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2. A fruitful approach

2. A fruitful approach  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0002
Item type: 
chapter
ISBN: 
9780199588077
‘A fruitful approach’ shows how the vertices and edges of graphs identify relations between things and how Jacob Moreno became the first to apply this to the analysis of social networks ... More
2. Origins of symmetry

2. Origins of symmetry  

Ian Stewart

in Symmetry: A Very Short Introduction

Print Publication Year: 
May 2013
Published Online: 
Sep 2013
eISBN: 
9780191778292
DOI: 
10.1093/actrade/9780199651986.003.0003
Item type: 
chapter
ISBN: 
9780199651986
‘Origins of symmetry’ investigates the discovery of symmetry. Symmetry was recognized for millennia before it was mathematically defined. Mathematicians believed that the only obstacle to ... More
8. Perfect storms in networks

8. Perfect storms in networks  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0008
Item type: 
chapter
ISBN: 
9780199588077
‘Perfect storms in networks’ shows that the range of possible dynamics in networks is enormous. Domino effects, co-extinctions, cascading failures, breakdown avalanches, systemic failure of ... More
7. Digging deeper into networks

7. Digging deeper into networks  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0007
Item type: 
chapter
ISBN: 
9780199588077
‘Digging deeper into networks’ shows that to capture the more subtle structure of networks one has to find measures that describe the surroundings of a node — degree distribution is not ... More
6. Unknot or knot to be?

6. Unknot or knot to be?  

Richard Earl

in Topology: A Very Short Introduction

Print Publication Year: 
Dec 2019
Published Online: 
Dec 2019
eISBN: 
9780191871252
DOI: 
10.1093/actrade/9780198832683.003.0006
Item type: 
chapter
ISBN: 
9780198832683
‘Unknot or knot to be?’ explains that a knot is a smooth, simple, closed curve in 3D space. Being simple and closed means the curve does not cross itself except that its end returns to its ... More
6. Emergence of networks

6. Emergence of networks  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0006
Item type: 
chapter
ISBN: 
9780199588077
‘Emergence of networks’ considers a range of network models that explain how local mechanisms, without global planning, can generate large-scale, complex, ordered, and efficient structures. ... More
9. All the world’s a net; or not?

9. All the world’s a net; or not?  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0009
Item type: 
chapter
ISBN: 
9780199588077
‘All the world's a net; or not?’ summarizes the extent and limitations of network science. There are warnings about the generalizations drawn from network theory, but the results of network ... More
Epilogue

Epilogue  

Richard Earl

in Topology: A Very Short Introduction

Print Publication Year: 
Dec 2019
Published Online: 
Dec 2019
eISBN: 
9780191871252
DOI: 
10.1093/actrade/9780198832683.003.0007
Item type: 
chapter
ISBN: 
9780198832683
Topology remains a large, active research area in mathematics. Unsurprisingly its character has changed over the last century—there is considerably less current interest in general ... More
3. Fractal dimension

3. Fractal dimension  

Kenneth J. Falconer

in Fractals: A Very Short Introduction

Print Publication Year: 
Sep 2013
Published Online: 
Sep 2013
eISBN: 
9780191778599
DOI: 
10.1093/actrade/9780199675982.003.0003
Item type: 
chapter
ISBN: 
9780199675982
‘Fractal dimension’ shows how fractals are measured as we examine them ever more closely. Traditional geometric methods in three dimensions are inadequate for measuring fractals, so a ... More
Networks: A Very Short Introduction

Networks: A Very Short Introduction  

Guido Caldarelli and Michele Catanzaro

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.001.0001
Item type: 
book
ISBN: 
9780199588077
Networks: A Very Short Introduction considers the basic elements of network theory and its applications using everyday examples from society, technology, nature, and history. ... More
5. Flavours of topology

5. Flavours of topology  

Richard Earl

in Topology: A Very Short Introduction

Print Publication Year: 
Dec 2019
Published Online: 
Dec 2019
eISBN: 
9780191871252
DOI: 
10.1093/actrade/9780198832683.003.0005
Item type: 
chapter
ISBN: 
9780198832683
From the mid-19th century, topological understanding progressed on various fronts. ‘Flavours of topology’ considers other areas such as differential topology, algebraic topology, and ... More
3. Thinking continuously

3. Thinking continuously  

Richard Earl

in Topology: A Very Short Introduction

Print Publication Year: 
Dec 2019
Published Online: 
Dec 2019
eISBN: 
9780191871252
DOI: 
10.1093/actrade/9780198832683.003.0003
Item type: 
chapter
ISBN: 
9780198832683
Many topologists might choose to describe their subject as the study of continuity. There are continuous and discontinuous functions in our everyday routines. ‘Thinking continuously’ aims ... More
Topology: A Very Short Introduction

Topology: A Very Short Introduction  

Richard Earl

Print Publication Year: 
Dec 2019
Published Online: 
Dec 2019
eISBN: 
9780191871252
DOI: 
10.1093/actrade/9780198832683.001.0001
Item type: 
book
ISBN: 
9780198832683
Topology, the mathematical study of the properties that are preserved through the deformations, twistings, and stretchings of objects, is an important area of modern mathematics. Topology: ... More
1. What is topology?

1. What is topology?  

Richard Earl

in Topology: A Very Short Introduction

Print Publication Year: 
Dec 2019
Published Online: 
Dec 2019
eISBN: 
9780191871252
DOI: 
10.1093/actrade/9780198832683.003.0001
Item type: 
chapter
ISBN: 
9780198832683
Topology is now a major area of modern mathematics, but an appreciation of topology came late in the history of mathematics. The word topology—meaning ‘the study of place’—was not coined ... More
4. The plane and other spaces

4. The plane and other spaces  

Richard Earl

in Topology: A Very Short Introduction

Print Publication Year: 
Dec 2019
Published Online: 
Dec 2019
eISBN: 
9780191871252
DOI: 
10.1093/actrade/9780198832683.003.0004
Item type: 
chapter
ISBN: 
9780198832683
Most functions have several numerical inputs and produce more than one numerical output. But even generally continuity requires that we can constrain the difference in outputs by suitably ... More
2. Making surfaces

2. Making surfaces  

Richard Earl

in Topology: A Very Short Introduction

Print Publication Year: 
Dec 2019
Published Online: 
Dec 2019
eISBN: 
9780191871252
DOI: 
10.1093/actrade/9780198832683.003.0002
Item type: 
chapter
ISBN: 
9780198832683
‘Making surfaces’ considers the shape of surfaces and discusses the work of some of the early topologists, Möbius, Klein, and Riemann. It introduces the torus shape and shows how its Euler ... More

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