Maths for Economists



Overview

Mathematics plays a central role in the formulation and analysis of modern economic theory. This course offers students an accessible and structured introduction to the essential mathematical techniques used in economic analysis. Topics covered include algebra, equations, logarithmic and exponential functions, calculus, optimisation, integration, and matrix algebra. Throughout the course, emphasis is placed on applying these methods to real-world economic problems such as utility maximisation, cost minimisation, equilibrium analysis, and economic growth models.

Designed for first-year undergraduate or equivalent students, the course is particularly suited to those pursuing economics, politics, or social science subjects who want to strengthen their mathematical foundations. The course adopts a hands-on approach, incorporating weekly tutorials, problem-solving exercises, and online quizzes to reinforce learning.

Programme details

Courses starts: 30 Sept 2025

The course will be delivered over ten weeks in Michaelmas Term 2025, with each week consisting of a one-hour lecture followed by a one-hour tutorial. Students will work through core topics drawn from the recommended textbook Mathematics for Economics and Business by Ian Jacques (9th edition), supported by regular practice problems and weekly quizzes.

Week 1: Review of Basic Mathematical Concepts
Topics: Fractions, powers, roots, order of operations, and manipulation of algebraic expressions.
Economic Application: Lays the foundation for interpreting and manipulating basic economic formulas, such as elasticity and index numbers.

Week 2: Linear and Quadratic Equations
Topics: Solving and graphing linear and quadratic equations, completing the square, discriminant analysis.
Economic Application: Used to model cost, revenue, and profit functions; helps identify break-even points and analyze market scenarios with non-linear dynamics.

Week 3: Simultaneous Equations
Topics: Solving linear systems using substitution, elimination, and matrix methods.
Economic Application: Core to solving supply-demand equilibrium, input-output models, and price-setting in competitive markets.

Week 4: Exponential and Logarithmic Functions
Topics: Properties, transformations, natural logarithms, and inverse functions.
Economic Application: Models compound interest, economic growth, inflation, and depreciation; key for understanding time value of money and utility functions.

Week 5: Introduction to Differentiation
Topics: First principles, rules of differentiation (product, quotient, chain), tangent lines, and rates of change.
Economic Application: Crucial for marginal analysis—examining marginal cost, marginal revenue, and optimizing firm behavior.

Week 6: Higher-Order Derivatives and Optimisation
Topics: Second and higher-order derivatives, concavity, inflection points, and local optimization.
Economic Application: Identifying profit-maximizing output levels and cost-minimizing input combinations using second derivative tests.

Week 7: Multivariable Functions and Partial Derivatives
Topics: Functions of several variables, partial derivatives, cross-partials, and gradient interpretation.
Economic Application: Applied to utility maximization, cost functions, production functions, and marginal rate of substitution.

Week 8: Unconstrained Optimisation
Topics: Critical points in multivariable functions, Hessian matrix, and second-order conditions.
Economic Application: Optimization of multivariable economic models such as firm output with multiple inputs or utility with multiple goods.

Week 9: Integration and Economic Applications
Topics: Indefinite and definite integrals, integration by substitution, area under curves.
Economic Application: Calculation of consumer and producer surplus, aggregate demand, and total cost/revenue functions.

Week 10: Matrix Algebra and Economic Modelling
Topics: Matrix operations, inverses, determinants, solving systems with matrices.
Economic Application: Matrix algebra is used in input-output models, which show how different industries depend on each other for inputs. A key example is the Leontief Model, which represents the flow of goods between sectors in an economy to help analyse the impact of changes in one sector on the others. It's widely used in national economic planning and forecasting.

 

Certification

Credit Accumulation Transfer Scheme (CATS) Points

Only those who have registered for assessment and accreditation will be awarded CATS points for completing work to the required standard. Please note that assignments are not graded but are marked either pass or fail. Please follow this link for more information on Credit Accumulation Transfer Scheme (CATS) points

Digital Certificate of Completion 

Students who are registered for assessment and accreditation and pass their final assignment will also be eligible for a digital Certificate of Completion. Information on how to access the digital certificate will be emailed to you after the end of the course. The certificate will show your name, the course title and the dates of the course attended. You will be able to download the certificate and share it on social media if you choose to do so.

