國立虎尾科技大學 |

Explorations in number theory = commuting through the numberverse /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Explorations in number theory/ by Cam McLeman, Erin McNicholas, Colin Starr.
Reminder of title:	commuting through the numberverse /
Author:	McLeman, Cam.
other author:	McNicholas, Erin.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	xiii, 372 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Number theory. -
Online resource:	https://doi.org/10.1007/978-3-030-98931-6
ISBN:	9783030989316

Explorations in number theory = commuting through the numberverse /
McLeman, Cam.

Explorations in number theorycommuting through the numberverse /[electronic resource] :by Cam McLeman, Erin McNicholas, Colin Starr. - Cham :Springer International Publishing :2022. - xiii, 372 p. :ill. (some col.), digital ;24 cm. - Undergraduate texts in mathematics,2197-5604. - Undergraduate texts in mathematics..

This innovative undergraduate textbook approaches number theory through the lens of abstract algebra. Written in an engaging and whimsical style, this text will introduce students to rings, groups, fields, and other algebraic structures as they discover the key concepts of elementary number theory. Inquiry-based learning (IBL) appears throughout the chapters, allowing students to develop insights for upcoming sections while simultaneously strengthening their understanding of previously covered topics. The text is organized around three core themes: the notion of what a "number" is, and the premise that it takes familiarity with a large variety of number systems to fully explore number theory; the use of Diophantine equations as catalysts for introducing and developing structural ideas; and the role of abstract algebra in number theory, in particular the extent to which it provides the Fundamental Theorem of Arithmetic for various new number systems. Other aspects of modern number theory - including the study of elliptic curves, the analogs between integer and polynomial arithmetic, p-adic arithmetic, and relationships between the spectra of primes in various rings - are included in smaller but persistent threads woven through chapters and exercise sets. Each chapter concludes with exercises organized in four categories: Calculations and Informal Proofs, Formal Proofs, Computation and Experimentation, and General Number Theory Awareness. IBL "Exploration" worksheets appear in many sections, some of which involve numerical investigations. To assist students who may not have experience with programming languages, Python worksheets are available on the book's website. The final chapter provides five additional IBL explorations that reinforce and expand what students have learned, and can be used as starting points for independent projects. The topics covered in these explorations are public key cryptography, Lagrange's four-square theorem, units and Pell's Equation, various cases of the solution to Fermat's Last Theorem, and a peek into other deeper mysteries of algebraic number theory. Students should have a basic familiarity with complex numbers, matrix algebra, vector spaces, and proof techniques, as well as a spirit of adventure to explore the "numberverse.".

ISBN: 9783030989316

Standard No.: 10.1007/978-3-030-98931-6doiSubjects--Topical Terms:

527883
Number theory.

LC Class. No.: QA241

Dewey Class. No.: 512.7

Explorations in number theory = commuting through the numberverse /
LDR:03364nam a2200325 a 4500 001 1097931
003 DE-He213
005 20221218004625.0
006 m d
007 cr nn 008maaau
008 230419s2022 sz s 0 eng d
020 $a 9783030989316 $q (electronic bk.)
020 $a 9783030989309 $q (paper)
024 7 $a 10.1007/978-3-030-98931-6 $2 doi
035 $a 978-3-030-98931-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA241
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 512.7 $2 23
090 $a QA241 $b .M164 2022
100 1 $a McLeman, Cam. $e author. $3 1393317
245 1 0 $a Explorations in number theory $h [electronic resource] : $b commuting through the numberverse / $c by Cam McLeman, Erin McNicholas, Colin Starr.
260 $a Cham : $c 2022. $b Springer International Publishing : $b Imprint: Springer,
300 $a xiii, 372 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Undergraduate texts in mathematics, $x 2197-5604
520 $a This innovative undergraduate textbook approaches number theory through the lens of abstract algebra. Written in an engaging and whimsical style, this text will introduce students to rings, groups, fields, and other algebraic structures as they discover the key concepts of elementary number theory. Inquiry-based learning (IBL) appears throughout the chapters, allowing students to develop insights for upcoming sections while simultaneously strengthening their understanding of previously covered topics. The text is organized around three core themes: the notion of what a "number" is, and the premise that it takes familiarity with a large variety of number systems to fully explore number theory; the use of Diophantine equations as catalysts for introducing and developing structural ideas; and the role of abstract algebra in number theory, in particular the extent to which it provides the Fundamental Theorem of Arithmetic for various new number systems. Other aspects of modern number theory - including the study of elliptic curves, the analogs between integer and polynomial arithmetic, p-adic arithmetic, and relationships between the spectra of primes in various rings - are included in smaller but persistent threads woven through chapters and exercise sets. Each chapter concludes with exercises organized in four categories: Calculations and Informal Proofs, Formal Proofs, Computation and Experimentation, and General Number Theory Awareness. IBL "Exploration" worksheets appear in many sections, some of which involve numerical investigations. To assist students who may not have experience with programming languages, Python worksheets are available on the book's website. The final chapter provides five additional IBL explorations that reinforce and expand what students have learned, and can be used as starting points for independent projects. The topics covered in these explorations are public key cryptography, Lagrange's four-square theorem, units and Pell's Equation, various cases of the solution to Fermat's Last Theorem, and a peek into other deeper mysteries of algebraic number theory. Students should have a basic familiarity with complex numbers, matrix algebra, vector spaces, and proof techniques, as well as a spirit of adventure to explore the "numberverse.".
650 0 $a Number theory. $3 527883
700 1 $a McNicholas, Erin. $e author. $3 1393318
700 1 $a Starr, Colin. $e author. $3 1393319
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Undergraduate texts in mathematics. $3 881276
856 4 0 $u https://doi.org/10.1007/978-3-030-98931-6
950 $a Mathematics and Statistics (SpringerNature-11649)