MATHEMATICS

Credit Points

20

Course Coordinator

Dr L Iancu

Pre-requisites

SCE H or GCE A level in Mathematics. This course may not be included in a minimum curriculum with EG 1006.

Overview

Calculus enables changing situations and complicated averaging processes to be described in precise ways. It was once of the leading intellectual achievements of the late 17-th and early 18-th Century. Early applications were made to modeling planetary motion and to calculating tax payable on land. Now the ideas are used in broad areas of mathematics and science and parts of the commercial world. The course develops the basic ideas of the differential and integral calculus of a single variable and explains some of the ways they are applied.

Structure

12 week course - 4 lectures and 1 tutorial per week.

Assessment

1st Attempt: 1 two-hour written examination paper (70%) and in-course assessment (30%).

Resit: 1 two-hour written examination paper (maximum of 100% resit and 70% resit with 30% in-course assessment).

Credit Points

20

Course Coordinator

Dr J Grbic

Pre-requisites

S or GCSE or equivalent in Mathematics. This course is not open to students with the equivalent of a Higher in Mathematics at grade B or above.

Overview

This is a basic course aimed primarily at helping students achieve greater accuracy, speed and confidence in mathematics. It is suitable both for those who may need mathematics in future study and for students who want to improve their abilities without any intention of studying the subject beyond first year. The course is taught using the interactive computer software CALMAT, enabling students to work in their own way and time but with immediate feedback. Support from staff is available on a daily basis. There is a requirement to attend a single weekly test for continuous assessment. The topics covered include basic arithmetic and algebraic operations, linear and quadratic equations, logarithms and the interpretation of graphs. As a final topic, students choose either an introduction to the calculus or an introduction to the language of probability and statistics.

Structure

12 week course - one class meeting and three supervised computer classes per week.

Assessment

100% in-course assessment for students who perform sufficiently well in weekly computerised tests. Any student who fails to attain a pass by in-course assessment or who wishes to upgrade CAS mark obtained, can take the end of course computerised examination or its resits.

Credit Points

20

Course Coordinator

Professor M Weiss

Pre-requisites

SCE H or GCE A level in Mathematics.

Overview

The standard numbers and their properties underline most mathematics. To improve understanding and breadth of applications, we need to develop another number system (complex numbers) and techniques to handle rectangular blocks of numbers (matrices and vectors). One can add or subtract matrices of the same size and multiply them by a single number. One can sometimes multiply matrices together using what initially seems a very strange procedure and if a matrix is square, we can try and find another matrix, called an inverse, such that the product of the two gives a simple "identity" matrix. Matrices have many uses in mathematics and its applications and the reasons for the strange way in which matrices are multiplied and why one seeks an inverse are dictated by the applications. We need also to develop methods of solving equations in these contexts.

This course includes ideas from discrete mathematics, including the key concept of induction and some elementary probability theory.

Structure

12 week course - 4 lectures and 1 tutorial per week.

Assessment

1st Attempt: 1 two-hour written examination paper (70%) and in-course assessment (30%).

Resit: 1 two-hour written examination paper (maximum of 100% resit and 70% resit with 30% in-course assessment).

Credit Points

20

Course Coordinator

Dr S Theriault

Pre-requisites

MA 1004 or equivalent.

Overview

This course is the natural successor to 'Introductory Mathematics 1' (MA 1004). (It is an inappropriate course to follow on from MA 1002). The course emphasizes accuracy in performing calculations involving trigonometry, exponentials, techniques and application of differentiation and integration, vectors, complex numbers and matrices. The course is taught and examined using the CALMAT computer software.

Structure

12 week course: 1 class meeting and 3 computer classes per week.

Assessment

100% in-course assessment for students who perform sufficiently well in weekly computerised tests. Any students who fails to attain a pass by in-course assessment or who wishes to upgrade CAS mark obtained, can take the end of course computerised examination or its resits.

Credit Points

20

Course Coordinator

Professor G Hall

Pre-requisites

Maths Highers A or B.

