Instructor: Justin Sawon
                    sawon@math.sunysb.edu
                    Office hours: Tuesday 10am - 12noon in Math Tower 4-104, Thursday 5 - 6pm in the Math Learning Centre
                    phone: +1-631-632 8267

Course Synopses: The aim of this course is to develop your ability to solve problems drawn from a wide range of mathematical subjects (see the topics below). Each week we will concentrate on a particular topic and look at problems in that area, though you are encouraged to be creative in your methodology: if you can find a geometrical solution to a combinatorial problem, all the better. Ultimately you should try to solve a problem without classifying it first; indeed many problems do not fit neatly into a single subject area. Problems occuring in the Putnam competition are the kinds of problems we will be solving (though many of our problems will be easier), and students in this course are encouraged to enter the Putnam competition.

Topics may include (in no particular order): combinatorics, inequalities, geometry, number theory, functions, calculus, algebra, graph theory, probability.

There will be homework problems each week, but no exams. Grading is S/U (satisfactory/unsatisfactory), and will be determined by the effort you make in doing the homework and in your participation in the classroom.

Students with Disabilities: If you have a physical, psychological, medical, or learning disability that may impact on your ability to carry out assigned course work, you are strongly urged to contact the staff in the Disabled Student Services (DSS) office: Room 133 in the Humanities Building; 632-6748v/TDD. The DSS office will review your concerns and determine, with you, what accommodations are necessary and appropriate. A written DSS recommendation should be brought to your lecturer who will make a decision on what special arrangements will be made. All information and documentation of disability is confidential. Arrangements should be made early in the semester so that your needs can be accommodated.

Week 2 Homework : Combinatorics, postscript, pdf.

Week 3 Homework : The Binomial Theorem, postscript, pdf.

Week 4 Homework : Generating Functions, postscript, pdf.

Week 5 Homework : Inequalities, postscript, pdf.

Week 6 Homework : The Pigeonhole Principle, postscript, pdf.

Week 7 Homework : Series, postscript, pdf.

Week 8 Homework : Calculus, postscript, pdf.

Week 9 Homework : Number Theory, postscript, pdf.

Week 10 Homework : Geometry, postscript, pdf (note: you really need to take a copy of this from my outside my door, in order to get all the diagrams).

Week 11 Homework : Algebra, postscript, pdf.

The William Lowell Putnam Mathematical Competition: is a prestigious nationwide (USA and Canada) math competition held each December for undergraduates -- 12 questions, 6 hours (two sessions). This year the Putnam exam will be held on Saturday, December 4, 2004. Individual and team winners (and their schools, in the latter case) get some money and a few minutes of fame! Results for a given December's exam usually become available in early April of the following year.

The exam is run by the Mathematical Association of America. The competition is open to all SUNY at Stony Brook undergraduates who have not yet received a college degree. No individual may participate in the competition more than four times. If you think that you might want to participate in the 2004 competition, please contact me, Justin Sawon *before* October 1, 2004. I will add your name to the mailing list and keep you informed.

I hope to organize some coaching sessions, probably held at the Math Club (in room P-131 in the Math Tower, 7pm on Thursday). The best practice for the competition would be attempting the past problems. You can discuss the problems with me during my office hours (see above), or at another mutually convenient time.

The official web page for the competition (not yet updated from last year). Copies of the problems are available (back to 1980). Copies of the solutions back to 1995.

First problem of the week: Do there exist polynomials a(x), b(y), c(x), and d(y) which satisfy

Second problem of the week: Show that the number of partitions of a positive integer into odd (positive) integers is the same as the number of partitions into distinct (positive) integers. For example suppose the number is 5. Then we can write it as a sum of odd integers in three ways: 5, 3+1+1, and 1+1+1+1+1. We can also write it as a sum of distinct integers in three ways: 5, 4+1, 3+2. If the number is 7, then we can write it as a sum of odd integers in five ways: 7, 5+1+1, 3+3+1, 3+1+1+1+1, 1+1+1+1+1+1+1. We can also write it as a sum of distinct integers in five ways: 7, 6+1, 5+2, 4+3, 4+2+1. Again the number of ways agree.

Please leave your solutions in the envelope on my door!

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This page last modified by Justin Sawon
Monday, 15-Nov-2004 18:28:42 EST
Email corrections and comments to sawon@math.sunysb.edu