Glossary

Updated 05:08 PM • Jul 23, 2026 5.9k views

Summarize

1.A

1.1

1

1.2

3

1.3

absolute convergence

2

1.4

5

1.5

absolute value equations

1

1.6

absolute value function

1

1.7

absolute value inequality

1

1.8

absolute value integral

1

1.9

1

1.10

2

1.11

accumulation function

1

1.12

accumulation points

1

1.13

actual increment

1

1.14

addition formula for arctangent

1

1.15

1

1.16

affine subspace

1

1.17

algebra of limits

1

1.18

algebraic equation

1

1.19

algebraic multiplicity

1

1.20

alternating group

1

1.21

alternating series

1

1.22

analytic function

1

1.23

1

1.24

angular measure

1

1.25

1

1.26

5

1.27

1

1.28

2

1.29

1

1.30

arccosine function

1

1.31

2

1.32

archimedean property

1

1.33

1

1.34

arcsine function

1

1.35

3

1.36

area between curves

1

1.37

argument of a complex number

1

1.38

arithmetic mean

5

1.39

arithmetic sequence

2

1.40

arithmetic series

1

1.41

associative property

1

1.42

1

1.43

3

1.44

7

1.45

asymptotic analysis

1

1.46

asymptotic behavior

1

1.47

asymptotic comparison

2

1.48

asymptotic equivalence

2

1.49

asymptotic expansion

1

1.50

asymptotic growth

1

1.51

augmented matrix

1

1.52

automated deduction

1

1.53

automorphism group

1

1.54

average rate of change

1

1.55

1

1.56

axis of symmetry

1

2.B

2.1

backpropagation

1

2.2

2

2.3

1

2.4

bayesian inference

1

2.5

1

2.6

bernoulli distribution

1

2.7

bernoulli trial

2

2.8

beta distribution

1

2.9

bezout identity

1

2.10

2

2.11

bijective function

3

2.12

binary operation

1

2.13

1

2.14

1

2.15

binomial coefficient

5

2.16

binomial differential

1

2.17

binomial distribution

3

2.18

binomial equation

2

2.19

binomial identities

1

2.20

binomial theorem

6

2.21

biquadratic equation

1

2.22

bounded function

1

2.23

bounded sequence

3

2.24

1

3.C

3.1

1

3.2

cancellation law

1

3.3

1

3.4

cantor's theorem

1

3.5

6

3.6

cartesian coordinate plane

1

3.7

cartesian coordinates

1

3.8

cartesian equation

1

3.9

cartesian plane

2

3.10

cartesian product

2

3.11

1

3.12

1

3.13

1

3.14

cauchy convergence criterion

1

3.15

cauchy convolution

1

3.16

cauchy criterion

1

3.17

1

3.18

1

3.19

cauchy schwarz inequality

1

3.20

cauchy sequence

3

3.21

cauchy-schwarz inequality

1

3.22

cauchy's theorem

1

3.23

ceiling function

1

3.24

central limit theorem

1

3.25

6

3.26

2

3.27

change of basis

1

3.28

change of variable

1

3.29

characteristic polynomial

3

3.30

chi-square distribution

1

3.31

1

3.32

1

3.33

closed interval

2

3.34

1

3.35

1

3.36

2

3.37

2

3.38

coefficient matrix

1

3.39

cofactor method

1

3.40

1

3.41

commutative property

1

3.42

compact interval

1

3.43

comparison test

3

3.44

comparison theorem

1

3.45

2

3.46

completeness axiom

1

3.47

completing the square

4

3.48

complex analysis

1

3.49

complex argument

1

3.50

complex conjugate

4

3.51

complex exponential

1

3.52

complex logarithm

1

3.53

complex modulus

1

3.54

complex numbers

11

3.55

2

3.56

1

3.57

complex solution

4

3.58

composite function

2

3.59

composite power function

1

3.60

composition of limits

1

3.61

compound inequality

1

3.62

computational graph

1

3.63

4

3.64

conditional convergence

1

3.65

conditional probability

1

3.66

confidence intervals

1

3.67

1

3.68

1

3.69

conic classification

1

3.70

3

3.71

consistency of systems

1

3.72

7

3.73

continuous distribution

3

3.74

continuous function

4

