraw} 47 | \verb https://github.com/jon77lee/JLee_LinearOptimizationBook 48 | \endverb 49 | \verb{url} 50 | \verb https://github.com/jon77lee/JLee_LinearOptimizationBook 51 | \endverb 52 | \endentry 53 | \enddatalist 54 | \endrefsection 55 | \endinput 56 | 57 | -------------------------------------------------------------------------------- /MATH561-Linear-Programming/LinProg.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH561-Linear-Programming/LinProg.pdf -------------------------------------------------------------------------------- /MATH561-Linear-Programming/LinProg.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH561-Linear-Programming/LinProg.synctex.gz -------------------------------------------------------------------------------- /MATH561-Linear-Programming/LinProg.tex: -------------------------------------------------------------------------------- 1 | \documentclass[a4paper]{report} 2 | \input{~/Developer/LaTeX-Template/Note/header.tex} 3 | \author{Pingbang Hu} 4 | \title{MATH561/IOE510/TO518\\Linear Programming} 5 | 6 | \thispagestyle{empty} 7 | \addbibresource{reference.bib} 8 | 9 | \newcommand{\Primal}{\mathrm{P}} 10 | \newcommand{\Dual}{\mathrm{D}} 11 | \newcommand{\Main}{\mathrm{M}} 12 | \newcommand{\Sub}{\mathrm{SUB}} 13 | \newcommand{\CSP}{\mathrm{CSP}} 14 | \newcommand{\LB}{\mathrm{LB}} 15 | \newcommand{\UB}{\mathrm{UB}} 16 | \DeclareMathOperator{\Proj}{Proj} 17 | 18 | \begin{document} 19 | 20 | \maketitle 21 | 22 | \begin{abstract} 23 | This is the first course in the series of graduate-level, large-scale and rigorous mathematical programming courses taught by \href{https://sites.google.com/site/jonleewebpage/}{Jon Lee} at University of Michigan, and in particular, we will use the book write by professor Lee~\cite{Linear-Opt}. This is a dynamic book which may changes and update constantly. In this course, we focus on developing a rigorous understanding on large-scale linear programming problems and also introduce the basic concept of integer programming. 24 | 25 | \vfill 26 | \begin{center} 27 | \includegraphics[width=.8\linewidth]{Figures/cover.png} 28 | \end{center} 29 | \vfill 30 | This course is taken in Fall 2021, and the date on the cover page is the last updated time. 31 | \end{abstract} 32 | 33 | \tableofcontents 34 | 35 | %─────Lectures─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 36 | \newpage 37 | 38 | \lec{1}{24} 39 | 40 | \newpage 41 | %─────Reference────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 42 | \pagestyle{plain} 43 | \printbibliography{} 44 | 45 | \end{document} -------------------------------------------------------------------------------- /MATH561-Linear-Programming/reference.bib: -------------------------------------------------------------------------------- 1 | @book{Linear-Opt, 2 | title = {A First Course in Linear Optimization”}, 3 | author = {Jon Lee}, 4 | url = {https://github.com/jon77lee/JLee_LinearOptimizationBook}, 5 | year = {2022}, 6 | publisher = {Reex Press} 7 | } 8 | -------------------------------------------------------------------------------- /MATH592-Introduction-to-Algebraic-Topology/AlgTop.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH592-Introduction-to-Algebraic-Topology/AlgTop.pdf -------------------------------------------------------------------------------- /MATH592-Introduction-to-Algebraic-Topology/AlgTop.synctex.gz: -------------------------------------------------------------------------------- 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your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{680.31496063bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.29166667)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{3-torus.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- 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file 'eg:constructing-sphere-1.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not 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Department of Mathematics}, 4 | isbn = {9780521795401}, 5 | lccn = {00065166}, 6 | series = {Algebraic Topology}, 7 | url = {https://books.google.com/books?id=BjKs86kosqgC}, 8 | year = {2002}, 9 | publisher = {Cambridge University Press} 10 | } 11 | 12 | @book{atiyah1994introduction, 13 | title = {Introduction To Commutative Algebra}, 14 | author = {Atiyah, M.F. and MacDonald, I.G.}, 15 | isbn = {9780813345444}, 16 | series = {Addison-Wesley series in mathematics}, 17 | url = {https://books.google.com/books?id=HOASFid4x18C}, 18 | year = {1994}, 19 | publisher = {Avalon Publishing} 20 | } 21 | 22 | @book{armstrong2013basic, 23 | title = {Basic Topology}, 24 | author = {Armstrong, M.A.