Parents: Help your child or teen

Online Volumes (Book 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

More Site Areas 
1.  Solving Linear Equations  2005
2.-Fractions-Rates-Proportns-Units-2006
3.  Algebra, Odds & Ends, HS level-2001
4.-Euclidean-Geometry/Complex No.s 
5.  Analytic Geometry/Functions 2006
6.  Number Theory. 2006-7
7.  Complex Numbers More 2001
8.  Calculus Introduction 2005
More Site Areas 
9   Real  Analysis 1995
10. Secondary IV? maths 2006-7
11. Math Education Essays  2006-7
12. LaTeX2HotEqn: 2004
13. Electric Circuits Etc  2007
14. Quebec Math Education 2004
15-Prequel-to-the-How-TOs-06-2008
How TOs/ Ref.-08- 2008
1. Arithmetic Reference
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus
7. Logics in Maths


Employ an online or offline tutor at your own risk from 

AU:  tutorfinder.com.au
CDN :  findatutor.ca 
CDN: .i-tutor.ca
CDN: Montreal Tutors
NZ:   findatutor.co.nz
UK:   tutorhunt.com 
UK:  tutors4me.co.uk
USA:  wiziq.com
USA: ziizoo.com

YOU are better than YOU think. Show yourself  how:

      |      
//  _   _ \\
/\             /\
  <|  (o)   (o)   |> 
 \     | |      / 

 For better work & study skills, read logic chapters 1 to 5  in  Three Skills for Algebra. Sooner is better. Good luck.

 -/[]\- 
||
   / \_ 
 ||||||||||||||||||||||||||||


 Logic Mastery
 Amazing, Amusing, Amorous,  Delicious, Delightful, Edifying, Strengthening Elixir. 
It eases work & learning difficulties Makes the hard easier. Opens eyes. Leads to greater precision.
in reading and writing

Do not leave here without it -  Logic mastery  will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.

   |      
//  _   _ \\
/\             /\
<|   (o)   (o)  |> 
     | |     |
   \             /   
\    =   /

Caution: Site advice is approximately correct, for some circumstances, not all. Site How-TOs are logically developed, but not tried and tested. That leaves room for thought and refinement..

 -/[]\- 
||
  _ / \     
 ||||||||||||||||||||||||||||
 

After logic  (a) continue reading Three Skills for Algebra, chapters 8 to 14  and do so alongside site area on solving linear2007 Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes  & More Math, chapters 2 to 6;


For online automated help in senior high school maths & calculus, visit  quickmath.com  For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com  With  overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck.


Explore collaborative whiteboards from groupboardtwiddla  or scriblink.


Chains of Reason
Chapter 6

Previous: Chapter 5, Deception

This chapter shows how reliable rules and patterns can be directly employed one at a time, or one after another, to get conclusions or further reliable rules and patterns. The question of what rules are reliable is considered in the following chapters.

Rules used to get or suggest conclusions are called implications. Just as there are methods for adding and multiplying numbers carefully, there are also methods for using implication rules by themselves to get conclusions. There are also methods for linking, threading and chaining implication rules together to get more implication rules. This chapter uses examples to explain two basic ideas:

  1. how to directly use a single implication rule to get conclusions, and
  2. how to link, chain or thread implication rules together to obtain or derive more rules and more conclusions.

The examples are not important (and are perhaps ridiculous) but they illustrate some rule-based methods in reason. Examples which involved real-life situations might distract from mastering these methods. That is, in real-life situations, each of us may have opinions or prejudices about what should occur. That could spoil an explanation of the use and linkage of implication rules. There is a need for neutral examples to illustrate the use of implication rules one at a time or one after another.

Arithmetic, algebra and geometry give many neutral examples for this. The examples below involve no mathematics. Bon Appetite.

Chapter Subsections: Direct and Indirect Usage of a Single Rule ] Linking and Chaining Two Rules Together ] Linking and Chaining Several Rules Together ] Deductive, Inductive or Empirical Reason ] Chapter 6, Chains of Reason (Deductive Reason), Pattern Based Reason ] Linking and Chaining ] Putting Several Rules Together ] Deductive ]

Next: Direct and Indirect Usage of a Single Rule

 

www.whyslopes.com
Volume 1A, Pattern Based Reason

 Chapters 1 to 24

FOREWORD
Three Remarks

1 Introduction
2 Communication
3. Elements of Reason
4 Implication Rules
5. Deception
6 Chains of Reason
7 Longer Chains
For & From Consistency
8. Language Change
9 Next Chapters
10 Responsibility
11 Accidental Patterns
12 Knowledge Islands
13 Euclidean Logic
14 Deductive & Empirical 
     Views of Mathematics

15 Objectivity
16 Origin of Rules
and Patterns
17 Objective Ways

18. Waking up
19. Symbols  & Logic
20. Pronouns or Symbols
21. Truth Tables I.
22. Truth Tables II
22. Biconditional
22. Contrapositive
23. IF-THEN table
24. Indirect Reason Again

To reason often means to persuade someone of the need for an idea or action. That someone could be yourself. So be careful.

1A Logic Postscripts
- online only

+Proof by Absurdity alias proof by contradiction
+How the demand for consistency supports the law of the excluded middle
+Reality versus or with the aid of Imagination
+Links for reason, logic and crtical thinking
+Three Remarks
+History Lost or Missing

There is a difference between
knowing how to spend money,
and having money to spend.

There is likewise a difference
between mastering a skill
and having meeting a situation in which it applies.

 



 


 .


[Page Top] Back ] Area Intro ] Next ] 
If you find an error, please cut and paste its  web page location (URL) into an Email

Wordy Site Tour:  Not too Bad Vol 2. Foreword 1A Foreword2  Logic Puzzles,  
What is a Variable
  Calculus Starter Guide  Vol 1 Foreword,  
 
 
Favourite Sites
The World Clock - Time Zones Around the World  
 BBC News  and mathematics portion of  English National Curriculum  

All trademarks and copyrights on this page are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster. 
The Rest © 1995 onward by site author,   Alan Selby
All Rights Reserved.