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SETS, RELATIONS, STRUCTURES
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REFERENCES
TOC
DETAILED CONTENTS
NEWS & UPDATES
MAPS
OVERVIEW
HISTORY
AREAS
EDUCATION
LANGUAGE
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 / CALCULUS
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
(Moi Support de Cours Particuliers Maths de Base) V1 PDF
(Isoz 2024, Chap 2 Warnings & 4 Intro) V1 PDF
(Glaeser 1973, Sommaire, Chap 00 Activité & Chap 01 Langage) V1 PDF
TOC
HISTORY
(Caratini Collection, Histoire des maths) V1 PDF
TOC
AREAS
(Reinhardt Atlas différents domaines) V1 PDF
TOC
EDUCATION
TOC
LANGUAGE
(Pianeta 2022, Histoire des Notations) V1 PDF
(Pianeta 2020, Notions formelles, Vocabulaire et Notations) V1 PDF
TOC
FOUNDATIONS
Information theory . Philosophy of mathematics
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
(Wikipedia Fr Fondements) V1 PDF
TOC
LOGIC
(Isoz, Proof Theory) V1 PDF
(Moi, Symboles et Connecteurs Logiques) V1 PDF
(Bailly, Fonction Application Langage Logique) V1 PDF
(Bodin, Algèbre Cours 01, 01.01 Logique et Raisonnements) V1 PDF
(Lacombe, notes sur les 2 vidéos) 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, 1 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
(Bodin, Algèbre Cours 01, 01.02 Ens et App) V1 PDF
(Souriac, 26 Exemples Gr An Co Esp V Esp A) V1 PDF
TOC
SETS
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
TOC
RELATIONS
TOC
BINARY RELATION
(Bailly, Relations Binaires RE RO) V1 PDF
TOC
EQUIVALENCE RELATION
TOC
ORDER (THEORY, RELATIONS, STRUCTURE)
TOC
FUNCTIONS, APPLICATIONS
TOC
STRUCTURES
ALGEBRAIC STRUCTURES, MORPHISMS
(Bailly & Moi, Résumé de Notions Fondamentales & Structures Algébriques 1 2 4) V1 PDF
COMMON AXIOMS
EQUATIONAL AXIOMS
Commutativity
Associativity
Left distributivity
Right distributivity
Distributivity
EXISTENTIAL AXIOMS
Identity element
Inverse element
NON-EQUATIONAL AXIOMS
ONE SET WITH OPERATIONS
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
TWO SETS WITH OPERATIONS
MODULE-LIKE STRUCTURES
VECTOR SPACE
ALGEBRA OVER A FIELD
INNER PRODUCT SPACE
AFFINE SPACE
EUCLIDEAN SPACE
ALGEBRA-LIKE STRUCTURES
HYBRID STRUCTURES WITH NON-ALGEBRAIC STRUCTURES
NON-ALGEBRAIC STRUCTURES
ORDER STRUCTURE
TOPOLOGICAL STRUCTURE
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, Numération, Calcul sur nbs entiers, PGCD PPCM Caractères de divisibilité, Fractions et Rapports : Calcul sur fractions, Rapports et proportions, Nbs relatifs, Opérations
sur, Généralités, Polynomes, Fractions rationnelles) V1 PDF
(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
OVERVIEW
GROUP THEORY
RING THEORY
FIELD THEORY
MODULE THEORY
VECTOR SPACE VECTOR
TOC
LINEAR ALGEBRA
(Bailly, Alg Lin 1 2 3 4 5 6) V1 PDF
(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
TOC
AEROSPACE ENGINEERING
TOC
SOFTWARE ENGINEERING
TOC
INDUSTRIAL ENGINEERING
TOC
REFERENCES
SIMPLE CONTENTS
DIDACTIC
HISTORY
AREAS
EDUCATION
LANGUAGE
ENCYCLOPEDIAS
DICTIONARIES
FOUNDATIONS
LOGIC
SETS
RELATIONS & STRUCTURES
NUMBERS
REF
DIDACTIC
TOP-RATED RESOURCES
Caratini.
