Download or read book Mathematical Vistas written by Peter Hilton and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects nine related mathematical essays which will intrigue and inform. From the reviews: "The authors put their writing where their talents are, and students get to see just how alive mathematics is...there is much to commend the book. It contains plenty of interesting mathematics, often going in unusual directions. I like the diagrams; the authors have chosen mathematics that involves especially pretty ones." --THE MATHEMATICAL ASSOCIATION OF AMERICA

Download or read book Mathematical vistas written by Peter John Hilton and published by . This book was released on 2002 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Vistas written by Joseph Malkevitch and published by . This book was released on 1990 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Vistas From A Room With Many Windows written by Hilton and published by . This book was released on 2009-12-01 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Reflections written by Peter Hilton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A relaxed and informal presentation conveying the joy of mathematical discovery and insight. Frequent questions lead readers to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful ideas. The text presents eight topics that illustrate the unity of mathematical thought as well as the diversity of mathematical ideas. Drawn from both "pure" and "applied" mathematics, they include: spirals in nature and in mathematics; the modern topic of fractals and the ancient topic of Fibonacci numbers; Pascals Triangle and paper folding; modular arithmetic and the arithmetic of the infinite. The final chapter presents some ideas about how mathematics should be done, and hence, how it should be taught. Presenting many recent discoveries that lead to interesting open questions, the book can serve as the main text in courses dealing with contemporary mathematical topics or as enrichment for other courses. It can also be read with pleasure by anyone interested in the intellectually intriguing aspects of mathematics.

Download or read book Some Vistas of Modern Mathematics written by Richard Bellman and published by University Press of Kentucky. This book was released on 2014-07-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapid advances in the physical and biological sciences and in related technologies have brought about equally farreaching changes in mathematical research. Focusing on control theory, invariant imbedding, dynamic programming, and quasilinearization, Mr. Bellman explores with ease and clarity the mathematical research problems arising from scientific questions in engineering, physics, biology, and medicine. Special attention is paid in these essays to the use of the digital computer in obtaining the numerical solution of numerical problems, its influence in the formulation of new and old scientific problems in new terms, and to some of the effects of the computer revolution on educational and social systems. The new opportunities for mathematical research presage, Bellman concludes, a renaissance of mathematics in human affairs by involving it closely in the problems of society.

Download or read book Titu Andreescu and Mark Saul written by Titu Andreescu and published by American Mathematical Soc.. This book was released on 2016-12-19 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra is required of the student. The exposition is lean. Most of the learning occurs as the student engages in the problems posed in each chapter. And the learning is not “linear”. The central topic of inequalities is linked to others in mathematics. Often these topics relate to much more than algebraic inequalities. There are also “secret” pathways through the book. Each chapter has a subtext, a theme which prepares the student for learning other mathematical topics, concepts, or habits of mind. For example, the early chapters on the arithmetic mean/geometric mean inequality show how very simple observations can be leveraged to yield useful and interesting results. Later chapters give examples of how one can generalize a mathematical statement. The chapter on the Cauchy-Schwarz inequality provides an introduction to vectors as mathematical objects. And there are many other secret pathways that the authors hope the reader will discover—and follow. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Download or read book Elementary Analysis written by Kenneth A. Ross and published by Springer Science & Business Media. This book was released on 1980-03-03 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for students having no previous experience with rigorous proofs, this text can be used immediately after standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, as well as for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied, while many abstract ideas, such as metric spaces and ordered systems, are avoided completely. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics, and optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.

Download or read book The Joy of Sets written by Keith Devlin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naïve" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science.

Download or read book Short Calculus written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews "This is a reprint of the original edition of Lang’s ‘A First Course in Calculus’, which was first published in 1964....The treatment is ‘as rigorous as any mathematician would wish it’....[The exercises] are refreshingly simply stated, without any extraneous verbiage, and at times quite challenging....There are answers to all the exercises set and some supplementary problems on each topic to tax even the most able." --Mathematical Gazette

Download or read book Beginning Functional Analysis written by Karen Saxe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unifying approach of functional analysis is to view functions as points in abstract vector space and the differential and integral operators as linear transformations on these spaces. The author's goal is to present the basics of functional analysis in a way that makes them comprehensible to a student who has completed courses in linear algebra and real analysis, and to develop the topics in their historical contexts.

Download or read book From Combinatorics to Philosophy written by Ernesto Damiani and published by Springer Science & Business Media. This book was released on 2009-07-24 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Combinatorics to Philosophy: The Legacy of G. -C. Rota provides an assessment of G. -C. Rota's legacy to current international research issues in mathematics, philosophy and computer science. This volume includes chapters by leading researchers, as well as a number of invited research papers. Rota’s legacy connects European and Italian research communities to the USA by providing inspiration to several generations of researchers in combinatorics, philosophy and computer science. From Combinatorics to Philosophy: The Legacy of G. -C. Rota is of valuable interest to research institutions and university libraries worldwide. This book is also designed for advanced-level students in mathematics, computer science, and philosophy.

Download or read book A Mathematical Odyssey written by Steven G. Krantz and published by Springer. This book was released on 2014-05-10 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincaré conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the mass-production automobile was pioneered by Henry Ford, so everyone should know that the P/NP problem has implications for security and data manipulation that will affect everyone. This book endeavors to tell the story of the modern impact of mathematics, of its trials and triumphs and insights, in language that can be appreciated by a broad audience. It endeavors to show what mathematics means for our lives, how it impacts all of us, and what new thoughts it should cause us to entertain. It introduces new vistas of mathematical ideas and shares the excitement of new ideas freshly minted. It discusses the significance and impact of these ideas, and gives them meaning that will travel well and cause people to reconsider their place in the universe. Mathematics is one of mankind's oldest disciplines. Along with philosophy, it has shaped the very modus of human thought. And it continues to do so. To be unaware of modern mathematics is to miss out on a large slice of life. It is to be left out of essential modern developments. We want to address this point, and do something about it. This is a book to make mathematics exciting for people of all interests and all walks of life. Mathematics is exhilarating, it is ennobling, it is uplifting, and it is fascinating. We want to show people this part of our world, and to get them to travel new paths.

Download or read book Linear Algebra written by Charles W. Curtis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and updated fourth edition designed for upper division courses in linear algebra includes the basic results on vector spaces over fields, determinants, the theory of a single linear transformation, and inner product spaces. While it does not presuppose an earlier course, many connections between linear algebra and calculus are worked into the discussion. A special feature is the inclusion of sections devoted to applications of linear algebra, which can either be part of a course, or used for independent study, and new to this edition is a section on analytic methods in matrix theory, with applications to Markov chains in probability theory. Proofs of all the main theorems are included, and are presented on an equal footing with methods for solving numerical problems. Worked examples are integrated into almost every section, to bring out the meaning of the theorems, and illustrate techniques for solving problems. Many numerical exercises make use of all the ideas, and develop computational skills, while exercises of a theoretical nature provide opportunities for students to discover for themselves.

Download or read book The Nature and Growth of Modern Mathematics written by Edna Ernestine Kramer and published by Princeton University Press. This book was released on 1982 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful "ideals" of Dedekind and Emmy Noether; and the importance of "purifying" mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail.

Download or read book Mathematicians Don t Work With Numbers written by Richard Poulo and published by Springer Nature. This book was released on with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Expeditions written by Reinhard Laubenbacher and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stories of five mathematical journeys into new realms, pieced together from the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, others by more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realisation that still greater vistas remain to be explored. The authors tell these stories by guiding readers through the very words of the mathematicians at the heart of these events, providing an insightinto the art of approaching mathematical problems. The five chapters are completely independent, with varying levels of mathematical sophistication, and will attract students, instructors, and the intellectually curious reader. By working through some of the original sources and supplementary exercises, which discuss and solve -- or attempt to solve -- a great problem, this book helps readers discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics.