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 non-binding
recommendation about whether you should continue in the class. The quiz
does not count toward your course grade.
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, November 1, during class. The final will be
Wednesday, December 11, 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
Office hours during the last week of classes are: Thursday (Dec.5) 11-12 and 2-3 and Friday (Dec.6) 10-11. 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.
|Sep.27-Oct.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.4-9||Inequalities||Larson Ch.7.1-7.4, 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.11-16||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.18-23||Algebra||Larson Ch.4, AG Ch.2.2, 2.4||Problem Set 4. Solutions||Oct.25|
|Oct.25-30||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.1-6||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 s-n)(s choose s)]. Solutions||Nov.8|
|Nov.8-13||Recurrent sequences, probability||Larson Ch.5.4, AG Ch.6.2, 6.3||Problem Set 7. Solutions||Nov.15|
|Nov.15-20||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.22-Dec.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|