Course 1C: Algorithms and Optimization

by Daniel Sinderson

Course Description

This is course 1C in my DIY graduate program, a year-long course on foundational concepts and techniques from general computer science, and the subfields of approximation and optimization. This will include algorithms and data structures, approximating functions with series and wavelets, and linear and nonlinear optimization.

Course Materials

The primary text will be Foundations of Applied Mathematics vol. 2 by Jeffrey Humpherys, Tyler J. Jarvis, and Emily J. Evans.
This includes a freely available lab supplement.
Lastly, I’ll be supplementing the computer science portion of the course with Structure and Interpretation of Computer Programs by Harold Abelson, Gerald Jay Sussman, and Julie Sussman, which is freely available here.

Syllabus

#	Chapter	HW	Lab
1	Introduction to Algorithms and Analysis	Notes	-
2	-	Problem Sets	Binary Tree Search
3	Asymptotic Integrals	Notes	-
4	-	Problem Sets	Nearest Neighbor Search
5	Data Structures	Notes	-
6	-	Problem Sets	Breadth-first Search
7	Combinatorial Optimization	Notes	-
8	-	Problem Sets	Dijkstra’s Algorithm
9	Probability	Notes	-
10	-	Problem Sets	Markov Chains
11	Probabilistic Sampling and Estimation	Notes	-
12	-	Problem Sets	Sampling
13	Random Algorithms	Notes	-
14	-	Problem Sets	-
15	Harmonic Analysis	Notes	-
16	-	Problem Sets	The Discrete Fourier Transform
17	Polynomial Approximation and Interpolation	Notes	-
18	-	Problem Sets	Convolution and Filtering
19	Fundamentals of Numerical Approximation	Notes	-
20	-	Problem Sets	Introduction to Wavelets
21	Unconstrained Optimization	Notes	-
22	-	Problem Sets	One-dimensional Optimization
23	Linear Optimization	Notes	-
24	-	Problem Sets	The Simplex Method
25	Nonlinear Constrained Optimization	Notes	-
26	-	Problem Sets	Reinforcement Learning 1: Gymnasium
27	Convex Analysis and Optimization	Notes	-
28	-	Problem Sets	CVXPY
29	Dynamic Opimization	Notes	-
30	-	Problem Sets	Dynamic Programming

Written on: December 1, 2024