## Linear programming

Linear programming or Linear optimisation is a field of mathematics that deals with finding optimal values or solutions that can be described with linear equations and inequalities. Very often this involves finding the minimal or maximal values, ...

## Minimum spanning tree

A number of problems from graph theory are called Minimum spanning tree. In graph theory, a tree is a way of connecting all the vertices together, so that there is exactly one path from any one vertex, to any other vertex of the tree. If the grap ...

## Travelling salesman problem

The Traveling Salesman Problem is a classic algorithmic problem in the field of computer science and operations research. It is focused on optimization. In this context, better solution often means a solution that is cheaper, shorter, or faster. ...

## Theoretical computer science

Theoretical Computer Science is domain of Computer Science that looks at the notion of information and about how information can be processed. It also looks at the way models are built in computer science. Common divisions of theoretical computer ...

## Boolean satisfiability problem

The Boolean satisfiability problem is a kind of problem in math-based logic. In propositional logic, a formula is satisfiable if the variables it uses can be given values so that it becomes true. If however for a given formula, no values exist so ...

## Computability theory

Computability theory is part of computer science. Scientists want to know what can be computed, and what can not. There is a model of a computer that is used for this. It is called the Turing machine. A Turing machine basically is a special typew ...

## Computational complexity theory

Computational complexity theory is a part of computer science. It looks at algorithms, and tries to say how many steps or how much memory a certain algorithm takes for a computer to do. Very often, algorithms that use fewer steps use more memory. ...

## Cook–Levin theorem

The Cook–Levin theorem is a theorem from theoretical computer science, which says that the Boolean satisfiability problem is NP-complete. A deterministic Turing machine can change a problem in NP in polynomial time to the problem of determining w ...

## Cyclomatic complexity

Cyclomatic complexity is a measurement to see how difficult a computer program is to understand. The measurement was developed by Thomas J. McCabe, Sr. in 1976. It looks at the programs source code and measures the number of independent paths thr ...

## Decidability theory

Decidability theory is a branch of mathematics. Suppose there is a set, and there is an element. There is also an algorithm. The algorithm will simply check if the element belongs to the set or not. If the algorithm stops and has reached a decisi ...

## Information

The word information is used in many different ways. Originally, it comes from a word that meant to give a form to something. Information is something that people can learn, know about, or understand. For example, a newspaper contains information ...

## Information entropy

Information entropy is a concept from information theory. It tells how much information there is in an event. In general, the more certain or deterministic the event is, the less information it will contain. More clearly stated, information is an ...

## NP-complete

An NP problem is an algorithmic problem such that if you have a case of the problem of size n {\displaystyle n}, the number of steps needed to check the answer is smaller than the value of some polynomial in n {\displaystyle n}. It doesnt mean on ...

## NP-hardness

An NP-hard problem is a yes/no problem where finding a solution for it is at least as hard as finding a solution for the hardest problem whose solution can quickly be checked as being true. Some NP-hard problems are ones where a working solution ...

## Pseudorandom number generator

A pseudorandom number generator is a way that computers generate numbers. Computers arent good at creating random numbers. We use an "algorithm" to make a random number. A good analogy is a jar of numbered marbles. Humans can reach into the jar a ...

## Pseudorandomness

Pseudorandomness is a process which has a result that seems to be random. Even if the result seems to be random, the process can be predicted. This near random process is important to online security. Because the result can be predicted, it is im ...

## Turing complete

Turing complete is a term used in computability theory to describe abstract machines, usually called automata. Such an automaton is Turing complete, if it can be used to emulate a Turing machine. It is also called computationally universal. Most ...

## Conjecture

A conjecture is an idea in mathematics that appears likely to be true but that has not been proven to be true. After a conjecture is proven to be true, it becomes a theorem.

## Collatz conjecture

The Collatz conjecture is a conjecture in mathematics. It is named after Lothar Collatz. He first proposed it in 1937. It is about what happens when something is done repeatedly starting at some integer n: If n is even divisible by two, n is halv ...

## Goldbachs conjecture

Goldbachs conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states: Every even integer greater than 2 can be written as the sum of two primes.

## Riemann hypothesis

The Riemann hypothesis is a mathematical question. Lots of people think that finding a proof of the hypothesis is one of the hardest and most important unsolved problems of pure mathematics. Pure mathematics is a type of mathematics that is about ...

## Twin prime conjecture

The twin prime conjecture is a mathematical theory. It says that it is possible to find two twin primes that are as big as wanted. Twin primes are prime numbers that differ by two. For example, 3 and 5 are both prime and differ by two. They are t ...

## Digital signal processing

Digital signal processing is concerned with the processing of digital signals or analog signals after converting from analog to digital format. DSP includes subfields like: communication signals processing, radar signal processing, sensor array p ...

## Digital signal processor

A digital signal processor is a specialized microprocessor designed specifically for digital signal processing, generally used in real-time computing. Digital signal processing algorithms require a large number of mathematical operations to be pe ...

## Dirac delta function

The Dirac delta function, often written as δ {\displaystyle \delta }, is a made-up concept by mathematician Paul Dirac. It is a really pointy and skinny function that pokes out a point along a wave. Loosely speaking, it has the value of zero ever ...