}, 25 | isbn = {9781475717938}, 26 | series = {Undergraduate Texts in Mathematics}, 27 | url = {https://books.google.com/books?id=NJbuBwAAQBAJ}, 28 | year = {2013}, 29 | publisher = {Springer New York} 30 | } 31 | -------------------------------------------------------------------------------- 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\includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | 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\documentclass[a4paper]{report} 2 | \input{~/Developer/LaTeX-Template/Note/header.tex} 3 | \author{Pingbang Hu} 4 | \title{MATH595\\Stochastic Processes on Graphs} 5 | 6 | \usepackage[stable]{footmisc} 7 | \usepackage{accents} 8 | 9 | \thispagestyle{empty} 10 | \addbibresource{reference.bib} 11 | 12 | \begin{document} 13 | 14 | \maketitle 15 | 16 | \begin{abstract} 17 | This is an advanced graduate-level math course taught by \href{https://psdey.web.illinois.edu/}{Partha Dey} at University of Illinois Urbana-Champaign. 18 | 19 | We list some references of this course, although we will not follow any particular book page by page: \emph{Random Graph Dynamics}~\cite{durrett2010random}, \emph{Random Graphs}~\cite{janson2011random}, \emph{Random Graphs and Complex Networks}~\cite{van2024random}. 20 | 21 | \vfill 22 | \begin{center} 23 | \includegraphics[width=.8\linewidth]{Figures/cover.png} 24 | \end{center} 25 | \vfill 26 | This course is taken in Spring 2025, and the date on the cover page is the last updated time. 27 | \end{abstract} 28 | 29 | \tableofcontents 30 | 31 | \lec{1}{28} 32 | 33 | \newpage 34 | %─────Appendix──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 35 | \appendix 36 | \appendixpage{} 37 | 38 | \input{appendix.tex} 39 | 40 | \newpage 41 | %─────Reference────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 42 | \pagestyle{plain} 43 | \printbibliography{} 44 | 45 | \end{document} -------------------------------------------------------------------------------- /MATH595-Stochastic-Processes-on-Graphs/Lectures/lec_13.tex: -------------------------------------------------------------------------------- 1 | \lecture{13}{4 Mar.\ 9:30}{Preferential Attachment Model} 2 | -------------------------------------------------------------------------------- /MATH595-Stochastic-Processes-on-Graphs/Lectures/lec_20.tex: -------------------------------------------------------------------------------- 1 | \lecture{20}{3 Apr.\ 9:30}{Ising Model} 2 | -------------------------------------------------------------------------------- /MATH595-Stochastic-Processes-on-Graphs/Lectures/lec_21.tex: -------------------------------------------------------------------------------- 1 | \lecture{21}{8 Apr.\ 9:30}{Ising Model} 2 | -------------------------------------------------------------------------------- /MATH595-Stochastic-Processes-on-Graphs/Lectures/lec_25.tex: -------------------------------------------------------------------------------- 1 | \lecture{25}{22 Apr.\ 9:30}{SK Spin Glass Model} 2 | Consider 3 | \[ 4 | H_n(\sigma ) 5 | = \beta \frac{1}{\sqrt{n} } \sum_{i < j} J_{ij} \sigma _i \sigma _j + B \sum_{i=1}^{n} \sigma _i . 6 | \] 7 | Then, \((H_n(\sigma ))_{\sigma \in \{ \pm 1 \} ^n} \sim \mathcal{N} ^{2^n}(0, n (\beta ^2 R_{\sigma , \tau }^2 / 2)_{\sigma , \tau })\). Let \(\xi (x) = \beta ^2 x^2 / 2\) and \(R_{\sigma , \tau } = \langle \sigma , \tau \rangle / n \in [-1, 1]\). 8 | 9 | \begin{eg}[\(p\) spin-glass model] 10 | \(\xi (x) = \beta ^2 x^p\), \(p \in \{ 2, 3, \dots \} \) creates a spin-glass model. 11 | \end{eg} 12 | \begin{explanation} 13 | Consider taking \(J_{i_1, \dots , i_p} \overset{\text{i.i.d.} }{\sim } \mathcal{N} (0, 1)\) such that 14 | \[ 15 | H_{n, p}(\sigma ) 16 | = \frac{\beta }{n^{\frac{p-1}{2}}} \sum_{i_1, \dots , i_p \in [n]} J_{i_1, \dots , i_p} \sigma _{i_1} \cdots \sigma _{i_p}. 17 | \] 18 | The joint distribution is \(\mathcal{N} (0, n (\beta ^2 R_{\sigma , \tau }^p)_{\sigma , \tau })\). 19 | \end{explanation} 20 | 21 | \begin{eg}[Mixed-\(p\) spin-glass model] 22 | One can also consider \(\xi (x) = \sum_{p=2}^{\infty} \beta _p^2 \cdot x^p\) with \(\sum_{p=2}^{\infty} \beta _p^2 < \infty \). 23 | \end{eg} 24 | 25 | \begin{theorem}[Informal] 26 | The Paris formula holds for the general class of \(\xi \) as long as \(\beta _p\) decays fast enough. 