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AlgebraA 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
7. Introduction to matrices

7. Introduction to 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/9780198732822.003.0007
Item type: 
chapter
ISBN: 
9780198732822
Matrices represent the central algebraic vehicle for advanced computation throughout mathematics as well as the physical and social sciences. ‘Introduction to matrices’ explains that ... 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
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
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
6. Can you picture that? X‐rays, DNA, and photos

6. Can you picture that? X‐rays, DNA, and photos  

Alain Goriely

in Applied Mathematics: A Very Short Introduction

Print Publication Year: 
Feb 2018
Published Online: 
Feb 2018
eISBN: 
9780191815805
DOI: 
10.1093/actrade/9780198754046.003.0006
Item type: 
chapter
ISBN: 
9780198754046
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, ... More
2. Characteristica universalis, logical calculus, and mathematics

2. Characteristica universalis, logical calculus, and mathematics  

Maria Rosa Antognazza

in Leibniz: A Very Short Introduction

Print Publication Year: 
Sep 2016
Published Online: 
Nov 2016
eISBN: 
9780191788079
DOI: 
10.1093/actrade/9780198718642.003.0002
Item type: 
chapter
ISBN: 
9780198718642
How did Leibniz propose to pursue his all-embracing programme of scientific advancement? What were the core projects that held his wide-ranging intellectual life together? ‘Characteristica ... More

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