Канал: Arizona Math Camp

The Maximum Theorem

The Maximum Theorem

Lower Hemicontinuity of the Budget Set Correspondence

Lower Hemicontinuity of the Budget Set Correspondence

Upper Hemicontinuity of the Budget Set Correspondence

Upper Hemicontinuity of the Budget Set Correspondence

The Budget Set Correspondence

The Budget Set Correspondence

Hemicontinuity of Correspondences: Examples

Hemicontinuity of Correspondences: Examples

Lecture 8: Foundation for Vector Spaces: Geometry and Algebra of Rn (Revised)

Lecture 8: Foundation for Vector Spaces: Geometry and Algebra of Rn (Revised)

Lecture 22(B): Continuous Functions 2 (Revised)

Lecture 22(B): Continuous Functions 2 (Revised)

2021 Introductory Remarks

2021 Introductory Remarks

Hemicontinuous Correspondences

Hemicontinuous Correspondences

Correspondences

Correspondences

Lecture 45(B): Lexicographic Preference

Lecture 45(B): Lexicographic Preference

Lecture 45(A): Lexicographic Preference

Lecture 45(A): Lexicographic Preference

Lecture 44(B): Representation of Preferences by Utility Functions

Lecture 44(B): Representation of Preferences by Utility Functions

Lecture 44(A): Representation of Preferences by Utility Functions

Lecture 44(A): Representation of Preferences by Utility Functions

Lecture 43(B): Equivalence Relations & Partitions

Lecture 43(B): Equivalence Relations & Partitions

Lecture 43(A): Equivalence Relations & Partitions

Lecture 43(A): Equivalence Relations & Partitions

Lecture 42(B): Order Relations and Utility Functions Exercise Solution

Lecture 42(B): Order Relations and Utility Functions Exercise Solution

Lecture 42(A): Order Relations, Preferences, and Utility Functions

Lecture 42(A): Order Relations, Preferences, and Utility Functions

Lecture 41(B): Binary Relations

Lecture 41(B): Binary Relations

Lecture 41(A): Binary Relations

Lecture 41(A): Binary Relations

Addition of Sets and Production Theory

Addition of Sets and Production Theory

Lecture 3(A): Quantifiers and Functions 2

Lecture 3(A): Quantifiers and Functions 2

Lecture 2(B): Quantifiers and Functions 1

Lecture 2(B): Quantifiers and Functions 1

Lecture 17(B): Concave and Convex Functions

Lecture 17(B): Concave and Convex Functions

Lecture 33(C): Concave functions and global optimization

Lecture 33(C): Concave functions and global optimization

Lecture 33(B): Characterization of differentiable concave functions.

Lecture 33(B): Characterization of differentiable concave functions.

Lecture 33(A): Global Optimization

Lecture 33(A): Global Optimization

Lecture 32: Unconstrained Optimization 3

Lecture 32: Unconstrained Optimization 3

Lecture 35: Geometry of Constrained Optimization: Multiple and nonlinear constraints

Lecture 35: Geometry of Constrained Optimization: Multiple and nonlinear constraints

Lecture 34: Geometry of Constrained Optimization: Focus on Gradients

Lecture 34: Geometry of Constrained Optimization: Focus on Gradients

Lecture 39(C): The Envelope Theorem: Shephard's Lemma

Lecture 39(C): The Envelope Theorem: Shephard's Lemma

Lecture 39(B): The Envelope Theorem: Hotelling's Lemma

Lecture 39(B): The Envelope Theorem: Hotelling's Lemma

Lecture 39(A): The Envelope Theorem and Shadow Values

Lecture 39(A): The Envelope Theorem and Shadow Values

Lecture 38(B): The Envelope Theorem for Constrained Optimization

Lecture 38(B): The Envelope Theorem for Constrained Optimization

Lecture 37(D): The Implicit Function Theorem

Lecture 37(D): The Implicit Function Theorem

Lecture 37(C): The Implicit Function Theorem

Lecture 37(C): The Implicit Function Theorem

Lecture 37(B): The Implicit Function Theorem

Lecture 37(B): The Implicit Function Theorem

Lecture 38(A): The Envelope Theorem: How the Optimal Value Changes

Lecture 38(A): The Envelope Theorem: How the Optimal Value Changes

Lecture 37(A): The Implicit Function Theorem: How the solution changes when parameters change.

