An Experimental Introduction To Number Theory PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download An Experimental Introduction To Number Theory PDF full book. Access full book title An Experimental Introduction To Number Theory.
Author | : Benjamin Hutz |
Publisher | : American Mathematical Soc. |
Total Pages | : 376 |
Release | : 2018-04-17 |
Genre | : Number theory |
ISBN | : 1470430975 |
Download An Experimental Introduction to Number Theory Book in PDF, ePub and Kindle
This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.
Author | : Fernando Rodriguez Villegas |
Publisher | : Oxford University Press, USA |
Total Pages | : 231 |
Release | : 2007-05-24 |
Genre | : Mathematics |
ISBN | : 0198528221 |
Download Experimental Number Theory Book in PDF, ePub and Kindle
This graduate text shows how the computer can be used as a tool for research in number theory through numerical experimentation. Examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, are provided along with exercises and selected solutions.
Author | : Fernando Rodriguez Villegas |
Publisher | : |
Total Pages | : 0 |
Release | : 2023 |
Genre | : Number theory |
ISBN | : 9781383024647 |
Download Experimental Number Theory Book in PDF, ePub and Kindle
This graduate text shows how the computer can be used as a tool for research in number theory through numerical experimentation. Examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory and elliptic units are provided.
Author | : Álvaro Lozano-Robledo |
Publisher | : American Mathematical Soc. |
Total Pages | : 488 |
Release | : 2019-03-21 |
Genre | : Arithmetical algebraic geometry |
ISBN | : 147045016X |
Download Number Theory and Geometry: An Introduction to Arithmetic Geometry Book in PDF, ePub and Kindle
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.
Author | : Richard Friedberg |
Publisher | : Courier Corporation |
Total Pages | : 241 |
Release | : 2012-07-06 |
Genre | : Mathematics |
ISBN | : 0486152693 |
Download An Adventurer's Guide to Number Theory Book in PDF, ePub and Kindle
This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.
Author | : W.A. Coppel |
Publisher | : Springer Science & Business Media |
Total Pages | : 392 |
Release | : 2006-02-02 |
Genre | : Mathematics |
ISBN | : 9780387298511 |
Download Number Theory Book in PDF, ePub and Kindle
This two-volume book is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A is accessible to first-year undergraduates and deals with elementary number theory. Part B is more advanced and gives the reader an idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches a broad picture is obtained. The book contains a treasury of proofs, several of which are gems seldom seen in number theory books.
Author | : Anthony Vazzana |
Publisher | : CRC Press |
Total Pages | : 530 |
Release | : 2007-10-30 |
Genre | : Computers |
ISBN | : 1584889381 |
Download Introduction to Number Theory Book in PDF, ePub and Kindle
One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi
Author | : M. Pohst |
Publisher | : Cambridge University Press |
Total Pages | : 520 |
Release | : 1997-09-25 |
Genre | : Mathematics |
ISBN | : 9780521596695 |
Download Algorithmic Algebraic Number Theory Book in PDF, ePub and Kindle
Now in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.
Author | : Song Y. Yan |
Publisher | : Springer Science & Business Media |
Total Pages | : 454 |
Release | : 2013-11-11 |
Genre | : Computers |
ISBN | : 366204773X |
Download Number Theory for Computing Book in PDF, ePub and Kindle
This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.
Author | : A. G. Postnikov |
Publisher | : American Mathematical Soc. |
Total Pages | : 332 |
Release | : 1988-12-31 |
Genre | : Mathematics |
ISBN | : 0821813498 |
Download Introduction to Analytic Number Theory Book in PDF, ePub and Kindle
Aimed at a level between textbooks and the latest research monographs, this book is directed at researchers, teachers, and graduate students interested in number theory and its connections with other branches of science. Choosing to emphasize topics not sufficiently covered in the literature, the author has attempted to give as broad a picture as possible of the problems of analytic number theory.