Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
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Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II


Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math
, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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44 matches:

  1.    wt: 5:   12 Webvideo Lessons on Area and Volume Calculation/
  2.    wt: 5:   5 Lessons on Integration/
  3.    wt: 5:   4 Lessons on Using Derivatives/
  4.    wt: 5:   38 Lessons on Calculating Derivatives/
  5.    wt: 5:   13 Lessons on Limits and Continuity/
  6.    wt: 4:   70 Calculus Starter Lessons/
  7.    wt: 3:   10 Examples of Algebraic Reasoning/
  8.    wt: 3:   4 Computation Rules and Function Notation/
  9.    wt: 2:   15 Arc or Inverse Trigonometric Function/
  10.    wt: 2:   8 Unit Circle Trigonometry/
  11.    wt: 2:   6 Trigonometry first steps/
  12.    wt: 2:   B Real Numbers Extrinsic Development/
  13.    wt: 2:   A Origins of Counting and Figuring Methods/
  14.    wt: 2:   9 Proportionality Backwards and Forwards/
  15.    wt: 2:   8 Unifying Theme For Algebra/
  16.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  17.    wt: 2:   6 More Less Greater Than Inequalities and Comparison/
  18.    wt: 2:   5 Real Numbers/
  19.    wt: 2:   Step 4 Gaussian Elimination/
  20.    wt: 2:   Step 3 Easy systems in 2 or more unknowns/
  21.    wt: 2:   Step 2 Algebraic solutions for one unknown/
  22.    wt: 2:   Step 1 Stick diagram and fractions/
  23.    wt: 2:   3 Solving Linear Equations/
  24.    wt: 2:   2 Formula Forward Use Evaluation/
  25.    wt: 2:   1 Working With Sets/
  26.    wt: 2:   Algebra Starter Lessons/
  27.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  28.    wt: 1:   2 Natural Logarithms Exponentials Powers Roots/
  29.    wt: 1:   14 Degrees to Radians and Radians to Degrees/
  30.    wt: 1:   13 Vectors/
  31.    wt: 1:   12 Function Translating and Rescaling/
  32.    wt: 1:   11 Parallel Straight Lines and Transversals/
  33.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  34.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  35.    wt: 1:   7 Complex Numbers/
  36.    wt: 1:   5 What is Similarity/
  37.    wt: 1:   4 Lines and Slopes Take 1/
  38.    wt: 1:   3 Cartesian and Polar Coordinates/
  39.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  40.    wt: 1:   1 Maps Plans Measurement/
  41.    wt: 1:   Geometry maps plans trigonometry vectors/
  42.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  43.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  44.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

125 matches:

