Math 100: Problem Solving

Fall 2017

Instructor: Sucharit Sarkar.
Class: MWF 10-10:50am, MS 6221.
Office hours: 1-3pm, MS 6909.

Reader: Ken Willyard.

Textbook: Loren Larson (L), Problem Solving Through Problems, ISBN 9780387961712.
Additional reading: Titu Andreescu and Razvan Gelca (AG), Putnam and Beyond, ISBN 9780387257655.
Useful links: University page, MyUCLA, Putnam materials.

Prerequisite: The official prerequisite is MAT 31A. However, MAT 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 25 minute long quiz in class on 10/6. 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: MAT 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. The course can serve as basic preparation for the Putnam. 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.

Homework: Homeworks are due at the beginning of lecture on Monday. Do not submit homework by e-mail. No late homework will be accepted. However, your lowest homework score will be dropped when computing your grade.
HW Due on Problems
1 10/9 HW1
2 10/16 HW2
3 10/23 HW3
4 10/30
5 11/6
6 11/13
7 11/20
8 11/27
9 12/4
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
Quiz MS 6221 10/6 10-10:25am
Midterm MS 6221 11/3 10-10:50am
Final TBD 12/13 11:30am-2:30pm
There will be no make-up exams. Attending 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.
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 (12/15). 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.

Tentative schedule:
Week Topic
1-2 L 2, AG 1
2-3 L 7.1-7.4, AG 2.1
3-4 L 3, AG 5
4-5 L 4, AG 2.2, 2.4
5-6 L 5.2-3, AG 3.1
6-7 L 1.3, 5.1, AG 6
7-8 L 5.4, AG 6.2-3
8-9 L 8, AG 4
9-10 L 6, AG 3