### Module Details

 The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
 Title Analytic Techniques for Computer Science Code COMP116 Coordinator Professor PE Dunne Computer Science P.E.Dunne@liverpool.ac.uk Year CATS Level Semester CATS Value Session 2022-23 Level 4 FHEQ Second Semester 15

### Aims

To equip students with an awareness of the range of methodologies that have been brought to bear in the treatment of computational issues.
To provide practical experience in how various formal approaches can be used to address such issues.

### Learning Outcomes

(LO1) Students will have a basic understanding of the range of techniques used to analyse and reason about computational settings.

(LO2) Students will have the ability to solve problems involving the outcome of matrix-vector products as might arise in standard transformations.

(LO3) Students will have the ability to apply basic rules to differentiate and integrate commonly arising functions.

(LO4) Students will have a basic understanding of manipulating complex numbers and translating between different representations.

(LO5) Students will have a basic understanding of the role of Linear algebra (including eigenvalues and eigenvectors) in computation problems such as web page ranking.

(S1) Problem Solving - Numeracy and computational skills

(S2) Problem Solving – Analysing facts and situations and applying creative thinking to develop appropriate solutions.

### Syllabus

Computation as static measurement: Numbers and types of number: integer, rational, irrational. Structured forms: Vectors and vector operations. Linear transformations. Applications in video games and robot motion planning. (3 lectures)

Computation as dynamic measurement: Introduction to calculus; functions and their graphs: geometric interpretation of derivative; standard differentiation formulae and rules; maxima and minima, information obtained from second derivative; basic integral calculus; geometric interpretation of integral; standard integral formulae. (5-6 lectures)

Beyond traditional notions of number : Definition of complex number, representation forms (coordinate, polar), properties of complex numbers: conjugates, modulus, standard arithmetic operations. (3 lectures)

Computational approaches for hard calculations: Experimental analysis; the distinction between probability and statistics; providing support for experimental claims. (3-4 lectures)

Com putational models of richer structures: Linear and Matrix algebra; common computational objects described by matrices; weighted directed graphs; properties and operations on matrices: determinant, singularity and invertibility; eigenvalues and eigenvectors; conditions guaranteeing existence of useful forms - the Perron-Frobenius Theorem: notable applications of the PF-eigenvector: Google page ranking algorithm; ranking of sports leagues. (8-9 lectures)

A bit of information theory: Shannon's Fundamental questions: What is information? How is it measured? What limits storage and communication of information? Example contexts: MP3 files, CD, streaming video. Shannon's model of information transmission; probabilistic interpretation of information measure and Shannon's axioms; the notion of information entropy. (4-6 lectures)

### Teaching and Learning Strategies

Teaching Method 1 - Lecture
Description: 3 lectures per week throughout semester
Attendance Recorded: Yes

Teaching Method 2 - Tutorial
Description: 1 tutorial/problem class per week throughout semester
Attendance Recorded: Not yet decided

Due to Covid-19, in 2021/22, one or more of the following delivery methods will be implemented based on the current local conditions.
(a) Hybrid delivery
Teaching Method 1 - Lecture
Description: Mix of on-campus/on-line synchronous/asynchronous sessions
Teaching Method 2 - Tutorial
Description: Mix of on-campus/on-line synchronous/asynchronous sessions

(b) Fully online delivery and assessment
Teaching Method 1 - Lecture
Description: On-line synchronous/asynchronous lectures
Teaching Method 2 - Tutorial
Description: On-line synchronous/asynchronous sessions

(c) Standard on-campus delivery
Teaching Method 1 - Lecture
Description: Mix of on-campus/on-line synchronous/a synchronous sessions
Teaching Method 2 - Tutorial
Description: On-campus synchronous sessions

### Teaching Schedule

 Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL Study Hours 30 10 40 Timetable (if known) Private Study 110 TOTAL HOURS 150

### Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
(116) Final Exam There is a resit opportunity. Standard UoL penalty applies for late submission. This is an anonymous assessment. Assessment Schedule (When) :Semester 2 exam schedule  120    60
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
(116.1) Class Test 3 There is a resit opportunity. Standard UoL penalty applies for late submission. This is an anonymous assessment. Assessment Schedule (When) :Semester 2    15
(116.2) Class Test 2 There is a resit opportunity. Standard UoL penalty applies for late submission. This is an anonymous assessment. Assessment Schedule (When) :Semester 2, Week 8 or 9    15
(116.3) Class Test 1 There is a resit opportunity. Standard UoL penalty applies for late submission. This is an anonymous assessment. Assessment Schedule (When) :Semester 2, Week 4    10