## Fourier transform

The Fourier transform is a mathematical function that can be used to find the base frequencies that a wave is made of. Imagine playing a chord on a piano. When played, the sounds of the notes of the chord mix together and form a sound wave. This ...

## Harmonic analysis

Harmonic analysis is a branch of mathematics that looks at the theoretical foundations of digital signal processing. A continuous signal can be drawn as a wave, or as a combination of several waves. Fourier transforms and Fourier series are among ...

## Window function

In mathematics, a window function is a special function that can be applied to a signal, as it occurs in digital signal processing. A window function has a value of zero outside the domain which is of interest, and a non-zero value inside this do ...

## Equation

A mathematical equation is an expression containing two mathematical objects connected by an equals sign. The equals sign says that both sides are exactly equal, or of the same value. An equation can be as simple as x=0, or as complex as 4 + 76 = ...

## Algebraic equation

In mathematics, an algebraic equation, also called polynomial equation over a given field is an equation of the form P = Q {\displaystyle P=Q} where P and Q are polynomials over that field, and have one univariate or more than one multivariate va ...

## Diophantine equation

A Diophantine equation is an equation that only takes integer coefficients, and that can be written as f = 0 {\displaystyle f=0}, where f is a polynomial. Diophantine analysis is a branch of mathematical analysis, concerned with such equations. T ...

## Drake equation

In 1961, Frank Drake wrote down an equation for the chance of a contactable alien civilization from another planet in the Milky Way Galaxy. This is known as the Drake Equation. Carl Sagan mentioned the Drake equation often so it that has been mis ...

## Equation solving

Equation solving is field of mathematics that is about finding the functions or values that will make an equation true. An equation says that two expressions are equal. These expressions contain one or more unknowns, which are usually called free ...

## Maxwells equations

Maxwells equations describe how electric charges and electric currents create electric and magnetic fields. They describe how an electric field can generate a magnetic field, and vice versa. In the 1860s James Clerk Maxwell published equations th ...

## Ordinary differential equation

An ordinary differential equation is a differential equation which contains one free variable, and its derivatives. Ordinary differential equations are used for many scientific models and predictions. The term ordinary is used to differentiate th ...

## Partial differential equation

Partial Differential equations are a kind of mathematical equation. They are related to partial derivatives, in that obtaining an antiderivative of a partial derivative involves integration of partial differential equations.

## Cantor set

The Cantor set is a subset of real numbers with certain properties that are interesting to mathematicians. These properties relate to topology, measurement, geometry, as well as set theory. Some of them are: It has the same cardinality as the set ...

## Fractal

A fractal is any pattern, that when seen as an image, produces a picture, which when zoomed into will still make the same picture. It can be cut into parts which look like a smaller version of the picture that was started with. The word fractal w ...

## Mandelbrot set

The Mandelbrot set is an example of a fractal in mathematics. It is named after Benoit Mandelbrot, a Polish-French-American mathematician. The Mandelbrot set is important for chaos theory. The edging of the set shows a self-similarity, which is n ...

## Function (mathematics)

In mathematics, a function is a mathematical object that produces an output, when given an input. So a function is like a machine, that takes values of x and returns an output y. The set of all values that x can have is called the domain, and the ...

## Calculus of variations

The calculus of variations is a field of mathematical analysis. It usually deals with functions defined on the real numbers, and with finding minima and maxima of such functions. When finding a minimum or maximum, there are often additional condi ...

## Cauchys integral formula

In mathematics, Cauchys integral formula is a central statement in complex analysis. The statement is named after Augustin-Louis Cauchy. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on ...

## Convex function

In mathematics, a convex function is any function with value of the weighted average of 2 points is less than or equal to the weighted average of the function at those points. Also, a function is convex if and only if its epigraph is a convex set.

## Fourier analysis

Fourier analysis is a branch of analysis that looks at how more complex functions can be built with simpler ones. It is also known as classical harmonic analysis. It is named after Joseph Fourier who first used it in the 19th century. The process ...

## Geometric distribution

In probability, the geometric distribution with probability of success p {\displaystyle p}, written Geo ⁡ {\displaystyle \operatorname {Geo} }, is a discrete probability distribution defined on non-negative integers. It is used to model the numbe ...

## Linear mapping

In mathematics, a linear mapping is a mapping f between vector spaces that preserves addition and scalar multiplication.

## Linear predictor function

In statistics and in machine learning, a linear predictor function is a linear function of a set of coefficients and explanatory variables, whose value is used to predict the outcome of a dependent variable. Functions of this sort are standard in ...

## Matrix function

In mathematics, a function maps an input value to an output value. In the case of a matrix function, the input and the output values are matrices. One example of a matrix function occurs with the Algebraic Riccati equation, which is used to solve ...

## Newtons method

Newtons method provides a way for finding the real zeros of a function. This algorithm is sometimes called the Newton–Raphson method, named after Sir Isaac Newton and Joseph Raphson. The method uses the derivative of the function in order to find ...

## Riemann zeta function

In mathematics, the Riemann zeta function is an important function in number theory. It is related to the distribution of prime numbers. It also has uses in other areas such as physics, probability theory, and applied statistics. It is named afte ...