Copyright 2024
Hardback
ISBN 9781032697246
410 Pages
March 22, 2024 by Chapman & Hall
This book provides a general, unified approach to the theory of polyadic groups, their normal subgroups and matrix representations.
The author focuses on those properties of polyadic groups which are not present in the binary case. These properties indicate a strong relationship between polyadic groups and various group-like algebras, as well as ternary Hopf algebras and n-Lie algebras that are widely used in theoretical physics.
The relationships of polyadic groups with special types of binary groups called covering groups and binary retracts is described. These relationships allow the study of polyadic groups using these binary groups and their automorphisms.
The book also describes the affine geometry induced by polyadic groups and fuzzy subsets defined on polyadic groups. Finally, we discuss the category of polyadic groups and the relationships between the different varieties of polyadic groups. In many cases, we give elegant new proofs of known theorems. We also give many interesting examples and applications.
The book contains many little-known results from articles previously published in hard-to-reach Russian, Ukrainian and Macedonian journals. These articles are not in English.
Copyright 2024
Hardback
ISBN 9781032302669
668 Pages 345 B/W Illustrations
March 14, 2024 by Chapman & Hall
Using meaningful examples, credible applications, and incisive technology, this book strives to empower students, enhance their critical thinking skills, and equip them with the knowledge and skills to succeed in the major or discipline they ultimately choose to study. An engaging style and clear writing make the language of mathematics accessible, understandable, and enjoyable, with a high standard for mathematical rigor.
A calculus book must tell the truth.This book is carefully written in the acceptedlanguageofmathematics in a readable exposition.It includes useful and fascinating applications, acquaints students with the history of the subject and offers a sense of what mathematics is all about.
Technique is presented, yet so are ideas. The author helps students to master basic methods and how to discover and build their own concepts in a scientific subject. There is an emphasis on using modeling and numerical calculation. Additional features include:
A Quick Quiz and Problems for Practice, Further Theory and Practice and Calculator/Computer Exercises appear at the end of each section.
All exercise sets are step laddered.
A Look Back and A Look Forward help students put the ideas in context.
Every chapter ends with a section called Genesis and Development, giving history and perspective on key topics in the evolution of calculus.
Boxed Insights clear up a point or answer commonly asked question.
The text has an extra-large offering of examples.
Examples are illustrated with meaningful and useful graphics.
The goal is to empower students, enhance their critical thinking skills, and give them the intellectual equipment to proceed successfully in whatever major or discipline they ultimately choose to study. This text is intended to be a cornerstone of that process.
The pedagogical features make the subject more interesting and accessible to students than other texts, while maintaining an appropriate rigor. ?Daniel Cunningham, CSU-Fresno
This text is truly well written and organized. I do like the fact the book is quite rigorous, yet full of illustrative examples. ?Bob Devaney, Boston University
I. Vectors
II. Vector-Valued Functions
III. Functions of Several Variables
IV. Multiple Integrals
V. Vector Calculus
Copyright 2024
Hardback
ISBN 9781032637112
144 Pages
April 2, 2024 by Chapman & Hall
Classical Clifford Algebras: Operator-Algebraic and Free-Probabilistic Approaches offers novel insights through operator-algebraic and free-probabilistic models. By employing these innovative methods, the author sheds new light on the intrinsic connections between Clifford algebras and various mathematical domains. This monograph should be an essential addition to the library of any researchers interested in Clifford Algebras or Algebraic Geometry more widely.
Includes multiple examples and applications
Suitable for postgraduates and researchers working in Algebraic Geometry
Takes an innovative approach to a well-established topic.
Part I. Motivation: On the Quaternions H. 1. Introduction of Part I. 2. On the Quaternions H. 3. Spectral Analysis on H Under (C2; ƒÎ). 4. 4. On Noncommutative Field H Under (C2; ƒÎ). 5. Free-Probabilistic Data Induced by H. Part II. On the Classical Clifford Algebras. 6. Introduction of Part II. 7. Classical Clifford Algebras. 8. Free Probability on the Clifford-Group C*-Probability Space (MG ; T). 9. Free Probability on Certain Sub-Structures of (MG; T). Part III. The Clifford Group G and the Semicircular Law. 10. Introduction of Part III. 11. On the Tensor Product C*-Probability C-Spaces (MG O A; T O ?). 12. Deformed Semicircular Laws on (MG O A; T O ?). 13. Applications. Part IV. Representations of the Clifford Algebra C. 14. Introduction of Part IV. 15. The Clifford Algebra C Embedded in the CG C*-Algebra MG. 16. On the R-Banach *-Algebra C. 17. R-Adjointable-Operator-Theoretic Properties on C. 18. Discussions.
Copyright 2024
Paperback
ISBN 9781032370910
Hardback
ISBN 9781032367019
314 Pages 38 B/W Illustrations
April 11, 2024 by Chapman & Hall
Fundamentals of Abstract Algebra is a primary textbook for a one year first course in Abstract Algebra, but it has much more to offer besides this. The book is full of opportunities for further, deeper reading, including explorations of interesting applications and more advanced topics, such as Galois theory. Replete with exercises and examples, the book is geared towards careful pedagogy and accessibility, and requires only minimal prerequisites. The book includes a primer on some basic mathematical concepts that will be useful for readers to understand, and in this sense the book is self-contained.
Self-contained treatments of all topics.
Everything required for a one-year first course in Abstract Algebra, and could also be used as supplementary reading for a second course.
Copious exercises and examples.
Section I. Groups. 1. Background Material. 2. Basic Group Theory. 3. Simple Groups. 4. Group Action. Group Presentation and Representations. 5. Solvable and Nilpotent Groups. Section II. Rings and Fields. Chapter 7. Ring Theory. 8. Integral Domain Theory. 9. Field Theory. 10. Galois Theory.
Copyright 2024
Hardback
ISBN 9781032581200
368 Pages
April 4, 2024 by Chapman & Hall
Set theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. Nearly every branch of Mathematics depends upon set theory and thus knowledge of set theory is of interest to every mathematician. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not only possible, but also valuable.
The book has two parts. The first one presents, from the sole intuition just mentioned of 'collection' and 'object', the axiomatic ZFC-theory. Then we present the basics of the theory: the axioms, well-orderings, ordinals and cardinals are the main subjects of this part. In all, one could say that we give some standard interpretation of set theory; but this standard interpretation results in a multiplicity of universes.
The second part of the book deals with the independence proofs of the continuum hypothesis (CH) and the axiom of choice (AC) and forcing is introduced as a necessary tool; and again the theory is developed intuitively, without the use of formal logic. The independence results belong to the metatheory, as they refer to things that cannot be proved; but the greater part of the arguments leading to the independence results, including forcing, are purely set-theoretic.
The book is self-contained and accessible to beginners in set theory. There are no prerequisites other than some knowledge of elementary mathematics. Full detailed proofs are given for all the results.