27 | \end{theorem} -------------------------------------------------------------------------------- /MATH595-Stochastic-Processes-on-Graphs/appendix.tex: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH595-Stochastic-Processes-on-Graphs/appendix.tex -------------------------------------------------------------------------------- /MATH595-Stochastic-Processes-on-Graphs/indent.log: -------------------------------------------------------------------------------- 1 | INFO: latexindent version 3.24.5, 2025-03-13, a script to indent .tex files 2 | latexindent lives here: /usr/local/texlive/2025/texmf-dist/scripts/latexindent/ 3 | Thu May 1 10:42:55 2025 4 | Filename: /Users/pbb/University/Notes/MATH595-Stochastic-Processes-on-Graphs/Lectures/__latexindent_temp_lec_28.tex 5 | INFO: Processing switches: 6 | -y|--yaml: YAML settings specified via command line 7 | -c|--cruft: cruft directory 8 | INFO: Directory for backup files and log file /Users/pbb/University/Notes/MATH595-Stochastic-Processes-on-Graphs/indent.log: 9 | /Users/pbb/University/Notes/MATH595-Stochastic-Processes-on-Graphs/ 10 | INFO: YAML settings read: defaultSettings.yaml 11 | Reading defaultSettings.yaml from /usr/local/texlive/2025/texmf-dist/scripts/latexindent/defaultSettings.yaml 12 | INFO: YAML reading settings 13 | Home directory is /Users/pbb 14 | latexindent.pl didn't find indentconfig.yaml or .indentconfig.yaml 15 | see all possible locations: https://latexindentpl.readthedocs.io/en/latest/sec-appendices.html#indentconfig-options) 16 | INFO: YAML settings read: -y switch 17 | YAML setting: defaultIndent:'\t' 18 | single-quoted string found in -y switch: '\t', substitute to 19 | Updating mainSettings with defaultIndent: 20 | INFO: Phase 1: searching for objects 21 | INFO: Phase 2: finding surrounding indentation 22 | INFO: Phase 3: indenting objects 23 | INFO: Phase 4: final indentation check 24 | INFO: Output routine: 25 | Not outputting to file; see -w and -o switches for more options. 26 | -------------- 27 | INFO: Please direct all communication/issues to: 28 | https://github.com/cmhughes/latexindent.pl 29 | -------------------------------------------------------------------------------- /MATH595-Stochastic-Processes-on-Graphs/reference.bib: -------------------------------------------------------------------------------- 1 | @book{durrett2010random, 2 | author = {Durrett, Rick}, 3 | title = {Random graph dynamics}, 4 | publisher = {Cambridge university press}, 5 | volume = {20}, 6 | year = {2010} 7 | } 8 | 9 | @book{janson2011random, 10 | author = {Janson, Svante and Luczak, Tomasz and Rucinski, Andrzej}, 11 | title = {Random graphs}, 12 | publisher = {John Wiley \& Sons}, 13 | year = {2011} 14 | } 15 | 16 | @book{van2024random, 17 | author = {Van Der Hofstad, Remco}, 18 | title = {Random graphs and complex networks}, 19 | publisher = {Cambridge university press}, 20 | volume = {54}, 21 | year = {2024} 22 | } -------------------------------------------------------------------------------- /MATH597-Analysis-II/Figures/thm:caratheodory-extension-1a.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH597-Analysis-II/Figures/thm:caratheodory-extension-1a.pdf -------------------------------------------------------------------------------- /MATH597-Analysis-II/Figures/thm:hahn-decomposition.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH597-Analysis-II/Figures/thm:hahn-decomposition.pdf -------------------------------------------------------------------------------- /MATH597-Analysis-II/ReAnalysis.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH597-Analysis-II/ReAnalysis.pdf -------------------------------------------------------------------------------- /MATH597-Analysis-II/ReAnalysis.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH597-Analysis-II/ReAnalysis.synctex.gz -------------------------------------------------------------------------------- /MATH597-Analysis-II/ReAnalysis.tex: -------------------------------------------------------------------------------- 1 | \documentclass[a4paper]{report} 2 | \input{~/Developer/LaTeX-Template/Note/header.tex} 3 | \author{Pingbang Hu} 4 | \title{MATH597\\Analysis II} 5 | 6 | \thispagestyle{empty} 7 | \addbibresource{reference.bib} 8 | 9 | \usetikzlibrary{lindenmayersystems} 10 | \pgfdeclarelindenmayersystem{cantor set}{ 11 | \rule{F -> FfF} 12 | \rule{f -> fff} 13 | } 14 | \usetikzlibrary{arrows} 15 | \newcommand{\nMAX}{63} 16 | \newcommand{\xGrSamp}{8} 17 | 18 | \usepackage{pgfplots} 19 | 20 | \newcommand{\GL}{\mathrm{GL}} 21 | \newcommand{\loc}{\mathrm{loc}} 22 | \DeclareMathOperator{\BV}{BV} 23 | \DeclareMathOperator{\NBV}{NBV} 24 | 25 | \begin{document} 26 | 27 | \maketitle 28 | 29 | \begin{abstract} 30 | This is the graduate-level real analysis course taught by \href{http://www.math.lsa.umich.edu/~baik/Welcome.html}{Jinho Baik} at University of Michigan. Everything is built up from measure theory, like integration and differentiation. Topics include measure theory, Hilbert/Banach spaces, \(L^p\) spaces, and some Fourier Analyses. 