3.75

continuous random variable

3

3.76

7

3.77

convergent sequence

1

3.78

convergent series

1

3.79

1

3.80

1

3.81

coordinate transformation

1

3.82

1

3.83

1

3.84

correlation coefficient

1

3.85

2

3.86

4

3.87

cosine function

2

3.88

cosine inequality

1

3.89

cosine similarity

1

3.90

3

3.91

cotangent function

1

3.92

1

3.93

1

3.94

1

3.95

1

3.96

1

3.97

1

3.98

cumulative distribution function

3

3.99

cumulative probability

1

3.100

1

3.101

1

3.102

1

3.103

cyclotomic polynomial

1

3.104

cylindrical shell

1

4.D

4.1

darboux criterion

1

4.2

1

4.3

darboux's theorem

1

4.4

de moivre's theorem

2

4.5

1

4.6

de morgan's laws

1

4.7

decimal expansion

1

4.8

decimal representation

1

4.9

decreasing function

1

4.10

1

4.11

definite integral

7

4.12

definite integrals

7

4.13

degenerate conic

1

4.14

3

4.15

1

4.16

degrees of freedom

1

4.17

1

4.18

1

4.19

13

4.20

derivative of the inverse function

1

4.21

6

4.22

4

4.23

1

4.24

diagonalization

1

4.25

1

4.26

difference of squares

1

4.27

difference quotient

2

4.28

differentiability

2

4.29

differentiable function

1

4.30

differentiable functions

1

4.31

1

4.32

differential calculus theorems

3

4.33

differential equation

1

4.34

differentiation

1

4.35

differentiation rules

1

4.36

2

4.37

1

4.38

direction vector

1

4.39

1

4.40

dirichlet criterion

1

4.41

dirichlet function

1

4.42

1

4.43

1

4.44

3

4.45

discontinuity set

1

4.46

discrete distributions

2

4.47

discrete random variable

1

4.48

discrete random variables

2

4.49

11

4.50

1

4.51

2

4.52

distance from a point to a line

1

4.53

distributive property

3

4.54

1

4.55

divergent sequence

1

4.56

division algorithm

1

4.57

division of complex numbers

1

4.58

10

4.59

domain of a function

2

4.60

domain restrictions

4

4.61

1

4.62

2

4.63

double angle formulas

1

4.64

double argument formulas

1

4.65

1

5.E

5.1

1

5.2

2

5.3

2

5.4

2

5.5

elementary functions

1

5.6

elementary symmetric polynomials

1

5.7

elimination method

1

5.8

1

5.9

equation with parameters

1

5.10

5

5.11

equilibrium solutions

1

5.12

equivalence classes

2

5.13

equivalent transformations

1

5.14

1

5.15

1

5.16

euclidean algorithm

2

5.17

euclidean distance

2

5.18

euclidean division

1

5.19

1

5.20

4

5.21

1

5.22

euler substitution

1

5.23

euler totient function

1

5.24

Euler's formula

2

5.25

2

5.26

2

5.27

1

5.28

eventual monotonicity

1

5.29

exact differential equations

1

5.30

existence and uniqueness

1

5.31

existence of roots

1

5.32

7

5.33

1

5.34

1

5.35

exponential distribution

1

5.36

exponential equations

2

5.37

exponential form

3

5.38

exponential function

7

5.39

exponential inequalities

1

5.40

exponential integral

1

5.41

exponential inverse

1

5.42

exponential limits

1

5.43

2

5.44

extraneous solutions

4

5.45

extreme value theorem

1

6.F

6.1

1

6.2

6

6.3

factoring trinomials

1

6.4

1

6.5

1

6.6

fermat's theorem

2

6.7

fibonacci sequence

1

6.8

1

6.9

field extensions

1

6.10

field structure

1

6.11

1

6.12

1

6.13

finite population

1

6.14

1

6.15

first derivative

1

6.16

first-order differential equation

1

6.17

first-order differential equations

1

6.18

first-order logic

1

6.19

1

6.20

5

6.21

1

6.22

2

6.23

2

6.24

fourier coefficients

1

6.25

2

6.26

fractional part

1

6.27

fractional powers

1

6.28

1

6.29

1

6.30

1

6.31

function analysis