Lecture 37(A): The Implicit Function Theorem: How the solution changes when parameters change.

Lecture 26(B): Approximation & Taylor Polynomials in Rn

Lecture 26(B): Approximation & Taylor Polynomials in Rn

Lecture 26(A): Approximation & Taylor Polynomials in Rn

Lecture 26(A): Approximation & Taylor Polynomials in Rn

Lecture 25(B): Derivatives

Lecture 25(B): Derivatives

Lecture 25(A): Derivatives

Lecture 25(A): Derivatives

Lecture 24(B): Approximation and Taylor Polynomials, with example

Lecture 24(B): Approximation and Taylor Polynomials, with example

Lecture 24(A): Approximation and Taylor Polynomials

Lecture 24(A): Approximation and Taylor Polynomials

Lecture 22(A): Continuous Functions 2

Lecture 22(A): Continuous Functions 2

Lecture 23(B): Compact Sets, Weierstrass Theorem, examples and counterexamples

Lecture 23(B): Compact Sets, Weierstrass Theorem, examples and counterexamples

Lecture 23(A): Compact Sets and Metric Spaces; Bolzano-Weierstrass Theorem

Lecture 23(A): Compact Sets and Metric Spaces; Bolzano-Weierstrass Theorem

Lecture 29(C): Quadratic Forms: Determinant conditions for definiteness

Lecture 29(C): Quadratic Forms: Determinant conditions for definiteness

Lecture 29(B): Quadratic Forms: Determinant conditions for definiteness

Lecture 29(B): Quadratic Forms: Determinant conditions for definiteness

Lecture 29(A): Quadratic Forms: Necessary & sufficient conditions for definiteness

Lecture 29(A): Quadratic Forms: Necessary & sufficient conditions for definiteness

