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33528871
Elementary Number Theory (Springer Undergraduate Mathematics Series)
88% of respondents would recommend this to a friend
Item #:
33528871
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An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples.
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What Stands Out
Comprehensive Coverage
This edition offers in-depth explanations of fundamental concepts in number theory, making it suitable for undergraduates seeking a thorough understanding of the subject.
Pedagogical Approach
Designed for learners, it includes numerous examples and exercises that reinforce concepts, ensuring students can apply theoretical knowledge practically.
Accessibly Priced
As part of the Springer Undergraduate Mathematics Series, this corrected edition is affordably priced, providing high-quality educational content for budget-conscious students.
Product Details
- Our intention in writing this book is to give an elementary introduction to number theory which does not demand a great deal of mathematical back ground or maturity from the reader, and which can be read and understood with no extra assistance. Our first three chapters are based almost entirely on A-level mathematics, while the next five require little else beyond some el ementary group theory. It is only in the last three chapters, where we treat more advanced topics, including recent developments, that we require greater mathematical background; here we use some basic ideas which students would expect to meet in the first year or so of a typical undergraduate course in math ematics. Throughout the book, we have attempted to explain our arguments as fully and as clearly as possible, with plenty of worked examples and with outline solutions for all the exercises. There are several good reasons for choosing number theory as a subject. It has a long and interesting history, ranging from the earliest recorded times to the present day (see Chapter 11, for instance, on Fermat's Last Theorem), and its problems have attracted many of the greatest mathematicians; consequently the study of number theory is an excellent introduction to the development and achievements of mathematics (and, indeed, some of its failures). In particular, the explicit nature of many of its problems, concerning basic properties of inte gers, makes number theory a particularly suitable subject in which to present modern mathematics in elementary terms.
| Publisher | Springer |
| Publication date | January 14, 1998 |
| Edition | Corrected |
| Language | English |
| Print length | 200 pages |
| ISBN-10 | 3540761977 |
| ISBN-13 | 978-3540761976 |
| Item Weight | 1.2 pounds (540 grams) |
| Dimensions | 7.01 x 0.72 x 9.25 inches (17.8 x 1.8 x 23.5 cm) |
| Part of series | Springer Undergraduate Mathematics |
Who Should Buy?
-
Students of Mathematics
Ideal for undergraduate students seeking a foundational understanding of number theory and its applications in mathematics.
-
Self-Learners
Great for individuals who wish to independently study number theory with structured explanations and exercises to enhance learning.
-
Instructors and Educators
Useful for teachers looking for a comprehensive resource to recommend to students or for structuring their number theory curriculum.
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Advanced Mathematicians
Less suitable for experts who may find the content too basic and lacking in advanced theoretical discussions.
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Number Theory Editorial Review
The Elementary Number Theory book in the Springer Undergraduate Mathematics series is a great source of topics for those looking to teach the subject at the elementary level. The writing is clear, and the book provides a unique way of looking at mathematical history that complements the straight timeline often seen. The combined introduction to number theory, practice of full proof writing, and exercises and solutions are laudable. However, it is not the meatiest text for those seeking a stripped-down introduction to number theory concepts without putting in work. Those who take the time to work through the book's questions will appreciate the pacing and the uniquely engaging way that the questions are presented in-chapter. The text struggles with difficult-to-understand solutions in the back of the book, which may lead to frustration among some readers. The book is also slightly more challenging than other number theory texts, and some readers may find the reading tough-going. Despite its limitations, the Elementary Number Theory book is an excellent source of material for teaching elementary number theory, and its engaging in-chapter questions are enough to make it among the best books on the subject.
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Pros
- Clear writing and unique perspective on mathematical history
- Good source of topics for elementary level teaching
- Combined introduction to number theory, proof writing practice, and exercises/solutions
- Engaging in-chapter questions
Cons
- Difficult-to-understand solutions in the back of the book
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Features & Benefits
- Fully-explained proofs
- Examples given
- Exercises and solutions integrated
- Includes ideas from algebra and analysis
- Covers quadratic residues and arithmetic functions
- Concise account of Fermat's Last Theorem
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