Icons Of Mathematics An Exploration Of Twenty Key Images

Author : Claudi Alsina ,Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 327 pages
File Size : 46,6 Mb
Release : 2020-06-01
Category : Education
ISBN : 9781470456160

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Icons of Mathematics: An Exploration of Twenty Key Images by Claudi Alsina ,Roger B. Nelsen Pdf

The authors present twenty icons of mathematics, that is, geometrical shapes such as the right triangle, the Venn diagram, and the yang and yin symbol and explore mathematical results associated with them. As with their previous books (Charming Proofs, When Less is More, Math Made Visual) proofs are visual whenever possible. The results require no more than high-school mathematics to appreciate and many of them will be new even to experienced readers. Besides theorems and proofs, the book contains many illustrations and it gives connections of the icons to the world outside of mathematics. There are also problems at the end of each chapter, with solutions provided in an appendix. The book could be used by students in courses in problem solving, mathematical reasoning, or mathematics for the liberal arts. It could also be read with pleasure by professional mathematicians, as it was by the members of the Dolciani editorial board, who unanimously recommend its publication.

Author : Claudi Alsina,Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 271 pages
File Size : 40,9 Mb
Release : 2015-12-31
Category : Mathematics
ISBN : 9781614442165

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A Mathematical Space Odyssey by Claudi Alsina,Roger B. Nelsen Pdf

Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. This book presents techniques for proving a variety of geometric results in three dimensions. Special attention is given to prisms, pyramids, platonic solids, cones, cylinders and spheres, as well as many new and classical results. A chapter is devoted to each of the following basic techniques for exploring space and proving theorems: enumeration, representation, dissection, plane sections, intersection, iteration, motion, projection, and folding and unfolding. The book includes a selection of Challenges for each chapter with solutions, references and a complete index. The text is aimed at secondary school and college and university teachers as an introduction to solid geometry, as a supplement in problem solving sessions, as enrichment material in a course on proofs and mathematical reasoning, or in a mathematics course for liberal arts students.--

Author : Keith Kendig
Publisher : MAA
Page : 211 pages
File Size : 45,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780883853535

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A Guide to Plane Algebraic Curves by Keith Kendig Pdf

An accessible introduction to the plane algebraic curves that also serves as a natural entry point to algebraic geometry. This book can be used for an undergraduate course, or as a companion to algebraic geometry at graduate level.

Author : C. Ray Rosentrater
Publisher : American Mathematical Soc.
Page : 325 pages
File Size : 53,6 Mb
Release : 2015-12-31
Category : Mathematics
ISBN : 9781614442172

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Varieties of Integration by C. Ray Rosentrater Pdf

Historical introduction -- The Riemann integral -- The Darboux integral -- A functional zoo -- Another approach : measure theory -- The Lebesgue integral -- The Gauge integral -- Stieltjes-type integrals and extensions -- A look back -- Afterword : L2 spaces and Fourier series

Author : Horst Martini,Luis Montejano,Déborah Oliveros
Publisher : Springer
Page : 486 pages
File Size : 52,9 Mb
Release : 2019-03-16
Category : Mathematics
ISBN : 9783030038687

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Bodies of Constant Width by Horst Martini,Luis Montejano,Déborah Oliveros Pdf

This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry. It examines bodies of constant width from several points of view, and, in doing so, shows surprising connections between various areas of mathematics. Concise explanations and detailed proofs demonstrate the many interesting properties and applications of these bodies. Numerous instructive diagrams are provided throughout to illustrate these concepts. An introduction to convexity theory is first provided, and the basic properties of constant width bodies are then presented. The book then delves into a number of related topics, which include Constant width bodies in convexity (sections and projections, complete and reduced sets, mixed volumes, and further partial fields) Sets of constant width in non-Euclidean geometries (in real Banach spaces, and in hyperbolic, spherical, and further non-Euclidean spaces) The concept of constant width in analysis (using Fourier series, spherical integration, and other related methods) Sets of constant width in differential geometry (using systems of lines and discussing notions like curvature, evolutes, etc.) Bodies of constant width in topology (hyperspaces, transnormal manifolds, fiber bundles, and related topics) The notion of constant width in discrete geometry (referring to geometric inequalities, packings and coverings, etc.) Technical applications, such as film projectors, the square-hole drill, and rotary engines Bodies of Constant Width: An Introduction to Convex Geometry with Applications will be a valuable resource for graduate and advanced undergraduate students studying convex geometry and related fields. Additionally, it will appeal to any mathematicians with a general interest in geometry.

Author : Paul R. Halmos
Publisher : American Mathematical Soc.
Page : 333 pages
File Size : 49,5 Mb
Release : 1995-12-31
Category : Mathematics
ISBN : 9781614442127

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Linear Algebra Problem Book by Paul R. Halmos Pdf

Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebraand today that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, for security and completeness, provide the detailed answer.

Author : Arthur T. Benjamin,Jennifer J. Quinn
Publisher : American Mathematical Society
Page : 210 pages
File Size : 49,5 Mb
Release : 2022-09-21
Category : Mathematics
ISBN : 9781470472597

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Proofs that Really Count by Arthur T. Benjamin,Jennifer J. Quinn Pdf

Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.