Souriac.
Kahn.
Reinhardt.
Bodin.
Caratini. Tout en 1. Mathématiques. 1994.
https://archive.org/details/toutenunlencyclo0000cara
Caratini. Encyclopédie. Mathématiques. 1972.
Caratini. Collection. Mathématiques. 1985.
https://archive.org/details/BibliothequePratiqueDeLEnseignantBordasTome.01Mathematiques/mode/2up
Caratini. Panorama Sciences. Mathématiques. 1993.
Souriac. MemoMath Bac Premières années de Faculté. 1977.
Download
[ Cf aussi du meme auteur le MemoMeca CF PHYSICS ]
Walusinski. Les bases des Maths en classes terminales. 1976.
Download
Pecastaings. Maths Bac en Poche. 1983.
Corne et al. ABC du BAC Mathématiques. 1983.
Kahn. Collection de Mathématiques du CNED. 1995.
Pianeta. Cours. Mathematiques.
https://www.dimitripianeta.fr/cours/mathematiques.html
Et informatique !
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 ]
Monka.
http://www.maths-et-tiques.fr/
Niveau Bac
Bodin. Exo7 Cours et Exercices de mathématiques.
Niveau L1/Math Sup, L2/Math Spé, L3/Licence
http://exo7.emath.fr/
https://www.youtube.com/@Exo7Math
https://fr.wikipedia.org/wiki/Exo7
Bodin.
https://arnbod.github.io/
Reinhardt. Atlas des Mathématiques. 1997.
[ Commentaire ] [ Commentaire Archive ] [ Download JPG ] [ Download PDF ]
Bailly-Maitre. YouTube MathsAdultes.
Excellent
https://www.youtube.com/@MathsAdultes
Isoz. Opera Magistris. Compendium of Elementary Applied Mathematics for Engineers. 4e. 2024. - 3e. 2018. - 9014 pages
[ sciences.ch ]
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/
https://ressources.unisciel.fr/sillages/mathematiques/cours_1a_mpsi_pcsi_ptsi_tsi/livre.pdf
Perret.
https://www.vive-les-maths.net/
Deschamps. Mathématiques Tout en Un MPSI. 3e. 2013. 1088 p
https://www.amazon.fr/Mathématiques-tout-en-MPSI-Conforme-programme
https://elmoukrie.com/wp-content/uploads/2022/08/mathematiques-tout-en-un-1re-annee-cours-et-exercices-corriges-claude-deschamps-andre-warusfel.pdf 2e
Wikibooks fr.
https://fr.wikibooks.org/wiki/Wikilivres:CDU/5/51
Geller. Mathématiques Abrégé. 1988. [ Cf BIOSTATISTICS ]
Geller. Statistique Abrégé. 1983. [ Cf BIOSTATISTICS ]
Bouvier. Théorie des Ensembles. 3e. 1982. [ Cf SETS ]
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/
(Poirier Premiers fondemenents brouillon) V1 PDF
très ardu selon moi mais génial
DIDACTIC : UNSORTED
https://www.sesamath.net/
http://villemin.gerard.free.fr/Referenc/Debutant/DebTdM.htm
https://pi.ac3j.fr/livres-de-mathematiques/
https://www.ukonline.be/cours/math/basehigher-summary
REF
TOPICS
REF
HISTORY
TOP-RATED
Boll. Histoire des Mathématiques.
Caratini. Collection.
Boll. Histoire des Mathématiques. 13e. 1979. - 128 pages
Pour commencer
Dieudonné. Abrégé d'histoire des mathématiques. 1978.