1

6.32

function approximation

1

6.33

function composition

1

6.34

function decomposition

1

6.35

function properties

1

6.36

function series

1

6.37

function symmetry

1

6.38

function transformation

1

6.39

6

6.40

fundamental theorem of algebra

3

6.41

fundamental theorem of calculus

3

7.G

7.1

gamma distribution

2

7.2

2

7.3

gauss-jordan elimination

1

7.4

1

7.5

gaussian elimination

6

7.6

gaussian function

1

7.7

general solution

1

7.8

generalized harmonic series

1

7.9

geometric distribution

1

7.10

geometric interpretation

1

7.11

4

7.12

geometric multiplicity

1

7.13

geometric sequence

3

7.14

geometric series

6

7.15

2

7.16

graphical interpretation

1

7.17

greatest lower bound

1

7.18

1

7.19

group presentations

1

7.20

1

8.H

8.1

half angle formulas

1

8.2

half argument formulas

1

8.3

half-angle substitution

1

8.4

3

8.5

harmonic motion

1

8.6

harmonic series

2

8.7

heaviside function

1

8.8

heaviside step function

1

8.9

heine-cantor theorem

1

8.10

1

8.11

heron's formula

1

8.12

1

8.13

higher-order derivative

1

8.14

1

8.15

homogeneous equation

1

8.16

homogeneous solution

1

8.17

homogeneous systems

2

8.18

homogeneous trigonometric equations

1

8.19

3

8.20

1

8.21

horizontal asymptotes

1

8.22

2

8.23

hyperbolic cosecant

1

8.24

hyperbolic cosine

3

8.25

hyperbolic cotangent

2

8.26

hyperbolic function

3

8.27

hyperbolic functions

3

8.28

hyperbolic identities

3

8.29

hyperbolic identity

2

8.30

hyperbolic secant

1

8.31

hyperbolic sine

3

8.32

hyperbolic tangent

2

8.33

hypergeometric distribution

1

8.34

1

8.35

2

9.I

9.1

2

9.2

identities and contradictions

1

9.3

identity and inverse

1

9.4

identity element

1

9.5

identity matrix

1

9.6

3

9.7

2

9.8

improper integral

3

9.9

inclusion-exclusion principle

1

9.10

incomplete quadratic equations

1

9.11

inconsistent system

1

9.12

increasing function

1

9.13

indefinite integral

3

9.14

indeterminate forms

3

9.15

1

9.16

2

9.17

1

9.18

5

9.19

1

9.20

infinite discontinuity

1

9.21

1

9.22

inflection point

1

9.23

initial value problems

2

9.24

1

9.25

injective function

2

9.26

1

9.27

1

9.28

2

9.29

2

9.30

3

9.31

integrals with radicals

1

9.32

integrating factor

1

9.33

1

9.34

integration by part

1

9.35

integration by parts

3

9.36

integration by substitution

4

9.37

integration rules

1

9.38

integration strategies

1

9.39

intermediate value property

1

9.40

intermediate value theorem

1

9.41

1

9.42

interpretations

1

9.43

interquantile range

1

9.44

intersecting curves

1

9.45

1

9.46

1

9.47

interval notation

2

9.48

interval of convergence

1

9.49

interval solutions

1

9.50

2

9.51

inverse element

1

9.52

inverse function

10

9.53

inverse function theorem

1

9.54

inverse functions

2

9.55

inverse hyperbolic function

1

9.56

1

9.57

inverse trigonometric function

3

9.58

inverse trigonometric functions

1

9.59

invertible functions

1

9.60

invertible matrix

3

9.61

irrational equations

4

9.62

irrational function

2

9.63

irrational inequalities

1

9.64

irrational numbers

3

9.65

irreducible polynomials

1

9.66

irreducible quadratic factors

2

9.67

3

10.J

10.1

jacobian matrix

1

10.2

joint probability density function

1

10.3

jump discontinuities

1

10.4

jump discontinuity

1

10.5

1

11.K

11.1

5

11.2

kernel and image

1

11.3

1

12.L

12.1

1

12.2

lagrange remainder

1

12.3

lagrange's theoreme

2

12.4

