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book details (version 2016-2017)

HANDBOOK OF

MATHEMATICS

Print version
. Hardcover-Hardback
Published on April 4, 2017
XVIII, 1132 p.
ISBN: 9782955199015
57,90 Euros

. Softcover-Paperback
Published on December 7, 2016
ISBN-13: 978-2-955-19900-8
EAN: 9782955199008
49,99 Euros
eBook version - Kindle
Published on May 23, 2017
ISBN: 9782955199022
39.99 Euros
Thierry Vialar (PhD).
HDBOM.
Language: English
Table of contents: pp i-xviii, 28 p.
Appendices: pp 1033-1051, 18 p.
Index: pp 1054-1110, 56 p.
Illustrations: Thousands illustrations and pictures.
Format: 15.5 x 6 x 22 cm - 6.1 x 2.36 8.66 in).
Format: Two-column format. Fontsize 7.5.
Weight (for paperback version): 1.5 kgs, or 3.3 pounds.
Typesetting with LaTeX, Scientific Word (MacKichan software), and AMS pachages, AMSFonts.
Paper: 80 grs.

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table of contents (level 1)

Introduction
Part I. Foundations of Mathematics.
Chap.1. Mathematical Logic.
  • Section 1. Propositions, Connections
  • Section 2. Propositional and Predicate Calculus
  • Section 3. Extension of First-order Predicate Calculus
  • Section 4. Formal System
  • Section 5. Demonstrations and Definitions
Chap.2. Set Theory.
  • Section 1. Basic Concepts
  • Section 2. Set Algebra
  • Section 3. Lattice Theory
  • Section 4. Foundations of Sets
  • Section 5. Problems of Set Theory
  • Section 6. Zermelo-Fraenkel Set Theory (ZFC)
  • Section 7. Banach-Tarski paradox and ZF
  • Section 8. Hahn-Banach Theorems
Chap.3. Relations and Structures.
  • Section 1. Relations
  • Section 2. Maps, Functions
  • Section 3. Families
  • Section 4. Laws of Composition
  • Section 5. Power, Cardinal, Denumerability
  • Section 6. Cardinals
  • Section 7. Structures
  • Section 8. Algebraic Structures
  • Section 9. Order Structure
  • Section 10. Ordinals
  • Section 11. Topological Structures
Chap.4. Arithmetic.
  • Section 1. Set of Natural Numbers ℕ
  • Section 2. Denumerability (Counting)
  • Section 3. Divisibility
  • Section 4. Integers ℤ
  • Section 5. Rational Numbers ℚ
  • Section 6. A General Exercise
Chap.5. Construction of Number System.
  • Section 1. Semigroup of Natural Numbers
  • Section 2. Ring of Integers
  • Section 3. Field of Rational Numbers
  • Section 4. Real Numbers
  • Section 5. Complex Numbers
  • Section 6. Synthesis, Generalization
Part II. Algebra.
Chap.6. Algebra
  • Section 1. Introduction
  • Section 2. Group Theory
  • Section 3. Rings and Fields
  • Section 4. Modules, Vector Spaces
  • Section 5. Linear Maps and Matrices
  • Section 6. Equation and System of Equations
  • Section 7. Algebra of Polynomials
  • Section 8. Polynomials over ℝ and ℂ
  • Section 9. Fractions and Rational Functions
  • Section 10. Polynomial Rings
  • Section 11. Field Extensions
  • Section 12. Prime fields, Finite fields
  • Section 13. Galois Theory
  • Section 14. Galois Theory Application
  • Section 15. Lie Groups
  • Section 16. Linear Algebra
  • Section 17. Eigenvalue, Eigensubspace
  • Section 18. Hermitian Form, Pre-Hilbert Space
  • Section 19. Exterior Algebra of Vector Space
Part III. Number Theory.
Chap.7. Number Theory
  • Section 1. Divisibility in an integral domain
  • Section 2. Diophantine Equations and Residues
  • Section 3. Absolute Value, Valuation
  • Section 4. Prime Numbers
Part IV. Geometry.
Chap.8. Geometry
  • Section 1. Contruction, and Overview
  • Section 2. Fundamental Concepts
  • Section 3. Absolute geometry
  • Section 4. Euclidean and non Euclidean Metrics
  • Section 5. Affine and Projective Planes
  • Section 6. Collineations and Correlations
  • Section 7. Ideal Plane, Coordinates
  • Section 8. Projective Metric
  • Section 9. Order and Orientation
  • Section 10. Angles and Measurements
  • Section 11. Rigid Transformations
  • Section 12. Similarity in Geometry
  • Section 13. Affine Maps
  • Section 14. Projective maps
  • Section 15. Analytic Representations
  • Section 16. Descriptive Geometry
  • Section 18. Hyperbolic Geometry