[ jusqu'à 1900 ]
https://fr.wikipedia.org/wiki/Abrégé_d'histoire_des_mathématiques
https://www.journals.uchicago.edu/doi/10.1086/354566
http://www.numdam.org/item/SPHM_1994___3_A1_0.pdf
https://www.researchgate.net/publication/336147786_Imagine_R
Wikipedia en.
https://en.wikipedia.org/wiki/History_of_mathematics
Escofier. Histoire des mathématiques. 1e. 2008. - 128 pages
https://refkol.ro/matek/mathbooks/ro.math.wikia.com%20wiki%20Fisiere_pdf_incarcate/Histoire-des-mathematiques.pdf
https://www.academia.edu/30445815/Jean_Pierre_ESCOFIER_Petite_histoire_des_mathématiques_Dunod_Paris_2016_in_Rep%C3%A8res_IREM_n_105_pp_81_82
https://irem.univ-rennes.fr/ouvrages-en-ligne-mathematiques-et-histoire
https://www.amazon.fr/Histoire-mathématiques-Jean-Baudet
https://fr.scribd.com/document/798506308/eBook-Jean-C-Baudet-Histoire-Des-Mathematiques
https://webusers.imj-prg.fr/~david.aubin/cours/lu3ma209.html
https://webusers.imj-prg.fr/~david.aubin/cours/lu3ma209t.html
https://www.amazon.fr/Une-histoire-mathématiques-Routes-dédales
https://fr.scribd.com/document/400993875/Amy-Dahan-Dalmedico-Jeanne-Peiffer-Une-histoire-des-mathematiques-1986-pdf
https://www.persee.fr/doc/rhs_0151-4105_1983_num_36_3_1957
https://irma.math.unistra.fr/~baumann/polyh.pdf
https://www.math93.com/histoire-des-maths.html
REF
OVERVIEW - CLASSIFICATION - AREAS
https://zbmath.org/classification/
https://zbmath.org/static/msc2020.pdf
Wikipedia en.
https://en.wikipedia.org/wiki/Mathematics
Wikipedia en.
https://en.wikipedia.org/wiki/Lists_of_mathematics_topics
Wikipedia en.
https://en.wikipedia.org/wiki/Wikipedia:Contents/Mathematics_and_logic
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/
REF
EDUCATION
Wikipedia fr.
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
Base de ressources pour l'enseignement des mathématiques
https://www.univ-irem.fr/
REF
LANGUAGE - GLOSSARY - SYMBOLS - NOTATIONS
Wikipedia en.
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
Wikipedia fr.
https://fr.wikipedia.org/wiki/Liste_d'abréviations_en_mathématiques
https://meltingmots.com/liste/abreviations/science
Wikipedia en.
https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols
Wikipedia it.
https://it.wikipedia.org/wiki/Glossario_della_simbologia_matematica
Cajori.
https://www.amazon.com/History-Mathematical-Notations-Dover-Mathematics/dp/0486677664
https://monoskop.org/images/2/21/Cajori_Florian_A_History_of_Mathematical_Notations_2_Vols.pdf
https://archive.org/details/historyofmathema031756mbp
https://www.maths.ed.ac.uk/~v1ranick/papers/cajorinot.pdf
REF
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
REF
DICTIONARIES
Bouvier. Dictionnaire des Mathématiques. 1993.
https://archive.org/details/dictionnairedesm0000bouv
[ Excellent ! ]
http://cefti35000.free.fr/@@PdF-/@Info/Dictionnaire_Des_Mathématiques.pdf
Verley. 1997.
https://pdfcoffee.com/dictionnaire-des-mathematiques-pdf-free.html
https://www.softouch.on.ca/kb/data/Concise-Oxford-Dictionary-of-Mathematics.pdf
REF
FOUNDATIONS
https://www.amazon.fr/Fondements-mathématiques-M-Combes/dp/2130314589
Wikipedia en.
https://en.wikipedia.org/wiki/Foundations_of_mathematics
https://u.osu.edu/friedman.8/
https://www.youtube.com/@harveyfriedman4465
Girard. 2000.
https://www.canal-u.tv/video/universite_de_tous_les_savoirs/les_fondements_des_mathematiques.1021
https://alistairsavage.ca/mat2762/notes/MAT2762-Fondements-des-mathematiques.pdf
REF
LOGIC
TOP-RATED
LOGIC : HISTORY
Boll. Histoire de la Logique. 5e. 1961. - 128 pages
https://gallica.bnf.fr/ark:/12148/bpt6k3350869f
https://www.babelio.com/livres/Boll-Histoire-de-la-logique/426534#!