Overview

Foundations of mathematics, including elementary set theory, Russell's paradox, logical argument and the important mathematical notation that goes with these topics.
Groups and symmetries and the idea of an axiomatic development of a topic in mathematics.
Elementary number theory, the division algorithm and the Chinese remainder theorem.
Elementary Astronomy, the seasons, solstices and equinoxes, latitude and longitude.
Elementary combinatories, permutations, combinations, partitions, Bell numbers, Fibonacci and Stirling numbers.
The role of mathematics in music, consonance, dissonance and the Western Scale.

Structure

3 one-hour lectures and 2 one-hour tutorials per week (to be arranged).

Assessment

1st Attempt: 1 two-hour written examinations (80%), in-course assessment (20%).

Resit: 1 two-hour written examination paper (maximum of 100% resit and 80% resit with 20% in-course assessment).

Credit Points

15

Course Coordinator

Professor D Benson

Pre-requisites

MA 1502 or, with the permission of the Head of Mathematical Sciences, MA 1504.

Overview

This course provides an introduction to algebraic structures and elementary number theory. The course includes a discussion of sets (notation, functions, maps, injections, surjections, bijections), countability of the rational numbers and uncountability of the real numbers, the integers and factorization (prime numbers, Euclidean algorithm, uniqueness of factorization), the integers ( mod n), equivalence relations, permutations, group axioms, the symmetric group, Lagrange's theorem, definition of communtative ring and of a field with examples, vector spaces and linear transformations.

Structure

3 one-hour lectures and 1 tutorial per week (to be arranged).

Assessment

1st Attempt: 1 two-hour written examination (80%); continuous assessment (20%).

Resit: 1 two-hour written examination paper (maximum of 100% resit and 80% resit with 20% in-course assessment).

Credit Points

15

Course Coordinator

Professor M Geck

Pre-requisites

MA 1002 or, with the permission of the Head of Mathematical Sciences, both MA 1004 and MA 1504. This course may not be included in a minimum curriculum with EG 2010.

Overview

This course aims to put on a sound footing many of the results and procedures used in the Calculus. It will include a discussion of fundamental properties of real numbers, sequences and limits, functions of one real variable (basic examples, continuity and differentiability), some applications (eg approximation by Taylor polynomials), integration of functions of one real variable, the "Fundamental Theorem of Calculus" and further applications (for example to are lengths of curves in the plane).

Structure

3 one-hour lectures and 1 one-hour tutorial per week (to be arranged).

Assessment

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%).

Resit: 1 two-hour written examination paper (maximum of 100% resit and 80% resit with 20% in-course assessment).

Credit Points

15

Course Coordinator

Dr A Libman

Pre-requisites

MA 1002, MA 1502

Co-requisites

To provide an introduction to the mathematical framework needed to handle events involving a certain degree of randomness. Applications range from game theory to financial mathematics.

Overview

The course provides the mathematical framework needed to model unpredictable events. Topics discussed include: motivating examples; probability space; discrete probability; combinatorics; generating functions; discrete distributions; branching processes; random walks; Markov chains.

Structure

2 one-hour lectures and 1 one-hour tutorial per week.

Assessment

1st Attempt: 1 two-hour written examination (80%), continuous assessment (20%).

Resit: 1 two-hour written examination paper (maximum of 100% resit and 80% resit with 20% in-course assessment).

Credit Points

15

Course Coordinator

Dr L Iancu

Pre-requisites

MA 1502 or, with permission of the Head of Mathematical Sciences, MA 1504.

Overview

The course provides an introduction to linear algebra. Topics discussed include solving systems of linear equations. Vector spaces over a field. Eigenvalues, eigenvectors and diagonalisation, bilinear forms and scalar products.

Structure

3 one-hour lectures and 1 one-hour tutorial per week (to be arranged).

Assessment

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%).

Resit: 1 two-hour written examination paper (maximum of 100% resit and 80% resit with 20% in-course assessment).

Credit Points

15

Course Coordinator

Professor R J Archbold

Pre-requisites

MA 2005

Overview

The course is concerned with the analysis of functions of several variables. Topics discussed include partial differentiation and its applications, multiple integration and an introduction to the theory of ordinary differential equations.

Structure

3 one-hour lectures, 1 one-hour tutorial per week and 4 one-hour practicals (to be arranged).

Assessment

1st Attempt: 1 two-hour written exmination (80%); continuous assessment (20%).

Resit: 1 two-hour written examination paper (maximum of 100% resit and 80% resit with 20% in-course assessment).