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REFERENCES
TOC
DETAILED CONTENTS
NEWS & UPDATES
MAPS
OVERVIEW
HISTORY
AREAS
FOUNDATIONS
LOGIC
SETS, RELATIONS, STRUCTURES
EQUIVALENCE, ORDER, ALGEBRAIC, TOPOLOGICAL...
SPACES (VECTOR, EUCLIDEAN, AFFINE, PROJECTIVE...)
MEASURE, METRIC (DISTANCE)
NUMBERS
ALGEBRA
LINEAR ALGEBRA
POLYNOMIALS & EQUATIONS
GROUP THEORY
RINGS & FIELDS
MODULES & VECTOR SPACES
LINEAR MAPS, MATRICES & DETERMINANTS
GALOIS THEORY
GEOMETRY
TRIGONOMETRY
ANALYTICAL GEOMETRY
ANALYSIS
REAL ANALYSIS
DIFFERENTIAL & INTEGRAL CALCULUS
COMPLEX ANALYSIS
TOPOLOGY
COMBINATORICS
PROBABILITIES
STATISTICS
APPLIED MATHEMATICS
MECHANICS
ELECTROMAGNETISM
ATOMISTIC
COSMOLOGY
CHEMISTRY
THEORETICAL COMPUTING
SOCIAL SCIENCES
ENGINEERING
REFERENCES
TOC
MAPS
TOC
OVERVIEW
(Caratini Tout en 1) V1 PDF
(Caratini Collection, Sommaire détaillé) V1 PDF
(Caratini Encyclopédie, Sommaire) V1 JPG
(Caratini Panorama, Sommaire Détaillé) V1 JPG
(Isoz, Contents & Chapter 3 Introduction) V1 PDF
(Walusinski Base Term, Sommaire détaillé & "Faire des Maths") V1 PDF
(Kahn Col CNED, Sommaire détaillé) V1 PDF
(Caratini Panorama, Sommaire Détaillé & Intro) V1 PDF
METHODS
VOCABULARY
SCIENCE & FAITH
SCIENTIFIC COMMUNICATION BACKFIRE
TOC
HISTORY
(Caratini Collection, Histoire des maths) V1 PDF
TOC
AREAS
(Reinhardt Atlas différents domaines) V1 PDF
TOC
FOUNDATIONS
Category theory - Information theory - Mathematical logic - Philosophy of mathematics - Set theory - Type theory
MATHEMATICAL LOGIC
Peano axioms -
Mathematical induction - Formal system - Axiomatic system -
Hilbert system - Natural deduction - Mathematical proof - Model theory
--Mathematical constructivism - Modal logic - List of mathematical
logic topics
SET THEORY
Set - Naive set
theory - Axiomatic set theory - Zermelo set theory - Zermelo–Fraenkel
set theory - Constructive set theory - Descriptive set theory -
Determinacy - Russell's paradox - List of set theory topics
TYPE THEORY
Axiom of
reducibility - Simple type theory - Dependent type theory -
Intuitionistic type theory - Homotopy type theory - Univalent
foundations - Girard's paradox
CATEGORY THEORY
Category - Topos
theory - Category of sets - Higher category theory - ∞-groupoid -
∞-topos theory - Mathematical structuralism - Glossary of category
theory - List of category theory topics
METALOGIC & METAMATHEMATICS
Cantor's
theorem - Entscheidungsproblem - Church–Turing thesis - Consistency -
Effective method - Foundations of mathematics (of geometry) - Gödel's
completeness theorem - Gödel's incompleteness theorems - Soundness -
Completeness - Decidability - Interpretation - Löwenheim–Skolem
theorem- Metatheorem - Satisfiability- Independence - Type–token
distinction - Use–mention distinction
TOC
MATHEMATICAL LOGIC
(Isoz, Proof Theory) V1 PDF
GENERAL
Axiom
(list) - Cardinality - First-order logic - Formal proof - Formal
semantics - Foundations of mathematics - Information theory - Lemma -
Logical consequence - Model - Theorem - Theory - Type theory
THEOREMS (LIST) & PARADOXES
Gödel's
completeness and incompleteness theorems - Tarski's undefinability -
Banach–Tarski paradox - Cantor's theorem, paradox and diagonal argument
- Compactness - Halting problem - Lindström's - Löwenheim–Skolem
- Russell's paradox
TRADITIONAL
Classical logic
- Logical truth - Tautology - Proposition- Inference - Logical
equivalence - Consistency - Equiconsistency - Argument - Soundness -
Validity - Syllogism - Square of opposition - Venn diagram
PROPOSITIONAL
Boolean algebra
- Boolean functions - Logical connectives - Propositional calculus -
Propositional formula - Truth tables- Many-valued logic 3 finite ∞
PREDICATE
First-order list - Second-order Monadic - Higher-order - Fixed-point - Free Quantifiers - Predicate - Monadic predicate calculus
FORMAL SYSTEMS (LIST), LANGUAGE AND SYNTAX
PROOF THEORY
MODEL THEORY
COMPUTABILITY THEORY
FOUNDATIONS CRISIS
PARADOXES
Hypothetical-Deductive Reasoning
PROPOSITIONAL CALCULUS
Propositions (premises)
Connectors
Decision procedures
Quantifiers
PREDICATE CALCULUS
Grammar
Languages
PROOFS
Rules of Proofs
TOC
SETS,
RELATIONS & STRUCTURES
(Caratini Collection, Généralités sur Ensembles Arithmétique Nombres Algèbre) V1 PDF
(Caratini Collection, Théorie des Ensembles) V1 PDF
(Souriac, Notions Fondamentales) V1 PDF
(Isoz, Set Theory) V1 PDF
(Caratini Panorama, AnnexeTheorie des ensembles & Algèbre des Structures) V1 PDF
(Caratini Collection, Algèbre des Structures) V1 PDF
