Math 17
An Introduction to Mathematics Beyond Calculus
Last updated June 27, 2016 13:25:43 EDT

## Math 17, Winter 2013: The Art of Counting

The course

This course is intended for prospective mathematics majors who want to learn at an early stage topics in mathematics outside of the standard calculus courses.

This term, the course is designed to introduce students to the beautiful subject of bijective and enumerative combinatorics. This is a subject which requires little mathematical background to reach the frontiers of current research.
Enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1; the number of ways to tile the figure

using vertical and horizontal dominoes is 210; and the number of polyominoes of area 4 (the pieces in the Tetris game), up to rotations and reflections, is 5. No formula is known, however, for the number of polyominoes of area n, where n is an arbitrary positive integer. Many similar problems are unsolved as well, despite being easy to state.
We will be concerned primarily with bijective proofs, that is, showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them.

Textbook

No textbook required for this course. The material will be based on notes and handouts, usually following the list of Bijective proof problems by Richard Stanley.

Some recommended books on bijective proofs are:

• A. T. Benjamin and J. J. Quinn, Proofs That Really Count: The Art of Combinatorial Proof, Dolciani Mathematical Expositions, Mathematical Association of America, 2003.
• N. Loehr, Bijective Combinatorics, CRC Press.
• D. Stanton and D. White, Constructive Combinatorics, Undergraduate Text in Mathematics, Springer.

Scheduled Lectures

 MWF 11:15 - 12:20 (x-hour) Tu 12:00-12:50 028 Haldeman

Instructor

 Sergi Elizalde Teaching Assistant: Natasha Komarov Office:   332 Kemeny Hall Office Hours:   Mon 12:20-1:30,     Wed 9:30-11:00 and by appointment Email:  first_name.last_name@dartmouth Email:   nkom {at} dartmouth

There will be no exams for this course. The course grade will be based on the written homework (50%), the homework solutions presented in class (20%), and an oral presentation (30%).

Homework Policy

• Homework will be assigned on most days. Written homework will be collected weekly.
• No late homework will be accepted unless arranged with the intructor in advance and for a very legitimate reason.
• Collaboration on the homework is encouraged, but the solutions must be written individually.
• Please mention on your problem set the names of the students that you worked with, and also reference any articles, books or websites if your solution takes significant ideas from them.

Disabilities

Students with disabilities who will be taking this course and may need disability-related classroom accommodations are encouraged to make an appointment to see their instructor as soon as possible. Also, they should stop by the Academic Skills Center in Collis Center to register for support services.

Last updated June 27, 2016 13:25:43 EDT