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Author:
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ISBN:
Category :
Languages : en
Pages : 2422
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 2422
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Author: Manuel Garcia Vida
Publisher:
ISBN: 9788426383341
Category :
Languages : es
Pages : 32
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Author:
Publisher:
ISBN:
Category : Catalogs, Publishers'
Languages : es
Pages : 1418
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Author: Strategies Teaching
Publisher: Teaching Strategies
ISBN: 9781933021126
Category :
Languages : es
Pages : 269
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Book Description
Author: I. Martin Isaacs
Publisher: American Mathematical Soc.
ISBN: 0821847945
Category : Mathematics
Languages : en
Pages : 242
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Book Description
One of the challenges many mathematics students face occurs after they complete their study of basic calculus and linear algebra, and they start taking courses where they are expected to write proofs. Historically, students have been learning to think mathematically and to write proofs by studying Euclidean geometry. In the author's opinion, geometry is still the best way to make the transition from elementary to advanced mathematics. The book begins with a thorough review of high school geometry, then goes on to discuss special points associated with triangles, circles and certain associated lines, Ceva's theorem, vector techniques of proof, and compass-and-straightedge constructions. There is also some emphasis on proving numerical formulas like the laws of sines, cosines, and tangents, Stewart's theorem, Ptolemy's theorem, and the area formula of Heron. An important difference of this book from the majority of modern college geometry texts is that it avoids axiomatics. The students using this book have had very little experience with formal mathematics. Instead, the focus of the course and the book is on interesting theorems and on the techniques that can be used to prove them. This makes the book suitable to second- or third-year mathematics majors and also to secondary mathematics education majors, allowing the students to learn how to write proofs of mathematical results and, at the end, showing them what mathematics is really all about.
Author: I. Martin Isaacs
Publisher: American Mathematical Society
ISBN: 1470471604
Category : Mathematics
Languages : en
Pages : 368
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The text begins with a review of group actions and Sylow theory. It includes semidirect products, the Schur–Zassenhaus theorem, the theory of commutators, coprime actions on groups, transfer theory, Frobenius groups, primitive and multiply transitive permutation groups, the simplicity of the PSL groups, the generalized Fitting subgroup and also Thompson's J-subgroup and his normal $p$-complement theorem. Topics that seldom (or never) appear in books are also covered. These include subnormality theory, a group-theoretic proof of Burnside's theorem about groups with order divisible by just two primes, the Wielandt automorphism tower theorem, Yoshida's transfer theorem, the “principal ideal theorem” of transfer theory and many smaller results that are not very well known. Proofs often contain original ideas, and they are given in complete detail. In many cases they are simpler than can be found elsewhere. The book is largely based on the author's lectures, and consequently, the style is friendly and somewhat informal. Finally, the book includes a large collection of problems at disparate levels of difficulty. These should enable students to practice group theory and not just read about it. Martin Isaacs is professor of mathematics at the University of Wisconsin, Madison. Over the years, he has received many teaching awards and is well known for his inspiring teaching and lecturing. He received the University of Wisconsin Distinguished Teaching Award in 1985, the Benjamin Smith Reynolds Teaching Award in 1989, and the Wisconsin Section MAA Teaching Award in 1993, to name only a few. He was also honored by being the selected MAA Pólya Lecturer in 2003–2005.
Author: I. Martin Isaacs
Publisher: American Mathematical Soc.
ISBN: 0821847996
Category : Mathematics
Languages : en
Pages : 531
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Book Description
as a student." --Book Jacket.
Author: Nima Rezaei
Publisher: Springer Nature
ISBN: 3031159632
Category : Medical
Languages : en
Pages : 513
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Book Description
Integrated Education and Learning aims to discuss novel approaches to offer integrated educational methods. Within the last few years, educational techniques have evolved to favour critical thinking and improve learning skills. This volume links thinking and learning in educational settings and discusses diverse mechanisms that influence this association; including meta-cognitive capacity, memory, cognitive style, conceptual approaches, digitalization, teaching approaches, echoing, and questioning. It embraces this discussion at all levels, from early childhood education to higher education. This book also includes teaching tips for creating a learning environment that cultivates students’ creativity and critical thinking on both online platforms and live-in-classroom. The book follows discussing the merits of an integrated educational paradigm that will help develop highly intellectual thinkers and will promote modern values to face current and future challenges. Finally, the book shows a balance between learning and education to enhance creativity, critical thinking and social skills.
Author:
Publisher:
ISBN:
Category : Education
Languages : en
Pages : 818
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Author: I. Martin Isaacs
Publisher: American Mathematical Soc.
ISBN: 1470434857
Category : Mathematics
Languages : en
Pages : 384
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This book, which can be considered as a sequel of the author's famous book Character Theory of Finite Groups, concerns the character theory of finite solvable groups and other groups that have an abundance of normal subgroups. It is subdivided into three parts: -theory, character correspondences, and M-groups. The -theory section contains an exposition of D. Gajendragadkar's -special characters, and it includes various extensions, generalizations, and applications of his work. The character correspondences section proves the McKay character counting conjecture and the Alperin weight conjecture for solvable groups, and it constructs a canonical McKay bijection for odd-order groups. In addition to a review of some basic material on M-groups, the third section contains an exposition of the use of symplectic modules for studying M-groups. In particular, an accessible presentation of E. C. Dade's deep results on monomial characters of odd prime-power degree is included. Very little of this material has previously appeared in book form, and much of it is based on the author's research. By reading a clean and accessible presentation written by the leading expert in the field, researchers and graduate students will be inspired to learn and work in this area that has fascinated the author for decades.
