國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Methods of solving number theory pro...

Grigorieva, Ellina.

Methods of solving number theory problems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Methods of solving number theory problemsby Ellina Grigorieva.
作者:	Grigorieva, Ellina.
出版者:	Cham :Springer International Publishing :2018.
面頁冊數:	xxi, 391 p. :digital ;24 cm.
Contained By:	Springer eBooks
標題:	Number theory.
電子資源:	http://dx.doi.org/10.1007/978-3-319-90915-8
ISBN:	9783319909158$q(electronic bk.)

Methods of solving number theory problems
Grigorieva, Ellina.

Methods of solving number theory problems[electronic resource] /by Ellina Grigorieva. - Cham :Springer International Publishing :2018. - xxi, 391 p. :digital ;24 cm.

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

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.

ISBN: 9783319909158$q(electronic bk.)

Standard No.: 10.1007/978-3-319-90915-8doiSubjects--Topical Terms:

189521
Number theory.

LC Class. No.: QA241 / .G754 2018

Dewey Class. No.: 512.7

Methods of solving number theory problems
LDR:03137nmm a2200313 a 4500 001 543126
003 DE-He213
005 20190129170355.0
006 m d
007 cr nn 008maaau
008 190411s2018 gw s 0 eng d
020 $a 9783319909158$q(electronic bk.)
020 $a 9783319909141$q(paper)
024 7 $a 10.1007/978-3-319-90915-8 $2 doi
035 $a 978-3-319-90915-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA241 $b .G754 2018
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
082 0 4 $a 512.7 $2 23
090 $a QA241 $b .G857 2018
100 1 $a Grigorieva, Ellina. $3 731710
245 1 0 $a Methods of solving number theory problems $h [electronic resource] / $c by Ellina Grigorieva.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2018.
300 $a xxi, 391 p. : $b digital ; $c 24 cm.
505 0 $a Preface -- Numbers: Problems Involving Integers -- Further Study of Integers -- Diophantine Equations and More -- Pythagorean Triples, Additive Problems, and More -- Homework.
520 $a 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.
650 0 $a Number theory. $3 189521
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Number Theory. $3 274059
650 2 4 $a Mathematics Education. $3 274700
650 2 4 $a Mathematical Logic and Foundations. $3 274479
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-90915-8
950 $a Mathematics and Statistics (Springer-11649)