Computer Science

ECM1416 - Computational Mathematics (2023)

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MODULE TITLEComputational Mathematics CREDIT VALUE15
MODULE CODEECM1416 MODULE CONVENERDr Tinkle Chugh (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 0
Number of Students Taking Module (anticipated) 70
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

Optimization and numerical search: Linear optimization.

Gradient descent, Newton method Numerical methods

Statistics and probabilities:

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

Bayesian inference & Markov Chains.

 

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 33.00 Guided Independent Study 117.00 Placement / Study Abroad 0.00
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 0 Written Exams 100 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written Exam 80 1 hour - Summer Exam Period 1,2,5,7,8 Orally, on request
Assignment 20 One assignment, 30 hours total    

 

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
Written exam Written Exam (1 hour) All August Ref Def Period
Assignment Assignment    

 

RE-ASSESSMENT NOTES

Reassessment will be by coursework and/or written exam in the failed or deferred element only. For referred candidates, the module mark will be capped at 40%. For deferred candidates, the module mark will be uncapped.

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

Basic reading:

 
 
 

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set Klein, Philip N. Coding the Matrix: Linear Algebra through Applications to Computer Science 1st [Library]
Set Mitrani, I. Probabilistic Modelling [Library]
Set Norris, J. R. Markov Chains Cambridge University Press 1998 978-0521633963 [Library]
Set Tenenbaum, Morris; Pollard, Harry Ordinary differential equation : an elementary textbook for students of mathematics, engineering, and the sciences [Library]
Set Blyth, T. S. Basic Linear Algebra Springer 2002 [Library]
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES None
CO-REQUISITE MODULES None
NQF LEVEL (FHEQ) 5 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Tuesday 10 July 2018 LAST REVISION DATE Wednesday 08 February 2023
KEY WORDS SEARCH Mathematics, statistics, probabilities, linear algebra, matrix, vectors, optimisation.