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Undergraduate Texts in Mathematics Ser.: Excursions in Number Theory, Algebra, and Analysis by Kenneth Ireland and Al Cuoco (2023, Hardcover)
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This textbook originates from a course taught by the late Ken Ireland in 1972. 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.
- Buy It NowExcursions in Number Theory, Algebra, and Analysis by Kenneth Ireland (English)
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About this product
Product Identifiers
PublisherSpringer International Publishing A&G
ISBN-103031130162
ISBN-139783031130168
eBay Product ID (ePID)26057275151
Product Key Features
Number of PagesXxv, 177 Pages
LanguageEnglish
Publication NameExcursions in Number Theory, Algebra, and Analysis
Publication Year2023
SubjectAlgebra / Abstract, General, Number Theory, Mathematical Analysis
TypeTextbook
AuthorKenneth Ireland, Al Cuoco
Subject AreaMathematics
SeriesUndergraduate Texts in Mathematics Ser.
FormatHardcover
Dimensions
Item Weight22.5 Oz
Item Length10 in
Item Width7 in
Additional Product Features
Reviews"Rather than being a book that one reads from cover to cover, Excursions is a curated collection problems followed by expository material aimed at providing background material useful for solving these problems. I imagine it would be a great experience to have a course taught out of this book. The second author clearly enjoyed the experience of studying this material under the guidance of the first author and wanted to make that experience available to others." (John D. Cook, MAA Reviews, June 17, 2023)
Dewey Edition23
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal512
Table Of ContentPreface.- 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.
SynopsisThis 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 .
LC Classification NumberQA241-247.5
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