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9. Aftermath

9. Aftermath  

Robin Wilson

in Number Theory: A Very Short Introduction

Print Publication Year: 
May 2020
Published Online: 
May 2020
eISBN: 
9780191839351
DOI: 
10.1093/actrade/9780198798095.003.0009
Item type: 
chapter
ISBN: 
9780198798095
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 ... More
6. Algebra and the arithmetic of remainders

6. Algebra and the arithmetic of remainders  

Peter M. Higgins

in Algebra: A Very Short Introduction

Print Publication Year: 
Oct 2015
Published Online: 
Oct 2015
eISBN: 
9780191797644
DOI: 
10.1093/actrade/9780198732822.003.0006
Item type: 
chapter
ISBN: 
9780198732822
‘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 ... 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
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
6. and beyond, to complex things

6. and beyond, to complex things  

Glen Van Brummelen

in Trigonometry: A Very Short Introduction

Print Publication Year: 
Jan 2020
Published Online: 
Jan 2020
eISBN: 
9780191851896
DOI: 
10.1093/actrade/9780198814313.003.0006
Item type: 
chapter
ISBN: 
9780198814313
‘ … 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 ... More
8. Atoms of symmetry

8. Atoms 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/9780199651986.003.0009
Item type: 
chapter
ISBN: 
9780199651986
‘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 ... More
6. Below the waterline of the number iceberg

6. Below the waterline of the number iceberg  

Peter M. Higgins

in Numbers: A Very Short Introduction

Print Publication Year: 
Feb 2011
Published Online: 
Sep 2013
eISBN: 
9780191777820
DOI: 
10.1093/actrade/9780199584055.003.0006
Item type: 
chapter
ISBN: 
9780199584055
‘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. ... More
3. Building a sine table with your bare hands

3. Building a sine table with your bare hands  

Glen Van Brummelen

in Trigonometry: A Very Short Introduction

Print Publication Year: 
Jan 2020
Published Online: 
Jan 2020
eISBN: 
9780191851896
DOI: 
10.1093/actrade/9780198814313.003.0003
Item type: 
chapter
ISBN: 
9780198814313
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 ... More
4. A combinatorial zoo

4. A combinatorial zoo  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0004
Item type: 
chapter
ISBN: 
9780198723493
‘A combinatorial zoo’ presents a menagerie of combinatorial topics, ranging from the box (or pigeonhole) principle, the inclusion–exclusion principle, the derangement problem, and the Tower ... More
4. Congruences, clocks, and calendars

4. Congruences, clocks, and calendars  

Robin Wilson

in Number Theory: A Very Short Introduction

Print Publication Year: 
May 2020
Published Online: 
May 2020
eISBN: 
9780191839351
DOI: 
10.1093/actrade/9780198798095.003.0004
Item type: 
chapter
ISBN: 
9780198798095
‘Congruences, clocks, and calendars’ demonstrates how we might apply the idea of congruence, first introduced by Gauss in 1801, to problems such as testing which Mersenne numbers are primes ... More
7. Conjectures and theorems

7. Conjectures and theorems  

Robin Wilson

in Number Theory: A Very Short Introduction

Print Publication Year: 
May 2020
Published Online: 
May 2020
eISBN: 
9780191839351
DOI: 
10.1093/actrade/9780198798095.003.0007
Item type: 
chapter
ISBN: 
9780198798095
‘Conjectures and theorems’ investigates a number of topics, such as the distribution of prime numbers, and two unsolved problems, Goldbach’s conjecture and the twin prime conjecture. The ... More
4. Connected and close

4. Connected and close  

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/9780199588077.003.0004
Item type: 
chapter
ISBN: 
9780199588077
‘Connected and close’ shows almost all the elements of networks take part in one large connected structure, called a giant connected component. Almost every node has a path of connections ... More
4. Cryptography: the secret life of primes

4. Cryptography: the secret life of primes  

Peter M. Higgins

in Numbers: A Very Short Introduction

Print Publication Year: 
Feb 2011
Published Online: 
Sep 2013
eISBN: 
9780191777820
DOI: 
10.1093/actrade/9780199584055.003.0004
Item type: 
chapter
ISBN: 
9780199584055
‘Cryptography: the secret life of primes’ shows how prime numbers can be used to encrypt sensitive data. All info can be communicated as numbers through computer systems, and cryptography ... More
8. Designs and geometry

8. Designs and geometry  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0008
Item type: 
chapter
ISBN: 
9780198723493
Block designs are used when designing experiments in which varieties of a commodity are compared. ‘Designs and geometry’ introduces various types of block design, and then relates them to ... 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
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
5. Dimension

5. Dimension  

Timothy Gowers

in Mathematics: A Very Short Introduction

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.003.0005
Item type: 
chapter
ISBN: 
9780192853615
A notable feature of advanced mathematics is that much of it is concerned with geometry in more than three dimensions. ‘Dimension’ looks at high-dimensional geometry, which is best ... 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
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
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

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