Math 100: Problem Solving

Web page: http://www.math.ucla.edu/~cm/100.1.12f/index.html

Prerequisite: The official prerequisite is completion of 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 25 minute long quiz in class on Friday, October 5. 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.

Course description: 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. The course can serve preparation for the Putnam Mathematical Contest. See the departmental Putnam web site for more information.

Topics to be covered are: 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.

Textbook: Loren C. Larson, Problem Solving Through Problems, Springer, 2006. Also recommended is (AG) Titu Andreescu and Razvan Gelca, Putnam and Beyond, Springer, 2007, available online. Other resources can be found at http://www.math.ucla.edu/~cm/putnam.html

Grading: 50% final, 30% midterm, 20% homework. The final grades will be Pass or No Pass.

Exams: There will be one in-class midterm and one final. The midterm will take place on Friday, October 26, during class. The final will be on Thursday, December 13, 8am-11am. No make-up exams will be given, except in case of a documented emergency. No books, notes or calculators will be allowed on the exams.

Here is a practice midterm with solutions. These are solutions to the midterm.

Here is a practice final and also an old final exam. During the week of the final the office hours will be: Monday 11-12 and Wednesday 2-3.

Homework: Homework will be assigned every week and will be due in class on Friday. The lowest homework score will be dropped.

The homework assignments will be posted on the web page. You are encouraged to talk about the problems with other students, but you should write up the solutions individually. You should acknowledge the assistance of any book, student or professor. No late homework will be accepted.