• Mathematics

Proof in Geometry

With "Mistakes in Geometric Proofs"
Author: A. I. Fetisov,Ya. S. Dubnov
Publisher: Courier Corporation
ISBN: 0486154920
Category: Mathematics
Page: 128
View: 6833
This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions.

    • Mathematics

College Geometry

An Introduction to the Modern Geometry of the Triangle and the Circle
Author: Nathan Altshiller-Court
Publisher: Courier Corporation
ISBN: 0486141373
Category: Mathematics
Page: 336
View: 6444
The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.

    • Mathematics

Linear Algebra


Author: Georgi? Evgen?evich Shilov
Publisher: Courier Corporation
ISBN: 9780486635187
Category: Mathematics
Page: 387
View: 1017
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

    • Mathematics

A New Look at Geometry


Author: Irving Adler
Publisher: Courier Corporation
ISBN: 0486320499
Category: Mathematics
Page: 416
View: 859
Richly detailed survey of the evolution of geometrical ideas and development of concepts of modern geometry: projective, Euclidean, and non-Euclidean geometry; role of geometry in Newtonian physics, calculus, relativity. Over 100 exercises with answers. 1966 edition.

    • Mathematics

Perspectives on Projective Geometry

A Guided Tour Through Real and Complex Geometry
Author: Jürgen Richter-Gebert
Publisher: Springer Science & Business Media
ISBN: 9783642172861
Category: Mathematics
Page: 571
View: 4303
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.

    • Science

The Mathematical Mechanic

Using Physical Reasoning to Solve Problems
Author: Mark Levi
Publisher: Princeton University Press
ISBN: 0691154562
Category: Science
Page: 186
View: 6835
In this delightful book, Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can.

    • Mathematics

Analysis in Euclidean Space


Author: Kenneth Hoffman
Publisher: Courier Corporation
ISBN: 0486135845
Category: Mathematics
Page: 448
View: 892
Developed for a beginning course in mathematical analysis, this text focuses on concepts, principles, and methods, offering introductions to real and complex analysis and complex function theory. 1975 edition.

    • Mathematics

Mathematics

Its Content, Methods and Meaning
Author: A. D. Aleksandrov,A. N. Kolmogorov,M. A. Lavrent’ev
Publisher: Courier Corporation
ISBN: 0486157873
Category: Mathematics
Page: 1120
View: 2907
Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

    • Mathematics

Lectures on Hyperbolic Geometry


Author: Riccardo Benedetti,Carlo Petronio
Publisher: Springer Science & Business Media
ISBN: 3642581587
Category: Mathematics
Page: 330
View: 9207
Focussing on the geometry of hyperbolic manifolds, the aim here is to provide an exposition of some fundamental results, while being as self-contained, complete, detailed and unified as possible. Following some classical material on the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (including a complete proof, following Gromov and Thurston) and Margulis' lemma. These then form the basis for studying Chabauty and geometric topology; a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory; and much space is devoted to the 3D case: a complete and elementary proof of the hyperbolic surgery theorem, based on the representation of three manifolds as glued ideal tetrahedra.

    • Juvenile Nonfiction

Proofs

Reasoning with Mathematics
Author: Tammy Pelli
Publisher: N.A
ISBN: 9781930820463
Category: Juvenile Nonfiction
Page: 64
View: 7242
Strategies, Developing Lines of Reason, Working Backward, Creating Order, Formal Proofs

    • Mathematics

Introduction to Proof in Abstract Mathematics


Author: Andrew Wohlgemuth
Publisher: Courier Corporation
ISBN: 0486141683
Category: Mathematics
Page: 384
View: 5172
This undergraduate text teaches students what constitutes an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. 1990 edition.

    • Mathematics

Differential Geometry


Author: Heinrich W. Guggenheimer
Publisher: Courier Corporation
ISBN: 0486157202
Category: Mathematics
Page: 400
View: 7715
This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.

    • Mathematics

The Divine Proportion


Author: H. E. Huntley
Publisher: Courier Corporation
ISBN: 0486131874
Category: Mathematics
Page: 208
View: 6727
Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much more. Excellent bridge between science and art. Features 58 figures.

    • Mathematics

A Readable Introduction to Real Mathematics


Author: Daniel Rosenthal,David Rosenthal,Peter Rosenthal
Publisher: Springer
ISBN: 3319056549
Category: Mathematics
Page: 161
View: 2873
Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. Topics covered include: mathematical induction - modular arithmetic - the fundamental theorem of arithmetic - Fermat's little theorem - RSA encryption - the Euclidean algorithm -rational and irrational numbers - complex numbers - cardinality - Euclidean plane geometry - constructability (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass). This textbook is suitable for a wide variety of courses and for a broad range of students in the fields of education, liberal arts, physical sciences and mathematics. Students at the senior high school level who like mathematics will also be able to further their understanding of mathematical thinking by reading this book.

    • Geometry

The Elements of Euclid


Author: Euclid
Publisher: N.A
ISBN: N.A
Category: Geometry
Page: 416
View: 6181

    • Mathematics

Topology

A Geometric Approach
Author: Terry Lawson
Publisher: Oxford University Press on Demand
ISBN: 9780199202485
Category: Mathematics
Page: 388
View: 2876
This new-in-paperback introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of exercises and projects, which fosters a teaching style that encourages the student to be an active class participant. A wide range of material at different levels supports flexible use of the book for a variety of students. Part I is appropriate for a one-semester or two-quarter course, and Part II (which is problem based) allows the book to be used for a year-long course which supports a variety of syllabuses. The over 750 exercises range from simple checks of omitted details in arguments, to reinforce the material and increase student involvement, to the development of substantial theorems that have been broken into many steps. The style encourages an active student role. Solutions to selected exercises are included as an appendix, with solutions to all exercises available to the instructor on a companion website.

    • Mathematics

Proofs from THE BOOK


Author: Martin Aigner,Günter M. Ziegler
Publisher: Springer
ISBN: 3662442051
Category: Mathematics
Page: 308
View: 9627
This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questio ns so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011.

    • Mathematics

Advanced Calculus

Revised
Author: Lynn Harold Loomis,Shlomo Sternberg
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Category: Mathematics
Page: 596
View: 4798
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

    • Mathematics

A Book of Abstract Algebra

Second Edition
Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486474178
Category: Mathematics
Page: 384
View: 9754
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

    • Mathematics

Differential Geometry of Curves and Surfaces

Revised and Updated Second Edition
Author: Manfredo P. do Carmo
Publisher: Courier Dover Publications
ISBN: 0486806995
Category: Mathematics
Page: 512
View: 1260
One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems. The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.