Program Overview

Mathematik (B.Sc.)

Introduction to the Program

The Bachelor of Science in Mathematics program is designed to provide students with a comprehensive understanding of mathematical concepts and principles. The program covers a wide range of topics, including mathematical logic, number theory, algebra, geometry, and analysis.

Program Structure

• The program is divided into several modules, each focusing on a specific area of mathematics.
  • Grundlagenbereich (Foundation Module): This module provides an introduction to the fundamental concepts of mathematics, including set theory, logic, and proof techniques.
  • Vertiefungsbereich (In-Depth Module): This module delves deeper into specific areas of mathematics, such as algebra, geometry, and analysis.
  • Ergänzungsbereich (Supplementary Module): This module offers additional courses that complement the core modules, including topics such as mathematical physics and computer science.
• Allgemeine Berufsvorbereitung (ABV): This module focuses on preparing students for their future careers, including courses on communication, teamwork, and project management.
• Bachelorarbeit: The final module requires students to complete a bachelor's thesis, which involves original research and a written dissertation.

Mathematical Logic

Mathematical logic is a key component of the program, focusing on the formal systems and methods used to reason about mathematical structures. Topics include:

• Propositional and predicate logic
• Model theory
• Proof theory
• Computability theory

Examples of Mathematical Logic

• The Königsberger Brückenproblem (Seven Bridges of Königsberg)
• Äquivalenzrelationen (Equivalence Relations)
• Das Kartenspiel SET (The Card Game SET)
• Paradoxa (Paradoxes)
• Pascalsches Dreieck (Pascal's Triangle)

Study Life

The program aims to provide students with a well-rounded education, including:

• Interviews with current students
• Types of events and lectures
• Semester structure
• Student initiatives
• Family-friendly university policies

Career Prospects

Graduates of the program have a wide range of career opportunities, including:

• Research and development
• Finance and banking
• Data analysis and science
• Teaching and education
• Consulting and management

Alumni Perspectives

Notable alumni include:

• Christina Bracht, Master's student in Organizational Psychology
• Dr. Malte Wandel, Postdoc at the University of Kyoto
• Dr. Hendrik Süß, Lecturer at the University of Manchester
• Anne Kahnt, Founder and CEO of vismath
• Simon Winter, Lecturer in Mathematics at Dimler & Albroscheit
• Dr. Carmen Köhler, Research Scientist at the German Weather Service
• Dr. René Birkner, IT Consultant at the Federal Ministry for the Environment, Nature Conservation, and Nuclear Safety
• Dr. Sebastian Meinert, Management Consultant at The Boston Consulting Group

Tautology and Contradiction

A tautology is a statement that is always true, while a contradiction is a statement that is always false. Examples include:

• Tautology: "It is raining or it is not raining"
• Contradiction: "It is raining and it is not raining"

Wahrheitstafeln (Truth Tables)

Truth tables are used to determine the validity of statements, including:

• Tautology
• Contradiction
• Contingency

Examples of Tautologies and Contradictions

• (AB)(¬B¬A)
• ¬(AB)¬A¬B
• ((AB)¬B)A
• A¬(¬AB)
• ((AB)(BC))(AC)
• (AB)(¬BA)