1

12.5

laplace expansion

1

12.6

1

12.7

1

12.8

1

12.9

leading coefficient

1

12.10

least upper bound

1

12.11

lebesgue measure

1

12.12

left-hand derivative

1

12.13

leibniz criterion

1

12.14

Leibniz notation

1

12.15

1

12.16

1

12.17

1

12.18

1

12.19

limit evaluation

2

12.20

1

12.21

limit of a sequence

1

12.22

limit of consecutive terms

1

12.23

limit properties

1

12.24

1

12.25

4

12.26

1

12.27

1

12.28

1

12.29

linear approximation

1

12.30

linear combination

1

12.31

linear combinations

2

12.32

linear differential equation

1

12.33

linear differential equations

1

12.34

linear equations

5

12.35

linear independence

1

12.36

linear inequalities

1

12.37

2

12.38

2

12.39

6

12.40

linearity of the derivative

1

12.41

lipschitz continuity

1

12.42

literal inequality

1

12.43

little o notation

1

12.44

little-o notation

2

12.45

local boundedness

1

12.46

1

12.47

logarithmic branches

1

12.48

logarithmic differentiation

1

12.49

logarithmic equations

1

12.50

logarithmic function

4

12.51

logarithmic growth

1

12.52

logarithmic inequality

1

12.53

logarithmic limits

1

12.54

logarithmic properties

1

12.55

6

12.56

logical connectives

1

12.57

logical consequence

1

12.58

logical equivalence

1

12.59

1

12.60

1

12.61

loss of solutions

1

13.M

13.1

maclaurin series

3

13.2

1

13.3

matrix addition

1

13.4

matrix diagonalization

1

13.5

matrix multiplication

2

13.6

1

13.7

matrix representation

2

13.8

maximum and minimum

1

13.9

maximum and minimum points

1

13.10

maximum and minimum values

1

13.11

7

13.12

mean value theorem

4

13.13

1

13.14

1

13.15

1

13.16

1

13.17

modified harmonic series

1

13.18

modular arithmetic

1

13.19

module homomorphisms

1

13.20

1

13.21

1

13.22

2

13.23

modulus and argument

1

13.24

modulus of a complex number

2

13.25

1

13.26

1

13.27

monotone convergence theorem

2

13.28

monotone sequence

2

13.29

monotone sequences

1

13.30

monotonic function

2

13.31

4

13.32

multimodal distribution

1

13.33

1

13.34

multiplicity of a root

1

13.35

multiplicity of roots

1

14.N

14.1

natural exponential function

1

14.2

natural logarithm

2

14.3

natural numbers

3

14.4

2

14.5

1

14.6

neural networks

1

14.7

non-differentiable point

1

14.8

2

14.9

normal acceleration

2

14.10

normal distribution

6

14.11

1

14.12

notable products

2

14.13

2

14.14

1

14.15

numerical integration

1

15.O

15.1

oblique asymptotes

1

15.2

1

15.3

one-sided derivative

1

15.4

1

15.5

1

15.6

1

15.7

order of approximation

1

15.8

1

15.9

1

15.10

2

15.11

ordinary differential equation

1

15.12

1

15.13

orthonormal basis

1

15.14

oscillating functions

1

15.15

oscillating sequence

1

16.P

16.1

p-integral test

1

16.2

5

16.3

parallel and perpendicular planes

1

16.4

1

16.5

2

16.6

parametric curves

1

16.7

parametric equations

2

16.8

parametric solution

1

16.9

parametric substitution

1

16.10

partial derivative

1

16.11

partial derivatives

1

16.12

partial fraction

1

16.13

partial fraction decomposition

2

16.14

partial fractions

3

16.15

5

16.16

particular solution

1

16.17

pascal triangle

2

16.18

1

16.19

periodic function

3

16.20

periodic functions

1

16.21

2

16.22

piecewise continuity

1

16.23

piecewise function

1

16.24

plane equations

1

16.25

1

16.26

point-to-plane distance

1

16.27

pointwise convergence

1

16.28

poisson distribution

1

16.29

polar coordinates

