Author: Peter Jephson Cameron

Publisher: Oxford University Press, USA

ISBN: 9780198501954

Category: Mathematics

Page: 295

View: 9999

This book is an undergraduate textbook on abstract algebra, beginning with the theories of rings and groups. As this is the first really abstract material students need, the pace here is gentle, and the basic concepts of subring, homomorphism, ideal, etc are developed in detail. Later, as students gain confidence with abstractions, they are led to further developments in group and ring theory (simple groups and extensions, Noetherian rings, and outline of universal algebra, lattices andcategories) and to applications such as Galois theory and coding theory. There is also a chapter outlining the construction of the number systems from scratch and proving in three different ways that trascendental numbers exist.
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Author: Joseph Landin

Publisher: Courier Corporation

ISBN: 0486150410

Category: Mathematics

Page: 272

View: 4292

This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.
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Containing the Indeterminate and Diophantine Analysis, and the Application of Algebra to Geometry

Author: John Bonnycastle

Publisher: N.A

ISBN: N.A

Category: Algebra

Page: 288

View: 1691

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Author: Alekseĭ Ivanovich Kostrikin

Publisher: Springer Verlag

ISBN: N.A

Category: Mathematics

Page: 575

View: 7666

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Solving Equations from Mesopotamian Times to the Renaissance

Author: Jacques Sesiano

Publisher: American Mathematical Soc.

ISBN: 0821844733

Category: Mathematics

Page: 174

View: 9207

This text should not be viewed as a comprehensive history of algebra before 1600, but as a basic introduction to the types of problems that illustrate the earliest forms of algebra. It would be particularly useful for an instructor who is looking for examples to help enliven a course on elementary algebra with problems drawn from actual historical texts. --Warren Van Egmond about the French edition for MathSciNet This book does not aim to give an exhaustive survey of the history of algebra up to early modern times but merely to present some significant steps in solving equations and, wherever applicable, to link these developments to the extension of the number system. Various examples of problems, with their typical solution methods, are analyzed, and sometimes translated completely. Indeed, it is another aim of this book to ease the reader's access to modern editions of old mathematical texts, or even to the original texts; to this end, some of the problems discussed in the text have been reproduced in the appendices in their original language (Greek, Latin, Arabic, Hebrew, French, German, Provencal, and Italian) with explicative notes.
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Author: Phillip Griffiths,Sigurdur Helgason

Publisher: American Mathematical Soc.

ISBN: 0821845306

Category: Courbes algébriques

Page: 221

View: 5016

This book offers a comprehensive treatment of geometric analysis on symmetric spaces, with applications to representation theory. The author's thorough, accurate approach brings the reader up to date on current research in analysis on symmetric spaces and the analytic approach to the representation theory of semisimple Lie groups. The author is a 1988 Steele Prize recipient for his earlier books in this area.
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Author: R. Kochendorffer

Publisher: Springer Science & Business Media

ISBN: 9400981791

Category: Mathematics

Page: 414

View: 6581

This book is intended as a textbook for an undergraduate course on algebra. In most universities a detailed study ·of abstract algebraic systems commences in the second year. By this time the student has gained some experience in mathematical reasoning so that a too elementary book would rob him of the joy and the stimulus of using his ability. I tried to make allowance for this when I chose t4e level of presentation. On the other hand, I hope that I also avoided discouraging the reader by demands which are beyond his strength. So, the first chapters will certainly not require more mathematical maturity than can reasonably be expected after the first year at the university. Apart from one exception the formal prerequisites do not exceed the syllabus of an average high school. As to the exception, I assume that the reader is familiar with the rudiments of linear algebra, i. e. addition and multiplication of matrices and the main properties of determinants. In view of the readers for whom the book is designed I felt entitled to this assumption. In the first chapters, matrices will almost exclusively occur in examples and exercises providing non-trivial instances in the theory of groups and rings. In Chapters 9 and 10 only, vector spaces and their properties will form a relevant part of the text. A reader who is not familiar with these concepts will have no difficulties in acquiring these prerequisites by any elementary textbook, e. g. [10].
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Being the First Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges

Author: Jeremiah Day

Publisher: N.A

ISBN: N.A

Category: Algebra

Page: 332

View: 3322

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Author: Martin M. Zuckerman

Publisher: Rowman & Littlefield

ISBN: 9780912675022

Category: Mathematics

Page: 304

View: 6489

This book covers the basic topics in arithmetic and algebra with which every college student should be thoroughly familiar. It is written with the student in mind, in a style and at a level appropriate for student understanding.
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Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486152952

Category: Mathematics

Page: 208

View: 5566

This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.
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teacher's commentary, parts I-II

Author: School Mathematics Study Group

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 7315

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Author: Jacobs,Russell F. Jacobs

Publisher: Holt Rinehart & Winston

ISBN: 9780030769818

Category: Algebra

Page: 602

View: 4534

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Author: Joseph J. Rotman

Publisher: Springer Science & Business Media

ISBN: 1461245761

Category: Mathematics

Page: 437

View: 9802

A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.
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With Notes and Observations : Designed for the Use of Schools and Places of Public Education : to which is Added an Appendix on the Application of Algebra to Geometry

Author: John Bonnycastle

Publisher: N.A

ISBN: N.A

Category: Algebra

Page: 260

View: 3884

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Author: Steven Dale Cutkosky

Publisher: American Mathematical Soc.

ISBN: 1470435187

Category: Geometry, Algebraic

Page: 484

View: 1276

This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.
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