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Springer Undergraduate Mathematics Series

Exploring Mathematics

Problem-Solving and Proof

Authors: Grieser, Daniel

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  • Provides general and maths-specific problem-solving strategies
  • Contains many motivating examples and exercises
  • Engages the reader to explore mathematics and solve fun problems
  • Introduces fundamental ideas useful in all areas of mathematics
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eBook £23.99
price for United Kingdom (gross)
  • ISBN 978-3-319-90321-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover £29.99
price for United Kingdom (gross)
  • ISBN 978-3-319-90319-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics.

Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book.

Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses.

About the authors

Daniel Grieser is Professor of Mathematics at Carl von Ossietzky Universität Oldenburg. He works in geometry, analysis and combinatorics. He won a gold medal at the International Mathematics Olympiad and in 2014 he received the Ars Legendi Faculty award for excellent teaching, a national prize awarded in Germany, for developing the course on which this book is based.

Reviews

“This book sets out to teach the reader to be a successful problem-solver and to be able to produce our own mathematical proofs. In a carefully designed and well-documented journey we are taken through a wide variety of problems … . This is a very clear and helpful book. It would be a useful addition to every teacher’s repertoire and a very helpful source of interesting problems to share with students at all levels.” (Peter Hall, The Mathematical Gazette, Vol. 103 (557), July, 2019)
“Exploring Mathematics can be used as an introduction to mathematical problem-solving, but may be better used as a supplement. I personally found that this systematic review of mathematical topics was refreshing, helping to fill gaps in my problem-solving toolkit. The reader may find it beneficial to use the book to review the fundamentals and enrich their problem-solving knowledge.” (Jack Chen, MAA Reviews, January, 2019)​

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook £23.99
price for United Kingdom (gross)
  • ISBN 978-3-319-90321-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover £29.99
price for United Kingdom (gross)
  • ISBN 978-3-319-90319-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Exploring Mathematics
Book Subtitle
Problem-Solving and Proof
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-90321-7
DOI
10.1007/978-3-319-90321-7
Softcover ISBN
978-3-319-90319-4
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XI, 308
Number of Illustrations
62 b/w illustrations, 15 illustrations in colour
Additional Information
Original German edition published by Springer Vieweg, Wiesbaden, Germany, 2013
Topics