# Discrete Mathematics and Mathematical Reasoning

This module runs in the first semester. Lecture hours are:
• Monday 16:10-17:00, Teviot LT, MEDS
• Tuesday 10:00-10:50, Weeks 1 & 7 Lecture Theatre C, DHT; Weeks 2-6, 8-10 Lecture Theatre 4, Appleton Tower
• Thursday 16:10-17:00, Teviot LT, MEDS
The first and introductory lecture will take place on Monday 18 September.

### Summary of intended learning outcomes

- Reason mathematically about basic (discrete) structures (such as numbers, sets, graphs, and trees)used in computer science.
- Use of mathematical and logical notation to define and formally reason about mathematical concepts such as sets, relations, functions, and integers, and discrete structures like trees, graphs, and partial orders;
- Evaluate elementary mathematical arguments and identify fallacious reasoning
- Construct inductive hypothesis and carry out simple induction proofs;
- Use graph theoretic models and data structures to model and solve some basic problems in Informatics (e.g., network connectivity, etc.)
- Prove elementary arithmetic and algebraic properties of the integers, and modular arithmetic, explain some of their basic applications in Informatics, e.g., to cryptography.
- Compare the asymptotic growth growth rates of basic functions; derive asymptotic bounds, and limits, for simple series and recurrence relations. Use these to derive bounds on the resource consumption (e.g., running time) of simple iterative and recursive algorithms.
- Calculate the number of possible outcomes of elementary combinatorial processes such as permutations and combinations.
- Be able to construct discrete probability distributions based on simple combinatorial processes, and to calculate the probabilities and expectations of simple events under such discrete distributions.

### Coursework

Weekly tutorial sheet exercises. Discussed in tutorial groups. The last exercise on each tutorial sheet is marked, and students must submit the solution by the due date each week (see here).