## CSE 547: Discrete Mathematics (2015 Spring)

• Lecturer: David (Bong Jun) Choi
• Time: M,W 10:30-11:50, Academic Building 227
• Office Hours: T, Th 16:00-17:00, or by appointment
• Contact: +82-32-626-1216 / bjchoi@sunykorea.ac.kr / Academic Building 423

## Overview:

• This course introduces mathematical tools for solving problems, such as recurrent problems, summations, integer functions, number theory, binomial coefficients, generating functions, discreteprobability, and asymptotics. After completing the course, students will not only be familiar with existing theorem and combinatorial reasoning, but also be fluent in algebraic and manipulative techniques to solve problems with more concrete mathematical results.

## Pre-Requisites:

• AMS 301 (topics include: graph theory, tree, searching, permutation and combination, generation function, recurrence relation, and etc.)

## Topics:

We will cover book chapters 1-5. If time permits, we will also cover some chosen topics in discrete probability and generating functions.
• Chapter 1. Recurrent Problems: Tower of Hanoi, Linear algebra, Josephus Problem
• Chapter 2. Sums: Multiple Sums, General Methods, Finite/Infinite Calculus, Infinite Sums
• Chapter 3. Integer Functions: Floors and Ceilings, Modulus operation
• Chapter 4. Number Theory: Divisibility, Primes, Factorial, Residues
• Chapter 5. Binomial Coefficients: Identities, Generating Functions, Hypergeometric Functions/Transformations
• Chapter 6. Special Numbers (reading): Stirling, Eulerian, Harmonic, Bernoulli, Fibonacci
• Chapter 7. Generating Functions (if time permits)
• Chapter 8. Discrete Probability (if time permits)

## Textbook:

• R. L. Graham et al., “Concrete Mathematics: A Foundation for Computer Science (2nd Edition)”, Addison-Wesley Professional, 1994. (ISBN-10: 0201558025)