Lure of the Integers
Author | : Joe Roberts |
Publisher | : American Mathematical Soc. |
Total Pages | : 331 |
Release | : 2020-07-31 |
Genre | : Mathematics |
ISBN | : 1470457296 |
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Author | : Joe Roberts |
Publisher | : American Mathematical Soc. |
Total Pages | : 331 |
Release | : 2020-07-31 |
Genre | : Mathematics |
ISBN | : 1470457296 |
Author | : James J. Tattersall |
Publisher | : Cambridge University Press |
Total Pages | : 420 |
Release | : 1999-10-14 |
Genre | : Mathematics |
ISBN | : 9780521585316 |
This book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.
Author | : Richard Guy |
Publisher | : Springer Science & Business Media |
Total Pages | : 303 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 1489935851 |
Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material.
Author | : Liang-shin Hahn |
Publisher | : American Mathematical Soc. |
Total Pages | : 204 |
Release | : 2019-12-26 |
Genre | : Education |
ISBN | : 1470451824 |
The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained—no background in complex numbers is assumed—and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more.
Author | : Marc Chamberland |
Publisher | : Princeton University Press |
Total Pages | : 240 |
Release | : 2017-05-30 |
Genre | : Mathematics |
ISBN | : 0691175691 |
"The numbers one through nine have remarkable mathematical properties and characteristics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? Are there really "six degrees of separation" between all pairs of people? And how can any map need only four colors to ensure that no regions of the same color touch? In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics."--Jacket.
Author | : Asok Kumar Mallik |
Publisher | : #N/A |
Total Pages | : 197 |
Release | : 2017-07-27 |
Genre | : Mathematics |
ISBN | : 9813222948 |
'… this could make an ideal end-of-year prize for a high-school student who is fascinated by all aspects of number. The subsections provide ideas and opportunities for mathematical exploration. This book might also be deemed a suitable resource for first-year undergraduates in that, via independent study, it would allow such students to broaden their knowledge of various number-theoretic ideas. I would recommend it for the purposes given above.'The Mathematical GazetteThis book is more than a mathematics textbook. It discusses various kinds of numbers and curious interconnections between them. Without getting into hardcore and difficult mathematical technicalities, the book lucidly introduces all kinds of numbers that mathematicians have created. Interesting anecdotes involving great mathematicians and their marvelous creations are included. The reader will get a glimpse of the thought process behind the invention of new mathematics. Starting from natural numbers, the book discusses integers, real numbers, imaginary and complex numbers and some special numbers like quaternions, dual numbers and p-adic numbers.Real numbers include rational, irrational and transcendental numbers. Iterations on real numbers are shown to throw up some unexpected behavior, which has given rise to the new science of 'Chaos'. Special numbers like e, pi, golden ratio, Euler's constant, Gauss's constant, amongst others, are discussed in great detail.The origin of imaginary numbers and the use of complex numbers constitute the next topic. It is shown why modern mathematics cannot even be imagined without imaginary numbers. Iterations on complex numbers are shown to generate a new mathematical object called 'Fractal', which is ubiquitous in nature. Finally, some very special numbers, not mentioned in the usual textbooks, and their applications, are introduced at an elementary level.The level of mathematics discussed in this book is easily accessible to young adults interested in mathematics, high school students, and adults having some interest in basic mathematics. The book concentrates more on the story than on rigorous mathematics.
Author | : John J. Watkins |
Publisher | : Princeton University Press |
Total Pages | : 270 |
Release | : 2011-09-19 |
Genre | : Mathematics |
ISBN | : 1400840929 |
Across the Board is the definitive work on chessboard problems. It is not simply about chess but the chessboard itself--that simple grid of squares so common to games around the world. And, more importantly, the fascinating mathematics behind it. From the Knight's Tour Problem and Queens Domination to their many variations, John Watkins surveys all the well-known problems in this surprisingly fertile area of recreational mathematics. Can a knight follow a path that covers every square once, ending on the starting square? How many queens are needed so that every square is targeted or occupied by one of the queens? Each main topic is treated in depth from its historical conception through to its status today. Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery. Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries, Across the Board will captivate students and instructors, mathematicians, chess enthusiasts, and puzzle devotees.
Author | : Richard E. Crandall |
Publisher | : Springer Science & Business Media |
Total Pages | : 500 |
Release | : 2000-06-22 |
Genre | : Computers |
ISBN | : 9780387950099 |
This interdisciplinary book provides a compendium of projects, plus numerous example programs for readers to study and explore. Designed for advanced undergraduates or graduates of science, mathematics and engineering who will deal with scientific computation in their future studies and research, it also contains new and useful reference materials for researchers. The problem sets range from the tutorial to exploratory and, at times, to "the impossible". The projects were collected from research results and computational dilemmas during the authors tenure as Chief Scientist at NeXT Computer, and from his lectures at Reed College. The content assumes familiarity with such college topics as calculus, differential equations, and at least elementary programming. Each project focuses on computation, theory, graphics, or a combination of these, and is designed with an estimated level of difficulty. The support code for each takes the form of either C or Mathematica, and is included in the appendix and on the bundled diskette. The algorithms are clearly laid out within the projects, such that the book may be used with other symbolic numerical and algebraic manipulation products
Author | : John de Pillis |
Publisher | : Cambridge University Press |
Total Pages | : 364 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780883855409 |
Illustrated book showing that there are few degrees of separation between mathematics and topics that provoke interesting conversations.