This book began life as a set of notes that I developed for a course at the University of Washington entitled Introduction to Modern Algebra for Tea- ers. Originally conceived as a text for future secondary-school mathematics teachers, it has developed into a book that could serve well as a text in an - dergraduatecourseinabstractalgebraoracoursedesignedasanintroduction to higher mathematics. This book di?ers from many undergraduate algebra texts in fundamental ways; the reasons lie in the book’s origin and the goals I set for the course. The course is a two-quarter sequence required of students intending to f- ?ll the requirements of the teacher preparation option for our B.A. degree in mathematics, or of the teacher preparation minor. It is required as well of those intending to matriculate in our university’s Master’s in Teaching p- gram for secondary mathematics teachers. This is the principal course they take involving abstraction and proof, and they come to it with perhaps as little background as a year of calculus and a quarter of linear algebra. The mathematical ability of the students varies widely, as does their level of ma- ematical interest.

*"synopsis" may belong to another edition of this title.*

Mathematics is often regarded as the study of calculation, but in fact, mathematics is much more. It combines creativity and logic in order to arrive at abstract truths. This book is intended to illustrate how calculation, creativity, and logic can be combined to solve a range of problems in algebra. Originally conceived as a text for a course for future secondary-school mathematics teachers, this book has developed into one that could serve well in an undergraduate course in abstract algebra or a course designed as an introduction to higher mathematics. Not all topics in a traditional algebra course are covered. Rather, the author focuses on integers, polynomials, their ring structure, and fields, with the aim that students master a small number of serious mathematical ideas. The topics studied should be of interest to all mathematics students and are especially appropriate for future teachers.

One nonstandard feature of the book is the small number of theorems for which full proofs are given. Many proofs are left as exercises, and for almost every such exercise a detailed hint or outline of the proof is provided. These exercises form the heart of the text. Unwinding the meaning of the hint or outline can be a significant challenge, and the unwinding process serves as the catalyst for learning.

Ron Irving is the Divisional Dean of Natural Sciences at the University of Washington. Prior to assuming this position, he served as Chair of the Department of Mathematics. He has published research articles in several areas of algebra, including ring theory and the representation theory of Lie groups and Lie algebras. In 2001, he received the University of Washington's Distinguished Teaching Award for the course on which this book is based.

From the reviews:

"The book focuses mainly on the ‘doing’ of algebra. ... The chief aim of the author is for students ‘to master such skills as learning what a mathematical statement is, what a mathematical argument or proof is, how to present an argument orally ... and how to converse effectively about mathematics.’ ... the author strives to motivate students, gradually developing their insights and abilities. ... It is an excellent primer for beginners in the field of abstract algebra, especially for future school teachers." (P. Shiu, The Mathematical Gazette, Vol. 89 (516), 2005)

"This is an instructional exposition which treats some elementary number theory ... . It is apparent that the author has made every effort to motivate students resp. to put them in the right way. ‘I love algebra. I want my students to love algebra’ – I believe that the author succeeded even in this regard." (G. Kowol, Monatshefte für Mathematik, Vol. 144 (2), 2005)

"This is a very elementary introduction to elementary number theory and some related topics in algebra ... . The topics chosen are well suited for a student’s first exposure to ‘serious’ mathematics (much more so, in the reviewer’s opinion, than the calculus course that is the norm in almost all curricula almost everywhere)." (S. Frisch, Internationale Mathematische Nachrichten, Issue 196, 2004)

"The book ... represents a very special introduction to modern algebra ... . focuses less on contents and more on the ‘doing’ of algebra. ... Many proofs are left as exercises, together with detailed hints or outlines, and these exercises actually form the heart of the entire text. ... Summing up, this book is a great primer for beginners in the field ... . could serve well in an undergraduate course for non-mathematicians, and as a guide to self-education beyond academic training, too." (Werner Kleinert, Zentralblatt MATH, Vol. 1046 (2), 2004)

"Originally conceived as a text for a course for future secondary-school mathematics teachers, this book has developed into one that could serve well in an undergraduate course in abstract algebra ... . The topics studies should be of interest to all mathematics students and are especially appropriate for future teachers. ... Many proofs are left as exercises, and for almost every such exercise, a detailed hint or outline of the proof is provided. These exercises form the heart of the text." (Zentralblatt für Didaktik der Mathematik, November, 2004)

"Mathematics is often regarded as the study of calculation ... . It combines creativity and logic in order to arrive at abstract truths. This book is intended to illustrate how calculation, creativity, and logic can be combined to solve a range of problems in algebra. ... Many proofs are left as exercises, and for almost every such exercise, a detailed hint or outline of the proof is provided. These exercises form the heart of the text." (L’Enseignement Mathematique, Vol. 50 (1-2), 2004)

"The book is meant to be a structurally different abstract algebra textbook. ... the book is very unitary and it has a good flow. ... Integers, Polynominals and Rings is a unique book, and should be extremely useful for an audience of future high school teachers. It would also be a valuable supplement for students taking a traditional abstract algebra course, especially since it is very readable." (Ioana Mihaila, MathDL, January, 2004)

*"About this title" may belong to another edition of this title.*

US$ 22.16

**Shipping:**
US$ 9.62

From United Kingdom to U.S.A.