Author : Claudi Alsina,Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 304 pages
File Size : 51,6 Mb
Release : 2020-02-10
Category : Education
ISBN : 9781470453121

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A Cornucopia of Quadrilaterals by Claudi Alsina,Roger B. Nelsen Pdf

A Cornucopia of Quadrilaterals collects and organizes hundreds of beautiful and surprising results about four-sided figures—for example, that the midpoints of the sides of any quadrilateral are the vertices of a parallelogram, or that in a convex quadrilateral (not a parallelogram) the line through the midpoints of the diagonals (the Newton line) is equidistant from opposite vertices, or that, if your quadrilateral has an inscribed circle, its center lies on the Newton line. There are results dating back to Euclid: the side-lengths of a pentagon, a hexagon, and a decagon inscribed in a circle can be assembled into a right triangle (the proof uses a quadrilateral and circumscribing circle); and results dating to Erdős: from any point in a triangle the sum of the distances to the vertices is at least twice as large as the sum of the distances to the sides. The book is suitable for serious study, but it equally rewards the reader who dips in randomly. It contains hundreds of challenging four-sided problems. Instructors of number theory, combinatorics, analysis, and geometry will find examples and problems to enrich their courses. The authors have carefully and skillfully organized the presentation into a variety of themes so the chapters flow seamlessly in a coherent narrative journey through the landscape of quadrilaterals. The authors' exposition is beautifully clear and compelling and is accessible to anyone with a high school background in geometry.

Author : Fernando Q. Gouvêa
Publisher : American Mathematical Soc.
Page : 309 pages
File Size : 42,8 Mb
Release : 2012-12-31
Category : Mathematics
ISBN : 9781614442110

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A Guide to Groups, Rings, and Fields by Fernando Q. Gouvêa Pdf

Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.

Author : Steven G. Krantz
Publisher : American Mathematical Soc.
Page : 137 pages
File Size : 46,5 Mb
Release : 2013-12-31
Category : Mathematics
ISBN : 9781614442134

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A Guide to Functional Analysis by Steven G. Krantz Pdf

MAA guides series numbering on title page appears as # 49. It should read # 9.

Author : Tom M. Apostol,Mamikon A. Mnatsakanian
Publisher : American Mathematical Soc.
Page : 520 pages
File Size : 45,6 Mb
Release : 2017-10-24
Category : Mathematics
ISBN : 9781470443368

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New Horizons in Geometry by Tom M. Apostol,Mamikon A. Mnatsakanian Pdf

Author : Anonim
Publisher : Unknown
Page : 554 pages
File Size : 50,6 Mb
Release : 2002
Category : Encyclopedias and dictionaries
ISBN : UOM:39015051610437

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The World Book Encyclopedia by Anonim Pdf

An encyclopedia designed especially to meet the needs of elementary, junior high, and senior high school students.

Author : Roger B. Nelsen
Publisher : MAA
Page : 166 pages
File Size : 50,6 Mb
Release : 1993
Category : Logic, Symbolic and mathematical
ISBN : 0883857006

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Proofs Without Words by Roger B. Nelsen Pdf

Author : MICHELLE. MANES
Publisher : Unknown
Page : 128 pages
File Size : 46,5 Mb
Release : 2018
Category : Electronic
ISBN : OCLC:1096529964

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MATHEMATICS FOR ELEMENTARY TEACHERS. (PRODUCT ID 23864410). by MICHELLE. MANES Pdf

Author : Math Vault
Publisher : Math Vault Publishing
Page : 76 pages
File Size : 54,8 Mb
Release : 2020-06-13
Category : Mathematics
ISBN : 8210379456XXX

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Comprehensive List of Mathematical Symbols by Math Vault Pdf

Ever wonder if there's a reference guide out there summarizing most of the symbols used in mathematics, along with contextual examples and LaTeX code so that you can pick up the various topics of mathematics at an unusual speed? Well now there is! In this jam-packed 75-page eBook, the Comprehensive List of Mathematical Symbols will take you through thousands of symbols in 10+ topics and 6 main categories. Each symbol also comes with their own defining examples, LaTeX codes and links to additional resources, making the eBook both a handy reference and a powerful tool for consolidating one's foundation of mathematics. Highlights - Featuring 1000+ of symbols from basic math, algebra, logic, set theory to calculus, analysis, probability and statistics - Comes with LaTeX code, defining contextual examples and links to additional resources - Clear. Concise. Straight-to-the-point with no fluff. - Informative. Engaging. Excellent for shortening the learning/reviewing curve. Table of Contents 1) Constants Key Mathematical Numbers Key Mathematical Sets Key Mathematical Infinities Other Key Mathematical Objects 2) Variables Variables for Numbers Variables in Geometry Variables in Logic Variables in Set Theory Variables in Linear/Abstract Algebra Variables in Probability and Statistics Variables in Calculus 3) Delimiters Common Delimiters Other Delimiters 4) Alphabet Letters Greek Letters Used in Mathematics Other Greek Letters 5) Operators Common Operators Number-related Operators Common Number-based Operators Complex-number-based Operators Function-related Operators Common Function-based Operators Elementary Functions Key Calculus-related Functions and Transforms Other Key Functions Operators in Geometry Operators in Logic Logical Connectives Quantifiers Substitution/Valuation-based Operators Set-related Operators Operators in Algebra Vector-related Operators Matrix-related Operators Vector-space-related Operators Abstract-algebra-related Operators Operators in Probability and Statistics Combinatorial Operators Probability-related Operators Probability-related Functions Discrete Probability Distributions Continuous Probability Distributions and Associated Functions Statistical Operators Operators in Calculus Operators Related to Sequence, Series and Limit Derivative-based Operators Integral-based Operators 6) Relational Symbols Equality-based Relational Symbols Comparison-based Relational Symbols Number-related Relational Symbols Relational Symbols in Geometry Relational Symbols in Logic Set-related Relational Symbols Relational Symbols in Abstract Algebra Relational Symbols in Probability and Statistics Relational Symbols in Calculus 7) Notational Symbols Common Notational Symbols Intervals Notational Symbols in Geometry and Trigonometry Notational Symbols in Probability and Statistics Notational Symbols in Calculus