https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/abs/marcel-boll-and-jacques-reinhart-histoire-de-la-logique-que-saisje-no-225-5th-edn
Wikipedia fr.
https://fr.wikipedia.org/wiki/Histoire_de_la_logique
Wikipedia en.
https://en.wikipedia.org/wiki/History_of_logic
https://www.historyoflogic.com/
http://www.humbox.ac.uk//5497/1102/LOGIC%20GALLERY%20cgp01.pdf
LOGIC & SET THEORY : DIDACTIC
Caratini. Logique. [ Cf PHILOSOPHY ]
Chauvineau. La Logique Moderne. 1980. 1964 ? 1969 ? -
128 pages
https://www.amazon.fr/dp/213036621X?ref=ppx_yo2ov_dt_b_fed_asin_title
https://excerpts.numilog.com/books/9782130366218.pdf
https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/la-logique-moderne-by-jean-chauvineau-pp-128-presse-universitaires-de-france-paris
https://www.persee.fr/doc/phlou_0035-3841_1957_num_55_47_4925_t1_0402_0000_2
https://www.persee.fr/doc/lfr_0023-8368_1971_num_12_1_5565
Wagner 2024 La Logique -
128 pages
https://www.quesaisje.com/la-logique-1
https://www.amazon.fr/Logique-Pierre-Wagner-dp-2715422121/dp/2715422121/ref=dp_ob_title_bk
https://excerpts.numilog.com/books/9782715422124.pdf
Largeault 1998 La Logique -
128 pages
https://www.amazon.fr/Logique-Jean-Largeault/dp/2130460887
Commentaire Amazon :
Ce livre est évidemment génial, comme tout ce qu'écrit Jean Largeault, mais je ne le conseillerais pas à un débutant.
Il est vraiment très difficile, la parution en édition " Que sais-je ? " est trompeuse.
Pour commencer, lisez plutôt les ouvrages de Robert Blanché, Marie-Louise Roure ou Jean Salem.
Et il il toujours bon de rappeler que la " Logique " de Paul Mouy est
tout à fait remarquable.
https://www.persee.fr/doc/phlou_0035-3841_1950_num_48_18_7884_t1_0309_0000_2 Critique
https://fr.wikipedia.org/wiki/Paul_Mouy
Mouy. Logique
(Cours de philosophie), Librairie Hachette, 1944 [2° édition posthume,
remaniée et augmentée par Mle Bachelard et M. Dufresne, 1952]
https://fr.scribd.com/document/543070393/La-Logique-Et-Mathematique
Mouy.
Les
mathématiques et l’idéalisme philosophique, in F. Le Lionnais, Les
grands courants de la pensée mathématique, Cahiers du Sud, 1948
(réimpr. 1962, libr. A. Blanchard ; 1997, éd. Hermann), 533 p., p.
370-371.
https://www.amazon.fr/Grands-courants-pensée-mathématique-Cahiers/dp/290305990X
https://www.persee.fr/doc/rhs_0048-7996_1949_num_2_3_2716
https://archive.org/details/greatcurrentsofm0000leli
Math & Phys.
Logique Mathématique
https://www.youtube.com/playlist?list=PLPMCOIL54o6VMqB7Q7tDXEfzAUGWI0fMD
Logicomix.
https://fr.wikipedia.org/wiki/Logicomix
https://profesorvargasguillen.wordpress.com/wp-content/uploads/2013/11/logicomix.pdf
https://archive.org/details/Logicomix-Comic-EarlyLifeOfBertrandRussell
https://fillide.it/apostolos-doxiadis-christos-papadimitriou-logicomix-segnalazione/
Largeault 1992 . L'intuitionnisme.
