Math 320, section 001:  Algorithm Design & Optimization 1

Homework Assignments

Reading Assignments

Instructor:  Paul Jenkins
Office:  279 TMCB, 801-422-5868
Lecture:  10:00-10:50 AM MWF, 108 TMCB
Office hours:  3:00-3:50 PM MWF or by appointment
Textbook: Foundations of Applied Mathematics volume 2: Algorithms, Approximation, Optimization by Jeffrey Humpherys and Tyler J. Jarvis, ISBN 978-1611976052. The book can be purchased at; becoming a member of the BYU Student Chapter of SIAM gives a significant discount.

TAs: Kimberly McKeen ( and Jordan Sheppard (, office hours 1-1:50 TTh, 5-5:50 W).

Grading: Homework 35%, reading assignments 10%, two midterms 15% each, final exam 25%. Grades will be available on BYU Learning Suite.

Exams: Two midterm exams in the testing center on October 18-20 and November 27-29.  A study guide for the first midterm exam may be found here. A study guide for the second midterm exam may be found here. A study guide for the final exam may be found here. The final exam will be in the testing center during finals week. The final exam will cover all material studied this semester.

Homework: The assigned homework problems include all unstarred problems from the textbook section covered that day unless otherwise noted; homework is due at 9 AM through Gradescope on the next class day after it is assigned. Your homework should be neat and should include enough detail that another student from the class could follow your arguments. Homework that is is excessively sloppy or is not readable may receive less than full credit. Late homework will not be accepted.  Working in groups on homework is encouraged, but each student should write up each problem, without looking at other students’ written solutions.  Using tools like ChatGPT or CoPilot to type or write any part of your work is forbidden. The lowest three homework assignments will be dropped.

Prerequisites:  Math 112, 113, 213, 215, 290, 314, 341, and CS 111 or equivalent.

Minimal learning outcomes: Coverage of the fundamentals of algorithm analysis including convergence, stability, mathematics for algorithm analysis, data structures, probability, and introductory statistics. Discrete optimization and algorithms employing stochastic guessing are investigated. Additionally, students will learn about approximation methods including Fourier series.

Students will have a solid understanding of the concepts listed below. They will be able to prove many of the theorems that are central to this material. They will understand the model specifications for the optimization algorithms, and be able to recognize whether they apply to a given application or not. They will be able to perform the relevant computations on small, simple problems. They will be able to describe the optimization and approximation algorithms well enough that they could program simple versions of them, and will have a basic knowledge of the computational strengths and weaknesses of the algorithms covered.

Topics covered include:

  1. Algorithms and analysis: Complexity and leading order behavior, graph search algorithms, combinatorics and dynamic programming, graphs and trees, complexity
  2. Approximation theory: Stirling's approximation theorem, harmonic analysis, discrete Fourier transform
  3. Probability: Contitional probability, Bayes's rule, continuous/discrete/multivariate random variables
  4. Statistics: Law of large numbers, central limit theorem, Bayesian statistics
  5. Random algorithms: Monte Carlo methods, importance/inversion/rejection sampling

This is a 3 credit class.  The BYU Registration Policy states that “the expectation for undergraduate courses is three hours of work per week per credit hour for the average student who is appropriately prepared; much more time may be required to achieve excellence.”  Thus, an average student should expect to spend at least 6 hours per week outside of lecture on working problems, reading the textbook, reviewing concepts, and completing assignments.

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