Course Code:
MATH 154
Semester:
Spring
Course Type:
Core
P:
2
Lab:
2
Laboratuvar Saati:
0
Credits:
3
ECTS:
7
Course Language:
English
Course Objectives:
The aim of this course is to introduce the topics and techniques of discrete methods and combinatorial reasoning with wide variety of applications.
Course Content:

Fundamental principle of counting. Introduction to discrete probability. Pigeonhole principle. Fundamentals of logic. The principle of inclusion and exclusion. Recurrence relations. Introduction to graph theory.

Course Methodology:
1: Lecture, 2: Problem Solving
Course Evaluation Methods:
A: Written examination

## Vertical Tabs

### Course Learning Outcomes

 Learning Outcomes Teaching Methods Assessment Methods 1) Understands and solves problems in counting using the basic principles of counting. 1,2 A 2) Uses the principle of inclusion and exclusion to solve related problems indirectly. 1,2 A 3) Expresses  a given argument in symbolic logic and decides whether it is a valid argument or not using the laws of logic and inference rules. 1,2 A 4) Solves first-order linear recurrence relations, second-order linear homogeneous recurrence relations with constant coefficients and some particular nonhomogeneous recurrence relations. 1,2 A 5) Models a given particular situation or a problem  using  graph theory. 1,2 A 6) Decides whether or not given graphs are isomorphic. 1,2 A

### Course Flow

 Week Topics Study Materials 1 The rules of sum and product. Permutations 1.1, 1.2 2 Combinations: The binomial theorem 1.3 3 Combinations with repetition 1.4 4 An introduction to discrete probability. The pigeonhole principle ((II) 6.1), 5.5 5 Basic connectives and truth tables 2.1 6 Logical equivalence: The laws of logic 2.2 7 Logical implication: The rules of inference 2.3 8 The use of quantifiers 2.4 9 The principle of inclusion and exclusion 8.1 10 The first-order linear recurrence relation 10.1 11 The Second-order linear homogeneous recurrence relation with constant coefficients 10.2 12 The nonhomogeneous recurrence relation 10.3 13 An introduction to graph theory: Definitions and basic examples 11.1 14 Subgraphs, complements and graph isomorphism 11.2

### Recommended Sources

 Textbook Discrete and Combinatorial Mathematics, R.P. Grimaldi, Addison-Wesley, 5th edition, 2004. Additional Resources Discrete Mathematics and Its Applications, K. H. Rosen, Mc Graw Hill, 6th edition, 2007.

### Material Sharing

 Documents Assignments Exams

### Assessment

 IN-TERM STUDIES NUMBER PERCENTAGE Mid-terms 1 100 Quizzes Assignments Total 100 CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE 60 CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE 40 Total 100

 COURSE CATEGORY Core Courses

### Course’s Contribution to Program

 No Program Learning Outcomes Contribution 1 2 3 4 5 1 The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) x 2 Acquiring fundamental knowledge on fundamental research fields in mathematics x 3 Ability form and interpret the relations between research topics in mathematics x 4 Ability to define, formulate and solve mathematical problems x 5 Consciousness of professional ethics and responsibilty x 6 Ability to communicate actively x 7 Ability of self-development in fields of interest x 8 Ability to learn, choose and use necessary information technologies x 9 Lifelong education x

### ECTS

 Activities Quantity Duration (Hour) Total Workload (Hour) Course Duration (14x Total course hours) 14 4 56 Hours for off-the-classroom study (Pre-study, practice) 14 6 84 Mid-terms (Including self study) 1 15 15 Quizzes Assignments Final examination (Including self study) 1 20 20 Total Work Load 175 Total Work Load / 25 (h) 7 ECTS Credit of the Course 7