eBook Math Explained: The Britannica Guide to Numbers and Measurement, 1st Edition

  • Published By:
  • ISBN-10: 1615302182
  • ISBN-13: 9781615302185
  • DDC: 512.7
  • Grade Level Range: 9th Grade - 12th Grade
  • 288 Pages | eBook
  • Original Copyright 2011 | Published/Released April 2012
  • This publication's content originally published in print form: 2011
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About

Overview

Communication and, indeed, our comprehension of the world in general are largely ordered by the number and measurement systems that have arisen over time. This book delves into the history of mathematical reasoning and the progression of numerical thought around the world. With detailed biographies of seminal thinkers and theorists, readers develop a sophisticated understanding of some of the most fundamental arithmetical concepts as well as the individuals who established them.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
Contents.
Introduction.
1: Numbers.
2: Numerals and Numeral Systems.
3: Number Bases.
4: Numeral Systems.
5: Development of Modern Numerals and Numeral Systems.
6: Arithmetic.
7: Fundamental Definitions and Laws.
8: Theory of Divisors.
9: Modular Arithmetic.
10: Logarithms.
11: Number Theory.
12: From Prehistory Through Classical Greece.
13: Number Theory in the East.
14: Modern Number Theory.
15: Unsolved Problems.
16: Set Theory.
17: Introduction to Naive Set Theory.
18: Axiomatic Set Theory.
19: Great Arithmeticians and Number Theorists.
20: The Ancient World.
21: Aryabhata I.
22: Diophantus of Alexandria.
23: Muḥammad IBN Mūsā Al-Khwārizmī.
24: Nicomachus of Gerasa.
25: Leonardo Pisano.
26: Qin Jiushao.
27: Renaissance Europe.
28: Henry Briggs.
29: Joost Bürgi.
30: Pierre de Fermat.
31: Carl Friedrich Gauss.
32: Christian Goldbach.
33: Marin Mersenne.
34: John Napier.
35: The Modern Era.
36: Paul Isaak Bernays.
37: Georg Cantor.
38: Paul Joseph Cohen.
39: Richard Dedekind.
40: Peter Gustav Lejeune Dirichlet.
41: Gottlob Frege.
42: Kurt Gödel.
43: Bertrand Russell.
44: Alan Mathison Turing.
45: Ivan Matveyevich Vinogradov.
46: John von Neumann.
47: Numerical Terms and Concepts.
48: Algorithm.
49: Arithmetic Function.
50: Associative Laws.
51: Axiom of Choice.
52: Binary Code.
53: Binary Number System.
54: Cantor's Theorem.
55: Chinese Remainder Theorem.
56: Church's Thesis.
57: Commutative Laws.
58: Complex Number.
59: Continuum Hypothesis.
60: Decimal Number System.
61: Decision Problem.
62: Dedekind Cut.
63: Diophantine Equation.
64: Dirichlet's Theorem.
65: Distributive Law.
66: Equivalence Relation.
67: Euclidean Algorithm.
68: Euclid's Twin Prime Conjecture.
69: Factor.
70: Factorial.
71: Fermat Prime.
72: Fermat's Last Theorem.
73: Fermat's Little Theorem.
74: Fibonacci Numbers.
75: Fraction.
76: Fundamental Theorem of Arithmetic.
77: Geometric Series.
78: Goldbach Conjecture.
79: Harmonic Sequence.
80: Imaginary Number.
81: Incompleteness Theorems.
82: Inequality.
83: Infinite Series.
84: Infinity.
85: Integer.
86: Lagrange's Four-Square Theorem.
87: Mersenne Number.
88: Number.
89: Perfect Number.
90: Prime.
91: Prime Number Theorem.
92: Pseudoprime.
93: Rational Number.
94: Real Number.
95: Riemann Zeta Function.
96: Root.
97: Russell's Paradox.
98: Set.
99: Square Root.
100: Transfinite Number.
101: Transitive Law.
102: Turing Machine.
103: Vinogradov's Theorem.
104: Waring's Problem.
105: Wilson's Theorem.
106: Zorn's Lemma.
107: Measurements.
108: Measurement Systems.
109: Early Units and Standards.
110: The English and U.S. Customary Systems of Weights and Measures.
111: The Metric System of Measurement.
112: Measurement Instruments and Systems.
113: Measurement Theory.
114: Measurement Pioneers.
115: Norman Robert Campbell.
116: Anders Celsius.
117: Giovanni Giorgi.
118: Edmund Gunter.
119: Joseph-Louis Lagrange.
120: Pierre-Simon Laplace.
121: Pierre Mechain.
122: Jesse Ramsden.
123: Measurement Terms and Concepts.
124: Acre.
125: Amphora.
126: Angstrom (Å).
127: Apothecaries' Weight.
128: Are.
129: Avoirdupois Weight.
130: Barrel.
131: Bat.
132: British Imperial System.
133: Bushel.
134: Centimetre (cm).
135: Cord.
136: Cubit.
137: Cup.
138: Dram.
139: Fathom.
140: Finger.
141: Foot.
142: Furlong.
143: Gal.
144: Gill.
145: Grain.
146: Gram (gm or g).
147: Gunter's Chain.
148: Hand.
149: Hectare.
150: Inch.
151: International Bureau of Weights and Measures.
152: International System of Units.
153: International Unit (IU).
154: Kilometre (km).
155: Knot.
156: League.
157: Libra.
158: Litre (L).
159: Log.
160: Metre.
161: Metrētēs.
162: Metric System.
163: Micrometre.
164: Mile.
165: Millimetre (mm).
166: Mina.
167: Mou.
168: Ounce.
169: Peck.
170: Pint.
171: Pound.
172: Qa.
173: Quart.
174: Rod.
175: Scruple.
176: Shi.
177: Steradian.
178: Stere.
179: Stone.
180: Talent.
181: Ton.
182: Troy Weight.
183: Zhang.
Glossary.
Bibliography.
Index.