Notes

GOOD LUCK ON FINALS !!!!

• Lecture 1 (Wed 1/25), Introduction - Sections 1.1, 1.2
• Lecture 2 (Fri 1/27), Density, Absolute Value, Power Formula, Binomial Formula - Sections 1.2, 1.3
• Lecture 3 (Mon 1/30), Sequences, Properties of Convergence - Section 2.1
• Lecture 4 (Wed 2/1), Sequences, Closed Sets, Monotonicity - Sections 2.2, 2.3
• Lecture 5 (Fri 2/3), Sequences and Subsequences - Sections 2.3, 2.4
• Lecture 6 (Mon 2/6), Sequences, Continuous Functions - Section 3.1
• Lecture 7 (Wed 2/8), Continuous Functions, Closed Domain Functions - Sections 3.2, 3.3
• Lecture 8 (Fri 2/10), Bisection Method, Uniform Continuity - Sections 3.3, 3.4
• Lecture 9 (Mon 2/13), Continuity, Epsilon-Delta - Sections 3.4, 3.5
• Lecture 10 (Wed 2/15), Monotonicity, Inverse Functions - Section 3.6
• Lecture 11 (Fri 2/17), Limits - Section 3.7
• Lecture 12 (Mon 2/20), MATH410 Fall 22 Practice Exam
• Lecture 13 (Wed 2/22), MATH410 Spring 22 Practice Exam
• Lecture 14 (Fri 2/24), Exam 1
• Lecture 15 (Mon 2/27), Derivatives - Section 4.1
• Lecture 16 (Wed 3/1), Derivative Rules - Section 4.1, 4.2
• Lecture 17 (Fri 3/3), Rolle's Theorem, Mean Value Theorem - Section 4.3
• Lecture 18 (Mon 3/6), Identity Criterion, Monotonicity, Second Derivative Test - Section 4.3
• Lecture 19 (Wed 3/8), Concavity, Cauchy MVT - Section 4.4
• Lecture 20 (Fri 3/10), L'Hopital's Rule, Partitions, Refinements, Upper/Lower Integrals - Section 4.4, 6.1
• Lecture 21 (Mon 3/13), Integrals - Section 6.2
• Lecture 22 (Wed 3/15), Additivity, Monotonicity, and Linearity of Integrals - Section 6.3
• Lecture 23 (Fri 3/17), Area, Integrability - Section 6.4
• Lecture 24 (Mon 3/27), Fundamental Theorem of Calculus, Logarithms - Section 6.6
• Lecture 25 (Wed 3/29), First Fundamental Theorem, Integral IVT, Improper Integrals - Section 6.5
• Lecture 26 (Fri 3/31), MATH410 Exam 2 Fall 2022
• Lecture 27 (Mon 4/3), Exam 2
• Lecture 28 (Wed 4/5), Exam Review, Integration by Parts
• Lecture 29 (Fri 4/7), Trapezoidal Rule, Simpson's Rule
• Lecture 30 (Mon 4/10), Taylor Polynomials - Section 8.1
• Lecture 31 (Wed 4/12), Taylor Polynomials, Lagrange Remainder Theorem - Section 8.2
• Lecture 32 (Fri 4/14), Lagrange Remainder Theorem - Section 8.3
• Lecture 33 (Mon 4/17), Lagrange Remainder Theorem, Special Function - Sections 8.4, 8.6
• Lecture 34 (Wed 4/19), Cauchy Sequences, Convergence Tests - Sections 8.5, 9.1
• Lecture 35 (Fri 4/21), Convergence Tests - Section 9.1
• Lecture 36 (Mon 4/24), Convergence Tests (Root Test), Pointwise Convergence - Sections 9.1, 9.2
• Lecture 37 (Wed 4/26), Uniform Convergence of Functions - Sections 9.3, 9.4
• Lecture 38 (Fri 4/28), Uniformly Cauchy - Sections 9.4, 9.6
• Lecture 39 (Mon 5/1), Power Series - Section 9.5
• Lecture 40 (Wed 5/3), MATH410 Exam 3 Fall 2022
• Lecture 41 (Fri 5/5), Exam 3
• Lecture 42 (Mon 5/8), MATH410 Fall 2022 Final Exam
• Lecture 43 (Wed 5/10), Final Exam