Published by
Springer New York 2003-12-04, New York
(2003)

ISBN 10: 0387201726
ISBN 13: 9780387201726

New
paperback
Quantity Available: > 20

Seller:

Rating

**Book Description **Springer New York 2003-12-04, New York, 2003. paperback. Condition: New. Seller Inventory # 9780387201726

Published by
Springer-Verlag New York Inc., United States
(2003)

ISBN 10: 0387201726
ISBN 13: 9780387201726

New
Paperback
Quantity Available: 10

Seller:

Rating

**Book Description **Springer-Verlag New York Inc., United States, 2003. Paperback. Condition: New. 2004 ed.. Language: English. Brand new Book. This book began life as a set of notes that I developed for a course at the University of Washington entitled Introduction to Modern Algebra for Tea- ers. Originally conceived as a text for future secondary-school mathematics teachers, it has developed into a book that could serve well as a text in an - dergraduatecourseinabstractalgebraoracoursedesignedasanintroduction to higher mathematics. This book di?ers from many undergraduate algebra texts in fundamental ways; the reasons lie in the book's origin and the goals I set for the course. The course is a two-quarter sequence required of students intending to f- ?ll the requirements of the teacher preparation option for our B.A. degree in mathematics, or of the teacher preparation minor. It is required as well of those intending to matriculate in our university's Master's in Teaching p- gram for secondary mathematics teachers. This is the principal course they take involving abstraction and proof, and they come to it with perhaps as little background as a year of calculus and a quarter of linear algebra. The mathematical ability of the students varies widely, as does their level of ma- ematical interest. Seller Inventory # SPR9780387201726

Published by
Springer-Verlag New York Inc., United States
(2003)

ISBN 10: 0387201726
ISBN 13: 9780387201726

New
Paperback
Quantity Available: 10

Seller:

Rating

**Book Description **Springer-Verlag New York Inc., United States, 2003. Paperback. Condition: New. 2004 ed.. Language: English. Brand new Book. This book began life as a set of notes that I developed for a course at the University of Washington entitled Introduction to Modern Algebra for Tea- ers. Originally conceived as a text for future secondary-school mathematics teachers, it has developed into a book that could serve well as a text in an - dergraduatecourseinabstractalgebraoracoursedesignedasanintroduction to higher mathematics. This book di?ers from many undergraduate algebra texts in fundamental ways; the reasons lie in the book's origin and the goals I set for the course. The course is a two-quarter sequence required of students intending to f- ?ll the requirements of the teacher preparation option for our B.A. degree in mathematics, or of the teacher preparation minor. It is required as well of those intending to matriculate in our university's Master's in Teaching p- gram for secondary mathematics teachers. This is the principal course they take involving abstraction and proof, and they come to it with perhaps as little background as a year of calculus and a quarter of linear algebra. The mathematical ability of the students varies widely, as does their level of ma- ematical interest. Seller Inventory # SPR9780387201726

Published by
Springer-Verlag New York Inc.
(2003)

ISBN 10: 0387201726
ISBN 13: 9780387201726

New
Quantity Available: > 20

Seller:

Rating

**Book Description **Springer-Verlag New York Inc., 2003. PAP. Condition: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Seller Inventory # S0-9780387201726

Published by
Springer
(2003)

ISBN 10: 0387201726
ISBN 13: 9780387201726

New
Quantity Available: > 20

Seller:

Rating

**Book Description **Springer, 2003. PAP. Condition: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Seller Inventory # IQ-9780387201726

Published by
Springer
(2016)

ISBN 10: 0387201726
ISBN 13: 9780387201726

New
Paperback
Quantity Available: 1

Seller:

Rating

**Book Description **Springer, 2016. Paperback. Condition: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Seller Inventory # ria9780387201726_lsuk

Published by
Springer Verlag
(2003)

ISBN 10: 0387201726
ISBN 13: 9780387201726

New
Paperback
Quantity Available: 2

Seller:

Rating

**Book Description **Springer Verlag, 2003. Paperback. Condition: Brand New. 1st edition. 284 pages. 9.00x6.00x0.75 inches. In Stock. Seller Inventory # __0387201726

Published by
Springer
(2003)

ISBN 10: 0387201726
ISBN 13: 9780387201726

New
Paperback
Quantity Available: 1

Seller:

Rating

**Book Description **Springer, 2003. Paperback. Condition: New. 2004. Seller Inventory # DADAX0387201726

Published by
Springer
(2003)

ISBN 10: 0387201726
ISBN 13: 9780387201726

New
Paperback
Quantity Available: 1

Seller:

Rating

**Book Description **Springer, 2003. Paperback. Condition: NEW. 9780387201726 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Seller Inventory # HTANDREE0271739

Published by
Springer
(2018)

ISBN 10: 0387201726
ISBN 13: 9780387201726

New
Paperback
Quantity Available: > 20

Seller:

Rating

**Book Description **Springer, 2018. Paperback. Condition: New. Never used! This item is printed on demand. Seller Inventory # 0387201726