Overview
- 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
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
- MSC (2010): 00-01, 00A07, 00A09, 97D50
- problem solving
- mathematical proofs
- mathematical problem solving
- mathematical exploration
- problem solving strategies mathematics
- extremal principle
- invariance principle
- pigeonhole principle
- counting principles
- mathematical induction
- logic
- proofs
- elementary number theory
About this book
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.Reviews
“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)
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Exploring Mathematics
Book Subtitle: Problem-Solving and Proof
Authors: Daniel Grieser
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-319-90321-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-90319-4Published: 31 May 2018
eBook ISBN: 978-3-319-90321-7Published: 21 May 2018
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
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: Mathematics, general, Mathematics Education, Popular Science in Mathematics