A leading expert in Modern Combinatorics wants to share his vision of the subject with the students. The seminar is a perfect background for future specialists in mathematics, physics, computer science, biology, economics, for those who are curious what statistical physics is about, what is cryptography, and how stock market works, and for everyone who likes mathematics.
The course will be organized around the following topics:
- Puzzles: dimer covering, magic squares, 36 officers
- Combinations: from coin tossing to dice and poker
- Fibonacci numbers: rabbits, population growth, etc.
- Arithmetic: designs, cyphers, intro to finite fields
- Catalan numbers: from playing roulette to stock market
The students will learn about the history of Combinatorics, its connections with the theory of numbers, its fundamental role in the natural sciences and various applications.
It is an advanced research course; all students are expected to participate in projects under the supervision of I.Ch. and the Graduate Research Consultant (the GRC Program). This seminar is partially supported by Honors Carolina.
The grades will be based on the exam, bi-weekly home assignments and the participation in the projects. The course requires focus and effort, but, generally, the students are quite satisfied with the progress they make (and their grades too).
From the Course Evaluation: “A difficult but wholly worthwhile course: I feel more competent for having taken it”, “I would recommend this FYS to others ONLY if they have a VERY strong affinity for and ability in Algebra (I thought I did, but I was wrong)”.