  1.    wt: 3:   A Chain Rule Real Player video examples
  2.    wt: 3:   33 Chain Rule Real Player video examples
  3.    wt: 3:   25 Chain Rule Animated Examples Continued
  4.    wt: 3:   24 Chain Rule Animated Examples
  5.    wt: 2:   3 Two Chain Rule Method Exercises
  6.    wt: 2:   1 Chain Rule in Reverse Integration Method
  7.    wt: 2:   30Chain Rule A Proof
  8.    wt: 2:   29 Chain Rule Optional Reading
  9.    wt: 2:   28 Chain Rule Preparation for a Proof
  10.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  11.    wt: 2:   26 Chain Rule Recognising outer inner functions
  12.    wt: 2:   23 Chain Rule in general
  13.    wt: 2:   22 Chain Rule for polynomials
  14.    wt: 2:   21 Chain Rule for powers
  15.    wt: 2:   20 Chain Rule for Pulley Systems
  16.    wt: 2:   19 Chain Rule for linear functions
  17.    wt: 2:   18 Chain Rule Introduction
  18.    wt: 2:   12 Quotient rule examples
  19.    wt: 2:   6 Power rule from product rule
  20.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  21.    wt: 2:   Chapter 3 Algebra Starter Lessons
  22.    wt: 1:   Skills Chapter 5 Calculus
  23.    wt: 1:   5 logarithms and exponentials etc
  24.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  25.    wt: 1:   chapitre 06 00 Chaines de la raison
  26.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  27.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  28.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  29.    wt: 1:   19 Horizontal line rule and method
  30.    wt: 1:   18 Vertical Line Rule and Method
  31.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  32.    wt: 1:   1 Calculator Starter Exercises
  33.    wt: 1:   7 Links Lessons Elsewhere
  34.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  35.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  36.    wt: 1:   31 basic secant cosecant cotangent trig identities
  37.    wt: 1:   30 unit circle calculation of six trigonometric functions
  38.    wt: 1:   17E Trig Formulas for dot and cross Products
  39.    wt: 1:   17A The complex number valued trig function cis
  40.    wt: 1:   Unit Circle Development of Trigonometry
  41.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  42.    wt: 1:   21 Logarithms Powers and Exponentials
  43.    wt: 1:   13 Trig Formulas for dot and cross Products
  44.    wt: 1:   9 The complex number valued trig function cis
  45.    wt: 1:   8 Unit Circle Development of Trigonometry
  46.    wt: 1:   7 Trignometric Ratios Unit Circle
  47.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  48.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  49.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  50.    wt: 1:   3 Trigonometric Ratios sine and cosine
  51.    wt: 1:   Why Trigonometry the whyslopes view
  52.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  53.    wt: 1:   12 Links Lessons elsewhere
  54.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  55.    wt: 1:   6 Ruler and compass Angle Bisection
  56.    wt: 1:   A Measurement with Ruler Proper Use
  57.    wt: 1:   7 Decimals Multiplication Methods Examples
  58.    wt: 1:   3 Proportionality Examples
  59.    wt: 1:   1 Equivalent Computation Rules
  60.    wt: 1:   2 Computation Rules Evaluation
  61.    wt: 1:   4 GE III Animated Examples
  62.    wt: 1:   1 GE Substitution four examples
  63.    wt: 1:   4 Four Examples Fractional Coefficients
  64.    wt: 1:   3 Four Examples
  65.    wt: 1:   2 Three Examples
  66.    wt: 1:   9 Three Examples
  67.    wt: 1:   7 Two Examples
  68.    wt: 1:   6 Three Examples
  69.    wt: 1:   5 Three Examples
  70.    wt: 1:   4 Two Examples
  71.    wt: 1:   3 Two Examples
  72.    wt: 1:   2 Three Examples
  73.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  74.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  75.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  76.    wt: 1:   4 Counting with Trees Product Rule Take I
  77.    wt: 1:   D Remainders Modulo 11 Pair Rule
  78.    wt: 1:   12 Adding Integers More Examples
  79.    wt: 1:   11 Adding Integers Formulas and Examples
  80.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  81.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  82.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  83.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  84.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  85.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  86.    wt: 1:   11 Efficient Square Rule Use
  87.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  88.    wt: 1:   5 Prime Factorization and a Square Rule
  89.    wt: 1:   1 Divsion Physical Examples
  90.    wt: 1:   2 Subtraction Easy Case Examples
  91.    wt: 1:   5. How to add decimals C. Examples
  92.    wt: 1:   A Related lessons in Volume 3
  93.    wt: 1:   11 Quotient rule
  94.    wt: 1:   10 Power rule for negative integers
  95.    wt: 1:   9 Reciprocal rule
  96.    wt: 1:   7 Animated Differentiation Examples
  97.    wt: 1:   5 Product Rule
  98.    wt: 1:   4 Sum Rule
  99.    wt: 1:   11 Limits at infinity Three Examples
  100.    wt: 1:   8 Four Animated Examples
  101.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  102.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  103.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  104.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  105.    wt: 1:   Chapter 23 Links To Trigonometry
  106.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  107.    wt: 1:   Chapter 9 About First Courses in Calculus
  108.    wt: 1:   Fall 1983 Calculus Appetizer
  109.    wt: 1:   Chapter 25. Mathematical Induction Examples
  110.    wt: 1:   Chapter 18. Rules for Algebra
  111.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  112.    wt: 1:   Chapter 4 Longer Chains of Reason
  113.    wt: 1:   Chapter 3 Chains of Reason
  114.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  115.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  116.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  117.    wt: 1:   Chapter 7 Longer Chains of Reason
  118.    wt: 1:   Chapter 6 Chains of Reason
  119.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  120.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  121.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  122.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  123.    wt: 1:   More Algebra and Slope based Calculus Preview
  124.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  125.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

