Topology

Author: Richard Earl
Publisher: Oxford University Press, USA
ISBN: 0198832680
Category : MATHEMATICS
Languages : en
Pages : 169

Book Description
How is a subway map different from other maps? What makes a knot knotted? What makes the M�bius 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.

Symmetry: A Very Short Introduction

Author: Ian Stewart
Publisher: OUP Oxford
ISBN: 0191652741
Category : Mathematics
Languages : en
Pages : 161

Book Description
In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and 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.

Topology: A Very Short Introduction

Author: Richard Earl
Publisher: Oxford University Press
ISBN: 0192568981
Category : Mathematics
Languages : en
Pages : 144

Book Description
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.

Networks: A Very Short Introduction

Author: Guido Caldarelli
Publisher: Oxford University Press
ISBN: 0199588074
Category : Computers
Languages : en
Pages : 144

Book Description
Networks are involved in many aspects of everyday life, from food webs in ecology and the spread of pandemics to social networking and public transport. This Very Short Introduction explores the basics of network theory to understand the science of complexity and its importance, using examples from nature, technology, and society, and history.

Projects

Author: Andrew Davies
Publisher: Oxford University Press
ISBN: 0198727666
Category : Business & Economics
Languages : en
Pages : 177

Book Description
A project is a temporary coalition of people and resources brought together to achieve a one-off objective. Andrew Davies explains how and why the project approach is central to success in creating products and services, constructing major infrastructure, launching entrepreneurial ventures, implementing strategies, even landing a man on the moon.

Soft Matter: a Very Short Introduction

Author: Tom McLeish
Publisher: Oxford University Press, USA
ISBN: 0198807139
Category : Science
Languages : en
Pages : 177

Book Description
Tom McLeish delves into the growing field of soft matter - the study of materials such as polymers, colloids, liquid crystals, and foams. Looking beneath their appearance to their inner structure, he discusses their shared physical properties, the principle of Brownian Motion that underlies all soft matter, and the applications of these materials.

The American South

Author: Charles Reagan Wilson
Publisher: Oxford University Press
ISBN: 0199943516
Category : History
Languages : en
Pages : 162

Book Description
"The American South has a dramatic history that has made it a distinctive place on the world stage, one with continuing significance into the twenty-first century. Its early history illuminates the expansion of Europe into the New World, creating a colonial, plantation, slave society that made it different from other parts of the United States but fostered commonalities with other southern places that had similar colonial experiences. The Civil War and civil rights movement are historical events that transformed the South in differing ways and remain part of a vibrant public memory, one that the region's people and outsiders to the region often contest. In the twentieth century, the South's pronounced traditionalism in customs and values was in tension with the forces of modernization that only slowly forced change"--

Combinatorics: A Very Short Introduction

Author: Robin Wilson
Publisher: Oxford University Press
ISBN: 0191035254
Category : Mathematics
Languages : en
Pages : 144

Book Description
How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries. 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.

Introduction to Topology

Author: V. A. Vasilʹev
Publisher: American Mathematical Soc.
ISBN: 0821821628
Category : Mathematics
Languages : en
Pages : 165

Book Description
This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, homology and cohomology, intersection index, etc. The author notes, "The lecture note origins of the book left a significant imprint on itsstyle. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs." He concludes, "As a rule, only those proofs (or sketches of proofs) that are interesting per se and have importantgeneralizations are presented."

Introduction to Topology

Author: Bert Mendelson
Publisher: Courier Corporation
ISBN: 0486135098
Category : Mathematics
Languages : en
Pages : 226

Book Description
Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.