Math 100: Problem Solving

Fall 2022

Instructor: Sucharit Sarkar.
Class: MWF 12:00-12:50, MS 6627.
Office hours: M 13:30-14:30 15:00-15:30, MS 6909.

Reader: Gary Song

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. To help you decide if the course is right for you, we will have a small quiz. Based on the results of the quiz, I will give you a non-binding recommendation about whether you should continue in the class. The quiz does not count toward your course grade.

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.

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 every alternate year), 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: Homeworks are due at the beginning of lecture on Wednesday; submit paper copies of homeworks in class; do not submit homework by e-mail. Late homeworks will not be accepted; however, your lowest homework score will be dropped when computing your grade.
HW Due on Problems
1 2022-10-05 HW1
2 2022-10-12 HW2
3 2022-10-19 HW3
4 2022-10-26 HW4
5 2022-11-02 HW5
6 2022-11-09 HW6
7 2022-11-16 HW7
8 2022-11-23 HW8
9 2022-11-30 HW9
You are encouraged to work in groups on your homework; this is generally beneficial to your understanding and helps you learn how to communicate clearly about mathematics. However, you must write up all solutions yourself. Moreover, since crediting your collaborators is an important element of academic ethics, you should write down with whom you worked at the top of each assignment. You should also cite any sources (other than lectures and the textbook) that you use.

Exams: The exams are non-collaborative closed-book exams. You are not allowed to use books, notes, or any electronic devices (such as calculators, phones, computers) during the exams. There is a single quiz, a single midterm, and a single final exam on the following dates.
Exam Location Date Time Syllabus
Quiz MS 6627 2022-10-05 12:00-12:50 Chapter 2
Midterm MS 6627 2022-10-26 12:00-12:50 Chapters 2,3,4,7
Final MS 6627 2022-12-06 08:00-11:00 Chapters 1-8
Old finals: 2015, 2016, 2017.
There will be no make-up exams. Submitting the final exam is mandatory. 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, in which case, if the performance in the course is otherwise satisfactory, the grade might be I.

Grading: Numerical grades will be recorded in the MyUCLA gradebook and the composite numerical grade will be computed as 20% HW + 30% Midterm + 50% Final. 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 homework or an exam 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 due date of the assignment in question, or 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.