(Caratini Panorama, 3 Algèbres - Notion de Sructure - Théorie des groupes - Analyse Histoire ) V1 PDF
(Bouvier Théorie Ensembles Sommaire) V1 JPG
(Bouvier Théorie Ensembles QSJ) V1 PDF
SET THEORY
OVERVIEW
Cardinals
Cartesian Product
Intervals
Set
hereditary - Class(Ur-) - Element - Ordinal number - Extensionality -
Forcing - Relation equivalence partition - Set operations: intersection
union complement - Cartesian product power set identities
AXIOMS
Adjunction -
Choice (countable dependent global) - Constructibility (V=L) -
Determinacy - Extensionality - Infinity - Limitation of size - Pairing
- Power set - Regularity - Union - Martin's axiom
Axiom schema (replacement specification)
OPERATIONS
Cartesian
product - Complement (i.e. set difference) - De Morgan's laws -
Disjoint union - Identities - Intersection - Power set - Symmetric
difference - Union
Inclusion
Intersection
Union
Difference
Symmetric Difference
Product
Complementarity
CONCEPTS - METHODS
Almost -
Cardinality - Cardinal number (large) - Class - Constructible universe
- Continuum hypothesis - Diagonal argument - Element ordered pairtuple
- Family - Forcing - One-to-one correspondence - Ordinal number -
Set-builder notation - Transfinite induction -Venn diagram
SET TYPES
Countable
- Uncountable - Empty - Inhabited - Singleton - Finite - Infinite -
Transitive - Ultrafilter- Recursive - Fuzzy- Universal - Universe
constructible -Grothendieck -Von Neumann
Amorphous
- Countable-- Empty - Finite (hereditarily) - Filter basesubbase -
Ultrafilter - Fuzzy - Infinite (Dedekind-infinite) - Recursive -
Singleton - Subset · Superset - Transitive - Uncountable - Universal
MAPS & CARDINALITY
Function
/ Map domain codomain image In/Sur/Bi-jection - Schröder–Bernstein
theorem - Isomorphism - Gödel numbering - Enumeration - Large cardinal
inaccessible -Aleph number - Operation binary
THEORIES
Zermelo–Fraenkel
axiom of choice continuum hypothesis - General - Kripke–Platek
-Morse–Kelley -Naive - New Foundations- Tarski–Grothendieck - Von
Neumann–Bernays–Gödel- Ackermann - Constructive
Alternative - Axiomatic - Naive - Cantor's theorem
Zermelo
(General) - Principia Mathematica (New Foundations) - Zermelo-Fraenkel
(von Neumann–Bernays–Gödel (Morse–Kelley)-
Kripke–PlatekTarski–Grothendieck)
PARADOXES - PROBLEMS
Russell's paradox - Suslin's problem - Burali-Forti paradox
SET THEORISTS
Paul
Bernays - Georg Cantor - Paul Cohen - Richard Dedekind - Abraham
Fraenkel - Kurt Gödel - Thomas Jech - John von Neumann - Willard Quine
- Bertrand Russell -Thoralf Skolem - Ernst Zermelo
RELATIONS xxxxxxxxxxxx
BINARY RELATION
EQUIVALENCE RELATION
ORDER RELATION
FUNCTIONS, APPLICATIONS
STRUCTURES
MORPHISMS
ALGEBRAIC STRUCTURES
COMMON AXIOMS
EQUATIONAL AXIOMS
Commutativity
Associativity
Left distributivity
Right distributivity
Distributivity
EXISTENTIAL AXIOMS
Identity element
Inverse element
NON-EQUATIONAL AXIOMS
GROUP-LIKE STRUCTURES
MAGMA
MONOID & GROUP
ABELIAN GROUP
RING-LIKE STRUCTURES
RING
DIVISION RING
COMMUTATIVE RING
FIELD
LATTICE-LIKE STRUCTURES
COMPLETE LATTICE
BOUNDED LATTICE
DISTRIBUTIVE LATTICE
BOOLEAN ALGEBRA
MODULE-LIKE STRUCTURES
VECTOR SPACE
ALGEBRA OVER A FIELD
INNER PRODUCT SPACE
AFFINE SPACE
EUCLIDEAN SPACE
ALGEBRA-LIKE STRUCTURES
NON-ALGEBRAIC STRUCTURES
ORDER
TOPOLOGICAL
MEASURE
METRIC
GEOMETRY
DIFFERENTIAL
UNIFORM
EVENT
UNIVERSAL ALGEBRA
CATEGORY
TOC
NUMBERS
(Isoz) V1 PDF
(Caratini Collection, Arithmétique & Théorie des Nombres) V1 PDF
(Caratini Collection, Annexe Arithmétique élémentaire et Calcul algébrique classique) V1 PDF
(Caratini Collection, Annexe Arithmétique élémentaire : Numération, Calcul sur nbs entiers, PGCD PPCM Caractères de divisibilité)
(Caratini Collection, Annexe Fractions et Rapports : Calcul sur fractions, Rapports et proportions )
(Caratini
Collection, Annexe Calcul algébrique élémentaire : Nbs relatifs, Opérations
sur, Généralités, Polynomes, Fractions rationnelles)
(Caratini Collection, Nombres Réels et Nombres Complexes) V1 PDF
OVERVIEW
DIGITAL BASES
IRRATIONAL NUMBERS
TRANSFINITE NUMBERS
QUATERNION NUMBERS
ALGEBRAIC & TRANSCENDENTAL NUMBERS
UNIVERSE NUMBERS (NORMAL NUMBERS)
ABSTRACT NUMBERS (VARIABLES)
NATURAL INTEGER NUMBERS
(Souriac, N, dénombrements) V1 PDF
RELATIVE INTEGER NUMBERS
(Souriac, Z diviseurs multiples congruences numération ) V1 PDF
RATIONAL NUMBERS
(Souriac, Q intro à R) V1 PDF
REAL NUMBERS
(Souriac, R calculs approchés) V1 PDF
COMPLEX NUMBERS
(Souriac, C images géom) V1 PDF
TOC
ARITHMETIC OPERATORS
(Isoz) V1 PDF
BINARY RELATIONS