128 pages
https://www.erudit.org/fr/revues/philoso/1994-v21-n1-philoso1798/027263ar.pdf
https://fr.slideshare.net/elsavonlicy/loeuvre-de-jean-largeault
https://www.amazon.fr/Lintuitionnisme-Jean-Largeault-ebook/dp/B071F1JC68
http://wynen.chez-alice.fr/liens/intuitionnisme.pdf
Cori et Lascar.
Logique Mathématique. 1994.
amazon.fr
Cori.
Lascar.
Lassaigne et Rougemont. Logique et Fondements de l'informatique. 1993.
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
Rougemont.
Kreisel et Krivine. Elements de Logique Mathématique. 1967.
Kreisel.
https://www.irif.fr/~krivine/articles/Elements_logique.pdf
Krivine. Théorie axiomatique des Ensembles. 1972.
amazon.fr/Th%C3%A9orie-axiomatique-ensembles-Krivine-Jean-Louis/dp/B00GO376UY
https://fr.wikipedia.org/wiki/Jean-Louis_Krivine
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
Lacombe.
Grandeur et misère de l'implication
https://video.irem.univ-paris-diderot.fr/w/adfa20fa-0028-4782-a864-99a7003e1280
Lacombe.
https://www.imj-prg.fr/lm/deces-de-daniel-lacombe/
Girard.
https://girard.perso.math.cnrs.fr/Accueil.html
LOGIC : OVERVIEW
Wikipedia en.
https://en.wikipedia.org/wiki/Mathematical_logic
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
LOGIC : 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/
https://fr.scribd.com/document/729412333/Cours-de-logique-2022-2023-LMD
https://philosophy.stackexchange.com/questions/76083/what-separates-mathematics-from-logic-can-mathematical-operations-be-applied?newreg=7e1561b15cdf4ec684ccc1a6e04e025c
REF
SETS
SETS : DIDACTIC
Bouvier. Théorie des Ensembles. 3e. 1982. - 128 pages
[ Download ]
[ Excellent ! ]
SETS : OVERVIEW
https://en.wikipedia.org/wiki/Set_theory
SETS : 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
REF
RELATIONS & STRUCTURES
Wikipedia en.
https://en.wikipedia.org/wiki/Mathematical_structure
Wikipedia en.
https://en.wikipedia.org/wiki/Outline_of_algebraic_structures
https://orbilu.uni.lu/bitstream/10993/32380/1/SM.pdf
https://en.wikipedia.org/wiki/List_of_order_structures_in_mathematics
REF
NUMBERS
REF
ALGEBRA
REF
GEOMETRY
https://www.its.caltech.edu/~matilde/SpaceMath.pdf
REF
ANALYSIS
https://cel.hal.science/cel-00519301v2
REF
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
https://www.savoir-sans-frontieres.com/JPP/telechargeables/Francais/LE%20TOPOLOGICON.pdf
REF
PROBABILITY
https://fr.scribd.com/document/747699320/La-Probabilite-le-hasard-et-la-certitude-Paul-Deheuvels
REF
APPLIED
Wikipedia en.
