MSc Economics

Foundations of Mathematics

Winter Semester 2024/25

On this page you find information and course materials for Foundations of Mathematics.

Learning Outcomes

In this course you will gain or deepen your knowledge of mathematical methods that are obligatory to the understanding of economic literature. You then are able to understand and apply the formal methods required in microeconomics and macroeconomics. For various reasons (e.g., different syllabi in Bachelor programs) the prior knowledge in mathematical methods varies considerably among students of the master program "Economics". Depending on your prior knowledge the presented material may be quite new for you. So the course gives you the opportunity to learn all that methods. It also may happen that you are already are familiar with the presented matter. Then we hope that the course offers you some new points of view to these mathematical concepts and methods.

Topics:

• Linear Algebra
• Linear equation and Gaussian elimination
• Matrix and vector
• Vector space, linear dependency and rank
• Determinant and Cramer's rule
• Eigenvalues and vectors
• Analysis
• Limit and continuity
• Derivative and total differential
• Integration
• Taylor series
• Multivariate Function
• Gradient, directional derivative, Jacobian matrix and Hessian matrix
• Static Optimization
• Convex set
• Convex, concave and quasi-concave function
• Local and global extremum
• Constraint optimization
• Lagrange function
• Kuhn-Tucker conditions
• Dynamic analysis
• Differential equations
• Control theory and Hamiltonian
• Difference equations

Prerequisites

Prior knowledge about fundamental concepts and tools (like terms, sets, equations, sequences, limits, univariate functions, derivatives, integration) is obligatory for this course. These are (should have been) already known from high school and mathematical courses in your Bachelor program. For the case of knowledge gaps we offer the Bridging Course Mathematics to close possible knowledge gaps. course materials are available from the web page of this course.

The methods repeated in the Bridging Course Mathematics are relevant for the the final exam as you cannot solve the problems with knowledge of basic techniques like differentiation and integration of functions or solving equations.

Course Organization

The course instructor will present new mathematical concepts and methods and presents example problems with detailed solutions. Students will prepare solutions to homework problems that will be discussed during the next unit of the course.

Course Materials

• Homework problems (for one-sided printing  |  for two-sided printing  |  e-book)   
• Handouts for slides
• Bridging Course Mathematics
• Introduction to Maxima for Economics
• List of formulae for final test

Preview - Science Track

• Mathematics 1: Linear Spaces and Metric Concepts
• Mathematics 2: Analysis and Dynamic Optimization

Some Literature

• A. C. Chiang, K. Wainwright: Fundamental Methods of Mathematical Economics, McGraw-Hill, New York, 2005
• K. Sydsæter, P. Hammond: Essential Mathematics for Economics Analysis, Prentice Hall, 3rd edition, 2008.
• K. Sydsæter, P. Hammond, A. Seierstad, A. Strøm: Further Mathematics for Economic Analysis, Prentice Hall, 2005.
• J. Leydold: Mathematik für Ökonomen, 3. Auflage, Oldenbourg Verlag, München Wien, 2003. (in German)
• K. Houston: How to Think Like a Mathematician, Cambridge University Press, 2009.

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Last change: 2024-09-13 by josef leydold