عنوان

Methods of Solving Number Theory Problems

(Number (ISBN

9783319909158

Number

E2923

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Methods of Solving Number Theory Problems

First Statement of Responsibility

by Ellina Grigorieva.

Place of Publication, Distribution, etc.

Cham, Switzerland

Name of Publisher, Distributor, etc.

Birkhauser

Date of Publication, Distribution, etc.

2018.

Specific Material Designation and Extent of Item

xxi, 391 p.

Other Physical Details

16 illustrations, 12 illustrations in color.

Text of Note

Preface -- Numbers: Problems Involving Integers -- Further Study of Integers -- Diophantine Equations and More -- Pythagorean Triples, Additive Problems, and More -- Homework.

0

Text of Note

Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of abstract problems in a systematic, creative manner. New solutions often require the ingenious use of earlier mathematical concepts - not the memorization of formulas and facts. Questions also often permit experimental numeric validation or visual interpretation to encourage the combined use of deductive and intuitive thinking. The first chapter of the book covers topics like even and odd numbers, divisibility, prime, perfect, figurate numbers, and introduces congruence. The next chapter works with representations of natural numbers in different bases, as well as the theory of continued fractions, quadratic irrationalities, and also explores different methods of proofs. The third chapter is dedicated to solving unusual factorial and exponential equations, Diophantine equations, introduces Pell's equations and how they connect algebra and geometry. Chapter 4 reviews Pythagorean triples and their relation to algebraic geometry, representation of a number as the sum of squares or cubes of other numbers, quadratic residuals, and interesting word problems. Appendices provide a historic overview of number theory and its main developments from ancient cultures to the modern day. Drawing from cases collected by an accomplished female mathematician, Methods in Solving Number Theory Problems is designed as a self-study guide or supplementary textbook for a one-semester course in introductory number theory. It can also be used to prepare for mathematical Olympiads. Elementary algebra, arithmetic and some calculus knowledge are the only prerequisites. Number theory gives precise proofs and theorems of an irreproachable rigor and sharpens analytical thinking, which makes this book perfect for anyone looking to build their mathematical confidence.-- Provided by publisher

Entry Element

Number theory.

Edition

Class number

Book number

Entry Element

Grigorieva, Ellina,

Country

Iran

Agency

University of Tehran. Library of College of Science

Date of Transaction

20220312173224.0

Cataloguing Rules (Descriptive Conventions))

rda

Date and Hour of Consultation and Access

UT_SCI_BL_DB_1003180_0001.pdf

e

BL

278840

a

Y