# Computer Science

## ECM1416 - Computational Mathematics (2016)

MODULE TITLE CREDIT VALUE Computational Mathematics 15 ECM1416 Dr Jia Hu (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 0
 Number of Students Taking Module (anticipated) 56
DESCRIPTION - summary of the module content

Computer science draws from a wide range of essential mathematical techniques. This module will provide a solid foundation on the required mathematical tools and how to use them in solving computer science problems. This module will introduce linear algebra and vector spaces, statistics and probabilities and numerical optimization.  In the course of this module, you will learn to apply theoretical knowledge in concrete programming tasks.  This module complements previous mathematics module and is essential for all engaged in a Computer Science program.

AIMS - intentions of the module

In this module we aim to provide you with a foundation in the essential mathematical tools used in advanced computer science topics. We will teach you how to use vector and matrices, statistics and probabilities and numerical optimization methods and implement them in computer programs.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge

1. Show understanding of linear algebra, probabilities and numerical optimization
2. Display competence in using these mathematical tools
3. Design algorithms implementing these mathematical methods
4. Apply the techniques in practical programming context

Discipline Specific Skills and Knowledge

5. Show understanding of a range of mathematical methods used in computer science
6. Apply mathematical techniques to computer science problems

Personal and Key Transferable / Employment Skills and Knowledge

7. Solve problems using the appropriate mathematical tools
8. Adapt existing mathematical knowledge to learning new methods

SYLLABUS PLAN - summary of the structure and academic content of the module

Introduction to vector spaces and linear algebra:

• Vectors and multidimensional spaces, matrices and operations (interpolation)
• Matrices and operations, products transpose, inverse and determinants (with examples of rotation matrices).
• Eigen decomposition, solving systems of linear equations with linear algebra.
• Derivatives in vector spaces, differential equations, partial derivatives, grad and Hessian.
• Taylor expansion

Statistics and probabilities:

• Random variables & Distributions (Normal vs uniform distribution)
• Conditional probabilities, independence, marginalization
• Expectation, variance and covariance, significance.
• Bayesian inference & Markov Chains.

Optimization and numerical search:

• Linear optimization.
• Numerical methods
• Random sampling methods & Monte Carlo
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 33 117 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled Learning & Teaching 22 Lectures Scheduled Learning & Teaching 11 Workshops Guided independent study 30 Independent work on the two assignments Guided independent study 87 Independent study

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Linear Algebra programming coursework 15 hours 3,4,6,7,8 Individual Marksheet

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams Practical Exams 20 80 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written Exam 80 2 hours 1,2,5,7,8 Orally, on request
Assignment 20 15 hours 3,4,6,7,8 Individual Marksheet

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
All Summative Assessment Written Exam (100%) All August Ref Def Period

RE-ASSESSMENT NOTES
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE: http://vle.exeter.ac.uk/

Web based and Electronic Resources:

Other Resources: