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Author : Marta Sved
Publisher : American Mathematical Soc.
ISBN 13 : 1470457288
Total Pages : 201 pages
Book Rating : 4.4/5 (74 download)
Download or read book Journey into Geometries written by Marta Sved and published by American Mathematical Soc.. This book was released on 2020-07-31 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas Q. Sibley
Publisher : The Mathematical Association of America
ISBN 13 : 1939512085
Total Pages : 586 pages
Book Rating : 4.9/5 (395 download)
Download or read book Thinking Geometrically written by Thomas Q. Sibley and published by The Mathematical Association of America. This book was released on 2015-08-14 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thinking Geometrically: A Survey of Geometries is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers. There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. The text is self-contained, including appendices with the material in Euclid’s first book and a high school axiomatic system as well as Hilbert’s axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.
Author : Wladimir-Georges Boskoff
Publisher : Springer Nature
ISBN 13 : 303154823X
Total Pages : 556 pages
Book Rating : 4.0/5 (315 download)
Download or read book A Mathematical Journey to Relativity written by Wladimir-Georges Boskoff and published by Springer Nature. This book was released on with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Isaak Moiseevich I︠A︡glom
Publisher : Ishi Press
ISBN 13 : 9784871878364
Total Pages : 237 pages
Book Rating : 4.8/5 (783 download)
Download or read book Geometries, Groups and Algebras in the Nineteenth Century written by Isaak Moiseevich I︠A︡glom and published by Ishi Press. This book was released on 2009 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: I. M. Yaglom has written a very accessible history of 19th century mathematics, with emphasis on interesting biographies of the leading protagonists and on the subjects most closely related to the work of Klein and Lie, whose own work is not discussed in detail until late in the book. Starting with Galois and his contribution to the evolving subject of group theory Yaglom gives a beautiful account of the lives and works of the major players in the development of the subject in the nineteenth century: Jordan, who was a teacher of Lie and Klein in Paris and their adventures during the Franco-Prussian War. Monge and Poncelet developing projective geometry as well as Bolyai, Gauss and Lobachevsky and their discovery of hyperbolic geometry. Riemann's contributions and the development of modern linear Algebra by Grassmann, Cayley and Hamilton are described in detail. The last two chapters are devoted to Lie's development of Lie Algebras and his construction of the geometry from a continuous group and Klein's Erlanger Programm unifying the different approaches to geometry by emphasizing automorphism groups. These last pages are definitely the climax of the book.
Author : Owen Byer
Publisher : American Mathematical Soc.
ISBN 13 : 0883857634
Total Pages : 485 pages
Book Rating : 4.8/5 (838 download)
Download or read book Methods for Euclidean Geometry written by Owen Byer and published by American Mathematical Soc.. This book was released on 2010-12-31 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
Author : Ton Marar
Publisher : Springer Nature
ISBN 13 : 3031074424
Total Pages : 124 pages
Book Rating : 4.0/5 (31 download)
Download or read book A Ludic Journey into Geometric Topology written by Ton Marar and published by Springer Nature. This book was released on 2022-09-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book draws on elements from everyday life, architecture, and the arts to provide the reader with elementary notions of geometric topology. Pac Man, subway maps, and architectural blueprints are the starting point for exploring how knowledge about geometry and, more specifically, topology has been consolidated over time, offering a learning journey that is both dense and enjoyable. The text begins with a discussion of mathematical models, moving on to Platonic and Keplerian theories that explain the Cosmos. Geometry from Felix Klein's point of view is then presented, paving the way to an introduction to topology. The final chapters present the concepts of closed, orientable, and non-orientable surfaces, as well as hypersurface models. Adopting a style that is both rigorous and accessible, this book will appeal to a broad audience, from curious students and researchers in various areas of knowledge to everyone who feels instigated by the power of mathematics in representing our world - and beyond.
Author : C. R. Wylie
Publisher : Courier Corporation
ISBN 13 : 0486141705
Total Pages : 578 pages
Book Rating : 4.4/5 (861 download)
Download or read book Introduction to Projective Geometry written by C. R. Wylie and published by Courier Corporation. This book was released on 2011-09-12 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.
Author : Jordan Ellenberg
Publisher : Penguin
ISBN 13 : 1984879065
Total Pages : 481 pages
Book Rating : 4.9/5 (848 download)
Download or read book Shape written by Jordan Ellenberg and published by Penguin. This book was released on 2021-05-25 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: An instant New York Times Bestseller! “Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry"comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.
Author : Ian Stewart
Publisher : ReadHowYouWant.com
ISBN 13 : 1458716546
Total Pages : 466 pages
Book Rating : 4.4/5 (587 download)
Download or read book Flatterland written by Ian Stewart and published by ReadHowYouWant.com. This book was released on 2010-10-08 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: First there was Edwin A. Abbott's remarkable Flatland, published in 1884, and one of the all-time classics of popular mathematics. Now, from mathematician and accomplished science writer Ian Stewart, comes what Nature calls "a superb sequel." Through larger-than-life characters and an inspired story line, Flatterland explores our present understanding of the shape and origins of the universe, the nature of space, time, and matter, as well as modern geometries and their applications. The journey begins when our heroine, Victoria Line, comes upon her great-great-grandfather A. Square's diary, hidden in the attic. The writings help her to contact the Space Hopper, who tempts her away from her home and family in Flatland and becomes her guide and mentor through ten dimensions. In the tradition of Alice in Wonderland and The Phantom Toll Booth, this magnificent investigation into the nature of reality is destined to become a modern classic.
