First Year Modules Descriptions

CT101 Computing Systems

Semester One:

Introduction to Computing Systems, Data Representation, Numbering Systems, Computer Systems Organization, Introduction to Operating Systems, Electronic Circuits, Combinatorial Logic Circuit Design, Sequential Logic Design.

Semester Two:

Finite State Machine Design, Hardware Description Languages, CPU Programming Models, CPU Instruction Set, CPU Design, Pipeline Hazard, Memory Subsystem, Input Output Subsystem

CT102 Algorithms and Information Systems

Algorithmics. Conditionals. Looping. Abstract Data Types. Recursion. Information Systems and classifications. Information Languages.

CT103 Programming

Introduction. Simple Programming Tasks. Alternate and iterative commands in the Language. Working with abstract data types. Recursion. Recursive Problem-Solving.

CT1112 Professional Skills I

What are Professional Skills?; research skills; understanding plagiarism and referencing; academic writing; digital literacies; writing and publishing online; presentation skills.

CT1113 Next-Generation Technologies I

Introduction to programming in HTML and JavaScript

EE130 Fundamentals of Electrical & Electronic Engineering I

Introduction to electrical and electronic engineering. Overview of electronic system application areas (e.g. microprocessors, telecommunications, power systems, signal processing, electronic design processes). Elementary electrical concepts, including quantities and circuit elements. Basic circuit laws and DC analysis. Circuit simplification techniques. Voltage and current dividers. Analogue and digital signals. Introduction to digital electronics and logic gates. Boolean algebra. Basic logic circuits. Logic circuit representation and minimisation.

On completion of this module, students should be able to:

1. Show an understanding of the basic concepts of electrical and electronic engineering and be able to describe a range of application areas; 
2. Apply Kirchhoff's current and voltage laws in the analysis of simple electric circuits involving voltage sources, current sources, resistors, potentiometers, switches, etc.
3. Based on requirements for a logic system, derive an equivalent truth table and/or Boolean expression and equivalent digital logic representations.

MA160 Mathematics

Taught in Semester(s) I+II. Examined in Semester(s) I+II.

Workload: 96 hours (72 Lecture hours, 24 Tutorial hours).

Module Learning Outcomes. On successful completion of this module the learner should be able to:

1. use modular arithmetic and Euler's Phi function to detect errors in ISBNs, encipher messages using 1-dimensional affine and RSA cryptosystems, attack 1-dimensional affine cryptosystems, calculate with Chinese remainders. The student will also be able to present a proof of Fermat's little theorem;
2. use matrices to solve resource allocation problems, encipher messages using higher dimensional affine cryptosystems, attack higher dimensional affine cryptosystems, solve some geometric problems;
3. use eigenvalues, eigenvectors and the Principle of Induction to solve practical and theoretical problems about recurrence. The student will also be able to state the Hamilton-Cayley theorem and prove it in the $2\times2$ case;
4. sketch the graph of a number of basic functions; calculate the limit of a function at a point or at infinity; decide whether a given function has an inverse and, if it does, calculate it; use the Intermediate Value Theorem to find roots of equations. You will be able to apply the material learned to a variety of problems coming from physics and earth sciences;
5. use the definition of a derivative to compute the derivative of simple functions; apply different techniques of differentiation to calculate derivatives; apply the Mean Value Theorem to finding roots of equations; find maxima/minima/inflection points, and use these to sketch graphs of functions; apply differentiation techniques to solve optimisation problems;
6. be able to perform calculations with logarithms and the exponential function. You will be able to use anti-derivatives to solve some basic problems in biology, chemistry and physics;
7. be able to perform basic arithmetic operations with complex numbers, and factorize polynomials as a product of linear factors;
8. be able to quantify the likelihood of some simple events, and calculate the expected value of some simple random variables;
9. be able to describe data using the notions of median, mode, percentile, mean, standard deviation; you will be able to make inferences based on the estimated mean and standard deviation of a population;
10. be able to explain the connection between differential and integral calculus using the Fundamental Theorem of Calculus, and you will be able to apply this connection to some practical scientific problems;
11. be able to evaluate definite and indefinite integrals using a variety of techniques;
12. be able to solve separable differential equations and apply this skill to study population models in biology and physics.

