Essential Mathematics for Undergraduates
Springer International Publishing (Verlag)
978-3-030-87173-4 (ISBN)
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 Part 4 breaks down the traditional, outdated barriers between areas, exploring in particular the interplay between algebra and geometry.Two appendices form Part 5: the Greek etymology of frequent terms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.
lt;p>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.
Part I: Basic Objects and Formalisation - Round-up of Elementary Logic.- Naive Set Theory.- Functions.- More Set Theory and Logic.- Boolean Algebras. Part 2: Numbers and Structures - Intuitive Arithmetics.- Real Numbers.- Totally Ordered Spaces.- Part 3: Elementary Real Functions - Real Polynomials.- Real Functions of One Real Variables.- Algebraic Functions.- Elementary Transcendental Functions.- Complex Numbers.- Enumerative Combinatorics.- Part 4: Geometry through Algebra - Vector Spaces.- Orthogonal Operators.- Actions & Representations.- Elementary Plane Geometry.- Metric Spaces.- Part 5: Appendices - Etymologies.- Index of names.- Main figures.- Glossary.- References.
"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)
“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)
| Erscheinungsdatum | 18.02.2022 |
|---|---|
| Zusatzinfo | XXII, 490 p. 153 illus., 115 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 925 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Schlagworte | Algebra • Boolean Algebras • combinatorics • complex numbers • Functions • Geometry • Logic • metric structures • polynomials • Real Numbers • set theory • Topology • vector spaces |
| ISBN-10 | 3-030-87173-8 / 3030871738 |
| ISBN-13 | 978-3-030-87173-4 / 9783030871734 |
| Zustand | Neuware |
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