Some important mathematical concepts used by computer scientists are introduced in this module. More sophisticated than earlier modules, the applications can be found in cryptography, security, computer graphics, hardware and operating systems design

Learning Outcomes

On successful completion of this module the learner will be able to:

LO1

Perform calculations and solve linear identities with mod arithmetic.

LO2

Use the Euclidean Algorithm to find GCD.

LO3

Use modular arithmetic to generate pseudo-random numbers.

LO4

Apply modular encodings and decodings to text.

LO5

Apply matrix techniques to solve systems of linear equations.

LO6

Apply the Bisection Method and Newton’s Method to solve equations.

LO7

Apply the Trapezoidal Rule and Simpson's Rule to calculate integrals numerically.

LO8

Apply linear interpolation to make estimates.

Module Content & Assessment

Course Work

Assessment Type

Assessment Description

Outcome addressed

% of total

Assessment Date

Continuous Assessment

CA1 Project: Decode a message encrypted by a modular scheme.

1,4

15.00

n/a

Continuous Assessment

CA2 – in-class – Typical task: Performing modular arithmetics calculations. Finding GCD. Calculating pseudo-random numbers. Solving equations using numerical techniques. Solving systems of linear equations by matrix techniques

1,4,5,6

15.00

n/a

End of Module Formal Examination

Assessment Type

Assessment Description

Outcome addressed

% of total

Assessment Date

Formal Exam

End-of-Semester Final Examination

70.00

End-of-Semester

TU Dublin – Tallaght Campus reserves the right to alter the nature and timings of assessment

Module Workload

Workload: Full Time

Workload Type

Workload Description

Hours

Frequency

Average Weekly Learner Workload

Lecturer/Lab

Delivery of course material

4.00

Every Week

4.00

Independent Learning

Studying course notes

2.00

Every Week

2.00

Total Weekly Learner Workload

6.00

Total Weekly Contact Hours

4.00

Workload: Part Time

Workload Type

Workload Description

Hours

Frequency

Average Weekly Learner Workload

Lecture

Lecture/ tutorial

4.00

Every Second Week

2.00

Independent Learning

Studying course notes

3.00

Every Week

3.00

Total Weekly Learner Workload

5.00

Total Weekly Contact Hours

2.00

Module Resources

Required Book Resources

Course Notes

Recommended Book Resources

Paul Fannon, Vesna Kadelburg, Ben Woolley, Stephen Ward 2013, Mathematics Higher Level for the IB Diploma Option Topic 10 Discrete Mathematics, 1 Ed., Cambridge University Press [ISBN: 978-110766694]

Peter Grossman 2008, Discrete Mathematics for Computing, 3 Ed., Palgrave Macmillan [ISBN: 978-0230216112]

John C. Molluzzo, Fred Buckley 2001, A First Course in Discrete Mathematics [ISBN: 978-0881339406]

Rod Haggarty 2001, Discrete mathematics for computing [ISBN: 978-0201730470]

Stephen Barnett 1998, Introduction to Discrete Mathematics, 1 Ed., Addison Wesley [ISBN: 978-020134292]

This module does not have any article/paper resources