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Mathematics Glossary: Terms and Concepts, Cheat Sheet of Mathematics

Mathematics

Definitions and explanations for various mathematical terms and concepts, including cumulative, deviation, inferences, quantiles, point-biserial correlation, notation, axiom, tensor, fractal, functor, conjecture, lemma, corollaries, cardinality, array, subscript, heuristics, syntax, ansatz, singleton, disjunction, arbitrary, convention, dialectic, recursion, theorems, equinumerosity, indices, surjection, rigor, ontology, aliter, invariant, furlong, logarithm, tessellation, derivative, tangent, topology, postulate, asymptote, induction, matrix, permutations, lemniscate, metatheorem, porism, Euclidean geometry, googol, and googolplex.

Typology: Cheat Sheet

2021/2022

Uploaded on 11/13/2022

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1. Cumulative - increasing or increased in quantity, degree, or force by successive additions.
2. Deviation - a measure that is used to find the difference between the observed value and the
expected value of a variable or the distance from the center point.
3. Inferences - the process of drawing conclusions about a parameter one is seeking to measure or
estimate
4. Quantiles - cut points dividing the range of a probability distribution into continuous intervals with
equal probabilities, or dividing the observations in a sample in the same way.
5. Point-biserial - a special case of Pearson in which one variable is quantitative and the other variable is
dichotomous and nominal or a way of measuring the consistency of the relationship between a
candidate's overall exam mark (a continuous variable – i.e. anywhere from 0-100%) and a candidate's
item mark (a dichotomous variable i.e. with only two possible outcomes).
6. Notation - a set of well-defined rules for representing quantities and operations with symbols.
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  1. Cumulative - increasing or increased in quantity, degree, or force by successive additions.
  2. Deviation - a measure that is used to find the difference between the observed value and the expected value of a variable or the distance from the center point.
  3. Inferences - the process of drawing conclusions about a parameter one is seeking to measure or estimate
  4. Quantiles - cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way.
  5. Point-biserial - a special case of Pearson in which one variable is quantitative and the other variable is dichotomous and nominal or a way of measuring the consistency of the relationship between a candidate's overall exam mark (a continuous variable – i.e. anywhere from 0-100%) and a candidate's item mark (a dichotomous variable i.e. with only two possible outcomes).
  6. Notation - a set of well-defined rules for representing quantities and operations with symbols.
  1. Axiom - an unprovable rule or first principle accepted as true because it is self-evident or particularly useful.
  2. Tensor - an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space.
  3. Fractal - a type of mathematical shape that are infinitely complex.
  4. Functor - a mapping between categories. Functors were first considered in algebraic topology, where algebraic objects are associated to topological spaces, and maps between these algebraic objects are associated to continuous maps between spaces.
  5. Conjecture - a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases.
  1. Syntax - the part of mathematics that deals with symbols, and rules for manipulating them.
  2. Ansatz - A term of German origin meaning “initial placement of a tool at a work piece” (Wikipedia), and is used in mathematics to refer to the initial, additional mathematical assumptions made to kick start the problem solving process — but which are later confirmed to be parts of the actual solution as well.
  3. Singleton - also known as a unit set, is a set with exactly one element.
  4. Disjunction - A disjunction is a statement involving an or. For two statements p and q, it is written in mathematical notation as p ∨q.
  5. Arbitrary - A number which could be any number it is defined to be but for which no specific value is chosen. It is often used in proofs since it can represent any number but does actually have the value of any number so that the proof applies to more than one situation.
  1. Convention - is a fact, name, notation, or usage which is generally agreed upon by mathematicians.
  2. Dialectic - A dialectical understanding of mathematics recognises that every equation is a contradiction and the point is to draw upon the theory of knowledge of Marxism in order to discover and grasp contradiction within every object - in order to change it.
  3. Recursion - The phenomenon whereby a mathematical expression or a procedure is expressed as some instances of itself — in a way that does not involve any circularity or infinite loop.
  4. Theorems - A mathematical claim which has been proved to be true, and which is of special importance in its respective field.
  5. Equinumerosity - means "to have the same number of elements"
  6. Indices - plural form of index, the small floating number that appears after a number or letter. It shows how many times a number or letter has been multiplied by itself.
  1. Furlong - A unit of measurement representing the side length of one square acre. One furlong is approximately 1/8 of a mile, 201.17 meters, or 220 yards.
  2. Logarithm - The power to which a base must be raised to produce a given number. If nx = a, the logarithm of a, with n as the base, is x. Logarithm is the opposite of exponentiation.
  3. Tessellation - Congruent plane figures/shapes that cover a plane completely without overlapping.
  4. Derivative - are models that are used to show rates of change. They can be geometrical, like the slope of a curve, or physical models, which are drawn out in mathematical terms comprising numbers, letters, and symbols.
  5. Tangent - a straight line that passes through a curve and has the slope of the curve at the point of intersection. The concept can also be applied to planes intersecting with curves.
  1. Topology - the study of geometric objects whose shapes are preserved, even when twisted, stretched, or otherwise deformed.
  2. Postulate - are statements that are assumed to be true, even though there isn't any proof. They sometimes serve as starting points for proving other statements, and other times they are used to explain terms that are undefined.
  3. Asymptote - can be vertical, horizontal, or slanted lines that graphs can approach, but can never touch. It's the mathematical equivalent of walking toward a fixed object at a pace that gets gradually slower and slower. Although the object gets closer and closer, the person doing the walking will never actually reach it.
  4. Induction - a simple, two-step method that allows mathematicians to prove things. The first step is to show that something is true for the first occurrence. Step two is to show that if the first one is true, the next one is, too.
  5. Matrix - a group of numbers arranged in rows and columns in a rectangular pattern. More than one matrix are matrices.
  1. Googol - The number 10¹⁰⁰. This number can be written as a 1 followed by 100 zeros.
  2. Googolplex - The number 10googol, or 1 followed by a googol number of zeros. This is reputed to be the largest number with a name. Note: This can also be written 10¹⁰^¹⁰⁰..