31 | 32 | Some proofs are \textbf{intended} left as assignments, and for completeness, I put them in \autoref{Apx:Additional-Proofs}, use it in your \textbf{own risks}! You'll lose the chance to practice and really understand the materials. 33 | 34 | Additionally, we'll use Folland~\cite{folland1999real} as our main text, while using Tao~\cite{tao2013introduction} and Axler~\cite{axler2019measure} as supplementary references. 35 | 36 | \vfill 37 | This course is taken in Winter 2022, and the date on the cover page is the last updated time. 38 | \end{abstract} 39 | 40 | \tableofcontents 41 | 42 | \lec{1}{40} 43 | 44 | \newpage 45 | %─────Appendix──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 46 | \appendix 47 | \appendixpage{} 48 | 49 | \input{appendix.tex} 50 | 51 | \newpage 52 | %─────Reference────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 53 | \pagestyle{plain} 54 | \printbibliography{} 55 | 56 | \end{document} -------------------------------------------------------------------------------- /MATH597-Analysis-II/reference.bib: -------------------------------------------------------------------------------- 1 | @book{folland1999real, 2 | title = {Real Analysis: Modern Techniques and Their Applications}, 3 | author = {Folland, G.B. and FOLLAND, G.B.A.}, 4 | isbn = {9780471317166}, 5 | lccn = {98037260}, 6 | series = {A Wiley-Interscience publication}, 7 | url = {https://books.google.com/books?id=uPkYAQAAIAAJ}, 8 | year = {1999}, 9 | publisher = {Wiley} 10 | } 11 | 12 | @book{axler2019measure, 13 | title = {Measure, Integration \& Real Analysis}, 14 | author = {Axler, S.}, 15 | isbn = {9783030331429}, 16 | series = {Graduate Texts in Mathematics}, 17 | url = {https://books.google.com/books?id=8hCDyQEACAAJ}, 18 | year = {2019}, 19 | publisher = {Springer International Publishing} 20 | } 21 | 22 | @book{tao2013introduction, 23 | title = {An Introduction to Measure Theory}, 24 | author = {Tao, T.}, 25 | isbn = {9781470409227}, 26 | series = {Graduate studies in mathematics}, 27 | url = {https://books.google.com/books?id=SPGJjwEACAAJ}, 28 | year = {2013}, 29 | publisher = {American Mathematical Society} 30 | } 31 | 32 | @book{dym1972fourier, 33 | title = {Fourier Series and Integrals}, 34 | author = {Dym, H. and McKean, H.P.}, 35 | isbn = {9780122264511}, 36 | lccn = {73187225}, 37 | series = {Probability and Mathematical Statistics}, 38 | url = {https://books.google.com/books?id=atkQAQAAIAAJ}, 39 | year = {1972}, 40 | publisher = {Elsevier Science} 41 | } 42 | -------------------------------------------------------------------------------- /MATH602-Real-Analysis-II/Figures/orthogonality-principle.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH602-Real-Analysis-II/Figures/orthogonality-principle.pdf -------------------------------------------------------------------------------- /MATH602-Real-Analysis-II/Figures/separation-of-a-point-from-convex-set.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH602-Real-Analysis-II/Figures/separation-of-a-point-from-convex-set.pdf -------------------------------------------------------------------------------- /MATH602-Real-Analysis-II/Lectures/lec_14.tex: -------------------------------------------------------------------------------- 1 | \lecture{14}{13 Oct.\ 14:30}{Midterm} 2 | Good luck! -------------------------------------------------------------------------------- /MATH602-Real-Analysis-II/ReAnalysis-II.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH602-Real-Analysis-II/ReAnalysis-II.pdf -------------------------------------------------------------------------------- /MATH602-Real-Analysis-II/ReAnalysis-II.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH602-Real-Analysis-II/ReAnalysis-II.synctex.gz -------------------------------------------------------------------------------- /MATH602-Real-Analysis-II/ReAnalysis-II.tex: -------------------------------------------------------------------------------- 1 | \documentclass[a4paper]{report} 2 | \input{~/Developer/LaTeX-Template/Note/header.tex} 3 | \author{Pingbang Hu} 4 | \title{MATH602\\Real Analysis II} 5 | 6 | \thispagestyle{empty} 7 | \addbibresource{reference.bib} 8 | 9 | \newcommand{\HS}{\mathrm{HS}} 10 | \DeclareMathOperator{\codim}{codim} 11 | 12 | \begin{document} 13 | 14 | \maketitle 15 | 16 | \begin{abstract} 17 | This is a graduate-level functional analysis taught by \href{https://lsa.umich.edu/math/people/faculty/conlon.html}{Joseph Conlon} at University of Michigan. The prerequisites include linear algebra, complex analysis, and also \href{https://pbb.wtf/posts/Notes#real-analysis-math597-umich}{real analysis}. We'll use Peter Lax\cite{lax2002functional} and Reed-Simon\cite{reed1980functional} as textbooks. 