An Excursion through Elementary Mathematics, Volume I

An Excursion through Elementary Mathematics, Volume I
Author :
Publisher : Springer
Total Pages : 652
Release :
ISBN-10 : 3319538705
ISBN-13 : 9783319538709
Rating : 4/5 (05 Downloads)

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

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.

An Excursion through Elementary Mathematics, Volume II

An Excursion through Elementary Mathematics, Volume II
Author :
Publisher : Springer
Total Pages : 550
Release :
ISBN-10 : 9783319779744
ISBN-13 : 3319779745
Rating : 4/5 (44 Downloads)

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

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.

Mathematical Excursions to the World's Great Buildings

Mathematical Excursions to the World's Great Buildings
Author :
Publisher : Princeton University Press
Total Pages : 336
Release :
ISBN-10 : 9781400841998
ISBN-13 : 1400841992
Rating : 4/5 (98 Downloads)

Synopsis Mathematical Excursions to the World's Great Buildings by : Alexander J. Hahn

How mathematics helped build the world's most important buildings from early Egypt to the present From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines this with an in-depth look at their aesthetics, history, and structure. Whether using trigonometry and vectors to explain why Gothic arches are structurally superior to Roman arches, or showing how simple ruler and compass constructions can produce sophisticated architectural details, Alexander Hahn describes the points at which elementary mathematics and architecture intersect. Beginning in prehistoric times, Hahn proceeds to guide readers through the Greek, Roman, Islamic, Romanesque, Gothic, Renaissance, and modern styles. He explores the unique features of the Pantheon, the Hagia Sophia, the Great Mosque of Cordoba, the Duomo in Florence, Palladio's villas, and Saint Peter's Basilica, as well as the U.S. Capitol Building. Hahn celebrates the forms and structures of architecture made possible by mathematical achievements from Greek geometry, the Hindu-Arabic number system, two- and three-dimensional coordinate geometry, and calculus. Along the way, Hahn introduces groundbreaking architects, including Brunelleschi, Alberti, da Vinci, Bramante, Michelangelo, della Porta, Wren, Gaudí, Saarinen, Utzon, and Gehry. Rich in detail, this book takes readers on an expedition around the globe, providing a deeper understanding of the mathematical forces at play in the world's most elegant buildings.

Excursions in Geometry

Excursions in Geometry
Author :
Publisher : Courier Corporation
Total Pages : 191
Release :
ISBN-10 : 9780486265308
ISBN-13 : 0486265307
Rating : 4/5 (08 Downloads)

Synopsis Excursions in Geometry by : Charles Stanley Ogilvy

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.

Excursions in Number Theory

Excursions in Number Theory
Author :
Publisher : Courier Corporation
Total Pages : 196
Release :
ISBN-10 : 0486257789
ISBN-13 : 9780486257785
Rating : 4/5 (89 Downloads)

Synopsis Excursions in Number Theory by : Charles Stanley Ogilvy

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.

Arithmetical Excursions

Arithmetical Excursions
Author :
Publisher : London : Toronto : Dent ; New York : Dover Publications
Total Pages : 356
Release :
ISBN-10 : PSU:000031880954
ISBN-13 :
Rating : 4/5 (54 Downloads)

Synopsis Arithmetical Excursions by : Henry Bowers

Geometry Through History

Geometry Through History
Author :
Publisher : Springer
Total Pages : 356
Release :
ISBN-10 : 9783319741352
ISBN-13 : 3319741357
Rating : 4/5 (52 Downloads)

Synopsis Geometry Through History by : Meighan I. Dillon

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.

The Joy of X

The Joy of X
Author :
Publisher : Houghton Mifflin Harcourt
Total Pages : 333
Release :
ISBN-10 : 9780547517650
ISBN-13 : 0547517653
Rating : 4/5 (50 Downloads)

Synopsis The Joy of X by : Steven Henry Strogatz

A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."

Excursions in Classical Analysis

Excursions in Classical Analysis
Author :
Publisher : American Mathematical Soc.
Total Pages : 301
Release :
ISBN-10 : 9780883859353
ISBN-13 : 0883859351
Rating : 4/5 (53 Downloads)

Synopsis Excursions in Classical Analysis by : Hongwei Chen

Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof. The [Author]; presents a variety of solutions for the problems in the book. Some solutions reach back to the work of mathematicians like Leonhard Euler while others connect to other beautiful parts of mathematics. Readers will frequently see problems solved by using an idea that, at first glance, might not even seem to apply to that problem. Other solutions employ a specific technique that can be used to solve many different kinds of problems. Excursions emphasizes the rich and elegant interplay between continuous and discrete mathematics by applying induction, recursion, and combinatorics to traditional problems in classical analysis. The book will be useful in students' preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order.

Algebra II

Algebra II
Author :
Publisher : Springer
Total Pages : 370
Release :
ISBN-10 : 9783319508535
ISBN-13 : 3319508539
Rating : 4/5 (35 Downloads)

Synopsis Algebra II by : Alexey L. Gorodentsev

This book is the second volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses. This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.