### Discrete Mathematics (MATH 204)

2021 Spring
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
6.00 / 6.00 ECTS (for students admitted in the 2013-14 Academic Year or following years)
Kağan Kurşungöz kursungoz@sabanciuniv.edu, Mohammad Sadek mmsadek@sabanciuniv.edu,
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English
Undergraduate
--
Formal lecture,Recitation
Interactive,Communicative
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### CONTENT

Introduction to combinatorial problems and techniques. Sets, relations and functions. Graphs, trees, matching, network flows. Counting techniques. Recurrence relations and generating functions. Combinatorial circuits and finite state machines. Also part of the "core course" pools for the CS, MS,TE degree programs.

### OBJECTIVE

This course aims to introduce basic ideas of discrete mathematics such as formal mathematical reasoning techniques, basic counting techniques, relations, graphs and trees. The course gives students training to develop their mathematical skills, analytical and critical thinking abilities, their ability to apply these capabilities to practical problems, and to communicate their knowledge of these areas.

### LEARNING OUTCOME

Understand the notion of mathematical thinking, mathematical proofs, algorithmic thinking, and able to apply them in problem solving, Present simple proofs in a precise and formally correct way, Apply various methods of prof like mathematical induction, direct, indirect proofs.

Understand and manipulate sets, sequences and sums.
Understand the basic concept of an algorithm and apply appropriate algorithms to solve problems in combinatorial mathematics. Analyze simple algorithms.
Have a basic understanding of divisibility and prime numbers, basics of modular arithmetic.
Understand all of the basic counting techniques, and some of the advanced counting techniques. Be able to use factorials, binomial coefficients appropriately, solve linear recurrences of small order.
Understand the basic properties of graphs and trees and use these concepts to model simple applications.

### ASSESSMENT METHODS and CRITERIA

 Percentage (%) Final 30 Midterm 50 Exam 17 Participation 3

### RECOMENDED or REQUIRED READINGS

 Textbook Kenneth H. Rosen, Discrete Mathematics and Its Applications, McGraw-Hill Readings 1. Ronald L. Graham, Donald E. Knuth, Oren Patashnik, Concrete Mathematics, Addison-Wesley2. Alan Tucker, Applied Combinatorics, John Wiley Sons