18 | 19 | The focus of this course is rather standard, including Banach and Hilbert Spaces Theory, Bounded Linear, Compact, and Self-Adjoint Operators Theorem, Representation, Hahn-Banach, Open Mapping Theorem, and Spectral Theory. We also covered some point-set topology along the way. 20 | 21 | \vfill 22 | This course is taken in Fall 2022, and the date on the cover page is the last updated time. 23 | \end{abstract} 24 | 25 | \tableofcontents 26 | 27 | \lec{1}{28} 28 | 29 | \newpage 30 | %─────Appendix──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 31 | \appendix 32 | \appendixpage{} 33 | 34 | \input{appendix.tex} 35 | 36 | \newpage 37 | %─────Reference────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 38 | \pagestyle{plain} 39 | \printbibliography{} 40 | 41 | \end{document} -------------------------------------------------------------------------------- /MATH602-Real-Analysis-II/reference.bib: -------------------------------------------------------------------------------- 1 | @book{lax2002functional, 2 | title = {Functional Analysis}, 3 | author = {Lax, P.D.}, 4 | isbn = {9780471556046}, 5 | lccn = {01046547}, 6 | series = {Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts}, 7 | url = {https://books.google.com/books?id=18VqDwAAQBAJ}, 8 | year = {2002}, 9 | publisher = {Wiley} 10 | } 11 | 12 | @book{reed1980functional, 13 | title = {I: Functional Analysis}, 14 | author = {Reed, M. and Simon, B.}, 15 | isbn = {9780125850506}, 16 | lccn = {75182650}, 17 | series = {Methods of Modern Mathematical Physics}, 18 | url = {https://books.google.com/books?id=hInvAAAAMAAJ}, 19 | year = {1980}, 20 | publisher = {Elsevier Science} 21 | } 22 | -------------------------------------------------------------------------------- /MATH635-Riemannian-Geometry/Figures/2nd-variation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH635-Riemannian-Geometry/Figures/2nd-variation.pdf 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\setlength\multicolsep{0pt} 10 | 11 | \newcommand{\GL}{\mathrm{GL}} 12 | \DeclareMathOperator{\Ind}{Ind} 13 | \DeclareMathOperator{\Inj}{Inj} 14 | \DeclareMathOperator{\Crit}{Crit} 15 | \DeclareMathOperator{\Ric}{Ric} 16 | 17 | \begin{document} 18 | 19 | \maketitle 20 | 21 | \begin{abstract} 22 | This is the advanced graduate-level differential geometry course focused on Riemannian geometry taught by \href{http://www-personal.umich.edu/~lbieri/}{Lydia Bieri} at University of Michigan. Topics include local and global aspects of differential geometry and its relation to the underlying topology. We'll use do Carmo's \emph{Riemannian Geometry}~\cite{flaherty2013riemannian} as our reference. Apart from this, I also found~\cite{Frederic2015} very useful. 23 | 24 | A noticeable different is that we introduce \hyperref[def:geodesic]{geodesics} differently from do Carmo~\cite{flaherty2013riemannian}, where we set the solution of the variations of \hyperref[def:energy]{energy} to define a \hyperref[def:geodesic]{geodesic} first, and then draw connection to the ``\hyperref[def:curve]{curve} with zero acceleration'' after introduce the \hyperref[def:covariant-derivative]{covariant derivative}; however, do Carmo~\cite{flaherty2013riemannian} first introduce \hyperref[def:covariant-derivative]{covariant derivative} and then return the variation viewpoint much later. 25 | 26 | \vfill 27 | \begin{center} 28 | \includegraphics[width=.8\linewidth]{Figures/cover.png} 29 | \end{center} 30 | \vfill 31 | This course is taken in Winter 2023, and the date on the cover page is the last updated time. 32 | \end{abstract} 33 | 34 | \tableofcontents 35 | 36 | \lec{1}{28} 37 | 38 | \newpage 39 | %─────Appendix──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 40 | \appendix 41 | \appendixpage{} 42 | 43 | \input{appendix.tex} 44 | 45 | \newpage 46 | %─────Reference────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 47 | \pagestyle{plain} 48 | \printbibliography{} 49 | 50 | \end{document} -------------------------------------------------------------------------------- /MATH681-Mathematical-Logic/Figures/cell.