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7. Nature's laws

7. Nature's laws  

Ian Stewart

in Symmetry: A Very Short Introduction

Print Publication Year: 
May 2013
Published Online: 
Sep 2013
eISBN: 
9780191778292
DOI: 
10.1093/actrade/9780199651986.003.0008
Item type: 
chapter
ISBN: 
9780199651986
‘Nature's laws’ investigates instances of symmetry in the laws of nature. Noether's theorem states that wherever a Hamiltonian system has a continuous symmetry, there is a conserved ... More
3. Proofs

3. Proofs  

Timothy Gowers

in Mathematics: A Very Short Introduction

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.003.0003
Item type: 
chapter
ISBN: 
9780192853615
‘Proofs’ is concerned with the concept of a proof, that is, an argument that puts a statement beyond all possible doubt. One of the most famous proofs in mathematics shows that the square ... More
5. The algebra of polynomials and cubic equations

5. The algebra of polynomials and cubic equations  

Peter M. Higgins

in Algebra: A Very Short Introduction

Print Publication Year: 
Oct 2015
Published Online: 
Oct 2015
eISBN: 
9780191797644
DOI: 
10.1093/actrade/9780198732822.003.0005
Item type: 
chapter
ISBN: 
9780198732822
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 ... More
5. Reciprocity

5. Reciprocity  

Ken Binmore

in Game Theory: A Very Short Introduction

Print Publication Year: 
Oct 2007
Published Online: 
Sep 2013
eISBN: 
9780191776991
DOI: 
10.1093/actrade/9780199218462.003.0005
Item type: 
chapter
ISBN: 
9780199218462
‘Reciprocity’ examines the effects of reciprocal behaviour. Reciprocity should only be possible in repeated games, and if this series of games has a finite end backwards induction should ... More
2. The economic theory of efficient pollution control

2. The economic theory of efficient pollution control  

Stephen Smith

in Environmental Economics: A Very Short Introduction

Print Publication Year: 
Sep 2011
Published Online: 
Sep 2013
eISBN: 
9780191777813
DOI: 
10.1093/actrade/9780199583584.003.0003
Item type: 
chapter
ISBN: 
9780199583584
Where pollution reductions come at a cost, how much cost are we willing to pay? ‘The economic theory of efficient pollution control’ looks at how to balance environmental and economic ... More
8. Some frequently asked questions

8. Some frequently asked questions  

Timothy Gowers

in Mathematics: A Very Short Introduction

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.003.0008
Item type: 
chapter
ISBN: 
9780192853615
Is it true that mathematicians are past it by the time they are 30? Why are there so few women mathematicians? Do mathematics and music go together? Why do so many people positively dislike ... More
7. Estimates and approximations

7. Estimates and approximations  

Timothy Gowers

in Mathematics: A Very Short Introduction

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.003.0007
Item type: 
chapter
ISBN: 
9780192853615
For many problems it would be miraculous and totally unexpected if somebody were to find a precise formula for the solution. ‘Estimates and approximations’ shows that most of the time one ... More
Algebra: A Very Short Introduction

Algebra: A Very Short Introduction  

Peter M. Higgins

Print Publication Year: 
Oct 2015
Published Online: 
Oct 2015
eISBN: 
9780191797644
DOI: 
10.1093/actrade/9780198732822.001.0001
Item type: 
book
ISBN: 
9780198732822
Algebra marked the beginning of modern mathematics, moving it beyond arithmetic, which involves calculations featuring given numbers, to problems in which some quantities are unknown. Now, ... More
1. Numbers and algebra

1. Numbers and algebra  

Peter M. Higgins

in Algebra: A Very Short Introduction

Print Publication Year: 
Oct 2015
Published Online: 
Oct 2015
eISBN: 
9780191797644
DOI: 
10.1093/actrade/9780198732822.003.0001
Item type: 
chapter
ISBN: 
9780198732822
‘Numbers and algebra’ introduces the number system and explains several terms used in algebra, including natural numbers, positive and negative integers, rational numbers, number ... More
10. Vector spaces

10. Vector spaces  

Peter M. Higgins

in Algebra: A Very Short Introduction

Print Publication Year: 
Oct 2015
Published Online: 
Oct 2015
eISBN: 
9780191797644
DOI: 
10.1093/actrade/9780198732822.003.0010
Item type: 
chapter
ISBN: 
9780198732822
‘Vector spaces’ discusses the algebra of vector spaces, which are abelian groups with an additional scalar multiplication by a field. Every finite abelian group is the direct product of ... More
3. Historical sketch

