Nowadays mathematical tools have become an important prerequisite for all those who want to understand the economic and business literature. Students of economics and business are required to achieve a solid understanding of mathematics. This includes mathematical tools such as infinitesimal calculus for functions of one or several variables, optimization with and without constraints, linear algebra and difference equations. Mathematics is also a way to logically structure arguments in order to obtain new hypotheses or statements to be tested on real data.

At the University of St. Gallen, Mathematics is taught at the Assessment and Bachelor Levels. Students entering the master programs in economics and finance are expected to have solid a background in Mathematics before entering the programs. Good knowledge of calculus in one and several variables, linear algebra, differential equations, and some experience with proofs and formal mathematical arguments is required.

**e-maths.ch** allows prospective master students to test their knowledge in the above mentioned topics.

**e-maths.ch** follows the book “Mathematics” written by Prof. Enrico De Giorgi, which covers the following topics treated at the Assessment and Bachelor Levels.

**Part I: Introduction**

Chapter 1: Why Mathematics for Economics?

Chapter 2: Mathematical Logic

Chapter 3: Set Theory

Chapter 4: Combinatorics

Chapter 5: Numbers

**Part II: Fundamentals**

Chapter 6: Sequences

Chapter 7: Series

Chapter 8: Financial Mathematics

**Part III: Univariate Calculus**

Chapter 9: Basic Notions

Chapter 10: Continuity and Differentiability

**Part IV: Multivariate Calculus**

Chapter 11: Function of Several Variables

Chapter 12: Optimisation

**Part V: Integration**

Chapter 13: Definite Integral

Chapter 14: Indefinite Integral

Chapter 15: Applications

**Part V: Linear algebra**

Chapter 16: Matrices and Determinants

Chapter 17: Vectors

Chapter 18: System of Linear Equations

Chapter 19: Eigenvalues and Eigenvectors

**Part VI: Dynamics**

Chapter 20: Difference Equations

Chapter 21: Differential Equations