Discrete mathematics
The discrete mathematics as a part of mathematics concerned with mathematical operations over finite or at least countable infinite sets. In contrast to other areas such as the analysis, which is not countable with continuous functions or curves, infinite sets has the property of continuity has no meaning for those considered in the discrete mathematics consequences.
That are present in discrete mathematics areas (such as number theory or graph theory ) are already quite old at the time, but discrete mathematics was long in the shadow of "continuous " mathematics, since the development of calculus through its diverse applications in the natural sciences ( especially physics ) came into the limelight. Only in the 20th century was created by the possibility of rapid digital data processing by computer ( the work -related nature with discrete states ) a variety of new applications of discrete mathematics. At the same time, there was a rapid development of discrete mathematics ( algorithms, etc., theoretical computer science ) has been driven largely by issues related to the computer.
An example of an area that lies at the intersection of analysis and discrete mathematics, the numerical mathematics that deals with the approximation of continuous by discrete sizes, as well as the estimate ( and minimization) of this error occurring.
Core areas
The core areas of discrete mathematics include:
- Combinatorics,
- Number theory,
- Coding theory,
- Graph theory,
- Game theory,
- Cryptography,
- Information Theory and
- Statistics.
In addition, discrete mathematics has provided additional contributions in the following areas:
- More Articles of numerics to improve the discrete arithmetic can be in the areas of linear and discrete optimization ( beyond combinatorial tasks) find
- Discrete mathematics has many points of contact with the algebra and mathematical logic,
- In geometry, there is a branch of discrete geometry and
- In computability theory which is a branch of theoretical computer science, one needs finite automata, which are studied in discrete mathematics.
Science Award
The Department of Discrete Mathematics German Mathematical Society awards the two- year cycle named after the German mathematician Richard Rado Richard Rado Prize for the best dissertation in discrete mathematics.
Study
A study of discrete mathematics is at various universities (among TU Berlin) by an appropriate focus within the mathematics study possible. Among other things, the Philipps- University of Marburg, Georg- August- University Göttingen, the Hochschule Bremerhaven, University of Applied Sciences in Münster University of Applied Sciences Northwestern Switzerland and the Friedrich -Schiller- University Jena treat discrete mathematics as a compulsory module in the basic study of computer science. Among the colleges, the university Mittweida in the context of a specialized master's program this possibility. In the Fachhochschule Rhein Main in Wiesbaden discrete mathematics is a compulsory module in the Master's program in computer science.