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Appetizers and Lessons for Mathematics and Reason
  online logic chapters  - the best starting point for further site exploration.  Bon Appetite.

Knowledge & Story Telling
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Pattern
Based
Reason
Volume 1A
Printed in Canada
ISBN 0-9697564-5-3

Volume 1 = 1A+1B
bounded together







Foreword
PS. Three Remark
1. What is reason
2. Inductive Ed Principles
2. Communication
3. Elements of Reason
4. Implication Rules [10]
5. Hype & Deception
5. Hype & Ethics
6. Chains of Reason [4]
7.  Longer Chains of Reason
7. Mathematical Induction
8. Language Change [2]
9. Next Chapters, About.
10. Limits to Freedom [2]
11. Accidental Patterns
12. Two Analogies
12.  Knowledge Islands
13. Euclidean Model
13. Euclidean Reason
14 Math: Deductive/Empirical [6]
15. Objectivity
15. Objectivity, More
16 Rules-Patterns Origins [10]
Knowledge & Story Telling
17. Objective Ways
17. Trial & Error Discovery
18. Conciousness
19. Symbols & Logic
20. Pronouns & Symbols
21. Truth Tables I. [3]
22. Contrapositive
22. Vacuously True
24. Indirect Reason More
24PS. Excluded Middle Law
24PS.  Proof by Absurdity
PS. Reality vs Imagination
PS. Ahistorical Logic
Links Elsewhere - Go GoGo
Book Entrance

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
+History Lost or Missing

Would you like to show yourself or others how to be algebra power users? Professor WhySlopes shouts his methods for algebra skill development are likely to work. Try them. They are different.

Postscript (5th October, 2009):   The ability to tell, invent and follow stories is transformed in education and research into the ability  to tell, invent and follow explanations and instructions as a  means to enrich, advance and provide a context for observable skill development, and a means to share what is the mind. In essence telling stories, one step at a time, and one step after another (in order perhaps) is the key to knowledge of folklore, culture and technical knowledge. We may judge stories as fictional or not, to greater or lessor extent.  We judge the consistency of stories in accordance with our knowledge or view of what is possible or allowable. So a good alibi allows a detective to ease or remove suspicions about who committed a action.  In writing or inventing a story, an author will attempt to avoid immediate or implied inconsistencies.  What Louis Carroll's Alice sees in Wonderland or Through the Looking Glass provides an story to follow, one that is not realistic. Shakespeare and Moliere through their writing create pieces of fiction for us to follow on paper or even to act out. We may judge the characters and plots in stories and plays by our own ideas on what is not possible.  But in telling stories, the tellers provide us with a imaginary world to follow and judge. Likewise in telling theories or providing instructions for the operation of a machine or the creation of a product,  researchers and teachers are telling us stories, ones that may correspond to and be useful in practice. The composers of a story may adhere to rules and criteria for consistency, rules and criteria that say what is or should be possible or not, in order to decide or conclude what may be in the story or not.  Chains of reason may be employed to find what a story implies or requires. The composer may include or not,  those implications or requirements in the telling and extension  of a story or theory.  

The developers of empirical theories in science and technology tell many small technical stories which individually work and are practice in special cases, but not necessarily in all cases.  High school and college chemistry for example include alternative theories for the identification of acids, salts and bases.   The oxymoron acid-salt reflects the idea that what is an salt in one theory is an acid according to another (a litmus paper test say).  

See the online logic postscripts to learn more.  Good luck.

 

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1. Arithmetic   2. Algebra   3.  More Algebra  4.  Geometry 5 More Geometry 6.  Calculus
>> densely written 
>> use as skill checklists

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

Site Topics/Sections 

 1. Decimal Arith - Video Based ]
2   Fractions  
3.  Fractions  with Units  
3. Solving Linear Equations  - 
making alg easier
4. Formulas forwards & Backwards - unifying theme for Algebra
5.  Proportionality, Back- & For-wards - theme at work.
6.  Logic - Math Free, good for precision in  work & studies 
7. Euclidean-Geometry  (leanly)
8. Slopes and Lines 
9. Why Study Slopes - a context 
10.  Quadratics
11  Polynomials
12  Factored Polys - a context
13 Functions - For-& Back -wards
14  Number Theory, Richly
15. Exponents, Radicals & logs.  
16   Calculus - Examples & Advice 
17.   Real  Analysis 
18  Electric Circuits Etc (So So)
19 Maps, Similarity & Trig, (alt view)
20 Complex numbers  

21 Logic with Symbols+truth tables

22  Consistent Story Telling
23. Even More Logic

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