Math 100: Problem Solving

Fall 2025

Instructor: Sucharit Sarkar.
Class: MWF 12:00-12:50, MS 6221.
Office hours: M 08:00-09:00 16:00-17:00, MS 6909.

Textbook: Loren Larson, Problem Solving Through Problems, ISBN 9780387961712.
Additional reading: Titu Andreescu and Razvan Gelca, Putnam and Beyond, ISBN 9780387257655.
Useful links: MyUCLA, Department page, Putnam materials, Putnam information.

Prerequisite: The official prerequisite is MATH 31A. However, MATH 100 is aimed at the most talented students at UCLA, and you should only take it if you got A's in your lower division math classes. Freshmen and transfer students who have some experience in math contests are welcome to enroll. You may self-judge if the course is suitable for you by looking at the homework problems and the class problems below. We will hold weekly in-class quizzes, and you may use your performance in those quizzes to judge your readiness for this course.

Topics: MATH 100 is a course in problem solving. The problems are more varied and unexpected than in a typical undergraduate mathematics course. Often an original or imaginative step is required. Topics to be covered include: Induction, the pigeonhole principle, inequalities, modular arithmetic, closed form evaluation of sums and products, problems in combinatorics, probability, geometry, rational functions and polynomials, and calculus.
Schedule: We will try to follow the schedule from the Department page. The following is a list of problems, (a subset of) which we cover in class.
Class problems.

Putnam: MATH 100 can serve as basic preparation for the Putnam for students who had minimal exposure to problem solving. (There is a more intensive preparation course for Putnam, MATH 101, offered occasionally, aimed at students who are already familiar with problem solving.) These Putnam materials may be useful for Putnam prepration. See here for more information.

Homework and Quiz: Homeworks are not going to be graded. Nevertheless, you should work on the following homeworks, arranged by week, which will help significantly with your understanding of the course material. You may work in groups on your homework; this is generally beneficial to your understanding and helps you learn how to communicate clearly about mathematics. Every week, starting from Week 2, we will have an in-class quiz with one of the homework problems for that week.
Quiz Date Problems
1 Oct 8 HW1
2 Oct 15 HW2
3 Oct 20 HW3
4 Oct 27 HW4
5 Nov 3 HW5
6 Nov 14 HW6
7 Nov 21 HW7
8 Nov 24 HW8
9 Dec 3 HW9

Exams: There is a single 3 hour final exam, which is non-collaborative closed-book exams. You are not allowed to use books, notes, or any electronic devices (such as calculators, phones, computers). Submitting the final exam is mandatory, and there are no make-up exams. In particular, note that university policy requires that a student who misses the finals be automatically given F, unless the absence is due to extreme and documented circumstances, which were discussed with the instructor prior to the finals, and the performance in the course is otherwise satisfactory, in which case, the grade might be I (at the instructor's discretion).
The final will be on Thursday, December 11, 08:00-11:00, location TBD. Here are some old finals: 2015, 2016, 2017.

Grading: Numerical grades will be recorded in the MyUCLA gradebook and the composite numerical grade will be computed as 50% Quiz + 50% Final. (Your lowest quiz score will be dropped.) Based on that, the final grade will be Pass or No Pass; you will pass if your composite numerical score is more than 60%.
If you believe a problem on a quiz or the final has been graded incorrectly, or that your score was not correctly recorded in the MyUCLA gradebook, you must bring this to the attention of the instructor within 10 calendar days of the date of the exam, and before the end of the quarter. Grading complaints not initiated within this period of time will not be considered. Please verify in a timely manner that your scores are correctly recorded on MyUCLA.