Chapters and Appendices

Book Entrance

B  How to Learn
C. How to Read
D. What to do in School
PS. Study Tips
PS: Time and Effort
E. How to Study Math and Why

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

PS: How To Improve Learning

Previous: How to Study Math and Why

1. Adopt some goals or aims for your learning. Seek and find a reason, approximately correct, for studying a subject.  Reasons may be as crude as improving marks, or more fundamental.  Ask your instructors for reason approximately correct for studying a subject, or topics in it.  That may provide a context and motivation for learning. That being said,  a teacher saying a topic is required because of the final examinations or course requirement could be giving a full and honest answer. But in general we hope you and your teachers can find reasons and a context approximately correct for most topics in a course.
   

2. Mathematics mastery is best checked and proven on paper. As in English, apart from a few mistakes,  if we do not write exactly what we mean, we do not understand what we are writing and most likely what we are reading. Precision reading and writing, are musts for better study skills in all subjects, mathematics included. 
   

3. If one explanation here or elsewhere is not to your liking, hard or nonsensical, try again and try another here or elsewhere, alone or with help 
   
   Variety in the presentation and development of ideas means if one explanation here or elsewhere is not to your liking, another might be. Different people have different likes and dislikes.  Another explanation, written or in person,  could  be clearer. Different authors and different teachers all provide different ways to learn or introduce ideas and skills.  So again,  if one explanation here or elsewhere is not to your liking, try another.  May will, stubbornness and patience be with you.
   

4. Know-how without know-why is incomplete in mathematics. Mastery of fraction sense and operations, mastery of logic, mastery of algebra and mastery of geometry may help at home and work in money problems and in construction or maintenance problems. The know-why part of  mathematics  provides stories or theories to follow, one at a time and one after another, some independently, to  provide a greater context for know-how not only in mathematics but also in other quantitative disciplines. 
   

5. For skill and knowledge perfection,  ask your teachers or tutors to encourage you, say what you are doing right, but also ask  that all errors in your written work, concept and notation,  be caught and corrected.  Errors need to be corrected. Otherwise, they return  to slow or stop instruction. 
   

6. In each subject, you may further  focus your studies with the question: how can I transfer or teach to others the skills and concepts I am learning? A subject is not fully understood until you can explain it clearly and directly. 

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