• Lecture 1 (Wed 1/25), The Leontief Input-Output Method (Section 1)
• Lecture 2 (Fri 1/27), The Leontief Input-Output Method (Continued), invertibility of (I - A)
• Lecture 3 (Mon 1/30), Affine Combinations (Section 2.1)
• Lecture 4 (Wed 2/1), Affine Combinations, Homogeneous Form and Graphics, Affine Independence (Section 2.1, 2.2)
• Lecture 5 (Fri 2/3), Affine Combinations, Convex Combinations (Section 2.4)
• Lecture 6 (Mon 2/6), Convex Combinations, Singular Value Decomposition (Section 2.5)
• Lecture 7 (Wed 2/8), Singular Value Decomposition, Trace and Eigenvalues
• Lecture 8 (Fri 2/10), Principal Component Analysis, Image Compression
• Lecture 9 (Mon 2/13), Introduction to Markov Chains (Section 3.1)
• Lecture 10 (Wed 2/15), Markov Chains, Stable/Steady-State Vectors (Section 3.2)
• Lecture 11 (Fri 2/17), Markov Chains, Google PageRank
• Lecture 12 (Mon 2/20), Google PageRank, Communication Classes (Section 3.3)
• Lecture 13 (Wed 2/22), Exam 1 Review
• Lecture 14 (Fri 2/24), Exam 1
• Lecture 15 (Mon 2/27), Communication Classes
• Lecture 16 (Wed 3/1), Communication Classes, Classification of States and Periodicity (Section 3.4)
• Lecture 17 (Fri 3/3), Periodicity, The Fundamental Matrix (Section 3.5)
• Lecture 18 (Mon 3/6), Canonical Form, Fundamental Matrix
• Lecture 19 (Wed 3/8), Fundamental Matrix
• Lecture 20 (Fri 3/10), Markov Chain Examples
• Lecture 21 (Mon 3/13), Markov Chain Examples, Parity Domination Problem
• Lecture 22 (Wed 3/15), Parity Domination Problem
• Lecture 23 (Fri 3/17), Lights Out, Extremal Combinatorics
• Lecture 24 (Mon 3/27), Distance and Sets (Section 4.1)
• Lecture 25 (Wed 3/29), Oddtown and Eventown
• Lecture 26 (Fri 3/31), Exam 2 Review
• Lecture 27 (Mon 4/3), Exam 2
• Lecture 28 (Wed 4/5), Oddtown and Eventown, Other Results
• Lecture 29 (Fri 4/7), Polynomial Spaces (Section 4.2)
• Lecture 30 (Mon 4/10), Polynomial Spaces, Basics of Graphs (Section 5.1)
• Lecture 31 (Wed 4/12), Graph Spectrum (Section 5.2)
• Lecture 32 (Fri 4/14), Eigenvalues of Graphs
• Lecture 33 (Mon 4/17), Eigenvalues of Graphs, Two Proofs (Section 5.3)
• Lecture 34 (Wed 4/19), Friendship
• Lecture 35 (Fri 4/21), Bipartite Graphs (Section 5.4)
• Lecture 36 (Mon 4/24), Biclique Decomposition
• Lecture 37 (Wed 4/26), Biclique Decomposition, Independence (Section 5.5)
• Lecture 38 (Fri 4/28), Hoffman Ratio Bound, Kneser Graph
• Lecture 39 (Mon 5/1), Exam 3 Review
• Lecture 40 (Wed 5/3), Exam 3
• Lecture 41 (Fri 5/5), Graph Colorings (Section 5.6)
• Lecture 42 (Mon 5/8), Final Exam Review
• Lecture 43 (Wed 5/10), Final Exam Review

• Lecture 1 (Thurs 1/26), Introduction & Stable Matching Problem
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• Lecture 2 (Tues 1/31), Stable Matching Problem, Asymptotic Notation
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• Lecture 3 (Thurs 2/2), Asymptotic Complexity, Running Time Analysis, Graphs
• Lecture 4 (Tues 2/7), Connectivity, BFS
• Lecture 5 (Thurs 2/9), BFS, Bipartiteness
• Lecture 6 (Tues 2/14), Connectivity in Digraphs, DFS, Topological Sorting
• Lecture 7 (Thurs 2/16), Greedy Algorithms, Shortest Paths
• Lecture 8 (Tues 2/21), Minimum Spanning Trees (Kruskal, Prim)
• Lecture 9 (Thurs 2/23), Scheduling, Interval Partitioning
• Lecture 10 (Tues 2/28), Scheduling to Minimize Lateness, Divide and Conquer, Closest Points
• Lecture 11 (Thurs 3/2), Closest Points, Polynomial Multiplication/FFT
• Lecture 12 (Tues 3/7), Fast Fourier Transform
• Lecture 13 (Thurs 3/9), Exam 1
• Lecture 14 (Tues 3/14), Dynamic Programming, Weighted Interval Scheduling
• Lecture 15 (Thurs 3/16), Knapsack
• Lecture 16 (Tues 3/28), Sequence Alignment
• Lecture 17 (Thurs 3/30), Shortest Paths in Graphs with Negative Weights
• Lecture 18 (Tues 4/4), Negative Cycles, Network Flow
• Lecture 19 (Thurs 4/6), Network Flow
• Lecture 20 (Tues 4/11), Max-flow/Min-cut, Bipartite Matching
• Lecture 21 (Thurs 4/13), Bipartite Matching, Extensions to Max Flow
• Lecture 22 (Tues 4/18), Max Flow Extensions
• Lecture 23 (Thurs 4/20), Reductions, Polynomial Reducibility, Satisfiability Problem
• Lecture 24 (Tues 4/25), Complexity Classes (P/NP)
• Lecture 25 (Thurs 4/27), Intractability (NP-completeness of 3-SAT, NP-complete problems)
• Lecture 26 (Tues 5/2), Hamiltonian Cycle, Intractability, Approximation Algorithms
• Lecture 27 (Thurs 5/4), Load Balancing, Center Selection
• Lecture 28 (Tues 5/9), Center Selection, Randomized Algorithms
• Lecture 29 (Thurs 5/11), Global Minimum Cut