Overview
- Covers topics in abstract algebra, topology, analysis, and geometry in an innovative way
- Explains core elementary subjects of undergraduate mathematics in plain English
- Offers a rich set of exercises and references for self-study
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About this book
This textbook covers topics of undergraduate mathematics in abstract algebra, geometry, topology and analysis with the purpose of connecting the underpinning key ideas. It guides STEM students towards developing knowledge and skills to enrich their scientific education. In doing so it avoids the common mechanical approach to problem-solving based on the repetitive application of dry formulas. The presentation preserves the mathematical rigour throughout and still stays accessible to undergraduates. The didactical focus is threaded through the assortment of subjects and reflects in the book’s structure.
Part 1 introduces the mathematical language and its rules together with the basic building blocks. Part 2 discusses the number systems of common practice, while the backgrounds needed to solve equations and inequalities are developed in Part 3. Part 4 breaks down the traditional, outdated barriers between areas, exploring in particular the interplay between algebra and geometry.Two appendices form Part 5: the Greek etymology of frequent terms and a list of mathematicians mentioned in the book. Abundant examples and exercises are disseminated along the text to boost the learning process and allow for independent work.
Students will find invaluable material to shepherd them through the first years of an undergraduate course, or to complement previously learnt subject matters. Teachers may pick’n’mix the contents for planning lecture courses or supplementing their classes.
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Keywords
Table of contents (19 chapters)
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Front Matter
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Basic Objects and Formalisation
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Front Matter
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Numbers and Structures
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Front Matter
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Elementary Real Functions
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Front Matter
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Geometry Through Algebra
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Front Matter
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Reviews
“The book being reviewed is a collection of what the author considers to be essential material for undergraduates … . it has to be said that many students will find that there is plenty to learn from this well-written book, which would also be a useful reference text had there been a properly compiled index.” (Peter Shiu, The Mathematical Gazette, Vol. 107 (570), November, 2023)
Authors and Affiliations
About the author
Simon G. Chiossi is a lecturer at Fluminense Federal University in Brazil. He was awarded a Ph.D. in mathematics from the University of Genoa in 2003. His research interests lie in complex differential geometry and Lie theory, with focus on special geometry in dimensions 4--8.
Bibliographic Information
Book Title: Essential Mathematics for Undergraduates
Book Subtitle: A Guided Approach to Algebra, Geometry, Topology and Analysis
Authors: Simon G. Chiossi
DOI: https://doi.org/10.1007/978-3-030-87174-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-87173-4Published: 17 February 2022
Softcover ISBN: 978-3-030-87176-5Published: 18 February 2023
eBook ISBN: 978-3-030-87174-1Published: 16 February 2022
Edition Number: 1
Number of Pages: XXII, 490
Number of Illustrations: 38 b/w illustrations, 115 illustrations in colour
Topics: Linear Algebra, Mathematical Logic and Foundations, Geometry, Topology, Discrete Mathematics