Download Available for adoption from JOHNS HOPKINS UNIVERSITY PRESS

Available for adoption from
JOHNS HOPKINS UNIVERSITY PRESS
Algebra in Context
Introductory Algebra from Origins to Applications
Amy Shell-Gellasch, Montgomery College
J. B. Thoo, Yuba College
552 pp., 28 b&w illus., 12 line drawings, 9 maps
HC 978-1-4214-1728-8
September 2015 $99.50
An engaging new approach to teaching algebra that takes
students on a historical journey from its roots
to modern times.
This book’s unique approach to the teaching of mathematics lies in its use
of history to provide a framework for understanding algebra and related
fields. With Algebra in Context, students will soon discover why mathematics is such a crucial part not only of civilization but also of everyday life.
Even those who have avoided mathematics for years will find the historical stories both inviting and gripping.
Features:
— There is no other text that covers the material in college algebra that use
the history of mathematics as the vehicle to impart this material
—Classroom tested
—Keeps students engaged with a textbook that includes math woven
together with illustrations throughout history
—Exercises included at the end of every section
—An innovative alternative to teaching standard quantitative literacy
Request an exam copy: http://bit.ly/JHUPExamCopies
press.jhu.edu
Contents
Prefaceix
Introductionxv
Part I Numeration Systems
1
1 Number Bases
1.1 Base 6
1.2 Base 4
3
5
8
2 Babylonian Number System
11
2.1Cuneiform
2.2 Mathematical Texts
2.3 Number System
12
13
15
3 Egyptian and Roman Number Systems
21
3.1Egyptian
21
3.1.1 History
21
3.1.2 Writing and Mathematics 22
3.1.3 Number System
24
3.2Roman
27
3.2.1 History
27
3.2.2 Number System
29
4 Chinese Number System
4.1 History and Mathematics
4.2 Rod Numerals
35
35
37
5
41
42
44
44
49
Mayan Number System
5.1Calendar
5.2Codices
5.3 Number System
5.4 Native North Americans
6 Indo-Arabic Number System
6.1 India
6.1.1 History
6.1.2 Mathematics
6.2 The Middle East
6.2.1 History
6.2.2 Mathematics
6.3 Number System
6.3.1 Whole Numbers
6.3.2 Fractions
51
51
52
53
55
55
59
60
64
66
7 Exercises
73
Part II Arithmetic Snapshots
87
8 Addition and Subtraction
89
9Multiplication
9.1 Roman Abacus
9.2 Grating or Lattice Method
¯ and Chinese
9.3 Ibn Labban
Counting Board
9.4 Egyptian Doubling Method
95
95
97
98
100
10Division
10.1Egyptian
10.2 Leonardo of Pisa
10.3 Galley or Scratch Method
105
105
107
113
11 Casting Out Nines
117
12 Finding Square Roots
12.1 Heron of Alexandria 12.2 Theon of Alexandria
a i Manuscript
12.3 Bakhsh¯l¯
12.4 Nicolas Chuquet
121
122
124
129
131
13 Exercises
135
Part III Foundations
141
14 Sets
143
14.1 Set Relations
146
14.2 Finding 2n152
14.3 One-to-One Correspondence
and Cardinality
154
15 Rational, Irrational, and Real Numbers
159
15.1 Commensurable and Incommensurable Magnitudes 162
15.2 Rational Numbers
163
15.3 Irrational Numbers
168
15.4 I Is Uncountably Infinite
174
15.5 card(Q), card(I), and card(R)
177
15.6 Transfinite Numbers
179
16Logic
183
17 The Higher Arithmetic
197
17.1 Early Greek Elementary
Number Theory
198
17.1.1 Pythagoras
199
17.1.2 Euclid
200
17.1.3 Nicomachus and
Diophantus
202
17.2 Even and Odd Numbers
203
17.3 Figurate Numbers
207
17.3.1 Triangular Numbers
207
17.3.2 Square Numbers
208
17.3.3 Rectangular Numbers
210
17.3.4 Other Figurate Numbers 213
17.4 Pythagorean Triples 214
17.5 Divisors, Common Factors,
and Common Multiples 220
17.5.1 Factors and Multiples
220
17.5.2 Euclid’s Algorithm
223
17.5.3MultipleS
233
17.6 Prime Numbers
238
17.6.1 The Sieve of Eratosthenes240
17.6.2 The Fundamental Theorem
of Arithmetic
242
17.6.3 Perfect Numbers
248
17.6.4 Friendly Numbers 252
18 Exercises
253
Part IV Solving Equations
265
19 Linear Problems
19.1 Review of Linear Equations 19.2 False Position
19.3 Double False Position
267
270
273
284
20 Quadratic Problems
301
20.1 Solving Quadratic Equations
by Completing the Square
302
20.1.1Babylonian
304
20.1.2Arabic
312
20.1.3Indian
320
20.1.4 The Quadratic Formula
326
20.2 Polynomial Equations in One Variable
335
20.2.1Powers
337
20.2.2nth Roots
345
20.3 Continued Fractions
356
20.3.1 Finite Simple Continued
Fractions
359
20.3.2 Infinite Simple Continued Fractions
360
20.3.3 The Number 0
369
21 Cubic Equations and
Complex Numbers
21.1 Complex Numbers 21.2 Solving Cubic Equations
and the Cubic Formula
375
377
395
22 Polynomial Equations
415
22.1 Relation between Roots and Coefficients
416
22.2 Viète and Harriot 419
22.3 Zeros of a Polynomial
424
22.3.1 Factoring 424
22.3.2 Descartes’s Rule of Signs 434
22.4 The Fundamental Theorem
of Algebra
436
23 Rule of Three 23.1China
23.2 India
23.3 Medieval Europe
23.4 The Rule of Three in False
Position 23.5 Direct Variation, Inverse
Variation, and Modeling 439
439
442
446
447
450
24Logarithms
461
24.1 Logarithms Today
470
24.2 Properties of Logarithms
472
24.3 Bases of a Logarithm
475
24.3.1 Using a Calculator
476
24.3.2 Comparing Logarithms
478
24.4 Logarithm to the Base e
and Applications 480
24.4.1 Compound Interest
484
24.4.2Amortization
491
24.4.3 Exponential Growth and
Decay
494
24.5 Logarithm to the Base 10 and Application to Earthquakes
499
25 Exercises 505
Bibliography 521
Index
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