1

16.30

1

16.31

polar integration

1

16.32

polygonal approximation

1

16.33

1

16.34

polynomial addition

1

16.35

polynomial degree

1

16.36

polynomial division

4

16.37

polynomial equations

4

16.38

polynomial expansion

1

16.39

polynomial factorization

5

16.40

polynomial function

1

16.41

polynomial functions

1

16.42

polynomial inequalities

2

16.43

polynomial multiplication

1

16.44

polynomial rings

1

16.45

polynomial roots

1

16.46

polynomial subtraction

1

16.47

7

16.48

positive term series

2

16.49

1

16.50

1

16.51

1

16.52

1

16.53

3

16.54

2

16.55

power-reduction identities

1

16.56

1

16.57

1

16.58

primitive roots

1

16.59

principal logarithm

1

16.60

principal value

1

16.61

prior probability

1

16.62

3

16.63

probability axiom

1

16.64

probability density

1

16.65

probability density function

4

16.66

probability mass function

3

16.67

probability tables

1

16.68

2

16.69

1

16.70

propositional logic

2

16.71

prosthaphaeresis formulas

1

16.72

pythagorean identities

1

16.73

pythagorean identity

7

16.74

pythagorean theorem

2

17.Q

17.1

1

17.2

quadratic equation

2

17.3

quadratic equations

8

17.4

1

17.5

quadratic formula

5

17.6

quadratic inequalities

2

17.7

quadratic inequality

1

17.8

quadratic mean deviation

1

17.9

1

17.10

quadratic trinomial

1

17.11

quadratic trinomials

1

17.12

quadrature formulas

1

17.13

1

17.14

1

17.15

1

17.16

2

18.R

18.1

2

18.2

1

18.3

4

18.4

radius of convergence

2

18.5

random experiment

1

18.6

random variable

1

18.7

random variables

2

18.8

3

18.9

1

18.10

rank-nullity theorem

1

18.11

2

18.12

rational equations

2

18.13

rational exponents

1

18.14

rational expressions

1

18.15

rational functions

4

18.16

rational inequalities

2

18.17

rational numbers

2

18.18

rational root theorem

3

18.19

rationalization

2

18.20

2

18.21

3

18.22

reciprocal functions

1

18.23

rectifiable curves

1

18.24

recurrence relation

1

18.25

1

18.26

reduction formula

1

18.27

reduction formulas

1

18.28

reference angles

1

18.29

1

18.30

1

18.31

regular polygons

1

18.32

2

18.33

1

18.34

remainder theorem

2

18.35

remarkable limits

1

18.36

removable discontinuity

1

18.37

residue classes

1

18.38

2

18.39

reverse mode autodiff

1

18.40

reverse triangle inequality

1

18.41

riemann integrability

3

18.42

1

18.43

2

18.44

2

18.45

right-hand derivative

1

18.46

1

18.47

1

18.48

1

18.49

rolle's theorem

1

18.50

1

18.51

3

18.52

roots and coefficients

1

18.53

roots of an equation

1

18.54

1

18.55

1

18.56

rouché-capelli theorem

1

18.57

1

18.58

1

19.S

19.1

1

19.2

1

19.3

1

19.4

1

19.5

sample variance

1

19.6

sampling distribution

1

19.7

sampling without replacement

1

19.8

1

19.9

1

19.10

scalar multiplication

1

19.11

scalar velocity

2

19.12

1

19.13

schwarz's theorem

1

19.14

4

19.15

secant and cosecant integrals

1

19.16

1

19.17

second derivative

1

19.18

second derivative test

1

19.19

1

19.20

separable differential equation

1

19.21

separable differential equations

2

19.22

separation of variables

1

19.23

1

19.24

4

19.25

sequences of functions

1

19.26

sequential characterization

1

19.27

7

19.28

series convergence

3

19.29

series with positive terms

1

19.30

1

19.31

set intersection

1

19.32

1

19.33

1

19.34

1

19.35

1

19.36

sigmoid function

1

19.37

4

19.38

2

19.39

1

19.40

sign permanence

1

19.41

1

