Introduction to Discrete Mathematics

This course provides a foundation for Computer Science and Applied Statistics. Many areas of Computer Science and Applied Statistics require the ability to work with concepts from discrete structures, which include topics such as set theory, logic, graph theory, and probability theory. In this course, you will learn about (1) sets, relations and functions; (2) basic logic, including propositional logic, logical connectives, truth tables, propositional inference rules and predicate logic; (3) proof techniques, including the structure of mathematical proofs, direct proofs, disproving by counterexample, proof by contradiction; (4) basics of counting, including counting arguments, the pigeonhole principle, permutations and combinations, solving recurrence relation; (5) graphs and trees; (6) discrete probability, including finite probability space, axioms of probability, conditional probability; and, (7) linear algebra, including vectors, matrices and their applications. The course is offered in a blended-learning format. Students are provided with a set of video lectures that they can watch multiple times. Student contact time is in a tutorial format aimed at reinforcing the principles introduced in the online lectures and giving students time to do exercises under the supervision of tutors.

DP requirements: Class Record of at least 30% and attendance at 10 or more (out of 12) tutorials.

Assessment: Class Record counts 50% and Exam counts 50%.

The University of Cape Town awards credits based on the National Qualifications Framework (NQF) to determine course and contact hour recommendations per course. 1 NQF credit represents roughly 10 notional hours of work which includes study time, assignments and examinations. Notional hours may very per courses depending on the course level and modality therefore, CEA recommends using NQF credits as a basis to determine U.S. equivalencies (1 NQF=.222 semester credits)