Discrete mathematics is the study of mathematical relationships between distinct or individual parts. Its primary focus can be simplified as the realm of the integer. The concepts from discrete math are directly applicable to computing concepts. This has caused a rise in its popularity, especially as a required area of study for computer science and programming careers.
Discrete Math and Computers
Computers are based in binary. Their mechanical function depends on two things; the electrical current is there or it is not. Therefore, everything a computer can do, from turning on through complex calculations, stems from those electrical inputs. As that simple input is combined with others to form more complex pieces it still relies upon base two for its computations. Since it cannot have a fractional input of there or not, it is ideal for discrete mathematical concepts.
Discrete Math Topics
There are many integer-based mathematical concepts that can be considered part of discrete mathematics. The following lists some of those, specifically as they apply to computing.
- Algorithmics –how to create a list of generic instructions that is non-specific enough to be used in many situations. For example, consider the Order of Operations from Algebra where a specific order must be followed when finding the result to a multi-step equation.
- Boolean Algebra – how to calculate expressions given in base two. Also includes electronics concepts such as logic gates.
- Combinatorics – the overall concept of problem solving. It is related to common math concepts such as algebra and probability and is seen in computing through concepts such as iterations and recursion.
- Computability and Complexity Theories – strongly related to combinatorics and algorithmics, but focuses on the theoretical and practical limitations of the chosen problem solving method. In computer science it is frequently applied through Big-O notation.
- Counting – ranges from simple finger counting to enumerations and counting in different number systems.
- Graph Theory – the use of mathematical structures to create a model of information in order to discover relationships among information in a set.
- Information Theory – applying mathematics to communication. It relies heavily on probability and statistics and is applied in areas such as data analysis, networking and other electronic communications, quantum computing and neurobiology.
- Logic – once considered a branch of philosophy, it now is heavily used to understand reasoning through electronic logic gates. It is closely related to proofs.
- Mathematical Relations – related to set theory, relations are properties that assign a value for truth such as found when evaluating inequalities.
- Number Theory – a broad branch of mathematics concerned with the properties of integers.
- Proofs – logical demonstration that a mathematical expression is true.
- Set Theory – the study of a collection of objects.
- Trees – a division of graph theory, trees are specifically applied in computer science through the study of data structures.
Reference:
Rosen, K.H.(1999). Discrete Mathematics and its Applications. McGraw Hill.