19.42

1

19.43

1

19.44

5

19.45

sine and cosine

1

19.46

sine cosine tangent

1

19.47

1

19.48

sine inequality

1

19.49

singular matrix

1

19.50

1

19.51

1

19.52

smoothness classes

1

19.53

1

19.54

solid of revolution

2

19.55

solids of revolution

1

19.56

solution classification

1

19.57

solution methods

1

19.58

solution of linear systems

1

19.59

4

19.60

1

19.61

spherical coordinates

1

19.62

1

19.63

1

19.64

squaring inequalities

1

19.65

squeeze theorem

2

19.66

standard deviation

2

19.67

standard equation

1

19.68

standard normal distribution

5

19.69

standard normal z tables

2

19.70

standard position

1

19.71

stationary point

2

19.72

stationary points

1

19.73

stirling’s approximation

1

19.74

strong induction

1

19.75

student's t distribution

1

19.76

1

19.77

1

19.78

2

19.79

1

19.80

successor function

1

19.81

sum and difference formulas

2

19.82

1

19.83

2

19.84

supremum and infimum

1

19.85

surface element

1

19.86

surface of revolution

1

19.87

1

19.88

surjective function

2

19.89

symmetric equation

1

19.90

symmetric group

1

19.91

symmetric polynomials

1

19.92

1

19.93

1

19.94

synthetic division

1

19.95

1

19.96

systems of inequalities

2

19.97

systems of linear equations

2

20.T

20.1

4

20.2

tangent and cotangent

1

20.3

tangent function

2

20.4

tangent inequality

1

20.5

1

20.6

tangential acceleration

2

20.7

taylor expansion

1

20.8

taylor expansions

2

20.9

1

20.10

taylor polynomial

2

20.11

3

20.12

telescoping series

1

20.13

text similarity

1

20.14

1

20.15

1

20.16

theorem proving

1

20.17

2

20.18

thomae function

1

20.19

thomae’s function

1

20.20

three variables

1

20.21

three-sigma rule

1

20.22

1

20.23

torsion modules

1

20.24

1

20.25

transcendental equation

1

20.26

transcendental numbers

1

20.27

1

20.28

1

20.29

1

20.30

trapezoidal rule

1

20.31

triangle inequality

2

20.32

2

20.33

1

20.34

trigonometric equations

2

20.35

trigonometric form

1

20.36

trigonometric form of complex numbers

1

20.37

trigonometric function

1

20.38

trigonometric functions

3

20.39

trigonometric identities

7

20.40

trigonometric inequalities

1

20.41

trigonometric integral

2

20.42

trigonometric integrals

2

20.43

trigonometric limits

2

20.44

trigonometric substitution

4

20.45

6

20.46

trinomial equation

1

20.47

1

20.48

1

20.49

1

21.U

21.1

1

21.2

uniform continuity

2

21.3

uniform convergence

2

21.4

uniform distribution

1

21.5

uniform rectilinear motion

1

21.6

uniformly accelerated motion

1

21.7

unique factorization

1

21.8

uniqueness of the limit

1

21.9

8

21.10

upper and lower sums

1

22.V

22.1

vandermonde identity

1

22.2

vanishing gradient

1

22.3

4

22.4

vector addition

1

22.5

vector equation

1

22.6

vector representation

1

22.7

3

22.8

3

22.9

vector velocity

1

22.10

1

22.11

2

22.12

2

22.13

1

22.14

vertical asymptotes

3

22.15

vertical tangent

1

22.16

vieta's formulas

6

22.17

2

23.W

23.1

1

23.2

weierstrass criterion

1

23.3

Weierstrass substitution

2

23.4

weierstrass theorem

2

23.5

weighted geometric mean

1

23.6

weighted integral

1

23.7

well-formed formulas

1

23.8

werner formulas

1

24.Z

24.1

1

24.2

1

24.3

zero product property

1

24.4

zero-product property

1

24.5

zeros of a function

1

Content on Algebrica.org is licensed under a CC Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. For more details, see the full license.