Number Theory and Geometry: An Introduction to Arithmetic Geometry
Title | Number Theory and Geometry: An Introduction to Arithmetic Geometry PDF eBook |
Author | Álvaro Lozano-Robledo |
Publisher | American Mathematical Soc. |
Pages | 506 |
Release | 2019-03-21 |
Genre | Mathematics |
ISBN | 147045016X |
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.
An Introduction to Mathematical Cryptography
Title | An Introduction to Mathematical Cryptography PDF eBook |
Author | Jeffrey Hoffstein |
Publisher | Springer |
Pages | 549 |
Release | 2014-09-11 |
Genre | Mathematics |
ISBN | 1493917110 |
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.
A Key to the Introduction to the National Arithmetic
Title | A Key to the Introduction to the National Arithmetic PDF eBook |
Author | Benjamin Greenleaf |
Publisher | |
Pages | 158 |
Release | 1853 |
Genre | Arithmetic |
ISBN |
An Introduction to Arithmetic. [With] Key
Title | An Introduction to Arithmetic. [With] Key PDF eBook |
Author | John Newark |
Publisher | Palala Press |
Pages | 54 |
Release | 2015-09-19 |
Genre | |
ISBN | 9781343260733 |
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
A Key to the introduction to the national arithmetic, etc
Title | A Key to the introduction to the national arithmetic, etc PDF eBook |
Author | Benjamin GREENLEAF |
Publisher | |
Pages | 138 |
Release | 1845 |
Genre | |
ISBN |
An introduction to arithmetic. [With] Key
Title | An introduction to arithmetic. [With] Key PDF eBook |
Author | John Newark |
Publisher | |
Pages | 58 |
Release | 1856 |
Genre | |
ISBN |
A Key to the Introduction to the National Arithmetic
Title | A Key to the Introduction to the National Arithmetic PDF eBook |
Author | Benjamin Greenleaf |
Publisher | |
Pages | 136 |
Release | 1846 |
Genre | Arithmetic |
ISBN |