# CS130 Mathematics for Computer Scientists I

*CS130 15 CATS (7.5 ECTS) Term 1 *

## Availability

Core - CS and CMS. Option - CSE

## Academic Aims

- To provide students with sufficient mathematical knowledge to enable them to understand the foundations of their subject for both study purposes and later career development.
- To bridge the gap in style and content between A-level and university mathematics and to introduce students to the language and methods of professional mathematics.

## Learning Outcomes

By the end of the module the students should be able to:

- Understand and use basic mathematical terminology.
- Understand the role of formal definitions and proofs and be able to apply them in problem solving.
- Understand the basics of propositional and predicate logic.
- Understand the basics of elementary set theory.
- Understand the basics of mathematical relations and functions.
- Understand the basics of graph theory.
- Understand the basics of probability.

## Content

- The axiomatic method: Basic concepts, axioms, definitions, theorems, finite and infinte sets, natural numbers, induction.
- Logic: Statements, truth values, Boolean operators, laws of propositional logic, predicates, quantifiers, laws of predicate logic.
- Sets: Connection between sets and predicates, operations on sets, laws of set operations.
- Relations: Relation composition and inverse, properties of relations, equivalence relations, equivalence classes, quotient sets, partial orders.
- Functions: Properties of functions, equinumerous sets, countable and uncountable sets.
- Graphs: Graph isomorphism, graph connectivity, Eulerian and Hamiltonian graphs.
- Probability: Definitions, conditional probability, Bayes' theorem, expectation, variance, standard deviation.

## Books

- Ross KA and Wright CRB,
*Discrete Mathematics (5th ed)*, Prentice-Hall, 2003. - Rosen KH,
*Discrete Mathematics and Its Applications (6th ed)*, McGraw-Hill, 2006. - Truss JK,
*Discrete Mathematics for Computer Scientists (2nd ed)*, Addison-Wesley, 1999.

## Assessment

Three-hour examination (80%) and problem sheets (20%)

## Teaching

30 lectures and 9 seminars