Author : Stefan Schadwinkel
Publisher : Lulu.com
ISBN 13 : 1411636147
Total Pages : 111 pages
Book Rating : 4.4/5 (116 download)
Download or read book At the Edge of All-That-Is, a Journey Into the Art of the Universe written by Stefan Schadwinkel and published by Lulu.com. This book was released on 2005-06-09 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book unfolds a non-dualistic world view, a view of Unity. That view is applied to topical scientific and philosophical issues, like Time, the Brain, Chaos and Order, the Human Immune System and Quantum Physics. It is a practical guide to navigate around common scientific, philosophical and spiritual pitfalls. With powerful, inspiring lyric and vivid metaphors, the reader is guided to realize and engage the full human potential. Awe inspiring sacred geometry is described and very advanced Mer-Ka-Ba activation techniques are unveiled. The nature of Mer-Ka-Ba fields is explained and related to the universe as a whole. Connecting the eternal teachings of the ancient masters with state of the art quantum mechanics, the book is the perfect add-on to all systems of co-creation. If you have been delighted by movies like "What the bleep do we know ?!," then this book will open the gates to the mystery right before your eyes. Fasten your seatbelt and get ready for your Journey into the Art of the Universe.
Author : Judith V. Grabiner
Publisher : MAA
ISBN 13 : 0883855720
Total Pages : 307 pages
Book Rating : 4.8/5 (838 download)
Download or read book A Historian Looks Back written by Judith V. Grabiner and published by MAA. This book was released on 2010-10-14 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: An inspiring collection of a historian's work on the history of mathematics.
Author : Charles R. Hadlock
Publisher : MAA
ISBN 13 : 0883855798
Total Pages : 223 pages
Book Rating : 4.8/5 (838 download)
Download or read book Six Sources of Collapse written by Charles R. Hadlock and published by MAA. This book was released on 2012 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible investigation into the mathematics behind collapse processes, ranging from crashing financial markets to extreme weather to ecological disasters.
Author : the late Richard Courant
Publisher : Oxford University Press
ISBN 13 : 019975487X
Total Pages : 596 pages
Book Rating : 4.1/5 (997 download)
Download or read book What Is Mathematics? written by the late Richard Courant and published by Oxford University Press. This book was released on 1996-07-18 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics?, Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar--a matter of the correct application of local rules. Meaningful mathematics is like journalism--it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature--it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature--it opens a window onto the world of mathematics for anyone interested to view.
Author : Bonnie Gold
Publisher : MAA
ISBN 13 : 9780883855676
Total Pages : 392 pages
Book Rating : 4.8/5 (556 download)
Download or read book Proof and Other Dilemmas written by Bonnie Gold and published by MAA. This book was released on 2008 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sixteen original essays exploring recent developments in the philosophy of mathematics, written in a way mathematicians will understand.
Author : Peter Casazza
Publisher : The Mathematical Association of America
ISBN 13 : 0883855852
Total Pages : 289 pages
Book Rating : 4.8/5 (838 download)
Download or read book I, Mathematician written by Peter Casazza and published by The Mathematical Association of America. This book was released on 2015-03-10 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians have pondered the psychology of the members of our tribe probably since mathematics was invented, but for certain since Hadamard’s The Psychology of Invention in the Mathematical Field. The editors asked two dozen prominent mathematicians (and one spouse thereof) to ruminate on what makes us different. The answers they got are thoughtful, interesting and thought-provoking. Not all respondents addressed the question directly. Michael Atiyah reflects on the tension between truth and beauty in mathematics. T.W. Körner, Alan Schoenfeld and Hyman Bass chose to write, reflectively and thoughtfully, about teaching and learning. Others, including Ian Stewart and Jane Hawkins, write about the sociology of our community. Many of the contributions range into philosophy of mathematics and the nature of our thought processes. Any mathematician will find much of interest here.
Author : William Dunham
Publisher : American Mathematical Soc.
ISBN 13 : 147045744X
Total Pages : 328 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Genius of Euler: Reflections on his Life and Work written by William Dunham and published by American Mathematical Soc.. This book was released on 2020-08-03 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Martin Gardner
Publisher : MAA
ISBN 13 : 9780883855515
Total Pages : 386 pages
Book Rating : 4.8/5 (555 download)
Download or read book Aha! A Two Volume Collection written by Martin Gardner and published by MAA. This book was released on 2006-12-14 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Previously published separately, the two books aha! Gotcha and aha! Insight are here combined as a single volume. The aha! books, as they are referred to by fans of Martin Gardner, contain 144 wonderful puzzles from the reigning king of recreational mathematics. In this combined volume, you will find puzzles ranging over geometry, logic, probability, statistics, number, time, combinatorics, and word play. Gardner calls these puzzles aha! problems, that 'seem difficult, and indeed are difficult if you go about trying to solve them in traditional ways. But if you can free your mind from standard problem solving techniques, you may be receptive to an aha! reaction that leads immediately to a solution. Don't be discouraged if, at first, you have difficulty with these problems. After a while you will begin to catch the spirit of offbeat, nonlinear thinking, and you may be surprised to find your aha! ability improving.'
