Xah Math Notes

basic calculus

• Logarithm

• Antiderivative#cite note-1
• Integral

• E (mathematical constant)
• Euler's formula
• Exponential function
• Characterizations of the exponential function

• Closed-form expression
• Binomial theorem

complex analysis

• Euler's identity

• Holomorphic function
• Riemann sphere
• Riemann surface
• Möbius transformation

statistics, probability

• Descriptive statistics
• Probability theory

• Probability distribution
• Normal distribution
• Law of large numbers

• Random walk
• Markov chain

• Bertrand paradox (probability)
• Boy or girl paradox

Proof theory

• Proof theory
• Intuitionistic logic
• Model theory
• NP (complexity)
• Combinatory logic
• Constructive proof
• Tarski's undefinability theorem
• Sequent calculus
• Natural deduction
• Russell's paradox
• Foundations of mathematics
• Computability theory
• Rice's theorem
• Computable function
• Zermelo–Fraenkel set theory
• Nondeterministic algorithm

type theory

• Intuitionistic type theory

• Well-ordering theorem
• Partially ordered set
• Univalent foundations
• Typing rule

• Type theory
• Yoneda embedding
• Morphism
• Calculus of constructions
• Completed infinity
• Constructive mathematics
• Martin-Löf type theory
• Total function
• Category theory
• Axiom of choice
• Well-order
• Dependent type#Comparison of languages with dependent types
• Ackermann function
• Large numbers#Systematically creating ever-faster-increasing sequences

• Lambda cube
• Sudan function

logic

• https://johncarlosbaez.wordpress.com/2014/09/08/the-logic-of-real-and-complex-numbers/

• Robert Ammann
• Post's lattice
• Clone (algebra)
• Projection (set theory)

• First-order logic
• Second-order logic
• Primitive recursive function
• Effective method
• Completeness (logic)
• Soundness
• Axiom schema

• Emil Leon Post

• Post's lattice#cite note-2
• Curry–Howard correspondence
• Peano axioms#Models

• Linear logic
• Shift-and-add algorithm

algebra

• Algebraic theory
• Universal algebra
• Algebraic structure
• Ring (mathematics)
• Field (mathematics)
• Galois theory
• Monoid
• Binomial theorem
• Associativity
• Abel–Ruffini theorem

group theory

• Normal subgroup
• Quotient group

• Free group

• Lattice (group)

• Presentation of a group
• Absolute presentation of a group
• Abelian group#Historical remarks

• Field theory (mathematics)
• Valuation (algebra)
• Group extension
• Groupoid#Comparing the definitions

• Octonion
• Cayley–Dickson construction
• Group representation
• Group (mathematics)
• Subgroup
• Commutative#History and etymology
• Algebraic group
• Group homomorphism

• Generating set of a group
• Permutation group
• Group action
• Symmetric group
• Symmetry group
• Free group
• Normal subgroup
• Representation theory

linear algebra

• Inner product space

• Linear map
• Determinant
• Determinant#Abstract algebraic aspects

• Bounded operator

topology

• Topology

• Topological space

• Pointless topology
• Geometric topology
• Algebraic topology
• General topology#Baire category theorem

• Homeomorphism
• Diffeomorphic

• Arc connected#Path connectedness
• Locally connected space
• Neighbourhood (mathematics)

• Compact set
• Compact space
• Dense set
• Metric space

• Embedding
• Immersion (mathematics)

• Weierstrass function
• Koch snowflake
• Sierpiński triangle
• Cantor set
• Menger sponge

• Hausdorff dimension

• Simplicial set
• Simplex

• Topos theory

• Shape of the universe

algebraic topology

• Lie group

• Homotopy

• Fundamental domain

differential geometry

• Manifold
• Manifold theory

• Classifying space
• Euler characteristic
• Genus (mathematics)
• Gauss–Bonnet theorem

• Morse theory

• Calculus of variations

• Minimal surface

• Plateau's problem

algebraic geometry

• Homology (mathematics)

number theory

• Transcendental number
• Definable real number
• Continued fraction

• Riemann hypothesis

• Fibonacci number

projective geometry

• Projective space
• Projective plane
• Homogeneous coordinates
• Homogeneous space
• Incidence structure

randomness, chaos theory

• Entropy (computing)
• Entropy (information theory)
• Kolmogorov randomness
• Algorithmic randomness
• Logistic map

misc shit

• State of matter
• Modulation
• Isomorphic keyboard
• Radio wave
• Electromagnetic spectrum
• Song to the Auspicious Cloud

• Blockchain
• Bitcoin
• Fractional-reserve banking

functional analysis

• Functional analysis

• Open mapping theorem

• Function space

basic geometry

• Circles of Apollonius
• Apollonian circles

general geometry

• One-dimensional space
• Affine space
• Coordinate rotation
• A Guide to the Classification Theorem for Compact Surfaces
• Rotation system
• Erlangen Program

• Algebraic geometry
• Algebraic variety
• Élie Cartan
• Fundamental group
• Normed linear space
• Complete metric space

• Cubic plane curve
• Hilbert's Nullstellensatz
• Real projective plane

• Hilbert space

• Banach space

• Hyperbolic space

unsorted, misc math

• Non-Euclidean geometry

• Cantor function
• Splitting field
• Combinatorics
• Quadratic form
• Homogeneous polynomial
• List of unsolved problems in mathematics

• Hilbert's program
• History of mathematics
• Magic squares
• Hilbert's problems#The 24th problem
• Thomae's function