Equalities
Comparators
FUNDAMENTAL ARITHMETIC LAWS
Addition
Subtraction
Multiplication
Division
ARITHMETIC POLYNOMIALS
ABSOLUTE VALUE
CALCULATION RULES (OPERATORS PRIORITIES)
TOC
NUMBER THEORY
(Isoz) V1 PDF
PRINCIPLE OF GOOD ORDER
INDUCTION PRINCIPLE
DIVISIBILITY
Euclidean Division
Euclidean Algorithm
Least Common Multiple
Fundamental Theorem of Arithmetic
Congruences (modular arithmetic)
Continued fraction
TOC
ALGEBRA
TOC
LINEAR ALGEBRA
(Caratini Collection, Algèbre Linéaire) V1 PDF
LINEAR SYSTEMS
LINEAR TRANSFORMATIONS
MATRICES
Rank of a matrix
Matrix Algebra
Type of Matrices
Determinant
CHANGE OF BASIS (FRAMES)
EIGENVALUES AND EIGENVECTORS
Rotation Matrices and Eigenvalues
SPECTRAL THEOREM
MATRIX DECOMPOSITIONS
Singular Value Decomposition (SVD)
LU Decomposition
Cholesky’s Decomposition
QR Decomposition
TOC
SET ALGEBRA
GROUPS ALGEBRA & GEOMETRY
Cyclic Groups
Transformations Groups
Group of Symetries
Permutations Groups
GALOIS THEORY
Elementary symmetric and Invariant Polynomials
General Vieta’s formulas
TOC
POLYNOMIALS & EQUATIONS - CALCULUS
(Caratini Collection, Polynomes & Théorie des Equations) V1 PDF
EQUATIONS & INEQUATIONS
Equations
Inequations
REMARKABLE IDENTITIES
POLYNOMIALS
Euclidean Division of Polynomials
Factorization Theorem of Polynomials
Diophantine equation
First order univariate Polynomial and Equations
Solving by circular reference
Second order univariate Polynomial and Equations
Irrational Equations
Golden Ratio
Third order univariate Polynomial and Equations
Fourth order univariate Polynomial and Equations
Trigonometric Polynomials
Cyclotomic Polynomials
Legendre Polynomials
TOC
VECTOR CALCULUS
CONCEPT OF ARROW
SET OF VECTORS
Pseudo-Vectors
Normal vector
Multiplication by a scalar .
VECTOR SPACES
Linear Combinations
Sub-vector spaces
Generating families
Linear Dependence or Independence
Base of a vectorial space
Direction Angles
Dimensions of a vector space
Extension of a free family
Rank of a finite family
Direct Sums
Affine spaces
EUCLIDEAN VECTOR SPACES
Scalar Product (Dot Product)
Cross Product
Mixed Product (triple product)
VECTORIAL FUNCTIONAL SPACE
HERMITIAN VECTOR SPACE
Hermitian Inner Product
Types of Vectors Spaces
SYSTEM OF COORDINATES
Cartesian (rectangular) Coordinate System
Spherical Coordinate System
Cylindrical Coordinate System
Polar Coordinate System
DIFFERENTIAL OPERATORS
Gradients of Scalar Field
Gradients of Vector Field
Divergences of a Vector Field
Rotationals of a Vector Field (Curl)
Laplacians of Scalar Fields (Laplace Operator)
Laplacians of Vector Fields
Remarkable Identities
Summary
TOC
TENSOR CALCULUS
TENSOR
INDICIAL NOTATION
Summation on multiple index
Kronecker Symbol
Antisymmetric Symbol (Levi-Civita symbol)
METRIC AND SIGNATURE
GRAM’S DETERMINANT
CONTRAVARIANT AND COVARIANT COMPONENTS
OPERATION IN BASIS
Gram-Schmidt Orthogonalization Method
Change of Basis
Reciprocal Basis (Dual Basis)
EUCLIDEAN TENSORS (CARTESIAN TENSOR)
Fundamental Tensor
Tensor product (dyadic) of two vectors and matrices
Tensor Spaces
Linear combination of tensors
Contraction of indices
SPECIAL TENSORS
Symmetric Tensor
Antisymmetric Tensor
Fundamental Tensor
CURVILINEAR COORDINATES
Natural basis in spherical coordinates (curvilinear basis in spherical coordinates)
Natural basis in polar coordinates (curvilinear basis in polar coordinates)
Natural basis in cylindrical coordinates (cylindrical basis in polar coordinates)
CHRISTOFFEL SYMBOLS
RICCI THEOREM
RIEMANN-CHRISTOFFEL SYMBOLS
RICCI CURVATURE (RICCI TENSOR)
EINSTEIN TENSOR
TOC
SPINOR CALCULUS
UNIT SPINOR
GEOMETRIC PROPERTIES
Plane Symmetries
Rotations
Properties of Pauli Matrices
TOC
GEOMETRY
TOC
TRIGONOMETRY
(Souriac) V1 PDF
RADIAN
CIRCLE TRIGONOMETRY
Remarkable trigonometric triangle identities
HYPERBOLIC TRIGONOMETRY
Remarkable hyperbolic identities
SPHERICAL TRIGONOMETRY
SOLID ANGLE
TOC
EUCLIDEAN GEOMETRY
OBJECTS OF EUCLIDEAN GEOMETRY
Dimensions
EUCLID’S CONSTRUCTIONS
Segments and Lines
PLANE GEOMETRY
Displacements and Turnarounds
Plane angles
Triangles
Parallelism
Circle
HILBERT’S AXIOMS
Incidence Axioms (axioms of association)
Order Axioms
Congruence Axioms
Continuity Axioms
Parellels Axioms
BARYCENTER (CENTROID)
GEOMETRIC TRANSFORMATIONS
Translation
Homothety (scaling)
Shear (skew) transformation
Rotation
Reflection
TOC
NON-EUCLIDEAN GEOMETRY
CURVATURE(S)
AXIOMS OF NON-EUCLIDEAN GEOMETRY
GEODESIC AND METRIC EQUATION
RIEMANN SPACES
TOC
PROJECTIVE GEOMETRY
CONICAL PERSPECTIVE (CENTRAL PERSPECTIVE)
Images of Points
