9. Aftermath
Robin Wilson
in Number Theory: A Very Short Introduction
The Aftermath returns to some of the problems posed early in the book. The questions solved include: In which years does February have four Sundays? How many shuffles are needed to restore ...
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4. Agents, networks, degree, and recirculation
John H. Holland
in Complexity: A Very Short Introduction
‘Agents, networks, degree, and recirculation’ explains that when studying complex adaptive systems (CAS) in a grammar-like way, agents serve as the ‘alphabet’. The hierarchical organization ...
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6. Algebra and the arithmetic of remainders
Peter M. Higgins
in Algebra: A Very Short Introduction
‘Algebra and the arithmetic of remainders’ considers a new type of algebra, which is both an ancient topic and one that has found major contemporary application in Internet cryptography. It ...
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5. The algebra of polynomials and cubic equations
Peter M. Higgins
in Algebra: A Very Short Introduction
Polynomials are expressions of the form p(x) = a0 + a1x + a2x2 + ... + anxn
; the number ai
is the coefficient of xi
, a
0 is the constant ...
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9. All the world’s a net; or not?
Guido Caldarelli and Michele Catanzaro
in Networks: A Very Short Introduction
‘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 ...
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6. and beyond, to complex things
Glen Van Brummelen
in Trigonometry: A Very Short Introduction
‘ … and beyond, to complex things’ first considers the Taylor series for the exponential function. One of the most famous, yet enigmatic, numbers in mathematics, e is an irrational number ...
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7. Applications in science, medicine, and operations research
John Haigh
in Probability: A Very Short Introduction
‘Applications in science, medicine, and operations research’ applies theories of probability to a range of different subject areas. Brownian motion of particles in liquid was explained by ...
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8. Atoms of symmetry
Ian Stewart
in Symmetry: A Very Short Introduction
‘Atoms of symmetry’ introduces simple groups, which are the indivisible fragments of finite symmetry groups. A comparison can be made with prime numbers, but molecular structure provides a ...
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8. The banking crisis and its aftermath
Mark H. A. Davis
in Mathematical Finance: A Very Short Introduction
What happened to the banks in 2008 and what has been the fallout for mathematical finance? ‘The banking crisis and its aftermath’ explains that for mathematical finance it has meant a ...
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6. Below the waterline of the number iceberg
Peter M. Higgins
in Numbers: A Very Short Introduction
‘Below the waterline of the number iceberg’ introduces numbers other than positive integers. Integers are all whole numbers, positive and negative, and can be arranged along a number line. ...
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4. Big data analytics
Dawn E. Holmes
in Big Data: A Very Short Introduction
‘Big data analytics’ argues that big data is only useful if we can extract useful information from it. It looks at some of the techniques used to discover useful information from big data, ...
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5. Big data and medicine
Dawn E. Holmes
in Big Data: A Very Short Introduction
Big data analysis is changing the world of healthcare. Its potential has yet to be fully realized, but includes medical diagnosis, epidemic prediction, gauging public response to government ...
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8. Big data and society
Dawn E. Holmes
in Big Data: A Very Short Introduction
‘Big data and society’ considers how big data is changing the society we live in, through the development of sophisticated robots and their role in the workplace. It discusses smart ...
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7. Big data security and the Snowden case
Dawn E. Holmes
in Big Data: A Very Short Introduction
‘Big data security and the Snowden case’ looks at some of the security issues surrounding big data and the importance of encryption. Some of the problems facing big data systems include ...
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6. Big data, big business
Dawn E. Holmes
in Big Data: A Very Short Introduction
Since the use of computers became feasible in commercial enterprise, there has been interest in using computers to improve efficiency, cut costs, and generate profits. When IBM launched the ...
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3. Building a sine table with your bare hands
Glen Van Brummelen
in Trigonometry: A Very Short Introduction
Technological advances, so pervasive in almost every aspect of our modern lives, become mundane to us almost overnight. How does a calculator find out, apparently effortlessly, that ...
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6. Can you picture that? X‐rays, DNA, and photos
Alain Goriely
in Applied Mathematics: A Very Short Introduction
Applied mathematics is also concerned with the manipulation and analysis of signals and data. In our digital world, where huge amounts of data are routinely collected, transmitted, ...
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4. Chance experiments
John Haigh
in Probability: A Very Short Introduction
‘Chance experiments’ expands on the notion of distributions, which are central to analysing the consequences of chance experiments. For discrete data, probability can be determined using ...
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3. The classical theory of option pricing
Mark H. A. Davis
in Mathematical Finance: A Very Short Introduction
‘The classical theory of option pricing’ explains the theory of arbitrage pricing, which is closely related to the Dutch Book Arguments, but which brings in a new factor: prices in ...
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7. Co-evolution and the formation of niches
John H. Holland
in Complexity: A Very Short Introduction
What is a niche? ‘Co-evolution and the formation of niches’ explains that the term ‘niche’ is widely used to describe an important part of the hierarchical organization of complex adaptive ...
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