Computational & Discrete Mathematics

Computational & Discrete Mathematics

Objectives

not available

Prerequisites

not available

Syllabus

1. Logic and proof: Statements and Logic - Predicates and quantifiers - Proof techniques - Mathematical induction. 2. Combinatorics: sum and product rules - rules of combinatorics - binomial coefficients. 3. Discrete probability: events and probabilities - conditional probability - random variables and expected values - covariance and correlation. 4. Relations - Operations - Structures: binary relations - representation of binary relations - properties of relations - equivalence relations and partial orders - binary operations - internal operation and equivalence classes - structures - isomorphisms. 5. Modular arithmetic - Cyclic groups: Divisibility - Euclidean algorithm - residues - "exponents" - cyclic groups - computations with big integers. 6. Rings and finite fields: the problem of generators and discrete logarithm - polynomial arithmetic and applications - Algorithms for finite fields - applications. 7. Recursion: sequences - recurrence relations - computation of sums and products.