Images of Straight Lines
AFFINE PROJECTIONS
Isometric perspective
Oblique perspective
Orthogonal projection
SPHERICAL PROJECTIONS
Stereographic projection
Cylindrical projection
Mercator projection
Lambert’s equivalent projection (Peters projection)
OTHER PERSPECTIVES
HOMOGENEOUS COORDINATES (PROJECTION COORDINATES)
P2 Projective Space
P3 Projective Space
TOC
ANALYTICAL GEOMETRY
CONICS
Algebraic approach
Geometric Approach
Dudelin Theorem (Dudelin Spheres)
Classification of conical by the determinant
PARAMETRIZATIONS
Equation of the Plane
Equation of the Straight line
Equation of a Square
Equation of a Cycloid
Equation of an Epicycloid
Equation of an Hypocycloid
Surface of revolution
TOC
DIFFERENTIAL GEOMETRY
PARAMETRIC CURVES
ISOLINES
FRENET FRAME
SURFACE PATCHS
Metric of a Surface Patch
TOC
GEOMETRIC SHAPES
USUAL SURFACES (AREAS)
Polygons
Rectangle
Square
Unspecified Triangle
Isosceles Triangle
Equilateral Triangle
Right Triangle
Trapezoid
Parallelogram
Hexagon
Rhombus
Circle
Ellipse
USUAL VOLUMES
Polyhedron
Usual Solids of Revolution
TOC
GRAPH THEORY
Type of Graphs and Structures
Graph Adjacency Matrix
Categories
TOC
KNOT THEORY
Braids Representation
Braids Group
Knot Representation
Knots Group
Tait’s Knot
Mathematical Formalisation
Planar Representation
TOC
ANALYSIS
(Souriac, fonction cont lim) V1 PDF
(Souriac, der) V1 PDF
(Souriac, suites int log etc) V1 PDF
(Caratini Panorama, Analyse sauf Annexe - Intro) V1 PDF
TOC
FUNCTIONAL ANALYSIS
(Isoz) V1 PDF
REPRESENTATIONS
Tabular Representation
Graphical Representation
Analytical Representation
FUNCTIONS
Limits and Continuity of Functions
Asymptotes
Concavity/Convexity of a function
LOGARITHMS
CONVOLUTIONS
Continuous and Discrete Linear Convolution Product
Matrix Convolution
INTEGRAL TRANSFORMS
Fourier Transform
Laplace Transform
Z-Transform
Hilbert Transform
FUNCTIONAL DOT PRODUCT (INNER PRODUCT)
Cauchy-Schwarz inequality for integrals
TOC
DIFFERENTIAL & INTEGRAL CALCULUS
DIFFERENTIAL CALCULUS
Differentials
Usual Derivatives
Implicit Differentiation
Smoothness
INTEGRAL CALCULUS
Definite Integral
Indefinite Integral
Double Integral
Integration by Substitution
Integration by Parts
Usual Primitives
Integral representation of first kind Bessel’s function
Dirac Function
Gamma Euler Function
Curvilinear Integrals
Integrals involving parametric equations
Improper Integrals
Elliptic Integrals
DIFFERENTIAL EQUATIONS
First order differential equations
Linear differential equations
Resolution methods of differential equations
Classification of partial differential equations
SYSTEMS OF DIFFERENTIAL EQUATIONS
REGULAR METHODS OF PERTURBATIONS
Perturbation theory for algebraic equations
Perturbation theory of differential equations
TOC
SEQUENCES & SERIES
SEQUENCES
Arithmetic Sequences
Harmonic Sequences
Geometric Sequences
Cauchy Sequence
Fibonacci Sequence
Logic Sequences/Psychologist Sequences
SERIES
Gauss Series
Arithmetic Series
Geometric Series
Telescoping Series
Grandi’s Series
Taylor and Maclaurin Series
Fourier Series (trigonometric series)
Bessel Series
CONVERGENCE CRITERIA
Integral Test
D’Alembert Rule
Alternating Series Test
Fixed Point Theorem
GENERATING FUNCTIONS (TRANSFORMATION OF A SEQUENCE INTO A SERIES)
Ordinary Generating Functions (transformation of a sequence into a series)
Multivariate Generating Functions
Functional Generating Functions
TOC
COMPLEX ANALYSIS
LINEAR APPLICATIONS
HOLOMORPHIC FUNCTIONS
Orthogonality of real and imaginary iso-curves
COMPLEX LOGARITHM
COMPLEX INTEGRAL CALCULUS
Convergence of a complex series
PATH DECOMPOSITION
Inverse Path
LAURENT SERIES
SINGULARITIES
RESIDUE THEOREM
Pole at infinity
TOC
TOPOLOGY
GENERAL TOPOLOGY
Topological Spaces
METRIC SPACE AND DISTANCE
Equivalent Distances
Lipschitz Functions
Continuity and Uniform Continuity
OPENED AND CLOSED SET
Balls
Partititions
Formal Ball
Diameter
VARIETIES
Subvariety
Surfaces Homeomorphism
Differential Varieties
TOC
MEASURE THEORY
MEASURABLE SPACES
Monotone Classes
TOC
COMBINATORICS - COMBINATORIAL ANALYSIS
(Souriac) V1 PDF
(Caratini Collection, Analyse Combinatoire)
V1 PDF
Simple Arrangements with Repetitions
Simple Permutations without Repetitions
Simple Permutations with Repetitions
Simple Arrangements without Repetitions
Simple Combinations without Repetitions
Simple Combinations with Repetitions
TOC
PROBABILITIES
(Souriac) V1 PDF
(Caratini Collection Histoire et Notions) V1 PDF
EVENT UNIVERSE
Infinite monkey theorem
Do probabilities refute complex structures?