3. Historical sketch  

John Haigh

in Probability: A Very Short Introduction

Print Publication Year: 
Apr 2012
Published Online: 
Sep 2013
eISBN: 
9780191777943
DOI: 
10.1093/actrade/9780199588480.003.0003
Item type: 
chapter
ISBN: 
9780199588480
‘Historical sketch’ outlines some of the notable discoveries in the field of probability research. Fermat and Pascal both showed ways of determining the winner of a series based on partial ... More
8. Quantum light

8. Quantum light  

Ian Walmsley

in Light: A Very Short Introduction

Print Publication Year: 
Sep 2015
Published Online: 
Sep 2015
eISBN: 
9780191782442
DOI: 
10.1093/actrade/9780199682690.003.0008
Item type: 
chapter
ISBN: 
9780199682690
There are many kinds of quantum light source, each producing a distinct kind of quantum light. ‘Quantum light’ first considers sources that generate the primitive quantum state of light—a ... More
2. Quantifying risk

2. Quantifying risk  

Mark H. A. Davis

in Mathematical Finance: A Very Short Introduction

Print Publication Year: 
Jan 2019
Published Online: 
Jan 2019
eISBN: 
9780191829932
DOI: 
10.1093/actrade/9780198787945.003.0002
Item type: 
chapter
ISBN: 
9780198787945
A large part of the purpose of the financial markets is to manage, and indeed profit from, risk—the uncertainty surrounding future events, any event, in fact, that affects the views of ... More
5. Measurement in the behavioural sciences

5. Measurement in the behavioural sciences  

David J. Hand

in Measurement: A Very Short Introduction

Print Publication Year: 
Oct 2016
Published Online: 
Oct 2016
eISBN: 
9780191824609
DOI: 
10.1093/actrade/9780198779568.003.0005
Item type: 
chapter
ISBN: 
9780198779568
Concepts of measurement in psychology are particularly noteworthy for having encountered scepticism. While people have been happy to accept that psychological attributes can be compared, ... More
6. Measurement in the social sciences, economics, business, and public policy

6. Measurement in the social sciences, economics, business, and public policy  

David J. Hand

in Measurement: A Very Short Introduction

Print Publication Year: 
Oct 2016
Published Online: 
Oct 2016
eISBN: 
9780191824609
DOI: 
10.1093/actrade/9780198779568.003.0006
Item type: 
chapter
ISBN: 
9780198779568
Social measurement spans a vast range of topics. It underpins government, public policy, international relations, industrial relations, economics, academic social science research, aspects ... More
3. Permutations and combinations

3. Permutations and combinations  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0003
Item type: 
chapter
ISBN: 
9780198723493
Permutations and combinations have been studied for thousands of years. ‘Permutations and combinations’ considers selecting objects from a collection, either in a particular order (such as ... More
14. Halt! What goes there?

14. Halt! What goes there?  

Graham Priest

in Logic: A Very Short Introduction (2nd edn)

Print Publication Year: 
Oct 2017
Published Online: 
Oct 2017
eISBN: 
9780191848513
DOI: 
10.1093/actrade/9780198811701.003.0014
Item type: 
chapter
ISBN: 
9780198811701
‘Halt! What goes there?’ looks at some results about what formal reasoning can and can’t do, and some of the philosophical implications of these facts. It considers the workings of ... More
9. Determinants and matrices

9. Determinants and matrices  

Peter M. Higgins

in Algebra: A Very Short Introduction

Print Publication Year: 
Oct 2015
Published Online: 
Oct 2015
eISBN: 
9780191797644
DOI: 
10.1093/actrade/9780198732822.003.0009
Item type: 
chapter
ISBN: 
9780198732822
‘Determinants and matrices’ explains that in three dimensions, the absolute value of the determinant det(A) of a linear transformation represented by the matrix A is the multiplier of ... More
2. The laws of algebra

2. The laws of algebra  

Peter M. Higgins

in Algebra: A Very Short Introduction

Print Publication Year: 
Oct 2015
Published Online: 
Oct 2015
eISBN: 
9780191797644
DOI: 
10.1093/actrade/9780198732822.003.0002
Item type: 
chapter
ISBN: 
9780198732822
‘The laws of algebra’ explores the three laws that govern arithmetic operations and explains how these rules are extended so that they continue to be respected as we pass from one number ... More
2. How the Sun survives

2. How the Sun survives  

Andrew King

in Stars: A Very Short Introduction

Print Publication Year: 
Jul 2012
Published Online: 
Sep 2013
eISBN: 
9780191778155
DOI: 
10.1093/actrade/9780199602926.003.0002
Item type: 
chapter
ISBN: 
9780199602926
Two facts are central to our existence: the Sun radiates vast amounts of energy into space and the Sun's gravity keeps the Earth in an orbit that we complete every year. With only a few ... More

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