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH681-Mathematical-Logic/Figures/cell.pdf -------------------------------------------------------------------------------- /MATH681-Mathematical-Logic/Figures/cover.png: 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Accompanies image file 'disjoint-union-finite-graphs.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{680.31496063bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.04166667)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{disjoint-union-finite-graphs.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /MATH681-Mathematical-Logic/Figures/linear-order-ap.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH681-Mathematical-Logic/Figures/linear-order-ap.pdf -------------------------------------------------------------------------------- /MATH681-Mathematical-Logic/Figures/random-graph-qe.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH681-Mathematical-Logic/Figures/random-graph-qe.pdf -------------------------------------------------------------------------------- /MATH681-Mathematical-Logic/Figures/random-graph-qe.pdf_tex: -------------------------------------------------------------------------------- 1 | %% Creator: Inkscape 1.2.2 (b0a84865, 2022-12-01), www.inkscape.org 2 | %% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010 3 | %% Accompanies image file 'random-graph-qe.pdf' (pdf, eps, ps) 4 | %% 5 | %% To include the image in your LaTeX document, write 6 | %% \input{.pdf_tex} 7 | %% instead of 8 | %% \includegraphics{.pdf} 9 | %% To scale the image, write 10 | %% \def\svgwidth{} 11 | %% \input{.pdf_tex} 12 | %% instead of 13 | %% \includegraphics[width=]{.pdf} 14 | %% 15 | %% Images with a different path to the parent latex file can 16 | %% be accessed with the `import' package (which may need to be 17 | %% installed) using 18 | %% \usepackage{import} 19 | %% in the preamble, and then including the image with 20 | %% \import{}{.pdf_tex} 21 | %% Alternatively, one can specify 22 | %% \graphicspath{{/}} 23 | %% 24 | %% For more information, please see info/svg-inkscape on CTAN: 25 | %% http://tug.ctan.org/tex-archive/info/svg-inkscape 26 | %% 27 | \begingroup% 28 | \makeatletter% 29 | \providecommand\color[2][]{% 30 | \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}% 31 | \renewcommand\color[2][]{}% 32 | }% 33 | \providecommand\transparent[1]{% 34 | \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% 35 | \renewcommand\transparent[1]{}% 36 | }% 37 | \providecommand\rotatebox[2]{#2}% 38 | \newcommand*\fsize{\dimexpr\f@size pt\relax}% 39 | \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% 40 | \ifx\svgwidth\undefined% 41 | \setlength{\unitlength}{680.31496063bp}% 42 | \ifx\svgscale\undefined% 43 | \relax% 44 | \else% 45 | \setlength{\unitlength}{\unitlength * \real{\svgscale}}% 46 | \fi% 47 | \else% 48 | \setlength{\unitlength}{\svgwidth}% 49 | \fi% 50 | \global\let\svgwidth\undefined% 51 | \global\let\svgscale\undefined% 52 | \makeatother% 53 | \begin{picture}(1,0.17916667)% 54 | \lineheight{1}% 55 | \setlength\tabcolsep{0pt}% 56 | \put(0,0){\includegraphics[width=\unitlength,page=1]{random-graph-qe.pdf}}% 57 | \end{picture}% 58 | \endgroup% 59 | -------------------------------------------------------------------------------- /MATH681-Mathematical-Logic/Figures/random-graph-theory.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH681-Mathematical-Logic/Figures/random-graph-theory.pdf -------------------------------------------------------------------------------- /MATH681-Mathematical-Logic/Figures/square-free.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH681-Mathematical-Logic/Figures/square-free.pdf -------------------------------------------------------------------------------- /MATH681-Mathematical-Logic/Logic.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH681-Mathematical-Logic/Logic.pdf -------------------------------------------------------------------------------- /MATH681-Mathematical-Logic/Logic.synctex.gz: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH681-Mathematical-Logic/Logic.synctex.gz -------------------------------------------------------------------------------- /MATH681-Mathematical-Logic/Logic.tex: -------------------------------------------------------------------------------- 1 | \documentclass[a4paper]{report} 2 | \input{~/Developer/LaTeX-Template/Note/header.tex} 3 | \author{Pingbang Hu} 4 | \title{MATH681\\Mathematical Logic} 5 | 6 | \thispagestyle{empty} 7 | \addbibresource{reference.bib} 8 | 9 | \newcounter{stoppedhere} 10 | 11 | \newcommand{\ACF}{\mathrm{ACF}} 12 | \newcommand{\DLO}{\mathrm{DLO}} 13 | \newcommand{\RCF}{\mathrm{RCF}} 14 | \newcommand{\ZFC}{\mathrm{ZFC}} 15 | \newcommand{\DAG}{\mathrm{DAG}} 16 | \newcommand{\FV}{\mathrm{FV}} 17 | \DeclareMathOperator{\Diag}{Diag} 18 | \DeclareMathOperator{\Flm}{Flm} 19 | \DeclareMathOperator{\dcl}{dcl} 20 | \DeclareMathOperator{\acl}{acl} 21 | \DeclareMathOperator{\tp}{tp} 22 | \DeclareMathOperator{\Age}{Age} 23 | \DeclareMathOperator{\Th}{Th} 24 | 25 | \begin{document} 26 | 27 | \maketitle 28 | 29 | \begin{abstract} 30 | This is a graduate-level mathematical logic course taught by \href{http://www-personal.umich.edu/~matthhar/}{Matthew Harrison-Trainor} at University of Michigan, aiming to obtain insights into all other branches of mathematics, such as algebraic geometry, analysis, etc. Specifically, we will cover model theory beyond the basic foundational ideas of logic. 31 | 32 | While there are no required textbooks, some books do cover part of the material in the class. For example, Marker's \emph{Model Theory: An Introduction}~\cite{marker2002model}, Hodges's \emph{A Shorter Model Theory}~\cite{hodges1997shorter}, and Hinman's \emph{Fundamentals of Mathematical Logic}~\cite{hinman2005fundamentals}. 33 | 34 | \vfill 35 | \begin{center} 36 | \includegraphics[width=.8\linewidth]{Figures/cover.png} 37 | \end{center} 38 | \vfill 39 | This course is taken in Winter 2023, and the date on the cover page is the last updated time. 40 | \end{abstract} 41 | 42 | \tableofcontents 43 | 44 | \lec{1}{28} 45 | 46 | \newpage 47 | %─────Appendix──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 48 | \appendix 49 | \appendixpage{} 50 | 51 | \input{appendix.tex} 52 | 53 | \newpage 54 | %─────Reference────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 55 | \pagestyle{plain} 56 | \printbibliography{} 57 | 58 | \end{document} -------------------------------------------------------------------------------- /MATH681-Mathematical-Logic/appendix.tex: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/MATH681-Mathematical-Logic/appendix.tex -------------------------------------------------------------------------------- /MATH681-Mathematical-Logic/reference.bib: -------------------------------------------------------------------------------- 1 | @book{marker2002model, 2 | title = {Model Theory : An Introduction}, 3 | author = {Marker, D.}, 4 | isbn = {9780387987606}, 5 | lccn = {02024184}, 6 | series = {Graduate Texts in Mathematics}, 7 | url = {https://books.google.com/books?id=gkvogoiEnuYC}, 8 | year = {2002}, 9 | publisher = {Springer New York} 10 | } 11 | 12 | @book{hodges1997shorter, 13 | title = {A Shorter Model Theory}, 14 | author = {Hodges, W. and Hodges, S.M.S.W.}, 15 | isbn = {9780521587136}, 16 | lccn = {96036603}, 17 | url = {https://books.google.com/books?id=S6QYeuo4p1EC}, 18 | year = {1997}, 19 | publisher = {Cambridge University Press} 20 | } 21 | 22 | @book{hinman2005fundamentals, 23 | title = {Fundamentals of Mathematical Logic}, 24 | author = {Hinman, P.G.}, 25 | isbn = {9781568812625}, 26 | lccn = {2005050968}, 27 | url = {https://books.google.com/books?id=xA6D8o72qAgC}, 28 | year = {2005}, 29 | publisher = {Taylor \& Francis} 30 | } 31 | 32 | @article{robinson_1949, 33 | title = {Definability and decision problems in arithmetic}, 34 | volume = {14}, 35 | doi = {10.2307/2266510}, 36 | number = {2}, 37 | journal = {The Journal of Symbolic Logic}, 38 | publisher = {Cambridge University Press}, 39 | author = {Robinson, Julia}, 40 | year = {1949}, 41 | pages = {98-114} 42 | } -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Notes 2 | 3 |

4 | 5 |

6 | 7 |

8 | Source Code of my LaTeX Lecture Notes. 9 |

10 | 11 | ## Abstract 12 | 13 | This repo contains all $\LaTeX$ source codes of the lecture notes I took in university. A more readable version can be found [here](https://pbb.wtf/posts/Notes). 14 | 15 | The [`header.tex`](https://github.com/sleepymalc/LaTeX-Template/blob/main/Note/header.tex) can be found in [LaTeX Template](https://github.com/sleepymalc/LaTeX-Template), together with a simple, but complete [demo](https://github.com/sleepymalc/LaTeX-Template/blob/main/Note/master.pdf). 16 | 17 | > **You need to include this header to compile any of my notes!** The particular compile environment should not be that relevant since the packages this environment depends on are quite straightforward and minimal, hence a simple *pdflatex* should do the job. As for Inkscape figures, please look into [VSCode-LaTeX-Inkscape](https://github.com/sleepymalc/VSCode-LaTeX-Inkscape) for detailed configuration. 