Three Skills
For
Algebra
Volume 2
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Vol 2, Three
Skills for Algebra covers many topics in algebra
and logic that students starting calculus should have mastered or will
have to master. Also includes arithmetic review problems to catch common
mistakes of students starting calculus. A fourth skill in this
misnamed volume gives a unifying theme for high school maths.
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Chapters and Appendices
Book Entrance
Variation between Examples
Variation of Letters
When does a letter denote a variable
Cases of Double Variation
Three Notions of a Variable
Constants
Talking about numbers
Dependent or Independent Variables
Foreword
1. Introduction
2. Implication Rules [4]
3. Chains of Reason [3]
4. Induction Mathematical
4. Romeo and Juliet
6 Old Language
5 Knowledge Islands [2]
7 Arith Skill Check [4 X 2]
Arith Webvideos
7. The Next Chapters
8 The Three Skills
8 VNR-Concise-Encyclopedia
PS. What is a Variable [8]
9. Algebra Talk [7]
10 Two More Skills[5]
11 Why Shorthand
12 Shorthand Usage [10]
13 What's Next
PS: The 4-th Skill For Algebra
14 Compound Interest [6]
15 Linear Equations [5]
16 Painless Proofs
17 Pythagoras
PS I. Distributive Law
PS II. Polynomials
18 Rules of Algebra [20]
19 Functions & Sets
20 Degrees & Radians
21 What's Next
22. Arith & Geometric Sums [2]
23 Summation Notation
24 Your Money [3]
25 Induction & Recursion [4]
26 What's Next
27 Pronouns in Logic
28 Occurrence Tables
29 Contrapositive
30 Truth Tables
31 Indirect Reason
Pathways for Learning
Would you like to show yourself or others how to be algebra
power users?
What is a Variable?
Introduction
Variation between Examples
Variation of Letters
A letter denotes a variable
Cases of Double Variation
Three Notions of a Variable
Constants, Parameters
& Variables
Talking about numbers
Dependent
or Independent
Variable, a Matter of Choice
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Dependent or Independent Variables,
A Matter of Choice
The area A of a rectangle is given by the product of its dimensions, say
width W and length L. In algebraic shorthand notation
A = WL
That being said, if we choose to calculate A from the values of W and L, then
A will be called the dependent quantity or variable while W and L will be called
the independent variables or quantities. On the other hand, we choose to compute
W in the equation A = WL from the values of A and L, then W = A/L and we will
call W the dependent variable and will we call A and L the independent
variables. So which variable is dependent or not depends on how we choose to use
a formula, or which ones we choose to give or calculate. If we are situation
where we know A = WL but we do not know which will be given and which will
be given, we cannot say which one will be dependent, albeit the form A = WL
suggests A will be the dependent variable. What we can say for sure or
certain is the the equation A = WL links or relates the area, width and area of
a given rectangle. The set theoretic view or codification of a relation
will be given below.
Postscript - Another Reading Guide
Arithmetic and algebraic expressions and formulas are like pictures better
read in silence than spoken aloud. That situation has led to a lack of words
in mathematics. The Discussion of Three Skills for Algebra in Chapter
8 to 12 provide a wordy, or too wordy remedy. See how much you swallow
today, and return for the rest to perfect your skills and comprehension later.
Note too, further skills for algebra, a fourth and/or fifth appear in Chapter
14. That chapter introduces two unifying themes for secondary school
mathematics:
- The forward and backward use of almost all formulas and equations (those
in function form y = something)
- The connection between arithmetic (or numerical) solution and algebraic
solution methods in the backward use of formulas and equations. If you
understand the algebraic solution, you are halfway to understanding the full
strength use of algebra in senior high school mathematics and
calculus.
So now, read on and get a headstart or catch-up for
high school mathematics and/or calculus. Good luck.
See too Chapter 7 with its Arithmetic Skill Check
for Calculus and Pre-calculus Students - Is your arithmetic precise and
efficient?
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Online Volumes (orders)
1, Elements of
Reason. 1996
1A. Pattern
Based Reason 1995
1B. Math
Curriculum Notes 1996
2. Three
Skills for Algebra 1995
3 .Why.Slopes.&.More.Math.1995
Math
How-TOs etc 2008
1. Arithmetic
2. Algebra
3. More
Algebra
4. Geometry
5. More
Geometry
6. Calculus
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Flash Videos 11-2008
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9 Calculus
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10..Real
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11 Electric
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