## CS1MA20-Mathematics and Computation

Module Provider: Computer Science
Number of credits: 20 [10 ECTS credits]
Level:4
Terms in which taught: Autumn / Spring / Summer module
Pre-requisites:
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Current from: 2020/1

Module Convenor: Prof Richard Mitchell

Type of module:

Summary module description:

An introduction to mathematics which is relevant to computer science, including linear algebra, probability and statistics. The focus of the module is more on understanding the concepts and considering how they can be implemented on a computer, than in pure mathematics.

Aims:

The module introduces mathematics as it relates to computer science, covering topics in linear algebra, calculus, probability and statistics. These are related to computer science applications and applied through implementations in MATLAB.

On completion of this module, students will:

• Be able to represent and interpret data graphically;

• Be able to perform calculations using linear algebra;

• Understand how to implement these methods in programs;

• Understand and be able to implement numerical algorithms;

• Be able to perform calculations with complex numbers;

• Be able to calculate probabilities and statistics

• Be able to relate this knowledge to topics in computer science;

• Be able to use MATLAB to implement numerical methods;

• Understand the relevance of rounding errors in numerical methods.

Assessable learning outcomes:

• Ability to perform calculations with matrices and vectors

• Ability to draw and interpret graphs

• Implementation of numerical methods

• Calculations with complex numbers

• Ability to use probability and statistics

• Knowledge of applications of these methods in the context of the subject

• Students will be able to work with MATLAB

• Experience of group problem solving

• Planning

Outline content:

Linear algebra (7 credits):

• atrices, elementwise operations, trace, transpose, multiplication. Implementations as code (e.g. in MATLAB).

• Linear transformations

• Matrix determinant, inverse. Implementations as code (e.g. in MATLAB).

• Vectors

• Matrix rank

• Gaussian elimination. Implementation as code (e.g. in MATLAB).

• Eigenvalues and eigenvectors

• Introduce applications of linear algebra (computer graphics, machine learning)

Graphical Representation (3 credits)

• Introduction of relevant functions, including polynomials, trigonometrical, exponential and logarithmic.

• Draw graphs of relevant functions

• Interpret key aspects of graphs

• Use MATLAB for plotting graphs

Implementation of numerical algorithms in MA TLAB (4 credits), covering concepts of integration as area under curve, differentiation as gradient e.g.:

• Newton–Raphson method

• Euler's method for first order differential equations

• Computer science applications

Complex numbers (2 credits):

• Working with complex numbers

• Representations

• Modulus and argument of complex numbers
• Computer science applications of complex numbers

• Using complex numbers in programs.

Probability and Statistics (4 credits):

• Simple probabilities

• Probability Distributions

• Data analysis

• Correlation

Brief description of teaching and learning methods:

Lectures, reading and preparation outside of lectures.

Tutorials on assignments and group problem solving.

Lab sessions utilising appropriate software, such as MATLAB.

Contact hours:
 Autumn Spring Summer Lectures 20 20 2 Tutorials 5 5 Practicals classes and workshops 5 5 Guided independent study: Wider reading (independent) 10 10 Wider reading (directed) 10 10 Exam revision/preparation 18 Advance preparation for classes 10 10 Completion of formative assessment tasks 20 20 Reflection 10 10 Total hours by term 90 90 20 Total hours for module 200

Summative Assessment Methods:
 Method Percentage Written exam 30 Set exercise 70

Summative assessment- Examinations:

One 1.5 hour examination paper in May/June.

Summative assessment- Coursework and in-class tests:

Regular lab exercises where students have practice of mathematical techniques using software including MatLab.

Formative assessment methods:

Students will be provided with formative feedback through tutorial work and some online exercises. Some work will be in groups.

Penalties for late submission:

The Module Convenor will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:

A mark of 40% overall.

Reassessment arrangements:

One 3-hour examination paper in August/September.  Note that the resit module mark will be the higher of (a) the mark from this resit exam and (b) an average of this resit exam mark and previous coursework marks, weighted as per the first attempt (30% exam, 70% coursework).