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.
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.