Author: Kenneth Ownsworth MayPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The Impossibility of a Division Algebra of Vectors in Three Dimensional Space
Author: Kenneth Ownsworth MayLearn from the Masters!
Author: Frank SwetzPublisher: Cambridge University Press
ISBN: 9780883857038
Category : Mathematics
Languages : en
Pages : 322
Book Description
This book is for high school and college teachers who want to know how they can use the history of mathematics as a pedagogical tool to help their students construct their own knowledge of mathematics. Often, a historical development of a particular topic is the best way to present a mathematical topic, but teachers may not have the time to do the research needed to present the material. This book provides its readers with historical ideas and insights which can be immediately applied in the classroom. The book is divided into two sections: the first on the use of history in high school mathematics, and the second on its use in university mathematics. The articles are diverse, covering fields such as trigonometry, mathematical modeling, calculus, linear algebra, vector analysis, and celestial mechanics. Also included are articles of a somewhat philosophical nature, which give general ideas on why history should be used in teaching and how it can be used in various special kinds of courses. Each article contains a bibliography to guide the reader to further reading on the subject.
Handbook of Algebra
Author: Publisher: Elsevier
ISBN: 0080532977
Category : Mathematics
Languages : en
Pages : 1185
Book Description
Handbook of Algebra
Quaternion Algebras
Author: John VoightPublisher: Springer Nature
ISBN: 3030566943
Category : Mathematics
Languages : en
Pages : 877
Book Description
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
Numbers, Sequences and Series
Author: Keith HirstPublisher: Butterworth-Heinemann
ISBN: 0340610433
Category : Mathematics
Languages : en
Pages : 213
Book Description
Concerned with the logical foundations of number systems from integers to complex numbers.
Mathematical Conversations
Author: Robin WilsonPublisher: Springer Science & Business Media
ISBN: 1461301955
Category : Mathematics
Languages : en
Pages : 486
Book Description
Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.
Excursions in the History of Mathematics
Author: Israel KleinerPublisher: Springer Science & Business Media
ISBN: 0817682686
Category : Mathematics
Languages : en
Pages : 362
Book Description
This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.
The American Mathematical Monthly
Author: The History of Mathematics from Antiquity to the Present
Author: Joseph Warren DaubenPublisher: Scholarly Title
ISBN:
Category : Mathematics
Languages : en
Pages : 520
Book Description
History in Mathematics Education
Author: I. Grattan-GuinnessPublisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 220
Book Description