Partial Differential Equations

An introduction to the methods of solution for partial differential equations and to their applications.

15 points

(MATH201 and MATH202) or EMTH210

MATH361, EMTH391, EMTH413

Discrete Mathematics

Discrete mathematics underpins many areas of modern-day science. In MATH320, we explore selected topics in discrete mathematics in greater depth and detail. In particular, we investigate some technical methods that allow for elegant solutions to more advanced enumeration questions, and explore the structural properties of directed graphs and partially-ordered sets (posets). Topics covered: Term 1: Combinatorial enumeration: Binomial identities and direct enumeration. Principle of Inclusion and Exclusion; Generating functions (ordinary and exponential). Lagrange inversion and applications. Term 2: Directed graphs and posets: Basic Ramsey theory, theory of directed graphs (structural results, algorithms, algebraic methods, phase transitions) and partially-ordered sets (Möbius inversion, Dilworth Theorem).

15 points

30 points from MATH201, MATH202, MATH203, MATH220, MATH240, EMTH210, EMTH211.

Rings and Fields

An introduction to fields and rings, including applications to coding theory and the impossibility of constructions such as ‘squaring the circle’.

15 points

One of MATH203, MATH220, MATH240, or EMTH211, and a further 15 points from MATH201-294.

MATH439, MATH311

Metric, Normed and Hilbert Spaces

An introduction to those parts of modern analysis essential for many aspects of pure and applied mathematics, physics, economics and finance.

15 points

30 points from MATH201, MATH202, MATH203, MATH240, MATH270, EMTH210, EMTH211 or EMTH271.

Computational Mathematics and Applications

This course looks at a variety of methods for solving important computational problems that arise in science, engineering and commerce. In addition to applications, we will look at the methods' basic theoretical properties (stability, accuracy, computational complexity, convergence). During the course, you will learn about the performance of the methods through examples and counterexamples that highlight their pros and cons.

15 points

1) Either MATH201 or EMTH210; AND 2) One of MATH202, MATH203, MATH240, MATH270, EMTH211 or EMTH271. With the permission of the Head of School a high grade in either MATH201 or EMTH210 will suffice.

EMTH414

Special Topic

This special topic will allow flexibility to offer new or one-off courses of strategic importance to the Department. Its potential uses include: new staff developing a course in their areas of research specialisation; visiting Erskine fellows offering courses covering exciting new developments.

15 points

Subject to the approval of the Head of School.

Independent Course of Study

15 points

Subject to approval of the Head of School.

Applied Matrix Algebra

A continuation of 200-level linear algebra with computational and theoretical aspects and applications.

15 points

One of MATH203, EMTH211, or DATA203

MATH352, EMTH412

Cryptography and Coding Theory

This course deals with the mathematical ideas underlying modern cryptography, including algebra, number theory and probability theory.

15 points

ONE of MATH203, DATA203 or EMTH211, and ONE of MATH120, MATH220, MATH240

MATH391

Dynamical Systems

An introduction to nonlinear systems, the use of linearisation techniques and bifurcation theory.

15 points

MATH201 or EMTH210 and a further 15 points from (EMTH211, EMTH271, MATH202, MATH203, MATH240, MATH270).

EMTH415

Applications of Complex Variables

Applications of complex variable theory in the physical and engineering sciences. Contour integration. Conformal mappings.

15 points

MATH201 or MATH240; or, a high level of achievement in EMTH210 with Head of School approval

MATH342

Mathematics in Perspective

Topics in the history, philosophy, directions and culture of mathematics including significant results from the past and an outline of some major areas of progress in the 20th century.

15 points

30 points in Mathematics or Statistics or Engineering Mathematics at 100 level. 45 points from the BA or BSc Schedule at 200 level in Mathematics, Statistics, Engineering Mathematics, related subjects, or other subjects with good grades, as approved by the Head of School.

MATH301, MATH433, HAPS405

Special Topic

This special topic will allow flexibility to offer new or one-off courses of strategic importance to the Department. Its potential uses include: new staff developing a course in their areas of research specialisation; visiting Erskine fellows offering courses covering exciting new developments.

15 points

Subject to the approval of the Head of School.

Independent Course of Study

15 points

Subject to the approval of the Head of School.

Mathematics Project

This 150 hour course provides students with an opportunity to develop mathematical research skills to extend and strengthen their understanding of an area of mathematics. Note: This course cannot be included as part of the 300 level requirement for a Mathematics or Statistics major.

15 points

Subject to approval of the Head of School

MATH305