Richard Earl - Böcker

How is a subway map different from other maps? What makes a knot knotted? What makes the Möbius strip one-sided? These are questions of topology, the mathematical study of properties preserved by twisting or stretching objects. In the 20th century topology became as broad and fundamental as algebra and geometry, with important implications for science, especially physics.In this Very Short Introduction Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

With over 4,000 entries, this informative A to Z provides clear, jargon-free definitions on a wide variety of mathematical terms. Its entries cover both pure and applied mathematics, and include key theories, concepts, methods, programmes, people, and terminology.For this sixth edition, around 800 new terms have been defined, expanding on the dictionary's coverage of topics such as algebra, differential geometry, algebraic geometry, representation theory, and statistics. Among this new material are articles such as cardinal arithmetic, first fundamental form, Lagrange's theorem, Navier-Stokes equations, potential, and splitting field. The existing entries have also been revised and updated to account for developments in the field. Numerous supplementary features complement the text, including detailed appendices on basic algebra, areas and volumes, trigonometric formulae, and Roman numerals. Newly added to these sections is a historical timeline of significant mathematicians lives and the emergence of key theorems. There are also illustrations, graphs, and charts throughout the text, as well as useful web links to provide access to further reading.

Very Short Introductions: Brilliant, sharp, inspiringThe 17th-century calculus of Newton and Leibniz was built on shaky foundations, and it wasn't until the 18th and 19th centuries that mathematicians--especially Bolzano, Cauchy, and Weierstrass--began to establish a rigorous basis for the subject. The resulting discipline is now known to mathematicians as analysis.This book, aimed at readers with some grounding in mathematics, describes the nascent evolution of mathematical analysis, its development as a subject in its own right, and its wide-ranging applications in mathematics and science, modelling reality from acoustics to fluid dynamics, from biological systems to quantum theory.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Containing a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics. Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth form mathematics, thus enabling students to understand the more complex material. Exercises are carefully chosen to introduce students to some central ideas, without building up large amounts of abstract technology. There are over 1500 carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time.