Number Theory and Geometry by Alvaro Lozano-Robledo
Number Theory and Geometry - Table of Contents
PART 1. INTEGERS, POLYNOMIALS, LINES, AND CONGRUENCES
- 2. The Integers
- 3. The Prime Numbers
- 4. Congruences
- 5. Groups, Rings, and Fields
- 6. Finite Fields
- 7. The Theorems of Wilson, Fermat, and Euler
- 8. Primitive Roots
PART 2. QUADRATIC CONGRUENCES AND QUADRATIC EQUATIONS
- 9. An Introduction to Quadratic Equations
- 10. Quadratic Congruences
- 11. The Hasse–Minkowski Theorem
- 12. Circles, Ellipses, and the Sum of Two Squares Problem
- 13. Continued Fractions
- 14. Hyperbolas and Pell’s Equation
PART 3. CUBIC EQUATIONS AND ELLIPTIC CURVES
- 15. An Introduction to Cubic Equations
- 16. Elliptic Curves
What You Will Learn in Number Theory and Geometry
Number Theory and Geometry: An Introduction to Arithmetic Geometry by Alvaro Lozano-Robledo provides a concrete introduction to arithmetic geometry by examining polynomial equations through geometric intuition. Accessing this lozano robledo number theory geometry pdf offers undergraduate students clear proofs and computational insights.
The textbook covers Pythagorean triples, rational points on conics, elliptic curves, complex multiplication, modular forms, and Fermat's Last Theorem. Studying this complete number theory and geometry alvaro lozano robledo book bridges elementary number theory with modern research topics in algebra and topology.
Designed as an accessible number theory and geometry pdf reference, this text features numerous exercises, illustrative diagrams, and historical background notes in every chapter.
Book Details & Specifications
Title:
Number Theory and Geometry by Alvaro Lozano-Robledo
Publisher:
American Mathematical Society (AMS)
Year:
2019
Pages:
501
Type:
PDF
Language:
English
ISBN-10 #:
147045016X
ISBN-13 #:
978-1470450168
License:
External Educational Resource (with the permission of AMS)
Amazon:
Amazon
About the Author: Alvaro Lozano-robledo
The author Alvaro Lozano-robledo
is a Spanish-born mathematician and Professor of Mathematics at the University of Connecticut specializing in number theory, arithmetic geometry, and elliptic curves.
As the author of Number Theory and Geometry by Alvaro Lozano-Robledo, he is widely recognized for his engaging pedagogical style, expository writing, and research in Galois representations.
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