KOLMOGOROV’S AXIOMS
CONDITIONAL PROBABILITIES
Conditional Expectation and Variance
Bayesian Networks
MARTINGALES
Gambling
MARKOV CHAINS
TOC
STATISTICS
SAMPLES
AVERAGES
Laplace Smoothing
Means and Averages properties
TYPE OF VARIABLES
Discrete Variables and Moments
Continuous Variables and Moments
FUNDAMENTAL POSTULATE OF STATISTICS
DIVERSITY INDEX
DISTRIBUTION FUNCTIONS (PROBABILITIES LAWS)
Discrete Uniform Distribution
Bernoulli Distribution
Geometric Distribution
Binomial Distribution
Negative Binomial Distribution
Hypergeometric Distribution
Multinomial Distribution
Poisson Distribution
Normal & Gauss-Laplace Distribution
Log-Normal Distribution
Continuous Uniform Distribution
Triangular Distribution
Pareto Distribution
Exponential Distribution
Cauchy Distribution
Beta Distribution
Gamma Distribution
Chi-Square (Pearson) Distribution
Student Distribution
Fisher Distribution
General Folded Normal Distribution
Laplace Distribution
Benford Distribution
LIKELIHOOD ESTIMATORS
Normal Distribution MLE
Poisson Distribution MLE
Binomial Distribution MLE
Geometric Distribution MLE
Weibull Distribution MLE
Gamma Distribution MLE
Pareto Distribution MLE
Censored data MLE
Fisher Information Matrix
FINITE POPULATION CORRECTION FACTOR
CONFIDENCE INTERVALS (INFERENCE)
Frequentist Inference
Bayesian Inference
WEAK LAW OF LARGE NUMBERS
CHARACTERISTIC FUNCTION
CENTRAL LIMIT THEOREM
UNIVARIATE HYPOTHESIS AND ADEQUATION TESTS (NHST)
Direction of hypothesis test and p-values
Fisher’s method for multiple p-values
Power of a test
Power of the one sample Z-test
Power of the one and two samples P-test
A/B tests
Analysis Of VAriance (ANOVA)
Equivalence tests
Cochran C test
Adequation Tests (Goodness of Fit tests)
Kernel density estimation
Likelihood-ratio tests
Robustness and Nonparametric Statistics;
Rank Statistics
Range Statistics
Extreme Value Theory
MULTIVARIATE STATISTICS
Principal Component Analysis
Correspondence Factorial Analysis (AFC)
Chi-2 Test of Independence
Cramér’s V
Pearson’s phi coefficient
Exact Fisher’s Test
Cohen’s kappa agreement
McNemar’s test
SURVIVAL STATISTICS
Kaplan-Meier Survival Rate
Cochran–Mantel–Haenszel tests
Cox (Proportional Hazard) Model
Propagation of Errors (experimental uncertainty analysis) ;
Absolute and Relative Uncertainties (direct calculation of bias)
Statistical Errors
Repeatability
Error propagation (linearized approximation)
Error propagation (statistical approach)
Significant Numbers
Spatial statistics;
2D Poisson’s spatial distance model
SURVEYS
Survey designs
Survey Sampling Error and Non-Sampling Error
A WORLD WITHOUT STATISTICS
Data fallacies
TOC
APPLIED MATHEMATICS
TOC
MECHANICS
TOC
PRINCIPIA
SYSTEM OF UNITS
Dimensional Analysis
Scientific Notation and Metric Prefixes
Scales of Measurements
DISTRIBUTIONS
CONSTANTS
Mathematical Constants
Universal Constants (fundamental constants)
Astronomical/Astrophysical parameters and constants
Chemical parameters
Material parameters
Planck’s constants
PRINCIPLES OF PHYSICS
Principle of Causality
Principle of Conservation of Energy
Principle of Least Action
Noether’s Principle (Noether’s theorem)
Curie’s Principle
POINT SPACES
TOC
ANALYTICAL / LAGRANGIAN MECHANICS
TOC
CLASSICAL MECHANICS
TOC
WAVE MECHANICS
TOC
STATISTICAL MECHANICS
TOC
THERMODYNAMICS
TOC
CONTINUUM MECHANICS
TOC
ELECTROMAGNETISM
TOC
ELECTROSTATICS
TOC
MAGNETOSTATICS
TOC
ELECTRODYNAMICS
TOC
ELECTROKINETICS
TOC
OPTICS (RAY OPTICS)
TOC
WAVE OPTICS
TOC
ATOMISTIC
TOC
CORPUSCULAR QUANTUM PHYSICS
TOC
WAVE QUANTUM PHYSICS
TOC
RELATIVISTIC QUANTUM PHYSICS
TOC
NUCLEAR PHYSICS
TOC
QUANTUM FIELD THEORY
TOC
ELEMENTARY PARTICLE PHYSICS
TOC
COSMOLOGY
TOC
ASTRONOMY (CELESTIAL MECHANICS)
TOC
ASTROPHYSICS
TOC
SPECIAL RELATIVITY
TOC
GENERAL RELATIVITY
TOC
COSMOGONY
TOC
QUANTUM GRAVITY
TOC
STRING THEORY
TOC
CHEMISTRY
TOC
QUANTUM CHEMISTRY
TOC
MOLECULAR CHEMISTRY
TOC
ANALYTICAL CHEMISTRY
TOC
THERMOCHEMISTRY
TOC
THEORETICAL COMPUTING
TOC
NUMERICAL METHODS/ANALYSIS
TOC
FRACTALS
TOC
LOGICAL SYSTEMS
TOC
ERROR-CORRECTING CODES
TOC
AUTOMATA THEORY
TOC
CRYPTOGRAPHY
TOC
QUANTUM COMPUTING
TOC
SOCIAL SCIENCES
TOC
POPULATION DYNAMICS
TOC
GAME AND DECISION THEORY
TOC
ECONOMY
TOC
QUANTITATIVE MANAGEMENT
TOC
MUSIC MATHEMATICS (PHYSICS OF HEARING)
TOC
ENGINEERING
TOC
MARINE & WEATHER ENGINEERING
TOC
MECHANICAL ENGINEERING
TOC
ELECTRICAL ENGINEERING
TOC
CIVIL ENGINEERING
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AEROSPACE ENGINEERING
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SOFTWARE ENGINEERING
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INDUSTRIAL ENGINEERING
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REFERENCES
DIDACTIC
Caratini. Tout en 1. Mathématiques. 1994. [ Download ] [ Read ]
Caratini. Encyclopédie. Mathématiques. 1972.