https://en.wikipedia.org/wiki/Applied_mathematics
https://media.philosophy.ox.ac.uk/docs/people/williamson/appliedmaths.pdf
REF
AUTHORS
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
BOLL MARCEL
BOUVIER ALAIN
C
CARAMELLO OLIVIA
https://www.youtube.com/watch?v=RcpZm7-S4gI
https://savoirs.ens.fr/expose.php?id=3385
https://savoirs.ens.fr/expose.php?id=3259
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
KHÉLIF ANATOLE
https://www.youtube.com/watch?v=kO8zZZnxYmE&t=1433s
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
TALEB NASSIM NICHOLAS
https://www.fooledbyrandomness.com/
https://en.wikipedia.org/wiki/Antifragility
https://www.youtube.com/@nntalebproba
Map of the Incerto
https://www.fooledbyrandomness.com/incerto.pdf
THOM RENE
https://web.archive.org/web/20120117160729/http://people.math.jussieu.fr/~chaperon/HommageChaperon.pdf
https://www.amazon.fr/Paraboles-catastrophes-Entretiens-math%C3%A9matiques-philosophie/dp/2081251302
https://archive.org/details/parabolesetcatas0000thom/mode/2up
https://archive.org/details/stabilitestructu0000thom_y5k9
https://archive.org/search?query=Thom+Rene%CC%81
https://archive.org/details/apologiedulogos0000thom
U
V
W
X
Y
Z
REF
TOPICS A-Z
MATHEMATICS : 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
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
2025
(Ajouté le site de Pianeta Dimitri, il y a aussi un cours sur les cartes mentales sur son site)
(Fini Boll Que Sais Je ? Histoire des Maths)
(Kahn CNED 03.01 Initiation geom plane) V1 PDF
(Moi Support de Cours Particuliers Maths de Base) V1 PDF
(Pianeta 2022, Histoire des Notations) V1 PDF
(Pianeta 2020, Notions formelles, Vocabulaire et Notations) V1 PDF
(Moi, Symboles et Connecteurs Logiques) V1 PDF
(Bailly, Fonction Application Langage Logique) V1 PDF
(Bodin, Algèbre Cours 01, 01.01 Logique et Raisonnements) V1 PDF
(Bodin, Algèbre Cours 01, 01.02 Ens et App) V1 PDF
(Bailly, Relations Binaires RE RO) V1 PDF
(Bailly & Moi, Résumé de Notions Fondamentales & Structures Algébriques 1 2 4) V1 PDF
(Lacombe, notes sur les 2 vidéos) V1 PDF
(Kahn, II Geom 1, 03.02. Vecteurs et droites - sym & transl) V1 PDF
(Kahn, II Geom 1, 03.09. Gén EV et AL) V1 PDF
(Souriac, 26 Exemples Gr An Co Esp V Esp A) V1 PDF
(Bailly, Alg Lin 1 2 3 4 5 6) V1 PDF
(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
(Caratini Collection, Nombres Réels et Nombres Complexes) V1 PDF
VRAC
trouver système pour articles wik et autres liens
Car geom top
car réels revoir kahn avant pour RO
str atlas et OM ensemble !
OBJECTIF
Kahn Caratini sans problèmes ! Et aborder OM et physique ! JP Petit et Mountain ?
maitriser notion de limite CNED Exo7
PAR AUTEURS
Séquence Logique : pensée formelle - car log - atlas maths et philo log.....puis TE atlas Exo 7 et maths adultes
Séquence TE :
Walunsinski
bases
Caratini. Pan
Geom analyse dico top
Caratini. Col
IR IC
CNED
mais reprendre depuis le début avec som détaillé sur site
CNED 2 Algèbre et Algèbre Linéaire, Chap 1 et 2 Refaire
Souriac Maths
finir et reprendre en parallèle des autres Cned atlas etc
les chapitres finnaux !! EA clarifier EE
Souriac Méca
Glaeser
Logique aprés autres
Bodin Exo 7
Alg 1
Anal 1 chap 1 après CNED
Geom 1
Bouvier TE
ordre revoir
refaire avec Walunsinski
Opera Magistris
faire sommaire détaillé applied ! Classer déjà fait
str et Log aprés Tout logique dur je pense !
sommaire dans le détail reprendre depuis le début logique compris
Wikipedia
found & logic math
2 Abrégés med
stat après cned
Vallant philo
pensée formelle
Atlas philo nom auteur ?
log
Auroux philo
Voc log Aur et math
Reinhardt Atlas
Atlas Logique refaire ! et après TE !
ABC du BAC
ex de constructions alg d'ens reprendre quotient opera str et homomorp refaire ?
Bac en Poche
PAR THEMES
Logique
Log formelle et log philo car
Reinhardt Atlas logique et car philo logique !
Notes wiki tel et ici
Rel RE RO str ordre
Bailly-Maitre video
pour les structures d'ordre faire en paral Bouvier TE Atlas et Souriac et RE
car réels revoir kahn avant pour RO
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