## Trinity College Dublin, The University of Dublin

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# Mathematical and Statistical Methods

## Module Code: EC2040

### Module Title: Mathematical and Statistical Methods

(NB Students may take only one of EC2040 and ST2930)

• ECTS Weighting: 10
• Semester/Term Taught: Michaelmas + Hilary Term
• Contact Hours: 44 hours of lectures and 20 hours of tutorials
• Module Personnel: Lecturer - Professor Andrea Guariso / Lecturer - Professor Michael Wycherley

### Module Learning Aims

The first half of the module will develop the calculus (differentiation and integration) from the JF Maths module, with increased depth of coverage and further applications. The aim of the module is to consolidate and develop skills developed in JF Mathematics so as to provide a solid basis for any calculus you might meet in the Sophister years.

The second half of the module provides a broad, practically oriented introduction to inferential statistics of the kind used across the range of social science disciplines. It builds on the material on descriptive statistics and probability covered in the Introduction to Statistics module students will have taken in the JF year.

### Learning Outcomes

Having successfully completed this module, you will be able to:

• Explain and apply mathematical and statistical terminology.
• Solve problems related to statistical inference, mathematical optimization and applications.
• Formulate economic problems in the language and abstractions of mathematics and statistics.

Satisfactory completion of this module will contribute to the development of the following key skills:

• Abstraction from concrete problems to generic concepts.
• Problem-solving using quantitative methods.
• Ability to perform simple statistical analysis.

### Module Content

#### Mathematics

• Analysis of convexity and concavity.
• Optimisation of multivariate functions.
• Constrained optimisation.
• Integration.
• Applications in consumer theory, producer theory, labor supply and macroeconomics.

#### Statistics

• Construction of confidence intervals for estimators.
• Hypothesis testing.
• Analysis of variance.
• Simple linear regression.

### Recommended Reading List

Mathematics: Alpha C. Chiang and Kevin Wainwright, Fundamental Methods of Mathematical Economics, McGraw-Hill, 4th Edition, 2005.

Statistics: Jaggia and Kelly, Business Statistics: Communicating with Numbers, McGraw Hill.

### Assessment Details

#### Michaelmas Term:

Weekly problem sets worth 10% of the overall grade and a take home test worth 10% of the overall grade.

#### Hilary Term:

Weekly problem sets worth 10% of the overall grade and a take home test worth 10% of the overall grade. Late submissions that have not been agreed in writing beforehand will be penalised 10% per day.

#### Annual Exam:

60% of the overall grade

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