Key Appetizers and Lessons
(links to other parts of this site)

Below, you will links to further material in online books and other site folders. Bon Appetite.

For Better Study Skills	First Steps in Logic	Arithmetic & Fractions
A Appendices B How to Learn C How to Read D What to do in School and Why E. How to Study Mathematics	1. Introduction 2. Implication Rules 3. Chains of Reason 4. Induction (Longer Chains) 5 Knowledge Islands Indirect Logic	Arithmetic WebVideos 7 Arithmetic Review Problems See Solving Equations with stick diagrams if your fraction skills and sense need improvement
If you plan to study calculus, do the Arithmetic Review Problems and have them corrected by another. Problems like these catch errors that slow or undo too many students entering calculus. Ouch.

Altogether, the logic chapters provide a unique mathematics-free introduction to the direct and indirect definition and rule-based thinking that appeared in Euclid's work a long time ago (2300 years ago)

First Steps in Algebra Proper Use of Equal Sign (Very Important)
8 The Three Skills 9 First Skill What is a Variables 10 Two More Skills 11 Why Shorthand 12 Shorthand Usage 13 What's Next 14 Compound Interest 15_Solving_Linear_Equations 16 Painless Proofs 17 Pythagoras	Fractions and Solving Equations with stick diagrams (spring 2005 postscript) -
	A. Letters & Lengths B. Stick Diagrams C. Beyond Sticks D..Almost One E. Binary Systems F. Larger Systems	Stick Diagram Examples 2x + 5 = 20 3x + 10 = 32 5a + 16 = 3a+ 24 (½)x + 8 = 24½ (¾)a + 16 = (¼)a+ 24 (¾)q + 17 = 32
	Stick diagrams give a visual introduction to algebra which develops fraction sense and skills. Try them before or besides chapter 15, Solving Linear Equations, whatever works
Teachers: Here some algebra lesson plans for the more effective development of the shorthand ways of writing and reasoning.

Finite Mathematics Prep for Calculus	Further Logic
21 What's Next 22. Geometric and Arithmetic Sums 23 Summation Notation 24 Investments, Loans, Pensions - Personal Money Calculations 25 Mathematical Induction and Recursion Proofs, Product Notation, & Factorial Notation	26 What's Next 27 Pronouns in Logic 28 Occurrence Tables 29 Contrapositive 30 Truth Tables 31 Indirect Reason	Some of this logic chapters may be used in the above treatment of analytic geometry.

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Professor Whyslopes:

Site value lies in the difference between its ideas and yours.
If one site explanation is not to your liking, try another. Each one is different.

Two gaps

The Old Algebra Gap: Algebra appears with too few words of explanation in high school and college mathematics. Online Volumes 2 and 3 offer remedies. Chapters 8 to 12 in Volume 2 put more words into the explanation and comprehension of algebra. Chapter 14 in Volume 2 with its explicit discussion of the direct and indirect use a formulas identifies a unifying theme for mathematics and logic - all rules and patterns will be used forward and backwards. Chapters 2 to 6 and 12 to 18 in Volume 3 may further ease or avoid the very challenging use of algebra in the high level mathematics: calculus. Calculus requires earlier high school mathematics at full strength: (i) This logically complete but long lesson on complex numbers shows how to simplify the senior high school exposition of circular trig functions upto to formulas in the plane for vectors dot and cross-products. The lesson provides the route that would have been taken in course design if the key element of the lesson, a December 2009 invention, had been available in the 1950s. For further algebra skill development. See the site coverage of fraction with units, proportionality, ratios and rates, polynomials, quadratics functions and straight line slopes and equations.
The Arithmetic Gap: An exact and efficient mastery of arithmetic with decimals and fractions is best (required) for the high level study of mathematics alone and in science, technology and business. Pages here on arithmetic with decimals and integers, on fractions and solving linear equations with fractional operations on stick diagrams may help fill the gap. That exact and efficient command should be obtained in the last years of primary school and the first years of secondary school.

Skill mastery in mathematics has to be seen to believed. To that end, learn or teach how-to write and draw the steps in mathematical figuring or reasoning clearly. Do not try to save space by doing a sequence of step in one place. Instead, do or record the steps in sequence on a separate lines to make each step obvious and verifiable.

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20 pages in French: Algèbre
Définition d'une variable
La raison basée sur les
règles et modelés

Parents: Help your Child/Teen Learn covers Speaking Skills, Reading & Writing, Preparing for Science & Having Patience, etc

Math How-TOs
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

Skill & Concept
Review or Development

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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Key Appetizers and Lessons (links to other parts of this site)

Two gaps

Key Appetizers and Lessons
(links to other parts of this site)