To provide an introduction to, and grounding in, the basic principles and techniques of logic and discrete mathematics that are fundamental to Computer Science.
1. Introduction to Logic (1.1 1. Basic Connectives and Truth Tables , 1.2 2. Logical Equivalence and Logical Implication , 1.3 3. Quantifiers)
2. Set, function and counting (2.1 1. Sets revision, 2.2 2. Functions - injective, surjective, bijective, 2.3 3. The product rule and sum rule, 2.4 4. Permutations and Combinations)
3.1 1. Terminology, 3.2 2. Direct Proof, 3.3 3. If and only if proof, 3.4 4. Counter example, 3.5 5. Contrapositive proof, 3.6 6. Proof by contraction, 3.7 7. Weak Induction proof
4. Relation and recurrence relations (4.1 1. Relations - reflexive, symmetric and transitive, 4.2 2. Recurrence Relations - simple first and second order)
5. Modular arithmetic (5.1 1. Divisibility , 5.2 2. Prime numbers , 5.3 3. Greatest Common Divisors and Least Common Multiple, 5.4 4. Solving Linear Congruences)
By the end of the course, students should be able to do the following:
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SCQF Level: 7
Credits: 15