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Number Theory and Geometry by Alvaro Lozano-Robledo 2019 HC AMS
US $38.49
ApproximatelyRM 161.86
Was US $54.99 (30% off)
Condition:
Very Good
A book that has been read but is in excellent condition. No obvious damage to the cover, with the dust jacket included for hard covers. No missing or damaged pages, no creases or tears, and no underlining/highlighting of text or writing in the margins. May be very minimal identifying marks on the inside cover. Very minimal wear and tear.
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Free local pickup from Schenectady, New York, United States.
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US $6.72 (approx RM 28.26) USPS Media MailTM.
Located in: Schenectady, New York, United States
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Estimated between Sat, 13 Sep and Wed, 17 Sep to 94104
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eBay item number:357476917272
Item specifics
- Condition
- ISBN
- 9781470450168
About this product
Product Identifiers
Publisher
American Mathematical Society
ISBN-10
147045016X
ISBN-13
9781470450168
eBay Product ID (ePID)
8038757255
Product Key Features
Number of Pages
488 Pages
Language
English
Publication Name
Number Theory and Geometry : an Introduction to Arithmetic Geometry
Subject
Number Theory
Publication Year
2019
Type
Textbook
Subject Area
Mathematics
Series
Pure and Applied Undergraduate Texts
Format
Hardcover
Dimensions
Item Height
0.8 in
Item Weight
37 Oz
Item Length
10 in
Item Width
7 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
2018-056079
Illustrated
Yes
Table Of Content
Introduction Integers, polynomials, lines, and congruences: The integers The prime numbers Congruences Groups, rings, and fields Finite fields The theorems of Wilson, Fermat, and Euler Primitive roots Quadratic congruences and quadratic equations: An introduction to quadratic equations Quadratic congruences The Hasse-Minkowski theorem Circles, ellipses, and the sum of two squares problem Continued fractions Hyperbolas and Pell's equation Cubic equations and elliptic curves: An introduction to cubic equations Elliptic curves Bibliography Index
Synopsis
The field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book provides an introduction to number theory and arithmetic geometry, the goal being to use geometry as the motivation to prove the main theorems in the book., Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
LC Classification Number
QA242.5.L6945 2019
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