  • Section 19. Elliptic Geometry
Part V. Analytic Geometry.
Chap.9. Analytic Geometry
  • Section 1. Vector spaces V3
  • Section 2. Scalar, Vector and Mixed products
  • Section 3. Line and Plane Equations
  • Section 4. Sphere and Conics
  • Section 5. Displacement, Affine map in R3
  • Section 6. Quadrics
  • Section 7. Affine Space on Rn
Part VI. Topology.
Chap.10. Topology
  • Section 1. Overview
  • Section 3. Basic Topological Notions of ℝp
  • Section 4. Definition of a Topological Space
  • Section 5. Metric Space, Basis, Neighborhood Basis
  • Section 6. Topological Map, Topological Subspace
  • Section 7. Quotient, Product and Sum Spaces
  • Section 8. Connectedness, Arc-connected space
  • Section 9. Sequence Convergence and Filter Base
  • Section 10. Separation Axioms
  • Section 11. Compactness
  • Section 12. Metrization
  • Section 13. Dimension Theory
  • Section 14. Theory of Curves
  • Section 15. Completion
Chap.11. Topology II
  • Section 1. Introduction
  • Section 2. Prerequisites, Reminders
  • Section 3. Distances and Metric Spaces
  • Section 4. Limits and Cluster Points
  • Section 5. Compact and locally compact spaces
  • Section 6. Connected spaces
  • Section 7. Metric and Semi-metric Spaces
  • Section 8. Baire Spaces
  • Section 9. Mapping Spaces (or Function Spaces)
  • Section 10. Normed Vector Spaces
  • Section 11. Hilbert Spaces
Part VII. Algebraic Topology.
Chap.12. Algebraic Topology
  • Section 1. Homotopy
  • Section 2. Polyhedra
  • Section 3. Fundamental Group of a Connected Polyhedron
  • Section 4. Surfaces
  • Section 5. Homology Theory
  • Section 6. Graph Theory
  • Section 7. Bundles
Chap.13. Algebraic Topology II
  • Section 1. Introduction
  • Section 2. Some Topological Notions
  • Section 3. Simplexes
  • Section 4. The Fundamental Group
  • Section 5. Singular Homology
  • Section 6. Long Exact Sequences
  • Section 7. Excision
  • Section 8. Simplicial Complexes
  • Section 9. CW Complexes
  • Section 10. Natural Transformations
  • Section 11. Covering Spaces
  • Section 12. Homotopy Groups
  • Section 13. Cohomology
Part VIII. Analysis.
Chap.14. Real Analysis
  • Section 1. Structures on ℝ
  • Section 2. Sequences, Series
  • Section 3. Real Functions
Chap.15. Differential Calculus
  • Section 1. Overview
  • Section 2. Functions of Differentiable Real Variable
  • Section 3. Mean Value Theorems
  • Section 4. Expansion In Series
  • Section 5. Rational Functions
  • Section 6. Algebraic Functions
  • Section 7. Non-algebraic Functions
  • Section 8. Approximation Theory
  • Section 9. Interpolation Theory
  • Section 10. Numerical Resolution of Equations
  • Section 11. Differential Calculus in ℝn
Chap.16. Integral Calculus
  • Section 1. Overview
  • Section 2. Riemann Integral
  • Section 3. Integration Rules, R-integrable Functions
  • Section 4. Primitive Functions, Indefinite Integrals
  • Section 5. Integration Methods, Series Integration
  • Section 6. Approximation Methods, Generalized Integrals
  • Section 7. Riemann Integral of Functions of Several Variables
  • Section 8. Successive Integrations, Change of Variables
  • Section 9. Riemann Sums and Applications
  • Section 10. Curvilinear Integral, Surface Integral
  • Section 11. Field, force, work-done
  • Section 12. Integration Theorems
  • Section 13. Jordan Areolar Measure, Lebesgue Measure
  • Section 14. Measurable Functions, Lebesgue Integral
Chap.17. Functional Analysis
  • Section 1. Abstract Spaces
  • Section 2. Differentiable Operators
  • Section 3. Calculus of Variations
  • Section 4. Integral Equations
  • Section 5. Compact Operators
Chap.18. Differential Equations
  • Section 1. Classic Differential Equations
  • Section 2. First-order Differential Equations
  • Section 3. Second-order Differential Equations
  • Section 4. Linear n-order Differential Equations
  • Section 5. Systems of Differential Equations
  • Section 6. Existence and Uniqueness Theorems
  • Section 7. Numerical Methods
  • Section 8. Partial Differential Equations
Chap.19. Differential Geometry
  • Section 1. Curves in R3
  • Section 2. Plane Curves
  • Section 3. Regular Patches, Surfaces
  • Section 4. First Fundamental Form
  • Section 5. Second Fundamental Form, Curvature
  • Section 6. Fundamental Theorem
  • Section 7. Tensors
  • Section 8. Tensors II
  • Section 9. Differential Forms
  • Section 10. Manifolds, Riemannian Geometry
  • Section 11. Complements of Differential Geometry
Chap.20. Function Theory (Complex Analysis)
  • Section 1. Introduction
  • Section 2. Complex Numbers, Compactification
  • Section 3. Sequences and Complex Functions
  • Section 4. Holomorphy
  • Section 5. Cauchy Integral Theorem and Formulas
  • Section 6. Power Series Expansion
  • Section 7. Analytic Continuation
  • Section 8. Singularities, Laurent Series
  • Section 9. Meromorphy, Residues
  • Section 10. Riemann Surfaces
  • Section 11. Entire Functions
  • Section 12. Meromorphic functions on C
  • Section 13. Periodic functions
  • Section 14. Algebraic functions
  • Section 15. Conformal transformations
  • Section 16. Functions of several variables
Chap.21. Complex Analysis II
  • Section 1. Introduction
  • Section 2. Prerequisites
  • Section 3. Recall on Functions of Complex Variables
  • Section 4. Curvilinear Integral
  • Section 5. Differential Forms in the Plane
  • Section 6. Holomorphic Functions I
  • Section 7. Holomorphic Functions II
  • Section 8. Homotopy
  • Section 9. Topology of the Complex Plane
  • Section 10. Cauchy Theorem (Homology Version)
  • Section 11. Residues
  • Section 12. Runge Theorem, Applications
  • Section 13. Conformal Mapping
  • Section 14. Harmonic Functions
  • Section 15. Subharmonic Functions
  • Section 16. (A1) Convolution, Partition of Unity
  • Section 17. (A2) Distributions
  • Section 18. (A3) Topology of the Complex Plane II
Part IX. Category Theory.
Chap.22. Areas Involved in Category Theory
  • Section 1. Areas Involved
  • Section 2. Algebraic System, Universal Algebra
  • Section 3. Signatures
  • Section 4. Structures
  • Section 5. Interpretations
  • Section 6. Varieties
  • Section 7. Algebraic Structures
  • Section 8. Maps and Structure Homomorphisms
  • Section 9. Algebraic Structure Morphisms and Kernels
  • Section 10. Ring Theory
  • Section 11. Complexes
  • Section 12. Direct limits
  • Section 13. Topological spaces
  • Section 14. Manifolds
  • Section 15. Homology, Cohomology
  • Section 16. Sheaf Theory
  • Section 17. Bundles
  • Section 18. Scheme Theory
  • Section 19. Homotopy
Chap.23. Category Theory
  • Section 1. Introduction
  • Section 2. Universe
  • Section 3. Objects
  • Section 4. Categories
  • Section 5. Functors
  • Section 6. Morphisms
  • Section 7. Graphs and Diagrams
  • Section 8. Limits and Products
  • Section 9. Pullbacks and Pushouts
  • Section 10. Kernels and Cokernels
  • Section 11. Exact Sequences
  • Section 12. Sheaves
  • Section 13. Grothendieck topology, site, sieve
  • Section 14. Topos
  • Section 15. Étale
  • Section 16. Yoneda Lemma, Yoneda Embedding
Part X. Probability and Statistics.
Chap.24. Probability
  • Section 1. Combinatorial Analysis
Chap.25. Probability Calculation, Statistics
  • Section 1. Introduction
  • Section 2. Event, Probability
  • Section 3. Statistical Distribution, Cumulative Distribution
  • Section 4. Statistical Methods
  • Section 5. Statistical Models
Part XI. Applied Mathematics.
Chap.26. Miscellaneous
  • Section 1. Fourier Series and Fourier Transform
  • Section 2. Integral transformations
  • Section 3. Distribution Theory
Chap.27. Optimization
  • Section 1. Introduction
  • Section 2. Linear Optimization
  • Section 3. Simplex Method
  • Section 4. Other Optimizations
  • Section 5. Convex sets, concave and convex functions
  • Section 6. Marginal Optimality Conditions
Chap.28. Dynamical Systems
  • Section 1. Dynamical Systems
  • Section 2. Chaos Theory
  • Section 3. Example in Physics
  • Section 4. Examples in Economics
Appendices
Symbols, Tables
  • Mathematical Symbols
  • Transformation Tables
  • Statistical Tables
Bibliography
Index