Format: Paperback / softback, 490 pages, height x width: 235x155 mm, 115 Illustrations, color; 38 Illustrations, black and white;
XXII, 490 p. 153 illus., 115 illus. in color.; 115 Illustrations, color; 38 Illustrations, black and white; XXII, 490 p. 153 illus., 115 illus. in color.,
Pub. Date: 03-Mar-2023
ISBN-13: 9783030871765
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 Part 4 breaks down the traditional, outdated barriers between areas, exploring in particular the interplay between algebra and geometry.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.
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.
Format: Paperback / softback, 62 pages, height x width: 235x155 mm, weight: 136 g, 10 Tables, color;
13 Illustrations, color; 8 Illustrations, black and white; XIII, 62 p. 21 illus., 13 illus. in color.
Series: SpringerBriefs in Physics
Pub. Date: 26-Jan-2023
ISBN-13: 9783031256240
This book, written by two pioneers in the field, provides a clear and concise description of memristors and other memory elements. It stresses the difference between their mathematical definition and physical reality. The reader will then be able to distinguish between what is experimentally realizable and various fictitious claims that plague the scientific literature. The discussion is kept simple enough that the book should be easily accessible not only to graduate students and researchers in Physics and Engineering, but also to undergraduate students interested in this topic.
Massimiliano Di Ventra and Yuriy Pershin are both experts in the area of memristors and other memory elements (such as memcapacitors and meminductors). They started to work in this field in 2008, and have followed it since then. They introduced memcapacitors and meminductors together with Chua, experimentally demonstrated the first memristive neural network, and pioneered the use ofmemory elements in analog electronics and memcomputing. More recently, they introduced a memristor test that helps resolve the controversy about the discovery of the memristor. They have published over 60 papers on this topic which have garnered more than 6000 citations in total. MD has published four books: Introduction to Nanoscale Science and Technology, Springer, 2004; Electrical Transport in Nanoscale Systems, Cambridge University Press, 2008; The Scientific Method: Reflections from a Practitioner, Oxford University Press, 2018; and MemComputing: Fundamentals and Applications, Oxford University Press, 2022.
Format: Hardback, 171 pages, height x width: 235x155 mm, 10 Illustrations, color; 2 Illustrations, black and white; XIX, 171 p. 12 illus., 10 illus. in color., 1 Hardback
Series: Logic, Epistemology, and the Unity of Science 58
Pub. Date: 05-Apr-2023
ISBN-13: 9783031243622
This publication includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728-1777) written in the 1760s: Vorlaufige Kenntnisse fur die, so die Quadratur und Rectification des Circuls suchen and Memoire sur quelques proprietes remarquables des quantites transcendentes circulaires et logarithmiques. The translations are accompanied by a contextualised study of each of these works and provide an overview of Lambert's contributions, showing both the background and the influence of his work. In addition, by adopting a biographical approach, it allows readers to better get to know the scientist himself. Lambert was a highly relevant scientist and polymath in his time, admired by the likes of Kant, who despite having made a wide variety of contributions to different branches of knowledge, later faded into an undeserved secondary place with respect to other scientists of the eighteenth century. In mathematics, in particular, he is famous for his research on non-Euclidean geometries, although he is likely best known for having been the first who proved the irrationality of pi. In his Memoire, he conducted one of the first studies on hyperbolic functions, offered a surprisingly rigorous proof of the irrationality of pi, established for the first time the modern distinction between algebraic and transcendental numbers, and based on such distinction, he conjectured the transcendence of pi and therefore the impossibility of squaring the circle.
Part I: Antecedents.
1. From Geometry to Analysis.
2. The situation in the first half of the 18th century. Euler and continued fractions.- Part II: Johann Heinrich Lambert (1728-1777).
3. A biographical approach to Johann Heinrich Lambert.
4. Outline of Lambert's Memoire (1761/1768).
5. An anotated translation of Lambert's Memoire (1761/1768).
6. Outine of Lambert's Vorlaufige Kenntnisse (1766/1770).
6. An anotated translation of Lambert's Vorlaufige Kenntnisse (1766/1770).- Part III: The influence of Lambert's work and the development of irrational numbers.
8. The state of irrationals until the turn of the century.
9. Title to be set up.
Format: Paperback / softback, 6 pages, height x width: 235x155 mm, 41 Illustrations, black and white; CXXXVII, 6 p. 41 illus.
Series: SpringerBriefs in Mathematics
Pub. Date: 25-Mar-2023
ISBN-13: 9783031236754
This brief presents a global perspective on the geometry of spaces of polynomials. Its particular focus is on polynomial spaces of dimension 3, providing, in that case, a graphical representation of the unit ball. Also, the extreme points in the unit ball of several polynomial spaces are characterized. Finally, a number of applications to obtain sharp classical polynomial inequalities are presented. The study performed is the first ever complete account on the geometry of the unit ball of polynomial spaces. Nowadays there are hundreds of research papers on this topic and our work gathers the state of the art of the main and/or relevant results up to now. This book is intended for a broad audience, including undergraduate and graduate students, junior and senior researchers and it also serves as a source book for consultation. In addition to that, we made this work visually attractive by including in it over 50 original figures in order to help in the understanding of all the results and techniques included in the book.
Chapter.
1. IntroductionChapter.
2. Polynomials of degreeChapter.
3. Spaces of trinomialsChapter.
4. Polynomials on nonsymmetric convex bodiesChapter.
5. Sequence Banach spacesChapter.
6. Polynomials with the hexagonal and octagonal normsChapter.
7. Hilbert spacesChapter.
8. Banach spacesChapter.
9. Applications
Format: Paperback / softback, 347 pages, height x width: 235x155 mm, 8 Tables, color; 7 Illustrations, color;
73 Illustrations, black and white; VIII, 347 p. 80 illus., 7 illus. in color
Series: Springer Undergraduate Mathematics Series
Pub. Date: 03-Apr-2023
ISBN-13: 9783031254086
This textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master's students. It places special emphasis on motivation and understanding, while developing a solid intuition for the more abstract concepts. In contrast to graduate level references, the text relies on a minimal set of prerequisites: a solid grounding in linear algebra and multivariable calculus, and ideally a course on ordinary differential equations. Manifolds are introduced intrinsically in terms of coordinate patches glued by transition functions. The theory is presented as a natural continuation of multivariable calculus; the role of point-set topology is kept to a minimum. Questions sprinkled throughout the text engage students in active learning, and encourage classroom participation. Answers to these questions are provided at the end of the book, thus making it ideal for independent study. Material is further reinforced with homework problems ranging from straightforward to challenging. The book contains more material than can be covered in a single semester, and detailed suggestions for instructors are provided in the Preface.
1. Introduction2. Manifolds3. Smooth maps4. Submanifolds5. Tangent spaces6. Vector fields7. Differential forms8. Integration9. Vector bundlesNotions from set theoryNotions from algebraTopological properties of manifoldsHints and answers to in-text questionsReferencesList of SymbolsIndex