University of Debrecen -- Insitute of Mathematics

College Discrete Mathematics

Instructor: László Kozma, Associate Professor

Tuesday 8-10, Room E103 in the Chemistry building, and Friday 8-10, Room M316 Geo-Math Building

Textbook:

G. Horváth and Sz. Tengely: Lecture Notes for College Discrete Mathematics, 2013

Syllabus: Introduction to the course. Introductory combinatorial exercises. Sets, number of subsets. Division algorithm. Euclidean algorithm. Numeral systems. Number of subsets again. Sequences. Permutations. The number of ordered subsets. Anagrams. The number of subsets of a given size. Distributing money. Balls and urns. Number of positive integer solutions of linear equations. Proof techniques: Mathematical induction. Proof by contradiction. Pigeon hole principle. The Binomial Theorem. Pascal's triangle. Fibonacci numbers. Recursive sequences.

Week 1
Warming up...

Week 2
Set operations.

Week 3
Sums and products.

Week 4
Numeral systems. .. Further exercises.

Week 5
Counting.

Week 6
Review Exercises. Sample Test.
Midterm Test: October 28, Friday, 8:15 am, Room M316

Week 7
Mathematical Induction. Further exercises.

Week 8
Constructive proofs and others.

Week 9
Pascal Triangle.

Week 10
Recurrence sequences.

Week 11
Revision Exercises.
Proof by Induction. Proof by Contradiction. The Pigeonhole Priciple.

Week 12
Final test. December 16, Friday, 8:15 am, Room M316
Sample Test. 2nd Sample Test.