Intro-Week Mathematics

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. allows prospective master students to test their knowledge in the above mentioned topics. 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