# Module ICP-1016:Mathematics for Computing

### Module Facts

Run by School of Computer Science and Electronic Engineering

10 Credits or 5 ECTS Credits

Semester 2

Organiser: Prof Ludmila Kuncheva

### Overall aims and purpose

To give the students background in important areas of mathematics that will be needed in their further studies (matrix and vector calculation, geometry in 2D and 3D, elements of probability theory)

### Course content

• Introduction to matrices. Addition, multiplication, the identity matrix. Inverses.

• Introduction to vectors Vector addition and subtraction. Scalar product. Euclidean distance between points.

• Introduction to geometry in the plane and 3-space. Equation of a line in 2D and 3D. Equation of a plane in 3D. Intersection between 2 lines in 2D and 3D. Intersection between a line and a plane. Rotation matrix.

• Introduction to probability. Counting rule. Permutations. Combinations. Sample spaces, elementary events, compound events. Probability for equiprobable elementary events. Conditional probability from 2-by-2 contingency tables.

### Learning outcomes mapped to assessment criteria

threshold

40% The student has sufficient knowledge of elementary mathematical operations and is able to show basic problem solving skills.

good

60% The student has reasonable understanding of the concepts and operations taught in the module. They are able to solve most problems related to the material.

excellent

70% The student has excellent mathematical skills and understands the material in depth. They are knowledgeable in all parts of the module and are able to demonstrate efficient and accurate problem solving.

Perform simple matrix arithmetic.

Add and multiply matrices of any size. Understand the use of a matrix inverse for solving systems of linear equations Understand and carry out matrix operations

Perform vector operations

Calculate the length of a vector. Calculate the Euclidean distance between points in 2D and 3D. Understand and operate with the concept of orthogonality of 2 vectors. Manipulate vectors.

Express and manipulate equations of lines and planes. Calculate points of intersection.

Find the equation of a line through 2 points in 2D space. Find the equation of a line through a point and parallel/orthogonal to a given line in 2D. Find points of intersection of two lines, a line and a plane in 3D

Determine the number of ways of choosing r out of n different objects. Calculate probabilities for sample spaces of equiprobable elementary events

Solve simple problems involving permutations Calculate joint, marginal and conditional probabilities from 2-by-2 contingency tables Calculate binomial coefficient. Find the number of combinations. Solve simple probability problems

### Assessment Methods

Type Name Description Weight
EXAM Examination

Solve all problems.

60
COURSEWORK Assignment 1

A collection of problems individually prepared for each student.

20
COURSEWORK Assignment 2

A collection of problems individually prepared for each student.

20

### Teaching and Learning Strategy

Hours
Private study

Self-study. Revision for the exam after lectures and at the end of the semester.

32
Private study

Preparation of the individual assignments.

32
Lecture

Pen-and-paper introduction of all concepts and methods. Problem-solving in class. Taking notes simultaneously with the lecturer writing down the material.

36

### Transferable skills

• Numeracy - Proficiency in using numbers at appropriate levels of accuracy
• Self-Management - Able to work unsupervised in an efficient, punctual and structured manner. To examine the outcomes of tasks and events, and judge levels of quality and importance
• Exploring - Able to investigate, research and consider alternatives
• Critical analysis & Problem Solving - Able to deconstruct and analyse problems or complex situations. To find solutions to problems through analyses and exploration of all possibilities using appropriate methods, rescources and creativity.

### Subject specific skills

• Knowledge and understanding of facts, concepts, principles & theories
• Use of such knowledge in modelling and design
• Problem solving strategies
• Knowledge and understanding of mathematical principles

### Resources

#### Resource implications for students

A limited number of copies of the book are available in the library. The book is available from Lulu: http://www.lulu.com/shop/ludmila-kuncheva/a-first-course-in-mathematics-for-computing/paperback/product-21531308.html A pdf copy of the book is stored in Blackboard.