CSE 1103 Discrete Mathematics
Undergraduate course, Noakhali Science and Technology University, Institute of Information Technology, 2022
This was full pledged class after COVID-19 crisis.
Time
From Feb 2023 to August 2023
Course Contents
| Week | Course Contents |
|---|---|
| 1 | Logic: Introduction to Logic, Propositional Logic, What Is Proposition, Elements of Propositional Logic, Truth Table, Connectives, Construction of Proposition, Converse and Contrapositive, Negation, Implications, From English to Proposition, From Proposition to English, Logical Equivalences, Reasoning with Propositions |
| 2 | Logic: Predicate Logic, Predicate, Quantification, English to Logic Translation, Logic to English Translation, Quantifiers and Connectives, Logical Equivalences of Quantifiers, Reasoning with Predicate Logic |
| 3 | Proofs: Rules of Inferences: Rules, Build Arguments for Both Propositional Logic, Predicate Logic and Quantified statements Formal Proofs: Using theorem, axioms Informal Proof: Direct Proof, Indirect Proof: proof by contrapositive, proof by contradiction, proof by cases |
| 4 | Sets, Functions, Sequences: Sets: Introduction to Set Theory, Representation of Set, Equality, Subset, Set Operations, Properties of Set Operation, Fuzzy Set and its Operations, Sets in Programming Language Functions: Injective Function, Surjective Function, Bijective Function, Ceiling and Floor Function, Composition of Function, Growth of Function, Recursive Function, Functions in Programing Languages |
| 5 | Sets, Functions, Sequences (cont'd): Sequences: Representation of Sequences, Summations of Sequencences, Cardinality of Sets, Sequence and Strings in Programming Languages Recurences and Induction: Recursive Definition, Recursive Function, Recursive Algorims, Mathematical Induction |
| 6-8 | Number Theory: Divisibility, Primes, Prime Factorization, Greatest Common Divisor, Least Common Multiples, Cryptography Modular Arithmatic: Properties, Hashing, pseudo-random numbers, Ciphers Integers and Algorithm: Representation of Integers, Algorithm of Integer Operations, Modular Exponentiation, Euclidean Algorithm |
| 9 | Matrices: Properties, Matrix Arithmetics, Matrix Multiplication, Transpose and Power of Matrices, Zero-One Matrices and Operations |
| 10 | Counting: Basics of Counting, Pigeonhole Principle, Inclusion-Exclusion Principle, Permutation and Combination |
| 11 | Relations: Properties, n-ary relations and applications, representing relations, closure of relations, equivalence of relations |
| 12 | Graphs and Trees: Graphs and Graph Models, Graph Terminology, Special Types of Graphs, Representing Graphs, Introduction to Trees, Applications of Trees |
| 13 | Formal Specifications with Z: Z notation, Application of Z: Files, Birthday and PhoneBook |
Reference Books
- Discrete Mathematics and its Applications, Seventh Edition by Kenneth H. Rosen.