Prerequisite material is overviewed in a series of videos that are available under the "Prerequisites" topic in the navigation bar, which is to the left of this text.

The lectures were produced using technology that is described in this video:
https://youtu.be/ltOxgb28ZKY

No.	PDF	Video
	Week   1
∼		Labor Day
1	Class #01	Introduction To Optimization
1a		Course Overview
1b		Examples: Fermat's Problem
1c		Open Sets; Interior And Boundary Points
1d		Minimizers and Minima
2	Class #02	Basic Differential Calculus
2a		To Be Recorded
	Week   2
3	Class #03	Minimizing By Approximation
3a		Stationarity
3b		Conditions for Stationarity
3c		Convexity; Strict Convexity
3d		Gradient Inequality And Convexity
4	Class #04	Scalar Minimization
4a		Searching For A Scalar Minimizer
4b		Searching With A Fixed Stepsize
4c		Searching With a Variable Stepsize
4d		Armijo Backtracking
5	Class #05	Functions With A Vector Argument
5a		Functions of Multiple Variables
5b		The 1-Form as Linear Algebra
5c		Directional Derivative and the Chain Rule
5d		Gradient 1-Form And Jacobian Matrix
5e		Linear Forms And Quadratic Forms
5f		Level Curves
	Week   3
6	Class #06	Stationary Points
6a		Stationarity Example
6b		Conditions For Stationarity
6c		Second Derivative And Hessian Matrix
6d		Eigenvalues Of A Hessian Matrix
7	Quiz #1	Basic Scalar Optimization
8	Class #08	Methods Using Steepest Descent
8a		Introduction To Descent
8b		Descent Directions
8c		Fixed-Stepsize Descent
8d		Backtracking Descent
	Week   4
9	Class #09	Newton's Method
9a		Scaling Methods
9b		Manual Scaling
9c		Newton's Method
9d		Damped Newton's Method
10	Test #1	Basic Scalar Optimization
11	Class #11	Linear Algebra For Neural Networks
11a		To Be Recorded
	Week   5
12	Class #12	Single Artificial Neuron
12a		To Be Recorded
13	Quiz #2	Adaptive Vector Optimization
14	Class #14	Artificial Neural Networks
14a		To Be Recorded
	Week   6
15	Class #15	Back-Propagation Of Scale Factors
15a		To Be Recorded
16	Test #2	Adaptive Vector Optimization
17	Class #17	Nonlinear Least Squares
17a		GPS As Vector Optimization
17b		Descent Methods for NLS Problems
17c		The Levenberg-Marquardt Algorithm
17d		Fermat-Weber Problems
	Week   7
18	Class #18	Convexity And Level Sets
18a		Monotonicity And Convexity
18b		Convex Functions
18c		Convex Sets
18d		Level Sets
18e		Gradient Inequality
19	Class #19	Constrained Optimization
19a		Constraint Properties For A Minimizer
19b		Linear Constraints
19c		Linear Objective Functions
19d		Convex Problems
20	Class #20	Lagrange Multipliers
20a		Objective Gradient And Property Gradient
20b		Quadratic Objective And Quadratic Constraint
20c		Linear Objective And Non-Convex Constraint
20d		Existence Of Lagrange Multipliers
	Week   8
21	Class #21	The Lagrange Equations
21a		Single Linear Constraint
21b		Quadratic Objective With Linear Constraints
21c		Example Mechanical System
21d		Matrix Form Of Quadratic Problems
22	Quiz #3	Neural Networks and Back-Propagation
23	Class #23	Dual Formulation of Lagrange Equations
23a		Primal Form And Feasible Set
23b		Min-Max And Max-Min Expressions
23c		Closed Form For Minimization Step
23d		Dual Formulation For Quadratic Problems
	Week   9
24	Class #24	KKT Conditions For Constrained Optimization
24a		Linear Inequality Constraints
24b		Examples Of Linear Inequalities
24c		KKT Background And Examples
24d		Definition Of A KKT Point
25	Test #3	Neural Networks and Back-Propagation
26	Class #26	Geometry At KKT Points
26a		Algebraic Interpretation Of Lagrange Multipliers
26b		KKT Geometry Of Inactive Linear Inequalities
26c		KKT Geometry Of Active Linear Inequalities
26d		KKT Geometry Of Linear Equality
	Week   10
27	Class #27	The Support Vector Machine (SVM)
27a		Hyperplane Classification
27b		Hyperplane Optimization Using Support Vectors
27c		Hyperplane Margins
27d		Primal Formulation Of SVM
28	Quiz #4	Lagrange Multipliers and KKT Conditions
29	Class #29	Dual Formulation Of The SVM
29a		Design Matrix And Label Matrix
29b		Vectorization Of SVM Primal Formulation
29c		Dual Formulation Of SVM
30	Class #30	Slack Variables And Dual Formulations
	Week   11
30a		Separable Data Not Linearly Separable
30b		Slack Variables And Soft Margins
30c		Slack Variables In SVM Primal Formulation
30d		Slack Variables In SVM Dual Formulation
31	Test #4	Lagrange Multipliers and KKT Conditions
32	Class #32	Kernel Trick For Nonlinear SVM
32a		Nonlinearly Separable Data
32b		Kernel Functions
32c		Gram Matrix And The Kernel Trick
	Week   12
32	Class #33	Kernel Classification For SVM
33a		Convex Problem For Lagrange Multipliers
33b		Classifying Observations And The Kernel Trick
33c		Examples Using Gaussian Kernels
34	Quiz #5	Linear SVM
35	Class #35	Course Summary
	Week   13
36	Test #5	Linear SVM
	Symbols	Symbols used in these notes

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