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05 Math
01 Encyclopedia
Algebra
binomial coefficient
binomial
degree of a polynomial
greatest common divisor
polynomial
trinomial
Arithmetic
absolute value
addition
equation
expression
logarithm
multiplication
term
variable
Calculus
antiderivative
critical point
definite integral
derivative
l'Hopital's rule
limit
Code Theory
Hamming distance
minimum Hamming distance
Combinatorics
permutation
Complex Numbers
complex conjugate
Foundations
axiom
axiomatic system
corollary
interpretation
lemma
mathematical object
mathematical property
model
primitive notion
theorem
Functions
bijection
endofunction
equality as functions
function of a real variable
function
injection
inverse function
involution
real function
real-valued function
root
support
surjection
Fundamentals
counting
equality
formula
identity
juxtaposition
open formula
ordered pair
tuple
universe
value
Geometry
Coordinate
Cartesian coordinate system
coordinate system
polar coordinate system
Models
three-point geometry
Systems
incidence geometry
angle
area
collinearity
congruence
displacement
distance
graph
isometry
parallel
perimeter
point
position
space
transformation
transversal
Groups
abelian group
cyclic group
dihedral group
general linear group
group center
group
linearly ordered group
order in a group
order of a group
subgroup
Homogeneous Relations
antisymmetric relation
asymmetric relation
connected relation
equivalence relation
irreflexive relation
reflexive relation
strongly connected relation
symmetric relation
transitive relation
trichotomous relation
Linear Algebra
augmented matrix
eigenvector
identity matrix
invertible matrix
linear combination
linear independence
linear system
matrix
Logic
Logical Operations
alternative denial
biconditional
conjunction
converse implication
converse nonimplication
disjunction
exclusive disjunction
joint denial
logical connective
material implication
material nonimplication
negation
Logical Quantifiers
logical quantifier
fallacy
formal language
proposition
truth value
Measure
measurable function
measurable set
measurable space
measure space
measure
pushforward measure
sigma algebra
Metric
metric space axioms
metric space
metric
Morphism
automorphism
endomorphism
homomorphism
isomorphism
Numbers
Number Systems
algebraic number
complex number
imaginary number
integer
irrational number
rational number
transcendental number
whole number
Sequences
triangular number
Euler's number
imaginary unit
number
Operations
associativity
binary operation
Cartesian product
commutativity
distributivity
operation
operator
Order
Orderings
partial order
preorder
strict partial order
strict total order
strict weak order
strict well-order
total order
weak order
well-order
Hasse diagram
order-convex set
ordering
partially ordered set
preordered set
well-ordering principle
Probability
Distribution
Examples
Bernoulli distribution
binomial distribution
continuous uniform distribution
exponential distribution
normal distribution
Poisson distribution
cumulative distribution function
probability density function
probability distribution
probability mass function
Experiment
Bernoulli trial
binomial experiment
collectively exhaustive events
event space
event
experiment
mutually exclusive events
sample space
Structure
probability axioms
probability measure
probability space
conditional probability
probability
random variable
Proof
induction
reductio ad absurdum
Propositional Logic
contradiction
truth function
Real Analysis
continuous function
law of trichotomy
Riemann sum
Relations
Domain
codomain of definition
codomain
domain of definition
domain
Properties
Totality
surjective relation
total relation
Uniqueness
functional relation
injective relation
bijective relation
binary relation
complementary relation
composition of relations
converse relation
equivalence class
finitary relation
relation
Rings
endomorphism ring
ring
Sequences
arithmetic sequence
geometric sequence
sequence
Series
geometric series
partial sum
series
Sets
Intervals
interval
nested intervals
partition of an interval
Set Operations
set complement
set difference
set intersection
set union
bounded set
cardinality
closure
countable
De Morgan's laws
disjoint sets
element
empty set
equality as sets
identity element
inclusion-exclusion principle
indicator function
inverse element
multiplicity
multiset
partition of a set
power set
set
singleton
Shapes
Polygons
Quadrilaterals
kite
