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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
5. Who are the leaders?

5. Who are the leaders?  

Keith Grint

in Leadership: A Very Short Introduction

Print Publication Year: 
Jul 2010
Published Online: 
Sep 2013
eISBN: 
9780191777592
DOI: 
10.1093/actrade/9780199569915.003.0005
Item type: 
chapter
ISBN: 
9780199569915
‘Who are the leaders?’ considers the characteristics of leaders. What do they look like? How do they act? There is a lack of diversity amongst world and business leaders; in business, the ... More
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
4. Structure of groups

4. Structure of groups  

Ian Stewart

in Symmetry: A Very Short Introduction

Print Publication Year: 
May 2013
Published Online: 
Sep 2013
eISBN: 
9780191778292
DOI: 
10.1093/actrade/9780199651986.003.0005
Item type: 
chapter
ISBN: 
9780199651986
‘Structure of groups’ discusses the basic concepts of group theory. Isomorphism occurs when two technically distinct groups share the same abstract structure and order. Groups may also ... More
5. Groups and games

5. Groups and games  

Ian Stewart

in Symmetry: A Very Short Introduction

Print Publication Year: 
May 2013
Published Online: 
Sep 2013
eISBN: 
9780191778292
DOI: 
10.1093/actrade/9780199651986.003.0006
Item type: 
chapter
ISBN: 
9780199651986
‘Groups and games’ explores group theory applied to games and puzzles. Simple games can have large symmetry groups, raising questions that are hard to answer even with today's computational ... More
7. Racist identities: ambivalence, contradiction, and commitment

7. Racist identities: ambivalence, contradiction, and commitment  

Ali Rattansi

in Racism: A Very Short Introduction

Print Publication Year: 
Mar 2007
Published Online: 
Sep 2013
eISBN: 
9780191776137
DOI: 
10.1093/actrade/9780192805904.003.0008
Item type: 
chapter
ISBN: 
9780192805904
People are often accused of using racialized language but this is not the same as being called a racist. What constitutes an identity? An individual or group identity is only partly a ... More
6. Practical security

6. Practical security  

Fred Piper and Sean Murphy

in Cryptography: A Very Short Introduction

Print Publication Year: 
May 2002
Published Online: 
Sep 2013
eISBN: 
9780191775741
DOI: 
10.1093/actrade/9780192803153.003.0006
Item type: 
chapter
ISBN: 
9780192803153
‘Practical security’ reviews the levels of security offered by algorithms and how implementers decide which algorithms to use. Realistic security and different forms of attack are ... More
5. Intergroup relations

5. Intergroup relations  

Richard J. Crisp

in Social Psychology: A Very Short Introduction

Print Publication Year: 
Aug 2015
Published Online: 
Aug 2015
eISBN: 
9780191783319
DOI: 
10.1093/actrade/9780198715511.003.0005
Item type: 
chapter
ISBN: 
9780198715511
‘Intergroup relations’ considers a range of theories that encompass the perceived relationships between the individual, their own group, and other groups, and that provide a range of ... More
1. Choice and desire

1. Choice and desire  

Michael Allingham

in Choice Theory: A Very Short Introduction

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191775710
DOI: 
10.1093/actrade/9780192803030.003.0001
Item type: 
chapter
ISBN: 
9780192803030
‘Choice and desire’ explains that choice theory is the exploration of the reasoning which underlies coherent patterns of choice; it explores what it means to act rationally. The format of ... More
2. Symmetry

2. Symmetry  

A. M. Glazer

in Crystallography: A Very Short Introduction

Print Publication Year: 
Mar 2016
Published Online: 
Mar 2016
eISBN: 
9780191787072
DOI: 
10.1093/actrade/9780198717591.003.0002
Item type: 
chapter
ISBN: 
9780198717591
In order to explain what crystals are and how their structures are described, we need to understand the role of symmetry, for this lies at the heart of crystallography. ‘Symmetry’ explains ... More
8. Matrices and groups

8. Matrices and groups  

Peter M. Higgins

in Algebra: A Very Short Introduction

Print Publication Year: 
Oct 2015
Published Online: 
Oct 2015
eISBN: 
9780191797644
DOI: 
10.1093/actrade/9780198732822.003.0008
Item type: 
chapter
ISBN: 
9780198732822
‘Matrices and groups’ continues with the example of geometric matrix products to see what happens when we compose the mappings involved. It explains several features, including the identity ... More
4. Social work with groups

4. Social work with groups  

Sally Holland and Jonathan Scourfield

in Social Work: A Very Short Introduction

Print Publication Year: 
Jun 2015
Published Online: 
Jun 2015
eISBN: 
9780191785221
DOI: 
10.1093/actrade/9780198708452.003.0004
Item type: 
chapter
ISBN: 
9780198708452
‘Social work with groups’ discusses two types of social work with groups. First, group work when unrelated people are brought together to receive some form of social work help or ... More
Introduction

Introduction  

Ian Stewart

in Symmetry: A Very Short Introduction

Print Publication Year: 
May 2013
Published Online: 
Sep 2013
eISBN: 
9780191778292
DOI: 
10.1093/actrade/9780199651986.003.0001
Item type: 
chapter
ISBN: 
9780199651986
Symmetry has influenced art and natural philosophy for millennia, and is indispensable in mathematics and science. It was originally an informal description, often used metaphorically. ... 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
5. Struggling, surviving, thriving

5. Struggling, surviving, thriving  

Stephen Fineman

in Work: A Very Short Introduction

Print Publication Year: 
Nov 2012
Published Online: 
Sep 2013
eISBN: 
9780191778452
DOI: 
10.1093/actrade/9780199699360.003.0005
Item type: 
chapter
ISBN: 
9780199699360
We have an innate need to find meaning in what we do. To Karl Marx this was an ideological problem: the capitalist system separated workers from their own self-realization. By the late 20th ... More
7. Family, group, and interactive therapies

7. Family, group, and interactive therapies  

Tom Burns and Eva Burns‐Lundgren

in Psychotherapy: A Very Short Introduction

Print Publication Year: 
Jan 2015
Published Online: 
Jan 2015
eISBN: 
9780191781599
DOI: 
10.1093/actrade/9780199689361.003.0007
Item type: 
chapter
ISBN: 
9780199689361
‘Family, group, and interactive therapies’ considers and describes the widely established practice of systemic family therapy, couples therapy, and group therapy, and also introduces ... 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
Symmetry: A Very Short Introduction

Symmetry: A Very Short Introduction  

Ian Stewart

Print Publication Year: 
May 2013
Published Online: 
Sep 2013
eISBN: 
9780191778292
DOI: 
10.1093/actrade/9780199651986.001.0001
Item type: 
book
ISBN: 
9780199651986
Symmetry: A Very Short Introduction provides an introduction to the formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the ... More
6. Blood transfusion

6. Blood transfusion  

Chris Cooper

in Blood: A Very Short Introduction

Print Publication Year: 
Sep 2016
Published Online: 
Sep 2016
eISBN: 
9780191785467
DOI: 
10.1093/actrade/9780199581450.003.0006
Item type: 
chapter
ISBN: 
9780199581450
‘Blood transfusion’ outlines the history of transfusing animal blood dating back to the 17th century. The 19th century saw the first successful human blood transfusion, but two major issues ... More

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