An Excursion Through Elementary Mathematics Volume Iii

Author : Antonio Caminha Muniz Neto
Publisher : Springer
Page : 648 pages
File Size : 50,9 Mb
Release : 2018-04-17
Category : Mathematics
ISBN : 9783319779775

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An Excursion through Elementary Mathematics, Volume III by Antonio Caminha Muniz Neto Pdf

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This third and last volume covers Counting, Generating Functions, Graph Theory, Number Theory, Complex Numbers, Polynomials, and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.

Author : Antonio Caminha Muniz Neto
Publisher : Springer
Page : 652 pages
File Size : 41,7 Mb
Release : 2017-03-31
Category : Mathematics
ISBN : 9783319538716

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An Excursion through Elementary Mathematics, Volume I by Antonio Caminha Muniz Neto Pdf

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This first volume covers Real Numbers, Functions, Real Analysis, Systems of Equations, Limits and Derivatives, and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.

Author : Antonio Caminha Muniz Neto
Publisher : Springer
Page : 550 pages
File Size : 41,7 Mb
Release : 2018-04-16
Category : Mathematics
ISBN : 9783319779744

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An Excursion through Elementary Mathematics, Volume II by Antonio Caminha Muniz Neto Pdf

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This second volume covers Plane Geometry, Trigonometry, Space Geometry, Vectors in the Plane, Solids and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.

Author : Alexandre Borovik,Tony Gardiner
Publisher : Unknown
Page : 398 pages
File Size : 43,7 Mb
Release : 2019-06-11
Category : Mathematics
ISBN : 1783746998

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The Essence of Mathematics Through Elementary Problems by Alexandre Borovik,Tony Gardiner Pdf

Author : Merlyn J. Behr,Dale G. Jungst
Publisher : Elsevier
Page : 440 pages
File Size : 40,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483277790

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Fundamentals of Elementary Mathematics by Merlyn J. Behr,Dale G. Jungst Pdf

Fundamentals of Elementary Mathematics provides an understanding of the fundamental aspects of elementary mathematics. This book presents the relevance of the mathematical concepts, which are also demonstrated in numerous exercises. Organized into 10 chapters, this book begins with an overview of the study of logic to understand the nature of mathematics. This text then discusses mathematics as a system of structure or as a collection of substructures. Other chapters consider the four essential components in a mathematical or logical system or structure, namely, undefined terms, defined terms, postulates, and theorems. This book discusses as well several principles used in numeration systems and provides examples of some numeration systems that are in use to illustrate these principles. The final chapter deals with the classification of certain mathematical systems as groups, fields, or rings to demonstrate some abstract mathematics. This book is a valuable resource for students and teachers in elementary mathematics.

Author : Charles Stanley Ogilvy
Publisher : Courier Corporation
Page : 191 pages
File Size : 40,7 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 9780486265308

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Excursions in Geometry by Charles Stanley Ogilvy Pdf

A straightedge, compass, and a little thought are all that's needed to discover the intellectual excitement of geometry. Harmonic division and Apollonian circles, inversive geometry, hexlet, Golden Section, more. 132 illustrations.

Author : Alexander Hahn
Publisher : Princeton University Press
Page : 344 pages
File Size : 46,6 Mb
Release : 2012-07-22
Category : Architecture
ISBN : 9780691145204

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Mathematical Excursions to the World's Great Buildings by Alexander Hahn Pdf

Describes the mathematics behind the design of famous buildings, including the Parthenon, the Sydney Opera House, and the Bilbao Guggenheim.

Author : C. Stanley Ogilvy
Publisher : Courier Corporation
Page : 196 pages
File Size : 41,6 Mb
Release : 1994-01-01
Category : Science
ISBN : 048628283X

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Excursions in Mathematics by C. Stanley Ogilvy Pdf

This lively and accessible exploration of the nature of mathematics examines the role of the mathematician as well as the four major branches: number theory, algebra, geometry, and analysis.

Author : Gattegno
Publisher : Unknown
Page : 128 pages
File Size : 45,9 Mb
Release : 2011-01-21
Category : Electronic
ISBN : 0878253378

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For the Teaching of Mathematics Volume 3 by Gattegno Pdf

Author : Henry Bowers,Joan E. Bowers
Publisher : Unknown
Page : 320 pages
File Size : 42,9 Mb
Release : 1961
Category : Electronic
ISBN : OCLC:35100143

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Arithmetical Excursions by Henry Bowers,Joan E. Bowers Pdf

Author : Isaak Moiseevich I︠A︡glom
Publisher : Unknown
Page : 152 pages
File Size : 51,7 Mb
Release : 1962
Category : Transformations (Mathematics)
ISBN : UOM:39015049377784

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Geometric Transformations by Isaak Moiseevich I︠A︡glom Pdf

Author : Charles Stanley Ogilvy,John Timothy Anderson
Publisher : Courier Corporation
Page : 196 pages
File Size : 47,5 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 0486257789

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Excursions in Number Theory by Charles Stanley Ogilvy,John Timothy Anderson Pdf

Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.

Author : Loring W. Tu
Publisher : Springer
Page : 347 pages
File Size : 45,6 Mb
Release : 2017-06-01
Category : Mathematics
ISBN : 9783319550848

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Differential Geometry by Loring W. Tu Pdf

This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.

Author : Meighan I. Dillon
Publisher : Springer
Page : 350 pages
File Size : 40,9 Mb
Release : 2018-03-21
Category : Mathematics
ISBN : 9783319741352

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Geometry Through History by Meighan I. Dillon Pdf

Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the field.

Author : Richard J. Trudeau
Publisher : Courier Corporation
Page : 224 pages
File Size : 44,8 Mb
Release : 2013-04-15
Category : Mathematics
ISBN : 9780486318660

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Introduction to Graph Theory by Richard J. Trudeau Pdf

Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.