Indicative Content

1. Modular arithmetic, Euclidean algorithm, applications to ISBNs and cryptography Euler's Phi function, Fermat's little theorem (and its proof), application to public key cryptography, Chinese Remainder Theorem.
2. Matrix addition, multiplication, inversion, systems of equations, applications to resource allocation problems; linear transformations, applications to cryptography; Cross products, applications to geometry.
3. Calculation of eigenvalues, eigenvectors and matrix powers for $2\times2$ matrices, Hamilton-Cayley theorem (with proof for $2\times2$ matrices); proof by induction. Fibonacci sequence, golden ratio, applications to practical recurrence problems.
4. Definition of derivative and its physical interpretation; techniques of differentiation; differentiability implies continuity; Mean Value Theorem; roots of equations; detecting maxima/minima; monotonicity, concavity; application to graph sketching; optimisation problems.
5. Exponentials, logarithms and pH calculations; anti-derivatives; real-world problems involving anti-derivatives.
6. Cartesian and polar coordinates; geometric interpretation using Argand diagrams; roots of unity; roots of polynomials; complex conjugates.
7. Probability of events; conditional probability and independence of events; Bayes' Theorem; expected values.
8. Histograms; mode, median, mean, quartile; standard deviation. Population, samples and estimators; applications to practical problems in biology, chemistry and physics.
9. Definite integrals and the Fundamental Theorem of Calculus; applications of integration to real-world problems.
10. A range of techniques for calculating definite and indefinite integrals; further applications to real-world problems.
11. Separable differential equations; logistic equation; applications to radioactive decay and biological population models.

Module Resources

Calculus James Stewart Brooks Cole

MA190 Mathematics

Taught in Semester(s) I+II. Examined in Semester(s) I+II.

Workload: 96 hours (72 Lecture hours, 24 Tutorial hours).

Module Learning Outcomes. On successful completion of this module the learner should be able to:

1. use modular arithmetic and Euler's Phi function to detect errors in ISBNs, encipher messages using 1-dimensional affine and RSA cryptosystems, attack 1-dimensional affine cryptosystems, calculate with Chinese remainders. The student will also be able to present a proof of Fermat's little theorem;
2. use matrices to solve resource allocation problems, encipher messages using higher dimensional affine cryptosystems, attack higher dimensional affine cryptosystems, solve some geometric problems;
3. use eigenvalues, eigenvectors and the Principle of Induction to solve practical and theoretical problems about recurrence. The student will also be able to state the Hamilton-Cayley theorem and prove it in the 2x2 case;
4. sketch the graph of a number of basic functions; calculate the limit of a function at a point or at infinity; decide whether a given function has an inverse and, if it does, calculate it; use the Intermediate Value Theorem to find roots of equations;
5. apply the material learned to a variety of problems coming from Physics and Earth Sciences;
6. use the definition of derivative to compute the derivative of simple functions; apply different techniques of differentiation to calculate derivatives; apply the Mean Value Theorem to finding roots of equations; find maxima/minima/inflection points, and use these to sketch graphs of functions; apply differentiation techniques to solve optimisation problems arising from Business and Economics;
7. find the general solution of a number of basic separable differentiable equations;
8. solve basic word problems;
9. distinguish between finite, countably infinite and uncountable sets of real numbers, explain these distinctions and provide examples to support these explanations;
10. explain the meanings of the terms supremum and infimum, analyze boundedness properties of given sets and provide new examples of sets with prescribed properties;
11. explain the concept of convergence and its importance in mathematics, and discuss and relate various properties of sequences of real numbers;
12. determine with proof whether a given sequence of real numbers is convergent, and provide examples of sequences with certain specified properties;
13. explain the connection between differential and integral calculus using the Fundamental Theorem of Calculus;
14. evaluate definite and indefinite integrals using a variety of techniques;
15. communicate ideas in a precise and clear manner using the specialized language of written mathematics.

Indicative Content

1. Modular arithmetic, Euclidean algorithm, applications to ISBNs and cryptography Euler's Phi function, Fermat's little theorem (and its proof), application to public key cryptography, Chinese Remainder Theorem.
2. Matrix addition, multiplication, inversion, systems of equations, applications to resource allocation problems; linear transformations, applications to cryptography; Cross products, applications to geometry.
3. Calculation of eigenvalues, eigenvectors and matrix powers for 2x2 matrices, Hamilton-Cayley theorem (with proof for 2x2 matrices); proof by induction; Fibonacci sequence, golden ratio, applications to practical recurrence problems.
4. Basic functions and their graphs; inverse functions; limits; the intermediate value theorem; roots of equations.
5. Definition of derivative and its physical interpretation. Techniques of differentiation. Differentiability implies continuity (with proof). The Mean Value Theorem; roots of equations.
6. Detecting maxima/minima, monotonicity, concavity; application to graph sketching.
7. Optimisation word problems.
8. Exponentials and logarithms. Anti-derivatives and separable differential equations. World problems involving differential equations: radioactive decay, population models.
9. Bounded and unbounded sets. Finite and infinite sets. Different kinds of infinities. The order relation on the real numbers. Suprema and infima. The completeness property of the real numbers. Sequences of real numbers:convergence and divergence.
10. What is a sequence? Convergent and divergent sequences. Boundedness and monotonicity. The Mean Value Theorem and some applications.
11. Definite integrals and the Fundamental Theorem of Calculus. Techniques of Integration.

Module Resources

Calculus James Stewart Brooks Cole

PH150 Introduction to Physics

The aim of this module is to equip the learner with an overview of some of the basic rules of nature that physical systems follow. The student will learn how to express these rules in simple mathematical form and to apply these rules to solve simple problems. They will acquire transferable skills in numeracy and analysis.