Mathematics

Study Field Outline

Mathematics is divided into the two major branches of pure and applied mathemat- ics. The main areas of pure mathematics

are algebra, analysis, geometry, topology and numbers theory, while applied math- ematics focuses on numerical analysis, optimisation and stochastic theory and processes.

Pure mathematics deals with abstract structures and their internal relationships, attempting to derive as many statements or conclusions as possible from a few assumptions.

By contrast, applied mathematics aims to provide a set of instruments for using quantitative methods to process questions from the fields of natural sciences and engineering, medicine, as well as econom- ics and social sciences.

A major field of application in numeri- cal mathematics (numerics) involves the development and analysis of numerical algorithms, for example, for solving dif- ferential equations which, for their part, are fundamental to describing processes taking place in nature, in engineering and technology, or even in the financial markets.

Stochastic theory provides a quantitative description and a methodology for analys- ing random phenomena in our everyday sphere of experience. This includes, for example, deriving statistical procedures for analysing complex data structures, deter- mining price formulae for financial deriva- tives traded on the stock exchanges or for risk controlling in the field of actuarial (insurance) mathematics.

In contrast to computer science, mathe- matics focuses on theory-based algorithms or relations whose efficiency and preci- sion can be proven and whose improved efficiency cannot necessarily be achieved by using better computers. Conversely, improved computing provides opportuni- ties for not only examining complex mod-

els theoretically, but also places the appro- priate software at the disposal of the user. The fields of business or industrial math- ematics, statistics and technomathematics have evolved from mathematics to become independent disciplines. Both business and industrial mathematics perform func- tions in almost all branches of business and industry. Major fields of application are to be found in insurance and finance. Studies have a very strong practical focus. The objective for statistics is to develop mathematical methods for analysing empirical data. The computer-compatible development of mathematical models for solving and analysing engineering prob- lems is undertaken by technomathemat- ics (engineering mathematics). Applied systems science focuses on mathematical models for applications in environmental protection/ecology. Biomathematicians have special knowledge in various disci- plines from the field of biology as well as the requisite basic knowledge from other natural sciences. They define biological or medical questions in the language of mathematics and use or develop models and methods to solve these.

The study of mathematics aims to enable students to learn and master mathematical concepts and methods. It requires an abil- ity for abstract thinking which is a basic requirement for those wishing to work as mathematicians. A willingness to engage in interdisciplinary cooperation is just as important, and so is already considered in the degree programmes by obliging students to select a minor or subsidiary subject. The chosen minor or consolida- tion subject will usually be chosen from

Studies at Universities

Practical experience/internships:

Students generally complete a practical phase in business, industry or a research institution during their studies.

Studies: Based on a well-founded school knowledge of mathematics, the math- ematical principles are taught and consoli- dated in the fields of analysis (differential and integral calculus, complex analysis, integration theory), linear algebra and ana- lytical geometry, applied mathematics –

stochastic theory (probability calculus and statistics, modelling), numerical analysis and optimisation. Additional modules on the chosen technical, natural sciences, medical or economic fields of applica- tion. In addition, students acquire various methods and work techniques, principles of computer science and the use of pro- fessional software and learn advanced programming languages, including “com- puter practical courses”. Elective modules cover areas like pure mathematics or vari- ous applied subjects and enable students to create their own profiles.

the field of natural sciences or engineer- ing, economics or computer science, depending on the institution in question.

This choice already marks the first career- relevant decision for the students‘ later professional assignment fields.

Programmes in this field

Aachen TH • Augsburg U • Bayreuth U • Berlin FU • Berlin HU • Berlin TU • Bielefeld U • Bochum U • Bonn U • Braunschweig TU • Bremen Jacobs University • Bremen U • Chemnitz TU • Clausthal TU • Cottbus TU • Darmstadt TU • Dortmund TU • Dresden TU • Duisburg-Essen U (Duisburg) • Düsseldorf U • Eichstätt-Ingolstadt U (Eichstätt) • Erfurt U • Erlangen-Nürnberg U (Erlangen) • Flensburg U • Frankfurt am Main U • Freiberg TUBergAk • Freiburg U • Gießen U • Göttingen U • Greifswald U • Hagen FernU • Halle-Wittenberg U • Hamburg U • Hannover U • Heidelberg U • Hildesheim U • Ilmenau TU • Jena U • Kaiserslautern TU • Karlsruhe U • Kassel U • Kiel U • Koblenz-Landau U • Köln U •

Konstanz U • Leipzig U • Lüneburg U • Magdeburg U • Mainz U • Mannheim U • Marburg U • München TU (Garching) • München U • Münster U • Oldenburg U • Osnabrück U •

Paderborn U • Potsdam U • Regensburg U • Rostock U • Saarbrücken U • Siegen U • Stuttgart U • Trier U • Tübingen U • Ulm U • Vechta H • Wuppertal U • Würzburg U

Studies at Universities of Applied Sciences

Practical experience/internships: None generally required before studies begin.

Studies: Modules on the principles of mathematics, analysis, linear algebra, numerical mathematics, probability cal- culus and statistics, geometry, stochastic theory, data structures and algorithms.

Study Field Outline

Physics is a fundamental science which has perhaps had a greater impact on the technology, business and industry of our world than any other science. And our concepts of the world in general are also largely based on research findings pro- duced by physics. Precise measurements of natural phenomena, whether observed directly or in experimental surroundings, enable us to reduce natural phenomena down to numerical relationships (experi- mental physics) and mathematically for- mulated laws (theoretical physics). This has led to a progressive accumulation of knowledge and – by means of techni- cal application – to the utilisation and

exploitation of nature (applied physics). Recent examples of the implementation of physical research in technical applications include semiconductor engineering, opto- electronics, nanoengineering and laser physics. Due to the highly mathematical nature of theoretical physics, the field of mathematics is the foremost auxiliary sci- ence for physicists and makes very heavy demands on undergraduates in particular. Recent years have seen new interdiscipli- nary degree programmes with substantial proportions of physics established to allow students to specialise.

Astrophysics, which involves the physical examination of celestial bodies (planetary system, the Sun, fixed stars, interstellar Students also learn work techniques as

well as aspects from the field of compu- ter science/programming/mathematical software. In the advanced study stages, students consolidate their knowledge in subjects like numerical mathematics, differential calculus, database systems. Depending on the institution in question, students can set core study areas by choos- ing applied modules in business math- ematics (finance and insurance/actuarial mathematics, operational research), indus- trial mathematics/technical mathemat- ics and corresponding practical projects. Modules also deliver interdisciplinary key qualifications in the fields of business administration, law, foreign languages, presentation techniques.