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Algebra: A Very Short Introduction
Peter M. Higgins
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, ...
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1. Numbers and algebra
Peter M. Higgins
in Algebra: A Very Short Introduction
‘Numbers and algebra’ introduces the number system and explains several terms used in algebra, including natural numbers, positive and negative integers, rational numbers, number ...
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7. Introduction to matrices
Peter M. Higgins
in Algebra: A Very Short Introduction
Matrices represent the central algebraic vehicle for advanced computation throughout mathematics as well as the physical and social sciences. ‘Introduction to matrices’ explains that ...
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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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2. The laws of algebra
Peter M. Higgins
in Algebra: A Very Short Introduction
‘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 ...
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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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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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2. Characteristica universalis, logical calculus, and mathematics
Maria Rosa Antognazza
in Leibniz: A Very Short Introduction
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 ...
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