BA Modern Language and Business & Management (Russian)

This unit provides students with the essential mathematical toolkit required by economics students. At the core of the unit are constrained, multivariate optimisation problems. Such problems form a core element of many economics units and students who took Advanced Mathematics will be familiar with the required solution techniques.

Students will also be introduced to the principles of matrix algebra, and of modelling dynamic variables.

Students will be provided with detailed material through lectures, tutorial, reading and online videos. A discussion board will allow students to receive frequent feedback on their understanding.

A Level Maths or very good AS level

The aim of this course is to introduce mathematical techniques useful in the economic and social sciences to those students who have the appropriate mathematical background.

The objectives of this course are that students will be able to:

1. Solve simple linear equations, find roots a quadratic equations and understand the solution to non-linear equations.
2. Understand functions, continuity and basic differentiation.
3. Solve one and two-variable unconstrained and constrained optimisation problems using the Lagrangian method.
4. Demonstrate their understanding of linear univariate difference equations.

Provisional

The preliminary syllabus is

• Preliminaries and Pre-requisites. A review of your mathematical background and some observations on logic
• Functions & Univariate Calculus. Functions, continuity. Roots of equations. Limits and basic differentiation. Stationary points and optimisation. Concavity and convexity.
• Vectors and Matrices. An introduction to vectors and matrices: their mathematical manipulation - addition, multiplication. Inverse matrix. Determinants. Rank. Quadratic Forms.
• Bivariate Functions
  Surfaces in 3D, contours. Partial functions and partial differentiation: the Jacobian and Hessian. Optimisation; saddle points. Concavity/convexity. Finding maxima/minima of functions of two variables subject constraints; e.g., maximising utility subject to a budget constraint.
• Dynamics. Simple dynamics. Geometric Series. Linear difference equations

Synchronous activities (such as Lectures or Review and Q&A sessions, and tutorials), and guided self-study

30% Mid-Term Online Tests

70% Final Exam

• Mock exam.
• Online quizzes.
• Tutorial feedback.
• PASS sessions.
• Office hours.
• Discussion boards.

Recommended reading  

Detailed prescribed reading is provided on the BLACKBOARD site. The ESSENTIAL TEXT is:  

Essential Mathematics for Economic Analysis (3rd Edition), by Knut Sydsæter and Peter Hammond  

Further Mathematics for Economic Analysis (2nd Edition), by Knut Sydsæter, Peter Hammond, Atle Seierstad and Arne StrØm  

This text will be available as a free online textbook from the unit's Blackboard page.  

For every 10 course unit credits we expect students to work for around 100 hours. This time generally includes any contact times (online or face to face, recorded and live), but also independent study, work for coursework, and group work. This amount is only a guidance and individual study time will vary