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Excursions in number theory, algebra...

Ireland, Kenneth.

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Excursions in number theory, algebra, and analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Excursions in number theory, algebra, and analysis/ by Kenneth Ireland, Al Cuoco.
Author:	Ireland, Kenneth.
other author:	Cuoco, Al.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xxv, 177 p. :ill., digital ;24 cm.
[NT 15003449]:	Preface -- 1. Dialing In Problems -- 2. Polygons and Modular Arithmetic -- 3. The Fundamental Theorem of Arithmetic -- 4. The Fundamental Theorem of Algebra -- 5. Irrational, Algebraic and Transcendental Numbers -- 6. Fourier Series and Gauss Sums -- Epilogue -- Notation -- Bibliography -- Index.
Contained By:	Springer Nature eBook
Subject:	Number theory. -
Online resource:	https://doi.org/10.1007/978-3-031-13017-5
ISBN:	9783031130175

Excursions in number theory, algebra, and analysis
Ireland, Kenneth.

Excursions in number theory, algebra, and analysis[electronic resource] /by Kenneth Ireland, Al Cuoco. - Cham :Springer International Publishing :2023. - xxv, 177 p. :ill., digital ;24 cm. - Readings in mathematics,2945-5847. - Readings in mathematics..

Preface -- 1. Dialing In Problems -- 2. Polygons and Modular Arithmetic -- 3. The Fundamental Theorem of Arithmetic -- 4. The Fundamental Theorem of Algebra -- 5. Irrational, Algebraic and Transcendental Numbers -- 6. Fourier Series and Gauss Sums -- Epilogue -- Notation -- Bibliography -- Index.

This textbook originates from a course taught by the late Ken Ireland in 1972. Designed to explore the theoretical underpinnings of undergraduate mathematics, the course focused on interrelationships and hands-on experience. Readers of this textbook will be taken on a modern rendering of Ireland's path of discovery, consisting of excursions into number theory, algebra, and analysis. Replete with surprising connections, deep insights, and brilliantly curated invitations to try problems at just the right moment, this journey weaves a rich body of knowledge that is ideal for those going on to study or teach mathematics. A pool of 200 'Dialing In' problems opens the book, providing fuel for active enquiry throughout a course. The following chapters develop theory to illuminate the observations and roadblocks encountered in the problems, situating them in the broader mathematical landscape. Topics cover polygons and modular arithmetic; the fundamental theorems of arithmetic and algebra; irrational, algebraic and transcendental numbers; and Fourier series and Gauss sums. A lively accompaniment of examples, exercises, historical anecdotes, and asides adds motivation and context to the theory. Return trips to the Dialing In problems are encouraged, offering opportunities to put theory into practice and make lasting connections along the way. Excursions in Number Theory, Algebra, and Analysis invites readers on a journey as important as the destination. Suitable for a senior capstone, professional development for practicing teachers, or independent reading, this textbook offers insights and skills valuable to math majors and high school teachers alike. A background in real analysis and abstract algebra is assumed, though the most important prerequisite is a willingness to put pen to paper and do some mathematics.

ISBN: 9783031130175

Standard No.: 10.1007/978-3-031-13017-5doiSubjects--Topical Terms:

515832
Number theory.

LC Class. No.: QA241

Dewey Class. No.: 512.7

Excursions in number theory, algebra, and analysis
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245 1 0 $a Excursions in number theory, algebra, and analysis $h [electronic resource] / $c by Kenneth Ireland, Al Cuoco.
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300 $a xxv, 177 p. : $b ill., digital ; $c 24 cm.
490 1 $a Readings in mathematics, $x 2945-5847
505 0 $a Preface -- 1. Dialing In Problems -- 2. Polygons and Modular Arithmetic -- 3. The Fundamental Theorem of Arithmetic -- 4. The Fundamental Theorem of Algebra -- 5. Irrational, Algebraic and Transcendental Numbers -- 6. Fourier Series and Gauss Sums -- Epilogue -- Notation -- Bibliography -- Index.
520 $a This textbook originates from a course taught by the late Ken Ireland in 1972. Designed to explore the theoretical underpinnings of undergraduate mathematics, the course focused on interrelationships and hands-on experience. Readers of this textbook will be taken on a modern rendering of Ireland's path of discovery, consisting of excursions into number theory, algebra, and analysis. Replete with surprising connections, deep insights, and brilliantly curated invitations to try problems at just the right moment, this journey weaves a rich body of knowledge that is ideal for those going on to study or teach mathematics. A pool of 200 'Dialing In' problems opens the book, providing fuel for active enquiry throughout a course. The following chapters develop theory to illuminate the observations and roadblocks encountered in the problems, situating them in the broader mathematical landscape. Topics cover polygons and modular arithmetic; the fundamental theorems of arithmetic and algebra; irrational, algebraic and transcendental numbers; and Fourier series and Gauss sums. A lively accompaniment of examples, exercises, historical anecdotes, and asides adds motivation and context to the theory. Return trips to the Dialing In problems are encouraged, offering opportunities to put theory into practice and make lasting connections along the way. Excursions in Number Theory, Algebra, and Analysis invites readers on a journey as important as the destination. Suitable for a senior capstone, professional development for practicing teachers, or independent reading, this textbook offers insights and skills valuable to math majors and high school teachers alike. A background in real analysis and abstract algebra is assumed, though the most important prerequisite is a willingness to put pen to paper and do some mathematics.
650 0 $a Number theory. $3 515832
650 0 $a Algebra. $3 516203
650 0 $a Mathematical analysis. $3 516833
650 1 4 $a Number Theory. $3 891078
650 2 4 $a Group Theory and Generalizations. $3 893889
650 2 4 $a Real Functions. $3 891265
700 1 $a Cuoco, Al. $3 3632330
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830 0 $a Readings in mathematics. $3 3609269
856 4 0 $u https://doi.org/10.1007/978-3-031-13017-5
950 $a Mathematics and Statistics (SpringerNature-11649)