Further mathematics for economists

Описание мероприятия

Для кого эта программа

The course is designed to:

• enable students to acquire skills in further methods of calculus and linear algebra, as required for their use in advanced economics-based subjects
• enable students to understand the underlying theory behind these techniques and those of more basic mathematics courses (such as 05a Mathematics 1 and 05b Mathematics 2)
• prepare students for advanced study in theoretical aspects of economics-based subjects.

Описание программы

This course provides students with the mathematical techniques and methods which find application in economics and related areas, and enables students to understand why, and in what circumstances, these techniques work.

Assessment

This course is assessed by a three-hour unseen written examination.

Учебный план:

Linear algebra: Vector spaces, linear independence and dependence, bases and dimension, rank and nullity of a matrix. Linear mappings, their rank and nullity, their matrix representation, and change of basis. Eigenvalues and eigenvectors. Diagonalisation of matrices, with applications to systems of difference and differential equations (including stability). Quadratic forms and orthogonal diagonalisation. Inner product spaces, norms, orthogonality and orthonormalisation.

Functions and mathematical analysis: Sets and functions. Supremum and infinum of bounded sets. Limits of sequences in R and Rm . Limits and continuity of functions. Open subsets and closed subsets of Rm . Compact subsets of R m . Convex sets, convex and concave funstions. Gradients and directional derivatives. The Jacobian derivative. The Edgeworth Box and contract curves.

Optimisation: Inconstrained optimisation and the second-order conditions. Constrained optimisation and the Kuhn-Tucker theorem. Envelope Theorems. Theory of linear programming (computational methods will not be included). Duality, with applications. Basic Game Theory.

Результат обучения:

At the end of this course and having completed the essential reading and activities students should be able to:

• use the concepts, terminology, methods and conventions covered in the unit to solve mathematical problems in this subject.
• demonstrate an understanding of the underlying principles of the subject.
• solve unseen mathematical problems
• involving understanding of these concepts and application of these methods.
• prove statements and to formulate precise mathematical arguments.

Требования к поступающим:

If taken as part of a BSc degree, courses which must be passed before this course may be attempted:

• MT1174 Calculus or both
• MT105a Mathematics 1 and 05b
• Mathematics 2

Exclusion

This course may not be taken with:

• MT2116 Abstract mathematics
• MT2176 Further calculus
• MT2175 Further linear algebra