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Key Terms & Concepts for Mathematics

This document contains a curated list of important keywords, terms, and concepts related to Mathematics.

General

  • Truncate (1)
  • Functional (2)
  • MATLAB (3)
  • R (4)

Graph Theory

  • Graph theory (5)
  • Hamiltonian path (6)
  • Adjacency matrix (7)
  • Red-Black Tree (8)

Calculus

  • Calculus (9)
  • Derivative (10)
  • Integral (11)

Algebra

  • Vector (12)
  • Matrix (13)

Geometry

  • Theorem (14)
  • Pythagorean theorem (15)

Number Theory

  • RSA Encryption (16)
  • Chinese Remainder Theorem (17)

Algorithms

  • Dijkstra's algorithm (18)
  • A* search algorithm (19)
  • Levenshtein distance (20)
  • Hessian matrix (21)
  • Gradient (22)
  • Curvature (23)
  • Differential equation (24)
  • Euclidean geometry (25)
  • Simpson's paradox (26)
  • Huffman coding (27)
  • Euler's totient function (28)
  • Cyclic group (29)
  • Pick's theorem (30)
  • Miller–Rabin primality test (31)
  • P versus NP problem (32)
  1. To shorten a number by cutting off digits from the end. For example, truncating the number 3.14159 to two decimal places gives 3.14.
  2. In mathematics, a functional is a function that takes a function as its input and returns a scalar value.
  3. A proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.
  4. A programming language and free software environment for statistical computing and graphics supported by the R Foundation for Statistical Computing.
  5. The study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (or nodes) and lines called edges that connect them.
  6. A path in a graph that visits each vertex exactly once.
  7. A square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph.
  8. A kind of self-balancing binary search tree.
  9. A branch of mathematics that studies rates of change and accumulation. It is divided into two main branches: differential calculus (concerning rates of change and slopes of curves) and integral calculus (concerning accumulation of quantities and the areas under and between curves).
  10. A measure of how a function changes as its input changes. The derivative of a function at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
  11. A mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the fundamental objects of calculus.
  12. A mathematical object that has both a magnitude and a direction. Vectors are often represented as arrows and are used to describe quantities like velocity and force.
  13. A rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are used to represent transformations, solve systems of linear equations, and in many other applications.
  14. A statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms.
  15. A fundamental relation in Euclidean geometry among the three sides of a right-angled triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
  16. A public-key cryptosystem based on the presumed difficulty of factoring large integers, the factoring problem.
  17. A theorem which gives a unique solution to simultaneous linear congruences with coprime moduli.
  18. An algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks.
  19. A searching algorithm that searches for the shortest path between an initial and a final state. It is used in many fields of computer science for its completeness, optimality, and optimal efficiency.
  20. A string metric for measuring the difference between two sequences.
  21. A square matrix of second-order partial derivatives of a scalar-valued function, or scalar field.
  22. A multi-variable generalization of the derivative.
  23. A measure of how much a curve deviates from being a straight line, or a surface deviates from being a plane.
  24. An equation that relates one or more unknown functions and their derivatives.
  25. A mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
  26. A phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined.
  27. A lossless data compression algorithm.
  28. A function that counts the positive integers up to a given integer n that are relatively prime to n.
  29. A group that can be generated by a single element.
  30. A theorem that provides a formula for the area of a simple polygon with integer vertex coordinates.
  31. A primality test: an algorithm which determines whether a given number is prime.
  32. A major unsolved problem in computer science.