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Semester 1

Discrete Mathematics and Probability (INFR08031)







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Visiting students should have done a previous University-level mathematics course, be comfortable with univariate calculus (differentiation and integration), and have some familiarity with basic concepts from discrete mathematics such as binary numbers, sets, functions, and relations. A previous computer science course is recommended.

Course Summary

The first part of this course covers fundamental topics in discrete mathematics that underlie many areas of computer science and presents standard mathematical reasoning and proof techniques such as proof by induction. The second part of this course covers discrete and continuous probability theory, including standard definitions and commonly used distributions and their applications.*This course replaces "Discrete Mathematics and Mathematical Reasoning" (INFR08023). from academic year 2020/21*

Course Description

The course will cover roughly the following topics: Block 1: Discrete Mathematics - Logical equivalences, conditional statements, predicates and quantifiers - Methods of proof using properties of integers, rational numbers and divisibility - Set theory, properties of functions and relations, cardinality - Sequences, sums and products, Induction and Recursion - Modular arithmetic, primes, greatest common divisors and their applications - Introductory graph topics Block 2: Probability Theory - Counting techniques: product rule, permutations, combinations - Axioms of probability, sample space, events, De Morgan's Law - Joint and conditional probability, independence, chain rule, law of total probability, Bayes' Theorem - Random variables, expectation, variance, covariance - Common discrete and continuous distributions (e.g., Bernoulli, binomial, Poisson, uniform, exponential, normal) - Central limit Theorem

Assessment Information

Written Exam 40%, Coursework 60%, Practical Exam 0%

Additional Assessment Information

Assessment will consist of:30% Engagement activities (10% homework & 20% STACK quizzes)30% Class test on Discrete Maths at half-way stage40% Exam on Probability and challenging Discrete Maths problem(s)

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