18 | 19 | ## Contribution 20 | 21 | The works are partially contributed by some other students, TAs, and professors in JI, which would be listed if known. 22 | 23 | > If you find any problems in the repository, you are welcome to make an issue or pull request. 24 | -------------------------------------------------------------------------------- /STAT575-Large-Sample-Theory/Figures/cover.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/sleepymalc/Notes/74954f283b1a4afd00dc3884f8af4c1dfc45530f/STAT575-Large-Sample-Theory/Figures/cover.png -------------------------------------------------------------------------------- /STAT575-Large-Sample-Theory/LargeSample.pdf: -------------------------------------------------------------------------------- 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12 | \DeclareMathOperator{\KL}{KL} 13 | 14 | \begin{document} 15 | 16 | \maketitle 17 | 18 | \begin{abstract} 19 | This is a graduate-level theoretical statistics course taught by \href{https://publish.illinois.edu/fellouri/}{Georgios Fellouris} at University of Illinois Urbana-Champaign, aiming to provide an introduction to asymptotic analysis of various statistical methods, including weak convergence, Lindeberg-Feller CLT, asymptotic relative efficiency, etc. 20 | 21 | We list some references of this course, although we will not follow any particular book page by page: \emph{Asymnptotic Statistics}~\cite{vaartAsymptoticStatistics1998}, \emph{Asymptotic Theory of Statistics and Probability}~\cite{dasguptaAsymptoticTheoryStatistics2008}, \emph{A course in Large Sample Theory}~\cite{fergusonCourseLargeSample2017}, \emph{Approximation Theorems of Mathematical Statistics}~\cite{serflingApproximationTheoremsMathematical2009}, and \emph{Elements of Large-Sample Theory}~\cite{lehmannElementsLargeSampleTheory2004}. 22 | 23 | \vfill 24 | \begin{center} 25 | \includegraphics[width=.8\linewidth]{Figures/cover.png} 26 | \end{center} 27 | \vfill 28 | This course is taken in Spring 2024, and the date on the cover page is the last updated time. 29 | \end{abstract} 30 | 31 | \tableofcontents 32 | 33 | \lec{1}{30} 34 | 35 | \newpage 36 | %─────Appendix──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 37 | \appendix 38 | \appendixpage{} 39 | 40 | \input{appendix.tex} 41 | 42 | \newpage 43 | %─────Reference────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 44 | \pagestyle{plain} 45 | \printbibliography{} 46 | 47 | \end{document} -------------------------------------------------------------------------------- /STAT575-Large-Sample-Theory/appendix.tex: 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-------------------------------------------------------------------------------- /STAT576-Empirical-Process-Theory/EmpProcess.tex: -------------------------------------------------------------------------------- 1 | \documentclass[a4paper]{report} 2 | \input{~/Developer/LaTeX-Template/Note/header.tex} 3 | \author{Pingbang Hu} 4 | \title{STAT576\\Empirical Process Theory} 5 | 6 | \thispagestyle{empty} 7 | \addbibresource{reference.bib} 8 | 9 | \newcounter{stoppedhere} 10 | 11 | \DeclareMathOperator{\Subg}{Subg} 12 | \DeclareMathOperator{\SubExp}{SubExp} 13 | \DeclareMathOperator{\VC}{VC} 14 | \DeclareMathOperator{\GW}{GW} 15 | \DeclareMathOperator{\Proj}{Proj} 16 | \DeclareMathOperator{\Star}{Star} 17 | \DeclareMathOperator{\TV}{TV} 18 | \DeclareMathOperator{\BV}{BV} 19 | 20 | \begin{document} 21 | 22 | \maketitle 23 | 24 | \begin{abstract} 25 | This is a graduate-level theoretical statistics course taught by \href{https://sabyasachi.web.illinois.edu/}{Sabyasachi Chatterjee} at University of Illinois Urbana-Champaign, aiming to provide an introduction to empirical process theory with applications to statistical \(M\)-estimation, non-parametric regression, classification and high dimensional statistics. 26 | 27 | While there are no required textbooks, some books do cover (almost all) part of the material in the class, e.g., Van Der Vaart and Wellner's \emph{Weak Convergence and Empirical Processes}~\cite{vandervaartWeakConvergenceEmpirical1996}. 28 | 29 | \vfill 30 | \begin{center} 31 | \includegraphics[width=.8\linewidth]{Figures/cover.png} 32 | \end{center} 33 | \vfill 34 | This course is taken in Fall 2023, and the date on the cover page is the last updated time. 35 | \end{abstract} 36 | 37 | \tableofcontents 38 | 39 | \lec{1}{31} 40 | 41 | \newpage 42 | %─────Appendix──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── 43 | \appendix 44 | \appendixpage{} 45 | 46 | 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