Glimpses of algebra and geometry 2nd Edition by Gabor Toth ISBN 1441929622 978-1441929624 by Toth G. 9780387953458, 0387953450 instant download after payment.

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Product details:

ISBN 10: 1441929622

ISBN 13: 978-1441929624 

Author: Gabor Toth 

Glimpses of Algebra and Geometry is intended for a "Bridge Course" that facilitates the transition between undergraduate and graduate studies. This new edition includes innumerable improvements throughout the text, including an in-depth treatment of root formulas, a detailed and complete classification of finite Mobius groups a la Klein, and a quick, direct, and modern approach to Felix Klein's "Normalformsatz."

Table of contents:

Preface to the Second Edition

Preface to the First Edition

Acknowledgments

Section 1 “A Number Is a Multitude Composed of Units”—Euclid

Section 2 “... There Are No Irrational Numbers at All”—Kronecker

Section 3 Rationality, Elliptic Curves, and Fermat’s Last Theorem

Section 4 Algebraic or Transcendental?

Section 5 Complex Arithmetic

Section 6 Quadratic, Cubic, and Quantic Equations

Section 7 Stereographic Projection

Section 8 Proof of the Fundamental Theorem of Algebra

Section 9 Symmetries of Regular Polygons

Section 10 Discrete Subgroups of Iso (R²)

Section 11 Möbius Geometry

Section 12 Complex Linear Fractional Transformations

Section 13 “Out of Nothing I Have Created a New Universe”—Bolyai

Section 14 Fuchsian Groups

Section 15 Riemann Surfaces

Section 16 General Surfaces

Section 17 The Five Platonic Solids

Section 18 Finite Möbius Groups

Section 19 Detour in Topology: Euler–Poincaré Characteristic

Section 20 Detour in Graph Theory: Euler, Hamilton, and the Four Color Theorem

Section 21 Dimension Leap

Section 22 Quaternions

Section 23 Back to R³!

Section 24 Invariants

Section 25 The Icosahedron and the Unsolvable Quintic

Section 26 The Fourth Dimension

Appendix A Sets

Appendix B Groups

Appendix C Topology

Appendix D Smooth Maps

Appendix E The Hypergeometric Differential Equation and the Schwarzian

Appendix F Galois Theory

Solutions for 100 Selected Problems

Index

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Tags: Gabor Toth, Glimpses, Algebra, Geometry