parallelogram
quadrilateral
rectangle
rhombus
square
trapezoid
Triangles
triangle
regular polygon
curve
line
shape
Statistics
correlation coefficient
covariance
expected value
quantile
random sample
standard deviation
standard score
statistic
variance
Structures
algebraic structure
field
integral domain
linear subspace
magma
monoid
semigroup
structure
Trigonometry
cofunction
law of cosines
trigonometric function
trigonometry
Vectors
dot product
inner product space
inner product
vector space
Euclid's postulates
Euler's product formula
Euler's totient function
Markov chain
Pascal's identity
Pascal's triangle
pigeonhole principle
Russel's paradox
unit circle
02 Distinctions
comparable and incomparable elements
convergent and divergent series
degree wrt polynomial
discrete and continuous random variables
discrete and continuous variables
finite and infinite
greatest and least elements
homogeneous and heterogeneous relations
independent and dependent events
independent and dependent random variables
independent and dependent variables
maximal and minimal elements
subset and superset
supremum and infimum
upper and lower bounds
03 Theorems
Abstract Algebra
A group element of finite order generates a finite cyclic subgroup of that order.
A group element of infinite order generates an infinite cyclic subgroup.
Cyclic subgroups are equivalent if one power is expressible as the gcd of the other with the order of the base.
Every permutation is the product of disjoint cycles.
Every power of a group element with infinite order is unique.
Every subgroup of a cyclic group is itself cyclic.
For each factor of the order of a cyclic group, the number of elements in the group with the order of that factor is equal to the number of totatives of the factor.
Fundamental Theory of Cyclic Groups
Greatest Common Divisor is expressible as a linear combination of its arguments
Group Cancellation Laws
If a group is finite, then every element has finite order.
Powers distribute over an operation if and only if the group is abelian.
The group center is a subgroup.
The identity element of a group is unique.
The inverse of an element in a group is unique.
The order of a group element divides the difference in exponent of equivalent powers of that element.
The order of a group element to some power is equal to the order of the generator, divided by the gcd of the order of the generator with the power of the element.
The order of any cyclic subgroup divides the order of any cyclic group which contains it.
The product of two elements with finite order which commute in a group has finite order which divides the product of the orders of the elements.
There is exactly one subgroup of the order of each divisor of the order of its container cyclic group.
Algebra
Fundamental Theorem of Algebra
Calculus
decomposition of definite integral
Fundamental Theorem of Calculus
swapping limits of integration in definite integral
Code Theory
An error correcting code has disjoint Hamming balls.
Hamming distance for binary codes can be calculated using the binomial coefficient.
Sphere Packing Bound
The cardinality of a Hamming ball is the total number of elements that are any distance up to and including its radius.
Fallacy
Division by Zero Fallacy
Fundamentals
principle of mathematical induction
Geometry
triangle inequality
Linear Algebra
A regular Markov chain has a stationary distribution and it is unique.
Fundamental Theorem of Regular Markov Chains
Markov chain contraction mapping
Number Theory
An odd number squared is odd.
Pascal's rule
The square root of two is irrational.
Probability
Bayes's theorem
law of total probability
multiplication rule for conditional probability
Real Analysis
Archimedean property
Cantor's theorem
density theorem
Every number is between two natural numbers
nested intervals property
The infimum of the set of reciprocals of the natural numbers is zero.
Statistics
central limit theorem
Triangular Numbers
The sum of two consecutive triangular numbers is a square number.
Bernoulli's inequality
binomial theorem
Division Algorithm
Euler's formula
Euler's theorem
Euler's totient function is multiplicative for coprime values.
Pythagorean theorem
04 Explainers
converting between cartesian and polar coordinates
error detection and correction
horizontal transformation of functions
introduction to probability
synthetic division
15 LaTeX
01 Showcase
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