Lecture 28: Quadratic Forms: Definite and semidefinite forms

Lecture 28: Quadratic Forms: Definite and semidefinite forms

Lecture 27(B): Quadratic Forms: Geometric Example

Lecture 27(B): Quadratic Forms: Geometric Example

Lecture 27(A): Quadratic Forms: Symmetric matrices, geometric intuition

Lecture 27(A): Quadratic Forms: Symmetric matrices, geometric intuition

Lecture 21(A): Continuous Functions

Lecture 21(A): Continuous Functions

Lecture 21(B): Continuous Functions

Lecture 21(B): Continuous Functions

Lecture 20(C): Bounded Sequences: The Bolzano-Weierstrass Theorem

Lecture 20(C): Bounded Sequences: The Bolzano-Weierstrass Theorem

Lecture 20(B): Bounded Sequences: The Monotone Convergence Theorem

Lecture 20(B): Bounded Sequences: The Monotone Convergence Theorem

Lecture 20(A): Bounded Sequences and Subsequences

Lecture 20(A): Bounded Sequences and Subsequences

Lecture 19(C): Sequences

Lecture 19(C): Sequences

Lecture 19(B): Sequences

Lecture 19(B): Sequences

Lecture 19(A): Sequences

Lecture 19(A): Sequences

Lecture 4(B): Unifying n-tuples, Sequences, Functions, and Subsets

Lecture 4(B): Unifying n-tuples, Sequences, Functions, and Subsets

Lecture 4(A): Unifying n-tuples, Sequences, Functions, and Subsets

Lecture 4(A): Unifying n-tuples, Sequences, Functions, and Subsets

Lecture 18(D): Alternative Norms and Metrics

Lecture 18(D): Alternative Norms and Metrics

Lecture 18(C): Alternative Norms and Metrics

Lecture 18(C): Alternative Norms and Metrics

Lecture 18(B): Alternative Norms and Metrics

Lecture 18(B): Alternative Norms and Metrics

Lecture 18(A): Alternative Norms and Metrics

Lecture 18(A): Alternative Norms and Metrics

Lecture 17(A): Concave and Convex Functions

Lecture 17(A): Concave and Convex Functions

Lecture 16(C): Convexity

Lecture 16(C): Convexity

Lecture 16(B): Convexity

Lecture 16(B): Convexity

Lecture 16(A): Convexity

Lecture 16(A): Convexity

Lecture 14(A): Linear Independence and Basis

Lecture 14(A): Linear Independence and Basis

Lecture 14(B): Linear Independence and Basis

Lecture 14(B): Linear Independence and Basis

Lecture 13(B): Linear Combinations

Lecture 13(B): Linear Combinations

Lecture 13(A): Linear Combinations

Lecture 13(A): Linear Combinations

Lecture 12(B): Vector Subspaces

Lecture 12(B): Vector Subspaces

Lecture 12(A): Vector Subspaces

Lecture 12(A): Vector Subspaces

Lecture 11: Vector Spaces

Lecture 11: Vector Spaces

Lecture 10(B): Euclidean Space: Examples and Theorems

Lecture 10(B): Euclidean Space: Examples and Theorems

Lecture 10(A): Euclidean Space: Neighborhoods, Open and Closed Sets

Lecture 10(A): Euclidean Space: Neighborhoods, Open and Closed Sets

Lecture 9(B): Euclidean Space: Cauchy-Schwarz and Triangle inequalities, dot product, hyperplanes.

Lecture 9(B): Euclidean Space: Cauchy-Schwarz and Triangle inequalities, dot product, hyperplanes.

Lecture 9(A): Euclidean Space

Lecture 9(A): Euclidean Space

Lecture 7(B): Proof by Induction

Lecture 7(B): Proof by Induction

Lecture 7(A): Proof by Induction: What is it and how does it work?

Lecture 7(A): Proof by Induction: What is it and how does it work?

Lecture 6(C): Logic 2 (Strategy for proofs)

Lecture 6(C): Logic 2 (Strategy for proofs)

Lecture 6(B): Logic 2 (Strategy for proofs)

Lecture 6(B): Logic 2 (Strategy for proofs)

Lecture 6(A): Logic 2 (Implication issues)

Lecture 6(A): Logic 2 (Implication issues)

Lecture 5(C): Logic 1 (Implication; De Morgan's Laws)

Lecture 5(C): Logic 1 (Implication; De Morgan's Laws)

Lecture 5(B): Logic 1 (Truth tables and compound statements)

Lecture 5(B): Logic 1 (Truth tables and compound statements)

Lecture 5(A): Logic 1 (Statements and truth values)

Lecture 5(A): Logic 1 (Statements and truth values)

Lecture 30: Unconstrained Optimization 1

Lecture 30: Unconstrained Optimization 1

Lecture 31: Unconstrained Optimization 2

Lecture 31: Unconstrained Optimization 2

Lecture 36(A): Solution Function and Value Function

Lecture 36(A): Solution Function and Value Function

Lecture 36(B): Solution Function and Value Function

Lecture 36(B): Solution Function and Value Function

Lecture 1(B): Sets and n-tuples

Lecture 1(B): Sets and n-tuples

Lecture 1(A): Sets and n-tuples

Lecture 1(A): Sets and n-tuples

Lecture 3(B): Quantifiers and Functions 2

Lecture 3(B): Quantifiers and Functions 2

Replaced: Lecture 3(A) has been replaced

Replaced: Lecture 3(A) has been replaced

Lecture 2(A): Quantifiers and Functions 1

Lecture 2(A): Quantifiers and Functions 1

Lecture 40(B): The Kuhn-Tucker Conditions and Theorem

Lecture 40(B): The Kuhn-Tucker Conditions and Theorem

Lecture 40(D): The Kuhn-Tucker Conditions: Two examples

Lecture 40(D): The Kuhn-Tucker Conditions: Two examples

Lecture 40(A): Kuhn-Tucker Conditions: Conceptual and geometric insight

Lecture 40(A): Kuhn-Tucker Conditions: Conceptual and geometric insight

Lecture 40(C): The Kuhn-Tucker Conditions: An Example

Lecture 40(C): The Kuhn-Tucker Conditions: An Example

Lecture 40(E): The Kuhn-Tucker Conditions: A Corner (Boundary) Solution

Lecture 40(E): The Kuhn-Tucker Conditions: A Corner (Boundary) Solution

Lecture 15(C): Linear Functions

Lecture 15(C): Linear Functions

Lecture 15(B): Linear Functions

Lecture 15(B): Linear Functions

Lecture 15(A): Linear Functions

Lecture 15(A): Linear Functions