Discrete Structures (CMPC-205)

1- The course provides a solid theoretical foundation of discrete structures as they apply to computer science problems and structures.

2- The students will learn how to use mathematical notation and solve problems using mathematical tools.

Course Material

01 WEEK 1- 1st LECTURE (Introduction, Propositional Logic)

02 WEEK 1- 2nd LECTURE (Applications of Propositional Logic, Propositional Equivalences)

03 WEEK 2- 1st LECTURE (Predicates and Quantifiers, Nested Quantifiers)

04 WEEK 2- 2nd LECTURE (Introduction to Proofs, Proof Methods and Strategy)

05 WEEK 3- 1st LECTURE (Sets, Set Operations)

06 WEEK 3- 2nd LECTURE (Set Functions, Sequences and Summations)

07 WEEK 4- 1st LECTURE (Cardinality of Sets , Matrices)

08 WEEK 4- 2nd LECTURE (Algorithms)

09 WEEK 5- 1st LECTURE (The Growth of Functions)

10 WEEK 5- 2nd LECTURE (Complexity of Algorithms)

11 WEEK 6- 1st LECTURE (Divisibility and Modular Arithmetic)

12 WEEK 6- 2nd LECTURE (Integer Representations and Algorithms, Primes and Greatest Common Divisors)

13 WEEK 7- 1st LECTURE (Solving Congruences, Applications of Congruences, )

14 WEEK 7- 2nd LECTURE (Cryptography)

15 WEEK 8- 1st LECTURE (Applications of Recurrence Relations)

16 WEEK 8- 2nd LECTURE (Solving Linear Recurrence Relations)

17 WEEK 9- 1st LECTURE (Divide-and- Conquer Algorithms and Recurrence Relations)

18 WEEK 9- 2nd LECTURE (Generating Functions, Inclusion Exclusion, Applications of Inclusion Exclusion)

19 WEEK 10- 1st LECTURE (Relations and Their Properties , n-ary Relations and Their Applications)

20 WEEK 10- 2nd LECTURE (Representing Relations, Closures of Relations)

21 WEEK 11- 1st LECTURE (Equivalence Relations, Partial Orderings)

22 WEEK 11- 2nd LECTURE (Graphs and Graph Models)

23 WEEK 12- 1st LECTURE (Graph Terminology and Special Types of Graphs)

24 WEEK 12- 2nd LECTURE (Representing Graphs, Connectivity)

25 WEEK 13- 1st LECTURE (Shortest-Path Problems, Planar Graphs, Graph Coloring)

26 WEEK 13- 2nd LECTURE (Introduction to Trees, Applications of Trees)

27 WEEK 14- 1st LECTURE (Tree Traversal, Spanning Trees)

28 WEEK 14- 2nd LECTURE (Minimum Spanning Trees)

29 WEEK 14- 2nd LECTURE (Minimum Spanning Trees)

30 WEEK 15- Semester Project Evaluation