P1 2021 Introductory Remarks
P2 Lecture 1(A)： Sets and n-tuples
P3 Lecture 1(B)： Sets and n-tuples
P4 Lecture 2(A)： Quantifiers and Functions 1
P5 Lecture 2(B)： Quantifiers and Functions 1
P6 Lecture 3(A)： Quantifiers and Functions 2
P7 Lecture 3(B)： Quantifiers and Functions 2
P8 Lecture 4(A)： Unifying n-tuples, Sequences, Functions, and Subsets
P9 Lecture 4(B)： Unifying n-tuples, Sequences, Functions, and Subsets
P10 Lecture 5(A)： Logic 1 (Statements and truth values)
P11 Lecture 5(B)： Logic 1 (Truth tables and compound statements)
P12 Lecture 5(C)： Logic 1 (Implication; De Morgan's Laws)
P13 Lecture 6(A)： Logic 2 (Implication issues)
P14 Lecture 6(B)： Logic 2 (Strategy for proofs)
P15 Lecture 6(C)： Logic 2 (Strategy for proofs)
P16 Lecture 7(A)： Proof by Induction： What is it and how does it work？
P17 Lecture 7(B)： Proof by Induction
P18 Lecture 8： Foundation for Vector Spaces： Geometry and Algebra of Rn (Revise
P19 Lecture 9(A)： Euclidean Space
P20 Lecture 9(B)： Euclidean Space： Cauchy-Schwarz and Triangle inequalities, dot
P21 Lecture 10(A)： Euclidean Space： Neighborhoods, Open and Closed Sets
P22 Lecture 10(B)： Euclidean Space： Examples and Theorems
P23 Lecture 11： Vector Spaces
P24 Lecture 12(A)： Vector Subspaces
P25 Lecture 12(B)： Vector Subspaces
P26 Lecture 13(A)： Linear Combinations
P27 Lecture 13(B)： Linear Combinations
P28 Lecture 14(A)： Linear Independence and Basis
P29 Lecture 14(B)： Linear Independence and Basis
P30 Lecture 15(A)： Linear Functions
P31 Lecture 15(B)： Linear Functions
P32 Lecture 15(C)： Linear Functions
P33 Lecture 16(A)： Convexity
P34 Lecture 16(B)： Convexity
P35 Lecture 16(C)： Convexity
P36 Lecture 17(A)： Concave and Convex Functions
P37 Lecture 18(A)： Alternative Norms and Metrics
P38 Lecture 18(B)： Alternative Norms and Metrics
P39 Lecture 18(C)： Alternative Norms and Metrics
P40 Lecture 18(D)： Alternative Norms and Metrics
P41 Lecture 19(A)： Sequences
P42 Lecture 19(B)： Sequences
P43 Lecture 19(C)： Sequences
P44 Lecture 20(A)： Bounded Sequences and Subsequences
P45 Lecture 20(B)： Bounded Sequences： The Monotone Convergence Theorem
P46 Lecture 20(C)： Bounded Sequences： The Bolzano-Weierstrass Theorem
P47 Lecture 21(A)： Continuous Functions
P48 Lecture 21(B)： Continuous Functions
P49 Lecture 22(A)： Continuous Functions 2
P50 Lecture 22(B)： Continuous Functions 2 (Revised)
P51 Lecture 23(A)： Compact Sets and Metric Spaces; Bolzano-Weierstrass Theorem
P52 Lecture 23(B)： Compact Sets, Weierstrass Theorem, examples and counterexampl
P53 Lecture 24(A)： Approximation and Taylor Polynomials
P54 Lecture 24(B)： Approximation and Taylor Polynomials, with example
P55 Lecture 25(A)： Derivatives
P56 Lecture 25(B)： Derivatives
P57 Lecture 26(A)： Approximation & Taylor Polynomials in Rn
P58 Lecture 26(B)： Approximation & Taylor Polynomials in Rn
P59 Lecture 27(A)： Quadratic Forms： Symmetric matrices, geometric intuition
P60 Lecture 27(B)： Quadratic Forms： Geometric Example
P61 Lecture 28： Quadratic Forms： Definite and semidefinite forms
P62 Lecture 29(A)： Quadratic Forms： Necessary & sufficient conditions for defini
P63 Lecture 29(B)： Quadratic Forms： Determinant conditions for definiteness
P64 Lecture 29(C)： Quadratic Forms： Determinant conditions for definiteness
P65 Lecture 30： Unconstrained Optimization 1
P66 Lecture 31： Unconstrained Optimization 2
P67 Lecture 32： Unconstrained Optimization 3
P68 Lecture 33(A)： Global Optimization
P69 Lecture 33(B)： Characterization of differentiable concave functions.
P70 Lecture 33(C)： Concave functions and global optimization
P71 Lecture 34： Geometry of Constrained Optimization： Focus on Gradients
P72 Lecture 35： Geometry of Constrained Optimization： Multiple and nonlinear con
P73 Lecture 36(A)： Solution Function and Value Function
P74 Lecture 36(B)： Solution Function and Value Function
P75 Lecture 37(A)： The Implicit Function Theorem： How the solution changes when
P76 Lecture 37(B)： The Implicit Function Theorem
P77 Lecture 37(C)： The Implicit Function Theorem
P78 Lecture 37(D)： The Implicit Function Theorem
P79 Lecture 38(A)： The Envelope Theorem： How the Optimal Value Changes
P80 Lecture 38(B)： The Envelope Theorem for Constrained Optimization
P81 Lecture 39(A)： The Envelope Theorem and Shadow Values
P82 Lecture 39(B)： The Envelope Theorem： Hotelling's Lemma
P83 Lecture 39(C)： The Envelope Theorem： Shephard's Lemma
P84 Lecture 40(A)： Kuhn-Tucker Conditions： Conceptual and geometric insight
P85 Lecture 40(B)： The Kuhn-Tucker Conditions and Theorem
P86 Lecture 40(C)： The Kuhn-Tucker Conditions： An Example
P87 Lecture 40(D)： The Kuhn-Tucker Conditions： Two examples
P88 Lecture 40(E)： The Kuhn-Tucker Conditions： A Corner (Boundary) Solution
P89 Lecture 41(A)： Binary Relations
P90 Lecture 41(B)： Binary Relations
P91 Lecture 42(A)： Order Relations, Preferences, and Utility Functions
P92 Lecture 42(B)： Order Relations and Utility Functions Exercise Solution
P93 Lecture 43(A)： Equivalence Relations & Partitions
P94 Lecture 43(B)： Equivalence Relations & Partitions
P95 Lecture 44(A)： Representation of Preferences by Utility Functions
P96 Lecture 44(B)： Representation of Preferences by Utility Functions
P97 Lecture 45(B)： Lexicographic Preference
P98 Lecture 45(A)： Lexicographic Preference
P100 Hemicontinuous Correspondences
P101 Hemicontinuity of Correspondences： Examples
P102 The Budget Set Correspondence
P103 Upper Hemicontinuity of the Budget Set Correspondence
P104 Lower Hemicontinuity of the Budget Set Correspondence
