MATHEMATICS

Credit Points

15

Course Coordinator

Professor M Linckelmann

Pre-requisites

SCE H or GCE A level in Mathematics. This course may not be included in a minimum curriculum with EG 1503.

Notes

The course starts from the beginning of the subject, but it is advantageous to be familiar with the material on Calculus contained in the Scottish Highers syllabus.

Overview

Calculus allows for changing situations and complicated averaging processes to be described in precise ways. It was one of the great 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 begins with an introduction to fundamental mathematical concepts and then develops the basic ideas of the differential calculus of a single variable and explains some of the ways they are applied.

Structure

3 one-hour lectures and 1 one-hour tutorial per week; support tutorials to be arranged by the Course Coordinator, as need arises.

Assessment

1st Attempt: 1 two-hour written examination (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).

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinator for feedback on the final examination.

Credit Points

15

Course Coordinator

Dr J Kedra

Pre-requisites

SCE H or GCE A level in Mathematics.

Overview

The basic course includes a discussion of the following topics: complex numbers and the theory of polynomial equations, vector algebra in two and three dimensions, systems of linear equations and their solution, matrices and determinants.

Structure

3 one-hour lectures and 1 one-hour tutorial per week. Support tutorials to be arranged by the Course Coordinator, as need arises.

Assessment

1st Attempt: 1 two-hour written examination (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).

Formative Assessment

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact the Course Coordinator for feedback on the final examination.

Feedback

In-course assessment will be marked and feedback provided to the students.

Support tutorials to be arranged by the Course Coordinator, as need arises.

Credit Points

15

Course Coordinator

Dr S Theriault

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, and an introduction to the calculus.

Structure

1 one-hour lecture and 2 one-hour supervised computer classes per week.

Assessment

1st Attempt: In-course assessment (100%) for students who perform sufficiently well in weekly computerised tests. Any student who fails to achieve by in-course assessment or who wishes to upgrade CAS mark obtained, can take the end of course computerised examination or its resit.

Resit: Computerised examination similar to 1st attempt examination.

Formative Assessment

Regular computerised tests discussed during computer practicals.

Feedback

In-course assessment will be marked and feedback provided to the students.

Informal feedback at computer practicals.

Credit Points

15

Course Coordinator

Professor G Hall

Pre-requisites

SCE H at grades A or B or equivalent in Mathematics.

Overview

Various topics in mathematics and its applications are introduced. Topics such as the foundations of mathematics, groups and symmetries, elementary number theory, applications to astronomy, combinatorics, conic sections and the role of mathematics in music will be discussed.

Structure

3 one-hour lectures, 1 one-hour tutorial/discussion group per week.

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).

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials.

Credit Points

15

Course Coordinator

Professor V Gorbounov

Pre-requisites

MA 1007 or equivalent.

Overview

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

1 one-hour lecture and 2 one-hour supervised computer classes per week.

Assessment

1st Attempt: In-course assessment (100%) for students who perform sufficiently well in weekly computerised tests. Any student who fails to achieve by in-course assessment or who wishes to upgrade CAS mark obtained, can take the end of course computerised examination or its resit.

Resit: Computerised examination similar to 1st attempt examination.

Formative Assessment

Regular computerised tests discussed during computer practicals.

Feedback

In-course assessment will be marked and feedback provided to the students.

Informal feedback at computer practicals.

Credit Points

15

Course Coordinator

Dr W Turner

Pre-requisites

SCE H or GCE A level in Mathematics; MA 1005 (recommended). This course may not be included in a minimum curriculum with EG 1503.

Overview

The course is a continuation of Calculus I from the 1st session. It develops the basic ideas concerning the integration of a function of one variable. It introduces Taylor series and determines these series for the most common functions. It also provides a first introduction to differential equations which are fundamental in applications of Mathematics to other sciences.

Structure

3 one-hour lectures and 1 one-hour tutorial per week. Support tutorials to be arranged by the Course Coordinator, as need arises.

Assessment

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

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

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact the Course Coordinator for feedback on the final examination.

Credit Points

15

Course Coordinator

Professor D Benson

Pre-requisites

MA 1502 or, with the permission of the Head of Teaching, 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 commutative ring and of a field with examples, vector spaces and linear transformations.

Structure

12 week course - 3 one-hour lectures and 1 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 M Weiss

Pre-requisites

MA 1002 or, with the permission of the Head of Teaching, both MA 1004 and MA 1504.

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 lengths of curves in the plane).

Structure

12 week course - 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 2004, MA 2005

Overview

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

Structure

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

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 R Kessar

Pre-requisites

MA 1502 and MA 2004 or, with permission of the Head of Teaching, MA 1504 and MA 2004.

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

12 week course - 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 M Geck

Pre-requisites

MA 2005

Overview

The course is mainly 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. There is also a self-paced introduction to the computer algebra package Maple.

Structure

12 week course - 3 one-hour lectures per week, 1 one-hour tutorial per week and 4 one-hour practicals over 12 weeks.

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).