## COMP1421 Fundamental Mathematical Concepts

### 10 creditsClass Size: 500

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2021/22

This module is not approved as a discovery module

### Module summary

Computer Science, at its foundation, is a mathematical and engineering discipline. This module focuses on the mathematical concepts that are fundamental to the study of Computer Science. In order to fully understand the concepts of algorithms design, logical reasoning and programming it is necessary to understand how to apply mathematical arguments and how to apply mathematical knowledge to model real world problems.This module forms the vital core of the Computer Science curriculum and encourages students to view real world problems as mathematical problems and will prepare students for further mathematical study in Computer Science. The module will consider applications of the fundamental mathematical concepts into the contexts of verification and program correctness, systems security and complexity analysis.

### Objectives

To develop an appreciation and familiarity of mathematical concepts and their application in computer science in addition to equipping students with the appropriate problem solving techniques and transferable skills to tackle real world problems. To prepare students for further mathematical study in the discipline of Computer Science.

Learning outcomes
On successful completion of this module a student will have demonstrated the ability to:

- apply their mathematical knowledge to real world problems.
- identify appropriate mathematical tools to solve problems.
- construct mathematical arguments to prove theorems.
- deploy problem solving techniques to problems within the discipline.

### Syllabus

This module covers the following 5 topic areas:

- Logic : propositions, connectives, truth tables, tautologies, contradictions, predicates and quantifiers.

- Proof techniques : direct proof, proof by contradiction, proof by contraposition and mathematical induction.

- Set theory : sets, set operations, Venn diagrams, set equality, subsets and cardinality.

- Relations & Functions : relations of sets, inverse functions, equivalence relations, order relations, domain and range, inverse functions, composition of functions and properties of functions.

- Vectors & Matrices : addition, multiplication, distributive and associativity, non-commutativity, identity matrix and inverse of square matrices.

### Teaching methods

 Delivery type Number Length hours Student hours Example Class 11 1.00 11.00 Class tests, exams and assessment 1 2.00 2.00 Lecture 22 1.00 22.00 Tutorial 10 1.00 10.00 Private study hours 55.00 Total Contact hours 45.00 Total hours (100hr per 10 credits) 100.00

### Private study

Taught session preparation: 18 hours
Taught session follow-up: 18 hours
Self-directed study: 7 hours
Assessment activities: 23 hours

### Opportunities for Formative Feedback

Attendance and formative assessment

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Online Coursework 1 20.00 In-course Assessment Online Coursework 2 20.00 In-course Assessment Online Coursework 3 20.00 Total percentage (Assessment Coursework) 60.00

This module will be reassessed by an online time-constrained assessment.

Exams
 Exam type Exam duration % of formal assessment Online Time-Limited assessment 2 hr 40.00 Total percentage (Assessment Exams) 40.00

This module will be reassessed by an online time-constrained assessment.