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. |
# |
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. |
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.ussion, presentation |
15 |
Euclidian Algorithm Formal Languages Finite State Machines |
asynchronous lecturing, solving problems, discussing during office hours. |
16 |
Final Exam |
Exam |