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Title
Essential mathematics for undergraduates : a guided approach to algebra, geometry, topology and analysis / Simon G. Chiossi.
ISBN
9783030871741 (electronic bk.)
3030871746 (electronic bk.)
9783030871734
3030871738
Published
Cham : Springer, [2021]
Copyright
©2021
Language
English
Description
1 online resource : illustrations (chiefly color)
Item Number
10.1007/978-3-030-87174-1 doi
Call Number
QA37.3 .C55 2021
Dewey Decimal Classification
510
Summary
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 books 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 Part 4 breaks down the traditional, outdated barriers between areas, exploring in particular the interplay between algebra and geometry.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 picknmix the contents for planning lecture courses or supplementing their classes.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
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.