Please note students who do not register for assessment and accreditation during the enrolment process will not be able to do so after the course has begun.

Fees

Description Costs
Course fee (with no assessment) £300.00
Assessment and Accreditation fee £60.00

Funding

If you are in receipt of a UK state benefit, you are a full-time student in the UK or a student on a low income, you may be eligible for a reduction of 50% of tuition fees. Please see the below link for full details:

Concessionary fees for short courses

Tutor

Dr Sangaralingam Ramesh

Sangaralingam Ramesh is an Economics Tutor in the Department for Continuing Education at the University of Oxford and a Senior Teaching Fellow in Economics at University College London, UK. He has been an Associate Professor in Economics at the Université Paris Dauphine GBD and Economics Module Leader at Kings College London

Course aims

To introduce students to key mathematical techniques essential for understanding and applying economic theory at an intermediate undergraduate level. The course supports students in developing the analytical tools required for modules in microeconomics, econometrics, and related fields.

Course objectives

By the end of the course, students will be able to:

  • Solve linear, non-linear, and simultaneous equations relevant to economic problems.

  • Understand and apply exponential and logarithmic functions to model economic growth and decay.

  • Use differentiation and partial differentiation in the analysis of economic functions including those found in consumer and firm theory.

  • Solve unconstrained and constrained optimisation problems, particularly in applications such as profit maximisation and utility maximisation.

  • Apply matrix algebra and basic integration techniques to economic scenarios such as surplus analysis and equilibrium.

  • Translate real-world economic issues into mathematical models and interpret mathematical results in an economic context.

Teaching methods

The course will be taught over ten weeks in Michaelmas Term 2025 via a weekly one-hour lecture and one-hour tutorial. Lectures will introduce key mathematical concepts with economic relevance, and tutorials will provide structured opportunities for guided problem-solving, discussion, and clarification of concepts. Supplementary learning is provided through weekly Moodle-based quizzes and online resources. The learning experience is designed to be interactive, practical, and grounded in economic application.

Learning outcomes

By the end of the course, students will be able to:

  • Demonstrate proficiency in algebraic techniques including solving and interpreting equations and graphical analysis.

  • Apply exponential and logarithmic functions to economic growth and finance-related problems.

  • Differentiate single-variable and multivariable functions with direct application to economic models.

  • Identify and solve optimization problems using both unconstrained and constrained approaches.

  • Perform integration and apply matrix algebra in economic contexts such as cost analysis and surplus calculation.

  • Develop confidence in using mathematical tools in economic reasoning and further study.

Assessment methods

Students registered for assessment will complete the following:

  • Formative assessment: A problem set comprising 5 questions based on material from Weeks 1–4. This is intended to help students consolidate early learning and prepare effectively for the summative assessment.
  • Summative assessment: A problem set comprising 10 numerical problems covering material from Weeks 5–10.

Only those students who have registered for assessment and accreditation will submit coursework.

 

Application

To be able to submit coursework and to earn credit (CATS points) for your course you will need to register and pay an additional £60 fee per course. You can do this by ticking the relevant box at the bottom of the enrolment form or when enrolling online. Please use the 'Book now' button on this page. Alternatively, please complete an enrolment form (Word) or enrolment form (Pdf).

Students who do not register for assessment and credit during the enrolment process will not be able to do so after the course has begun. If you are enrolled on the Certificate of Higher Education you need to indicate this on the enrolment form but there is no additional registration fee.

Level and demands

The Department's Weekly Classes are taught at FHEQ Level 4, i.e. first year undergraduate level, and you will be expected to engage in a significant amount of private study in preparation for the classes. This may take the form, for instance, of reading and analysing set texts, responding to questions or tasks, or preparing work to present in class.

Terms & conditions for applicants and students

Information on financial support