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

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

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

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

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

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

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...

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 ---- 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 ...

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

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