Caratini. Collection. Mathématiques. 1985. [ View - Download - Backup ]
Caratini. Panorama Sciences. Mathématiques. 1993.
Souriac. MemoMath Bac Premières années de Faculté. 1977. [ Download - Backup ] [ Cf aussi du meme auteur le MemoMeca en physique ! ]
Walusinski. Les bases des Maths en classes terminales. 1976. [ Download - Backup ]
Kahn. Collection de Mathématiques du CNED. 1995. [ Bac + 2 ]
Corne et al. ABC du BAC Mathématiques. 1983.
Bouvier. Théorie des Ensembles. 3e. 1982. [ 128 pages ] [ Download ]
https://www.ukonline.be/cours/math/basehigher-summary
https://fr.wikibooks.org/wiki/Wikilivres:CDU/5/51
Bodin. Exo7 Cours et exercices de mathématiques. [ arnbod.github.io ] [ exo7.emath.fr ] [ youtube.com/@Exo7Math ]
Reinhardt. Atlas des Mathématiques. 1997. [ Commentaire ] [ Commentaire Archive ] [ Download JPG ] [ Download PDF ]
Isoz. Opera Magistris. Compendium of Elementary Applied Mathematics for Engineers (EAME). 4e. 2024. - 3e. 2018. [ 9014 pages ] [ sciences.ch ]
Glaeser. Mathématiques pour l'élève-professeur. 2e. 1973. [ Download ] [ Idées précieuses ! ]
Hadamard. Essai sur la psychologie de l'invention dans le domaine mathématique. 1975. [ Download Français ] [ Read Français ]
Hadamard. An Essay on the Psychology of Invention in the Mathematical Field. 1954. [ Download English ] [ Download English ] [ Read English ]
Soyeur.
Cours de Mathématiques Sup MPSI PCSI PTSI TSI
http://les.mathematiques.free.fr/pdf/livre.pdf [ référence utile couvrant toutes les mathématiques de première année ]
http://asoyeur.free.fr/
Perret.
https://www.vive-les-maths.net/
Monka.
http://www.maths-et-tiques.fr/
Pujo.
http://math.univ-lyon1.fr/~pujo/
http://math.univ-lyon1.fr/~pujo/PASSMaths.html
http://math.univ-lyon1.fr/~pujo/fondmath1.pdf
Poirier.
http://spoirier.lautre.net
http://settheory.net/
https://www.reddit.com/r/math/comments/15b3olx/is_anyone_familiar_with_this_websitebased/
Bailly-Maitre.
https://www.youtube.com/@MathsAdultes
Unsorted
https://www.sesamath.net/
http://villemin.gerard.free.fr/Referenc/Debutant/DebTdM.htm
https://pi.ac3j.fr/livres-de-mathematiques/
OVERVIEW
https://en.wikipedia.org/wiki/Mathematics
https://en.wikipedia.org/wiki/Lists_of_mathematics_topics
https://kevinbinz.com/quantitative/
http://serge.mehl.free.fr/
https://www.amazon.fr/Lunivers-math%C3%A9matique-Philip-J-Davis/dp/2040155880
https://statanalytica.com/blog/best-math-books/
NEWS
CLASSIFICATION
https://zbmath.org/classification/
EDUCATION
https://fr.wikipedia.org/wiki/Difficultés_en_mathématiques
https://mathvault.ca/
https://alibalilab.wiscweb.wisc.edu/wp-content/uploads/sites/371/2018/02/AlibaliNathan2012.pdf
https://fac.umc.edu.dz/fse/assets/img/Universit%C3%A9%20Fr%C3%A8res%20Mentouri%20Constantine%201.pdf
https://fac.umc.edu.dz/fse/assets/img/DDM-M1-%20%202015-2016.pdf
https://web.archive.org/web/20150219032809/http://welles.dm.unibo.it/rsddm/it/articoli/damore/395%20concettualizazione%20registri%20noetica.pdf
https://www.univ-irem.fr/
ENCYCLOPEDIAS
https://encyclopediaofmath.org/wiki/Main_Page
https://archive.org/details/CrcEncyclopediaOfMathematics/Weisstein__Eric_W_-_CRC_Concise_Encyclopedia_Mathematics_Vol_1__CRC_1999__4AH/
https://archive.org/details/encyclopedia-of-mathematics_202206
Tanton. https://doc.lagout.org/science/0_Computer%20Science/3_Theory/Mathematics/Encyclopedia%20of%20Mathematics.pdf
Wolfram. https://mathworld.wolfram.com/
https://planetmath.org/
https://archive.org/details/petite_encylopedie_des_mathematiques_dictionnaire_Pagoulatos_1980
DICTIONARIES
Bouvier.
