| Introduction |
|
ix | |
|
|
|
1 | (8) |
|
|
|
3 | (6) |
|
|
|
6 | (3) |
|
|
|
9 | (18) |
|
Forward, or Backward to Elementary Mathematics? |
|
|
11 | (16) |
|
The Meaning of the Arithmetic Operations |
|
|
13 | (1) |
|
|
|
14 | (1) |
|
|
|
15 | (2) |
|
|
|
17 | (1) |
|
Discrete and Continuous Quantities |
|
|
18 | (1) |
|
|
|
18 | (2) |
|
|
|
20 | (2) |
|
Expansion and Reduction of Fractions |
|
|
22 | (1) |
|
|
|
23 | (4) |
|
|
|
27 | (22) |
|
|
|
29 | (20) |
|
Meanings of Directed Numbers |
|
|
32 | (4) |
|
Operations with Directed Numbers |
|
|
36 | (4) |
|
The Order Among Directed Numbers |
|
|
40 | (1) |
|
The Directed Numbers on the Real Line |
|
|
41 | (1) |
|
|
|
41 | (3) |
|
Multiplication and Division of Directed Numbers |
|
|
44 | (2) |
|
|
|
46 | (3) |
|
|
|
49 | (18) |
|
|
|
51 | (16) |
|
Opening Boxes --- Distributivity |
|
|
55 | (2) |
|
Birds of a Feather Flock Together |
|
|
57 | (1) |
|
Opening Up Two Pairs of Brackets |
|
|
57 | (1) |
|
|
|
58 | (2) |
|
|
|
60 | (2) |
|
An Application to Geometry |
|
|
62 | (3) |
|
A Bit Beyond: Newton's Binomial Formula |
|
|
65 | (2) |
|
|
|
67 | (20) |
|
|
|
69 | (18) |
|
|
|
70 | (6) |
|
|
|
76 | (3) |
|
|
|
79 | (5) |
|
|
|
84 | (3) |
|
|
|
87 | (12) |
|
Equations: Going Back to Where You Started |
|
|
89 | (10) |
|
Equations with Two Operations |
|
|
94 | (1) |
|
|
|
94 | (2) |
|
|
|
96 | (3) |
|
|
|
99 | (14) |
|
Similarity and Proportion |
|
|
101 | (12) |
|
|
|
107 | (1) |
|
|
|
108 | (5) |
|
|
|
113 | (10) |
|
|
|
115 | (8) |
|
|
|
118 | (5) |
|
|
|
123 | (30) |
|
When Algebra Meets Geometry |
|
|
125 | (28) |
|
|
|
132 | (8) |
|
|
|
140 | (4) |
|
Ascending and Descending Functions |
|
|
144 | (1) |
|
Admonition: A Function is Not its Graph |
|
|
145 | (1) |
|
Functions Defined Separately in Different Domains |
|
|
146 | (1) |
|
|
|
147 | (1) |
|
|
|
148 | (5) |
|
|
|
153 | (10) |
|
Arithmetic Sequences and Their Sums |
|
|
155 | (8) |
|
|
|
157 | (6) |
|
|
|
163 | (10) |
|
|
|
165 | (8) |
|
|
|
168 | (5) |
|
|
|
173 | (14) |
|
Equations with Two Unknowns |
|
|
175 | (12) |
|
|
|
176 | (3) |
|
A Second Method: Expressing One Variable in Terms of the Other |
|
|
179 | (1) |
|
The Number of Solutions of a System of Linear Equations |
|
|
180 | (4) |
|
A Bit Beyond --- Determinants |
|
|
184 | (3) |
|
|
|
187 | (24) |
|
Quadratic Equations and Quadratic Expressions |
|
|
189 | (22) |
|
|
|
193 | (2) |
|
|
|
195 | (5) |
|
|
|
200 | (11) |
|
|
|
211 | (10) |
|
|
|
213 | (8) |
|
|
|
216 | (1) |
|
Inequalities Involving Absolute Value |
|
|
217 | (4) |
|
|
|
221 | |
|
|
|
223 | |
|
The Sum of a Geometric Sequence |
|
|
225 | |
