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Course Information

DISCRETE MATHEMATICS
Code	Semester	Theoretical	Practice	National Credit	ECTS Credit
		Hour / Week
MAT205	Fall	3	0	3	3

Prerequisites and co-requisites	NONE
Language of instruction	English
Type	Required
Level of Course	Bachelor's
Lecturer	Assistant Professor Türker ERTEM
Mode of Delivery	Face to Face
Suggested Subject	NONE
Professional practise ( internship )	None
Objectives of the Course	Discrete mathematics involves the study of objects which are distinct and separated from each other. For example, finite sets and the set of integers are discrete sets, while the set of real numbers would be considered to be a continuous (or non-discrete) set of objects. This places the subject of discrete mathematics at the opposite end of the spectrum from the study of calculus. Typical problems in discrete mathematics involve either listing or counting the elements of a given discrete set. Often we are interested in sets that carry additional structures such as an operation (addition, multiplication, concatenation, union or intersection, for example) or an inequality (less than or subset inclusion, for example) or an "equivalence relation" (equivalence of fractions or congruence modulo 3, would be examples). When present, such structures are likely to be instrumental in enumerating and counting processes. The basic concepts of discrete mathematics tend to lend themselves to being axiomatized (which means building a subject up starting from basic elementary definitions), and the subject is particularly well-suited for a first non-calculus course of engineering majors. Through this course, you can expect to develop your mathematical vocabulary and maturity and to enhance your ability to create, read, and analyze mathematical arguments. With both the subject itself, as well as the experience gained by working with mathematical arguments, the course is intended to provide an important foundation for moving into higher-level math understandings. Topics included are sets, relations, functions, induction and other methods of proof, recursion, combinatorics, graph theory, and algorithms. Emphasis is placed on the solution of problems and proofs.
Contents of the Course	Introduction to Discrete Mathematics. Set theory. Number theory. Combinatorics. Mathematical proof techniques, Logical methods. Relations and functions. Ordered sets. Algorithms. Logic.

Learning Outcomes of Course

#	Learning Outcomes
1	Define the discrete structures and basics of discrete mathematics.
2	Interpret computer applications of discrete mathematics
3	Analyze discrete structures
4	Define and analyze engineering problems by using the mathematics, scientific and engineering knowledge

Course Syllabus

#	Subjects	Teaching Methods and Technics
1	Set Theory Introduction to Sets Cartesian Products Subsets and Power Sets	asynchronous lecturing, solving problems, discussing during office hours.
2	Set Operations Indexed Sets and Well Ordering Principle Logic Introduction to Logic	asynchronous lecturing, solving problems, discussing during office hours.
3	Truth Tables Truth Table Proofs Logic Laws	asynchronous lecturing, solving problems, discussing during office hours.
4	Conditionals, Converses, Inverses, Contrapositives Rules of Inference Quantificational Logic	asynchronous lecturing, solving problems, discussing during office hours.
5	Counting Introduction to Counting Factorials and Permutations Permutation Practice	asynchronous lecturing, solving problems, discussing during office hours.
6	Combinations Binomial Theorem, Pascal’s Triangle Combinations with Repetition	asynchronous lecturing, solving problems, discussing during office hours.
7	Permutations and Combinations Practice Proof Techniques Direct Proof Proof by Case	asynchronous lecturing, solving problems, discussing during office hours.
8	Midterm	exam
9	Proof by Contraposition	asynchronous lecturing, solving problems, discussing during office hours.
10	Proof by Contradiction Mathematical Induction	asynchronous lecturing, solving problems, discussing during office hours.
11	Relations and Functions Introduction to Relations Partial Orders	asynchronous lecturing, solving problems, discussing during office hours.
12	Introduction to Functions Injections, Surjections, Bijections, Inverses	asynchronous lecturing, solving problems, discussing during office hours.nous
13	Number Theory and Formal Languages Pigeonhole Principle Divisibility	asynchronous lecturing, solving problems, discussing during office hours.
14	Modular Arithmetic Primes and GCD	asynchronous lecturing, solving problems, discussing during office hours.
15	Euclidian Algorithm Formal Languages Finite State Machines	asynchronous lecturing, solving problems, discussing during office hours.
16	Final Exam	exam

Course Syllabus

#	Material / Resources	Information About Resources	Reference / Recommended Resources
1	Kenneth H.Rosen, Discrete Mathematics and Its application	Mc.Graw Hill
2	Richard Johnsonbaugh Discrete Mathematics	Pearson Education
3	John C. Molluzzo and Fred Buckley, A First Course in Discrete Mathematics	Waveland Press

Method of Assessment

#	Weight	Work Type	Work Title
1	20%	Mid-Term Exam	Mid-Term Exam
2	80%	Final Exam	Final Exam

Relationship between Learning Outcomes of Course and Program Outcomes

#	Learning Outcomes	Program Outcomes	Method of Assessment
1	Define the discrete structures and basics of discrete mathematics.	1͵7	1͵2
2	Interpret computer applications of discrete mathematics	1͵7	1͵2
3	Analyze discrete structures	1͵7	1͵2
4	Define and analyze engineering problems by using the mathematics, scientific and engineering knowledge	1͵7	1͵2

PS. The numbers, which are shown in the column Method of Assessment, presents the methods shown in the previous table, titled as Method of Assessment.

Work Load Details

#	Type of Work	Quantity	Time (Hour)	Work Load
1	Course Duration	14	3	42
2	Course Duration Except Class (Preliminary Study, Enhancement)	14	2	28
3	Presentation and Seminar Preparation	0	0	0
4	Web Research, Library and Archival Work	0	0	0
5	Document/Information Listing	0	0	0
6	Workshop	0	0	0
7	Preparation for Midterm Exam	1	6	6
8	Midterm Exam	1	2	2
9	Quiz	0	0	0
10	Homework	0	0	0
11	Midterm Project	0	0	0
12	Midterm Exercise	0	0	0
13	Final Project	0	0	0
14	Final Exercise	0	0	0
15	Preparation for Final Exam	1	10	10
16	Final Exam	1	2	2
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