Quantitative Methods

The purpose of the course is to thoroughly cover some basic quantitative methods considered essential for a specialized financial analyst today. The course develops topics in the fields of mathematics, statistics, and econometrics, which form the background of the quantitative tools of modern financial theory. All concepts, rules, axioms, and tools developed during the course are framed with suitable graphical representations, numerical examples, and computational sub-models to achieve as complete an understanding as possible.

The course will be conducted in four three-hour weekly lectures. The course's grading will be done through written exams on a day, time, and room that will be announced in due time.

The course structure per week is as follows:

Week 1: Linear Algebra

• Introduction to Linear Algebra, Matrix Operations
• Vector Spaces, Linear Transformations
• Determinants, Inverse Matrices
• Eigenvalues and Eigenvectors
• Review and Problem Solving

Week 2: Differential Calculus

• Introduction to Differential Calculus, Limits
• Derivatives and Differentiation Rules
• Applications of Derivatives (Tangent lines, Rates of Change)
• Maxima, Minima, and Inflection Points
• Review and Problem Solving

Week 3: Probabilities

• Introduction to Probability, Basic Probability Rules
• Conditional Probability and Independence
• Discrete Random Variables and Probability Distributions
• Continuous Random Variables and Probability Density Functions
• Review and Problem Solving

Week 4: Distributions & Statistics

• Introduction to Statistics, Descriptive Statistics
• Normal Distribution, Standard Normal Distribution
• Sampling Distributions, Central Limit Theorem
• Confidence Intervals, Hypothesis Testing
• Review and Problem Solving

The course material comes from the following books:

1. Aczel, A.D. and Sounderpandian J., (2002), Complete Business Statistics, McGraw–Hill/Irwin, 5th edition (ISBN 0-07-112290-7). Chapters 1-8
2. Newbold, P., Carlson W.L. and Thorne B.M., (2003), Statistics for Business and Economics, Prentice Hall, 5th edition (ISBN 0-13-029320-2). Chapters 1-9
3. Bergin, J., (2020), Mathematics for Economists, with applications, Gutenberg Publications, (ISBN 9789600121582). Chapters 1-3 and 5-12.
4. Hoy, M., Livernois, J., McKenna, C., Rees, R. and Stengos, T., (2011), Mathematics for Economics, The MIT Press, 3rd edition (ISBN 978-0-262-01507-3). Chapters 1-9 and 11-13.