
Web page: http://www.math.ucla.edu/~cm/100.1.13f/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
4. Based on the results of the quiz, I will give you a nonbinding
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 inclass midterm and one final. The midterm
will take place on Friday, November 1, during class. The final will be
on
Wednesday, December 11, 8am11am.
No makeup exams will be given, except in case of
a documented emergency. No books, notes or calculators will be allowed on
the exams.
Office hours during the last week of classes are: Thursday (Dec.5) 1112
and 23 and Friday (Dec.6) 1011. I will be out of town during final week, but you
can email me questions.
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.
Week  Topic  Read  Homework  Due 
Sep.27Oct.3  Induction and Pigeonhole  Larson Ch.2, AG Ch.1  Larson 2.1.6, 2.1.9, 2.1.10, 2.2.4, 2.3.3 (a), 2.6.6, 2.6.7, 2.6.9, 2.6.10, 2.6.11 (a). Solutions  Oct. 4 
Oct.49  Inequalities  Larson Ch.7.17.4, AG Ch.2.1  Larson 7.1.7, 7.1.11, 7.2.6, 7.2.7, 7.2.9(b)(c), 7.2.11, 7.3.7(a)(b), 7.4.10, 7.4.11, 7.4.17. Solutions  Oct. 11 
Oct.1116  Number theory  Larson Ch.3, AG Ch.5  Larson 3.1.10, 3.1.12, 3.1.13, 3.1.14, 3.2.11, 3.2.14(c), 3.2.15 (b)(c), 3.2.23, 3.3.26, 3.4.7. Solutions  Oct.18 
Oct.1823  Algebra  Larson Ch.4, AG Ch.2.2, 2.4  Problem Set 4. Solutions  Oct.25 
Oct.2530  Summation of series  Larson Ch.5.2, 5.3, AG Ch.3.1  Larson 4.4.15, 4.4.26, 4.4.30 (a)(b), 5.2.7, 5.2.8, 5.2.10, 5.2.11 (a) [Typo: Set k=i], 5.3.6, 5.3.7 (a) [Typo: Sum should start at n=2], 5.3.9 (b). Solutions  Nov.1 
Nov.16  Combinatorics  Larson Ch.1.3, 5.1, AG Ch.6  Larson 1.3.9, 1.3.10, 1.3.12, 2.5.13(a), 5.1.9(a)(d), 5.1.12 [Typo in 5.1.12(a): The sum should end with the term (r choose sn)(s choose s)]. Solutions  Nov.8 
Nov.813  Recurrent sequences, probability  Larson Ch.5.4, AG Ch.6.2, 6.3  Problem Set 7. Solutions  Nov.15 
Nov.1520  Geometry and trigonometry  Larson Ch.8, AG Ch.4  Larson 8.2.6, 8.2.7, 8.2.10, 8.3.10, 8.3.11, 8.3.13, 8.3.18, 8.4.6, 8.4.7, 8.4.8. Solutions  Nov.22 
Nov.22Dec.6  Calculus  Larson Ch.6, AG Ch.3  Larson 6.1.4, 6.1.7, 6.2.4, 6.2.5, 6.3.5(b), 6.5.5, 6.7.3, 6.7.6, 6.8.4(c)(d), 6.9.8.  Dec.6 