**Instructor**: Paul Jenkins

**Office**: 279 TMCB, 801-422-5868

**Email**: jenkins@math.byu.edu

**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 http://bookstore.siam.org/ot166/; becoming a member of the BYU Student Chapter of SIAM gives a significant discount.

**TAs:** Kimberly McKeen (mkimba17@byu.edu) and Jordan Sheppard (jsheppard@mathematics.byu.edu, 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:

- Algorithms and analysis: Complexity and leading order behavior, graph search algorithms, combinatorics and dynamic programming, graphs and trees, complexity
- Approximation theory: Stirling's approximation theorem, harmonic analysis, discrete Fourier transform
- Probability: Contitional probability, Bayes's rule, continuous/discrete/multivariate random variables
- Statistics: Law of large numbers, central limit theorem, Bayesian statistics
- 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.

**Preventing Sexual Misconduct**: Brigham Young University prohibits all forms of sexual harassment—including sexual assault, dating violence, domestic violence, and stalking on the basis of sex—by its personnel and students and in all its education programs or activities. University policy requires all faculty members to promptly report incidents of sexual harassment that come to their attention in any way and encourages reports by students who experience or become aware of sexual harassment. Incidents should be reported to the Title IX Coordinator at t9coordinator@byu.edu or (801) 422-8692 or 1085 WSC. Reports may also be submitted online at https://titleix.byu.edu/report or 1-888-238-1062 (24 hours a day). BYU offers a number of resources and services for those affected by sexual harassment, including the university's confidential Sexual Assault Survivor Advocate. Additional information about sexual harassment, the university's Sexual Harassment Policy, reporting requirements, and resources can be found in the University Catalog, by visiting http://titleix.byu.edu, or by contacting the university's Title IX Coordinator.

**Student Disability**: Brigham Young University is committed to providing a working and learning atmosphere that reasonably accommodates qualified persons with disabilities. A disability is a physical or mental impairment that substantially limits one or more major life activities. Whether an impairment is substantially limiting depends on its nature and severity, its duration or expected duration, and its permanent or expected permanent or long-term impact. Examples include vision or hearing impairments, physical disabilities, chronic illnesses, emotional disorders (e.g., depression, anxiety), learning disorders, and attention disorders (e.g., ADHD). If you have a disability which impairs your ability to complete this course successfully, please contact the University Accessibility Center (UAC), 2170 WSC or 801-422-2767 to request a reasonable accommodation. The UAC can also assess students for learning, attention, and emotional concerns. If you feel you have been unlawfully discriminated against on the basis of disability, please contact the Equal Opportunity Office at 801-422-5895, eo_manager@byu.edu, or visit https://hrs.byu.edu/equal-opportunity for help.

**Honor Code**: In keeping with the principles of the BYU Honor Code, students are expected to be honest in all of their academic work. Academic honesty means, most fundamentally, that any work you present as your own must in fact be your own work and not that of another. Violations of this principle may result in a failing grade in the course and additional disciplinary action by the university. Students are also expected to adhere to the Dress and Grooming Standards. Adherence demonstrates respect for yourself and others and ensures an effective learning and working environment. It is the university's expectation, and every instructor's expectation in class, that each student will abide by all Honor Code standards. Please call the Honor Code Office at 422-2847 if you have questions about those standards.