https://archive.org/details/dictionnairedesm0000bouv
http://cefti35000.free.fr/@@PdF-/@Info/Dictionnaire_Des_Math%C3%A9matiques.pdf
https://www.softouch.on.ca/kb/data/Concise%20Oxford%20Dictionary%20of%20Mathematics.pdf
GLOSSARY - SYMBOLS
https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols
https://it.wikipedia.org/wiki/Glossario_della_simbologia_matematica
HISTORY
https://en.wikipedia.org/wiki/History_of_mathematics
LANGUAGE OF MATHEMATICS
https://en.wikipedia.org/wiki/Language_of_mathematics
https://librivox.org/uploads/xx-nonproject/Handboo for Spoken Mathematics.pdf
http://sgalex.free.fr/typo-maths_fr.pdf
FOUNDATIONS OF MATHEMATICS
https://en.wikipedia.org/wiki/Foundations_of_mathematics
https://u.osu.edu/friedman.8/ - https://www.youtube.com/@harveyfriedman4465
https://www.canal-u.tv/video/universite_de_tous_les_savoirs/les_fondements_des_mathematiques.1021
LOGIC
Wikipedia.
https://en.wikipedia.org/wiki/Logical_connective
https://en.wikipedia.org/wiki/List_of_logic_symbols
https://en.wikipedia.org/wiki/Truth_function
https://en.wikipedia.org/wiki/Logical_truth
https://en.wikipedia.org/wiki/Material_conditional
Wikipedia. Fr.
https://fr.wikipedia.org/wiki/Portail:Logique
https://fr.wikipedia.org/wiki/Liste_de_symboles_logiques
https://fr.wikipedia.org/wiki/Connecteur_logique
Exo7Math.
Logique & Raisonnements - https://youtube.com/playlist?list=PL8CE6188299CCFA23&si=JBKfgXDz-2usAJqv
Math & Phys.
Logique Mathématique - https://www.youtube.com/playlist?list=PLPMCOIL54o6VMqB7Q7tDXEfzAUGWI0fMD
Lacombe.
Tout ce que vous avez toujours voulu savoir sur la logique et qu’on n’a jamais voulu vous révéler - https://video.irem.univ-paris-diderot.fr/w/8wMr26FicscZ5s9ERHVTjB
Grandeur et misère de l'implication - https://video.irem.univ-paris-diderot.fr/w/adfa20fa-0028-4782-a864-99a7003e1280
https://www.imj-prg.fr/lm/deces-de-daniel-lacombe/
Girard.
https://girard.perso.math.cnrs.fr/Accueil.html
Cori.
Logique Mathématique. - amazon.fr
Lassaigne.
https://webusers.imj-prg.fr/~richard.lassaigne/ - amazon.fr/Logique-Fondements-LInformatique-Calculabilite-Lambda-Calcul/dp/2866013808
https://webusers.imj-prg.fr/~richard.lassaigne/coursM2/logique_07.pdf
Kreisel.
https://www.irif.fr/~krivine/articles/Elements_logique.pdf
Krivine.
amazon.fr/Th%C3%A9orie-axiomatique-ensembles-Krivine-Jean-Louis/dp/B00GO376UY - https://fr.wikipedia.org/wiki/Jean-Louis_Krivine
Unsorted.
https://encyclopediaofmath.org/index.php?title=Mathematical_logic
https://www.logicmatters.net/
https://www.reddit.com/r/math/comments/1418n9n/whats_a_good_book_to_learn_rigorous_mathematical/
https://www.pdfdrive.com/a-concise-introduction-to-logic-e185900044.html
https://www.historyoflogic.co/website-pdf/logic.pdf
https://les-mathematiques.net/vanilla/discussion/592553/livres-pour-debuter-la-logique
https://builds.openlogicproject.org/
SET THEORY
Wikipedia.
https://en.wikipedia.org/wiki/Set_theory
Unsorted.
