## Trinity College Dublin, The University of Dublin

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# Mathematics and Statistics

## Module Code: EC1030

### Module Name: Mathematics and Statistics

• ECTS Weighting: 10
• Semester/Term Taught: Michaelmas + Hilary Term
• Contact Hours: 44 hours of lectures and 20 hours of tutorials
• Lecturers : Lecturers – Professor Martina Kirchberger (MT) / Professor Alejandra Ramos (HT)

### Module Learning Aims

The modern practice of business, economics, and the social sciences requires at least a minimum knowledge of certain mathematical and statistical tools. In the study of statistics we ask the following question: how can we summarize data in a consistent way, so as to draw conclusions from them that can be used in decision-making. Many statistical methods use a particular field of mathematics called Probability Theory, which will be studied in some detail. In addition, statistics uses the same form of logical rigor as mathematics.

The academic literature in fields like finance and economics, in particular, has become highly mathematical over the past decades. But also business people, economic advisors, policy makers, journalists, etc., even if they do not actively use mathematics and statistics (although many of them do), are confronted with analyses that use the language of mathematics and statistics. In mathematics, as applied to business, economics, and the social sciences, we mainly ask questions like: how can we model and analyse individuals' decisions? How do these change if the environment changes?

### Module Content

Mathematics topics discussed during Michaelmas Term are:

• Indices and logarithms;
• Matrices;
• Differentiation;
• Optimisation of functions of one variable;
• Partial differentiation;
• Constrained and unconstrained optimisation of functions of several variables;
• Basic integration.

Statistics topics discussed during Hilary term are:

• Graphical and numerical data description;
• Probability theory;
• Discrete and continuous random variables;
• Sampling distributions of the (sample) mean and proportion;
• Confidence intervals for the (population) mean and proportion;
• Hypothesis tests for the (population) mean and proportion.

### Learning Outcomes

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

• Explain and apply mathematical and statistical terminology;
• Formulate simple problems in the language and abstractions of mathematics and statistics;
• Solve simple problems related to the topics in the module;
• Report the results of simple problems to others in clear, concise, and correct English.

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;
• Explaining quantitative reasoning in clear, concise, and correct English.

### Recommended Texts

Mathematics
Ian Jacques, Mathematics for Economics and Business, Pearson, 8th Edition. ISBN 9781292074337

This textbook comes with the MyMathLab online resource that will be used throughout this module. If you do not intend on purchasing the text book you can chose to purchase MyMathLab plus etext or simply the MyMathLab online resource. Please see mymathlab.com/global for more details. At least one of the above must be purchased by students as all continuous assessment for the course is conducted through this online resource. More information will be given at the first lecture.

Statistics
Jaggia and Kelly Business Statistics: Communicating with Numbers McGraw Hill, 2013 International Edition. ISBN: 9780077142346

This textbook comes with the McGraw Hill Connect online resource that will be used throughout this module. If you do not intend on purchasing the text book you can chose to purchase the McGraw Hill Connect online resource. To register with code from textbook or purchase online access please visit http://connect.mcgraw-hill.com/class/ec1030stats2013. As all continuous assessment for the course is conducted through this online resource, students are required to purchase access to the McGraw Hill Connect resource. More information will be given at the first lecture.

### Assessment Details

Michaelmas Term:
Midterm test in week 8 accounting for 5% of the overall grade, homeworks due periodically accounting for 15% of the overall grade.

Hilary Term:
Midterm test in week 8 accounting for 5% of the overall grade, homeworks due periodically accounting for 15% of the overall grade

Annual Exam: