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The Non-Euclidean, Hyperbolic Plane
The Non-Euclidean, Hyperbolic PlanePaul Kelly, Gordon MatthewsI. Some Historical Background
II. Absolute Plane Geometry
III. Hyperbolic Plane Geometry
IV. A Euclidean Model of the Hyperbolic Plane
Appendix: Distance Geometries
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Graphs and their Uses
Graphs and their UsesOystein Ore1. What is a Graph?
2. Connected Graphs
3. Trees
4. Matchings
5. Directed Graphs
6. Questions Concerning Games and Puzzles
7. Relations
8. Planar Graphs
9. Map Coloring
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Algebraic Curves
Algebraic CurvesWilliam Fulton1. Affine Algebraic Sets
2. Affine Varieties
3. Local Properties of Plane Curves
4. Projective Varieties
5. Projective Plane Curves
6. Varieties, Morphisms, and Rational Maps
7. Resolution of Singularities
8. Riemann-Roch Theorem
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Algebra - Erster Teil
Algebra - Erster TeilB.L. van der WaerdenUnter Benutzung von Vorlesungen von E. Artin und E. Noether
1. Zahlen und Mengen
2. Gruppen
3. Ringe und Körper
4. Vektorräume und Tensorräume
5. Ganzrationale Funktionen
6. Körpertheorie
7. Fortsetzung der Gruppentheorie
8. Die Theorie von Galois
9. Ordnung und Wohlordnung von Mengen
10. Unendliche Körpererweiterungen
11. Reelle Körper
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Algebra - Zweiter Teil
Algebra - Zweiter TeilB.L. van der WaerdenUnter Benutzung von Vorlesungen von E. Artin und E. Noether
12. Lineare Algebra
13. Algebren
14. Darstellungstheorie der Gruppen und Algebren
15. Allgemeine Idealtheorie der kommutativen Ringe
16. Theorie der Polynomideale
17. Ganze algebraische Grössen
18. Bewertete Körper
19. Algebraische Funktionen einer Variablen
20. Topologische Algebra
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Fundamentals of Galois Theory
Fundamentals of Galois TheoryM.M. PostnikovPart I. The elements of Galois theory
1. Elements of field theory
2. Basic information from group theory
3. Galois theory
Part II. The soltuion of equations in radicals
1. Supplementary information form the general theory of groups
2. Equations which are solvable in radicals
3. Structure of equations which are not solvable in radicals
4. Non-solvability in radicals of the general equation of degree n >= 5
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Introduction to Analytic Number Theory
Introduction to Analytic Number TheoryTom M. ApostolHistorical Introduction
1. The Fundamental Theorem of Arithmetic
2. Arithmetical Functions and Dirichlet Multiplication
3. Averages of Arithmetical Functions
4. Some Elementary Theorems on the Distribution of Prime Numbers
5. Congruences
6. Finite Abelian Groups and Their Characters
7. Dirichlet’s Theorem on Primes in Arithmetical Progressions
8. Periodic Arithmetical Functions and Gauss Sums
9. Quadratic Residues and the Quadratic Reciprocit...
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The Theory of Numbers and Diophantine Analysis
The Theory of Numbers and Diophantine AnalysisRobert D. CarmichaelI. Elementary Properties of Integers
II. On the Indicator of an Integer
III. Elementary Properties of Congruences
IV. The Theorems of Fermat and Wilson
V. Primitive Roots Modulo m
VI. Other Topics
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I. Introduction. Rational Triangles. Method of Infinite Descent
II. Problems Involving a Multiplicative Domain
III. Equations of the Third Degree
IV. Equations of the Fourth Degree
V. Equations of Degree Higher Than the Fourth. The ...
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Principia Mathematica to *56
Principia Mathematica to *56Alfred North Whitehead, Bertrand RussellIntroduction
I. Mathematical Logic
A. The Theory of Deduction
B. Theory of Apparent Variables
C. Classes and Relations
D. Logic of Relations
E. Products and Sums of Classes
II. Prolegomena to Cardinal Arithmetic
A. Unit Classes and Couples
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Theory of Sets
Theory of SetsE. KamkeI. The Rudiments of Set Theory
II. Arbitrary Sets and Their Cardinal Numbers
III. Ordered Sets and Their Order Types
IV. Well-Ordered Sets and Their Ordinal Numbers
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