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.

### Discrete Mathematics (MATH 204)

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Programs\Type | Required | Core Elective | Area Elective |

BA- Political Science | |||

BA-Cultural Studies | |||

BA-Cultural Studies | |||

BA-Economics | |||

BA-Economics | |||

BA-International Studies | |||

BA-International Studies | |||

BA-Management | |||

BA-Management | |||

BA-Political Sci.&Inter.Relat. | |||

BA-Political Sci.&Inter.Relat. | |||

BA-Social & Political Sciences | |||

BA-Visual Arts&Visual Com.Des. | |||

BA-Visual Arts&Visual Com.Des. | |||

BS-Biological Sci.&Bioeng. | * | ||

BS-Computer Science & Eng. | * | ||

BS-Computer Science & Eng. | * | ||

BS-Electronics Engineering | * | ||

BS-Electronics Engineering | * | ||

BS-Industrial Engineering | * | ||

BS-Manufacturing Systems Eng. | * | ||

BS-Materials Sci. & Nano Eng. | * | ||

BS-Materials Science & Eng. | * | ||

BS-Mechatronics | * | ||

BS-Mechatronics | * | ||

BS-Microelectronics | |||

BS-Molecular Bio.Gen.&Bioeng | * | ||

BS-Telecommunications | * | ||

Mathematics |

### CONTENT

### 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.

### Update Date:

### ASSESSMENT METHODS and CRITERIA

Percentage (%) | |

Final | 35 |

Midterm | 35 |

Assignment | 20 |

Participation | 10 |

### 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, 2. Alan Tucker, Applied Combinatorics, John Wiley Sons |