https://iep.utm.edu/set-theo/
https://plato.stanford.edu/entries/settheory-early/
https://handbook.assafrinot.com/
https://encyclopediaofmath.org/index.php?title=Axiomatic_set_theory
https://encyclopediaofmath.org/index.php?title=Set_theory
https://ghostarchive.org/varchive/hBcWRZMP6xs
Walter B. Rudin: "Set Theory: An Offspring of Analysis" - youtu.be/hBcWRZMP6xs?si=3gnC_Qe1E7CvWiOS
https://fr.quora.com/La-diff%C3%A9rence-entre-la-fonction-et-lapplication-en-math%C3%A9matiques-autrement-dit-est-ce-que-toute-fonction-est-une-application-ou-bien-toute-application-est-une-fonction
http://tomlr.free.fr/Math%E9matiques/Bourbaki/Theorie%20Des%20Ensembles.pdf
https://fr.scribd.com/doc/45501470/Goldrei-classic-Set-Theory-for-Guided-Independent-Study
https://vdoc.pub/download/classic-set-theory-for-guided-independent-study-5bovu2or7vr0
RELATIONS & STRUCTURES
GEOMETRY
https://www.its.caltech.edu/~matilde/SpaceMath.pdf
ANALYSIS
https://cel.hal.science/cel-00519301v2
TOPOLOGY
https://math.stackexchange.com/questions/354624/is-a-topological-space-a-structure
http://www.pdmi.ras.ru/~olegviro/topoman/index.html
http://www.felixnagel.org/publications.html
A B
C D E F G H I J K
L M N O P Q R S T
U V W X Y Z
A
B
BOUVIER ALAIN
C
CARATINI ROGER
D
E
F
G
GLAESER GEORGES
https://fr.wikipedia.org/wiki/Georges_Glaeser
http://www.numdam.org/article/SPHM_1983___14_A1_0.pdf
GODEL KURT
https://web.archive.org/web/20160304192140/https://www.cs.auckland.ac.nz/~chaitin/sciamer3.pdf
https://scienceetonnante.com/2016/12/09/theoreme-godel/
H
HADAMARD JACQUES
https://www.ams.org/journals/bull/1946-52-03/S0002-9904-1946-08528-6/S0002-9904-1946-08528-6.pdf
I
J
K
KRIVINE JEAN LOUIS
https://www.irif.fr/~krivine/
L
LACOMBE DANIEL
https://publimath.apmep.fr/publimath.php?r=%22Lacombe+Daniel%22
M
N
NIMIER JACQUES
https://fr.wikipedia.org/wiki/Jacques_Nimier
http://pedagopsy.eu/page75.html
O
P
Q
R
S
T
THOM RENE
https://web.archive.org/web/20120117160729/http://people.math.jussieu.fr/~chaperon/HommageChaperon.pdf
U
V
W
X
Y
Z
UNSORTED
http://licence-math.univ-lyon1.fr/doku.php?id=a22:s1_algebre1_maths:page
http://cache.media.education.gouv.fr/file/special_3_ESR/45/6/programme-MPSI_252456.pdf
https://www.math.u-bordeaux.fr/~ayger/coursmismi.pdf
https://maths-pdf.fr/
http://maths.ac-amiens.fr/IMG/pdf/explosion_des_mathematiques.pdf
https://sites.math.rutgers.edu/~zeilberg/akherim/PCM.pdf
https://www.pdfdrive.com/princeton-companion-to-mathematics-e38277874.html
https://zbmath.org/classification/
https://mathworld.wolfram.com/
https://pi.ac3j.fr/livres-de-mathematiques/
http://sgalex.free.fr/typo-maths_fr.pdf
https://math.typeit.org/
https://www.languefrancaise.net/forum/viewtopic.php?id=13045
https://perso.univ-rennes1.fr/matthieu.romagny/agreg/ecriture_mathematique.pdf
https://www.ventsetjardins.fr/pelican/comprendre/Bibliotheque-de-maths-physique.html
SEE ALSO BIOSTATISTICS
MORE REFERENCES
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NEWS & UPDATES
DONE 2024
(Walusinski "Faire des Maths") V1 PDF
(Caratini Collection, Histoire des maths) V1 PDF
(Caratini Collection, Généralités sur Ensembles Arithmétique Nombres Algèbre) V1 PDF
(Caratini Collection, Théorie des Ensembles) V1 PDF
(Caratini Collection, Arithmétique & Théorie des Nombres) V1 PDF
(Caratini Collection, Analyse Combinatoire)
V1 PDF
(Caratini Panorama, Sommaire Détaillé & Intro) V1 PDF
(Caratini Collection, Analyse Combinatoire)
V1 PDF
(Caratini Panorama, Sommaire Détaillé & Intro) V1 PDF
(Caratini Panorama, Annexe Theorie des ensembles & Algèbre des Structures) V1 PDF
(Caratini Collection, Algèbre des Structures) V1 PDF
(Caratini Panorama, 3 Algèbres - Notion de Sructure - Théorie des groupes - Analyse Histoire ) V1 PDF
(Bouvier Théorie Ensembles QSJ) V1 PDF
(Glaeser Sommaire, Chap 00 & Chap 01) V1 PDF
(Reinhardt Atlas différents domaines) V1 PDF
References Logic Logique Cori (Lascar Lassaigne Kreisel Krivine)
TO UPLOAD
Cned geom
TO DOWLOAD
TO DO
str wikip
Reinhardt Atlas logique et car philo logique !
(Reinhardt Atlas, Théorie des ensembles : Concepts Algèbre Treillis Problématique) V1 PDF
(Reinhardt
Atlas, Relations & Structures : Relation Application Fonction
Puissance Cardinal dénombrabilité Structures Algébriques Ordre Ordinaux
Topologiques) V1 PDF
(Souriac finir !!)
(Caratini Collection, Nombres Réels et Nombres Complexes) V1 PDF et car géométrie pan finir sauf analyse
R TE Bouvier QSJ
trouver système pour articles wik et autres liens !
DOING
(Kahn CNED 2 Algèbre et Algèbre Linéaire, Chap 1 et 2) Refaire
(Kahn CNED 1 3 4 5 6 )
Opera Magistris 23 Dec et sommaire dans le détail reprendre depuis le début logique compris !!!
ABC du BAC ex de constructions alg d'ens reprendre quotient opera str et homomorp refaire ?
Caratini logique dans philosophie str
Pensée formelle ?
geom CNED
Reinhardt Atlas Logique
Bodin exo 7 et videos
STOPPED
Exo 7
Caratini Panorama ET col !
Souriac
CNED mais reprendre depuis le début avec som détaillé sur site
TE QSJ refaire avec Walunsinski
pour logique trouver un ordre de lecture et de travail
Reinhardt Atlas Logique refaire ! et après TE !
Glaeser juste avant logique
PROGRAM
Séquence pensée formelle car log et atlas log.....puis TE atlas
LOGIC
Izoz quand ?
Exo 7 finir !
Reprise ABC et CNED et TE QSJ et Souriac
Atl
Log formelle et log philo car
2 Abrégés cri
Sour méca
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