Unit information: Intermediate Mathematical Methods for Economics and Data Science in 2030/31

Unit name	Intermediate Mathematical Methods for Economics and Data Science
Unit code	ECON20010
Credit points	20
Level of study	I/5
Teaching block(s)	Teaching Block 1 (weeks 1 - 12)
Unit director	Dr. Spini
Open unit status	Not open
Units you must take before you take this one (pre-requisite units)	EFIM10023 Mathematics for Economics ECON10006 Statistical Methods
Units you must take alongside this one (co-requisite units)	None
Units you may not take alongside this one	None
School/department	School of Economics
Faculty	Faculty of Social Sciences and Law

Unit Information

Why is this unit important?

This unit provides essential mathematical foundations for studying Economics and Data Science, integrating linear algebra, calculus, and computational methods. It will equip you with skills in matrix algebra, optimization techniques, and regression analysis, which are crucial for econometrics, statistical modelling, and machine learning. The inclusion of Python programming ensures that you will develop computational skills applicable to data-driven economic research and predictive analytics

How does this unit fit into your programme of study.

This unit serves as a bridge between foundational mathematics and advanced coursework in econometrics, data science, and applied machine learning, preparing students for statistical modelling, empirical research, and quantitative policy evaluation in later years.

Your learning on this unit

Overview of the content

This unit will introduce you to advanced topics in linear algebra and multivariable calculus, with applications in econometrics, optimization, and data science. The emphasis is on computational methods and their practical application in economic modelling, statistical estimation, and preparation for optional units in machine learning. The course integrates Python programming for numerical computations, matrix operations, and regression analysis.

Topics include:

• Linear Algebra: Matrices, determinants, eigenvalues, singular value decomposition (SVD)
• Systems of Equations: Gaussian elimination, least squares estimation
• Vector Spaces: Basis, rank, and linear independence
• Optimization: Linear programming, Gradient descent, Hessian matrices, and constrained optimization (Lagrange multipliers)
• Multivariable Calculus: Partial derivatives, Jacobians, and total differentials
• Applications: Regression models, Markov chains, principal component analysis (PCA)

How will students, personally, be different as a result of the unit?

You will develop the key skills of linear algebra that is essential for modern econometrics and data science, and will develop confidence in applying these techniques.

Learning Outcomes:

By the end of this unit, you will be able to:

1. Evaluate statistical and econometric problems using linear algebra techniques
2. Apply mathematical techniques to solving constrained and unconstrained multivariate optimisation problems
3. Apply and evaluate statistical models
4. Demonstrate an understanding of, and be able to apply programming tools for linear algebra and calculus.

How you will learn

Teaching will be delivered through a combination of large and small group classes, supported by online resources

How you will be assessed

Tasks which help you learn and prepare you for summative tasks:

• Weekly problem sets covering algebraic and calculus-based exercises.
• Computer lab exercises to practice optimization and numerical linear algebra.
• Group discussions on mathematical applications in econometrics.

Tasks which count towards your unit mark (summative):

• Portfolio of computer lab tasks: (50%)
• Exam (90 minutes): (50%)

Each element assesses all learning outcomes

When assessment does not go to plan

If students fail the unit such that credit points cannot be awarded at the first attempt, they will normally be provided reassessment in the failed element(s).

The reassessment tasks will be:

• Portfolio of computer lab tasks: (50%)
• Exam (90 minutes): (50%)

Each element assesses all learning outcomes

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. ECON20010).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the University Workload statement relating to this unit for more information.

Assessment
The assessment methods listed in this unit specification are designed to enable students to demonstrate the named learning outcomes (LOs). Where a disability prevents a student from undertaking a specific method of assessment, schools will make reasonable adjustments to support a student to demonstrate the LO by an alternative method or with additional resources.

The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates within the Regulations and Code of Practice for Taught Programmes.