578 matches:

  1.    wt: 8:   A Chain Rule Real Player video examples
  2.    wt: 8:   33 Chain Rule Real Player video examples
  3.    wt: 8:   25 Chain Rule Animated Examples Continued
  4.    wt: 8:   24 Chain Rule Animated Examples
  5.    wt: 7:   3 Two Chain Rule Method Exercises
  6.    wt: 7:   1 Chain Rule in Reverse Integration Method
  7.    wt: 7:   30Chain Rule A Proof
  8.    wt: 7:   29 Chain Rule Optional Reading
  9.    wt: 7:   28 Chain Rule Preparation for a Proof
  10.    wt: 7:   27 Chain Rule sinusoidal outer inner functions EGS
  11.    wt: 7:   26 Chain Rule Recognising outer inner functions
  12.    wt: 7:   23 Chain Rule in general
  13.    wt: 7:   22 Chain Rule for polynomials
  14.    wt: 7:   21 Chain Rule for powers
  15.    wt: 7:   20 Chain Rule for Pulley Systems
  16.    wt: 7:   19 Chain Rule for linear functions
  17.    wt: 7:   18 Chain Rule Introduction
  18.    wt: 7:   12 Quotient rule examples
  19.    wt: 7:   6 Power rule from product rule
  20.    wt: 6:   A Related lessons in Volume 3
  21.    wt: 6:   11 Quotient rule
  22.    wt: 6:   10 Power rule for negative integers
  23.    wt: 6:   9 Reciprocal rule
  24.    wt: 6:   7 Animated Differentiation Examples
  25.    wt: 6:   5 Product Rule
  26.    wt: 6:   4 Sum Rule
  27.    wt: 6:   11 Limits at infinity Three Examples
  28.    wt: 6:   8 Four Animated Examples
  29.    wt: 5:   Example 2 volume of a cone
  30.    wt: 5:   Example 1 volume of a pyramid
  31.    wt: 5:   Volume of Solid by Cross Sections Lesson
  32.    wt: 5:   Example 1. Area Between x and x squared
  33.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  34.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  35.    wt: 5:   Example 4 with x function of y
  36.    wt: 5:   Example 3
  37.    wt: 5:   Example 2
  38.    wt: 5:   Example 1
  39.    wt: 5:   Area Between Curves Lesson Take 2
  40.    wt: 5:   Area Between Curves Lesson Take 1
  41.    wt: 5:   Summary
  42.    wt: 5:   A Related Material in Volume 3
  43.    wt: 5:   5 Area Under Curve Exercise
  44.    wt: 5:   4 Definite Integrals Evaluation Exercises
  45.    wt: 5:   2 Indefinite Integrals Exercises
  46.    wt: 5:   4 Second derivative test exercise example
  47.    wt: 5:   3 Second derivative test
  48.    wt: 5:   2 Second derivative test prequel
  49.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  50.    wt: 5:   38 Formulas and derivatives for powers and roots
  51.    wt: 5:   36 Cube root derivative animated
  52.    wt: 5:   34 Derivative of exponential function
  53.    wt: 5:   31 Derivatives of inverse functions
  54.    wt: 5:   17 Derivatives of quotients of sine and cosine
  55.    wt: 5:   16 Derivatives of reciprocals of sine and cosine
  56.    wt: 5:   15 sine and cosine derivatives 3rd step
  57.    wt: 5:   14 sine and cosine derivatives 2nd step
  58.    wt: 5:   13 sine and cosine derivatives 1st step
  59.    wt: 5:   8 Differentiation of polynomials
  60.    wt: 5:   3 Motivation for Limit Definition Take 2
  61.    wt: 5:   2 Motivation for Limit Definition Take 1
  62.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  63.    wt: 5:   13 Limits with Parameters and Derivatives Take II
  64.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  65.    wt: 5:   10 Three one sided limits with infinite values
  66.    wt: 5:   9 Limits Continuity and Composition
  67.    wt: 5:   7 Evaluation by immediate or delayed substitution
  68.    wt: 5:   6 Continuity at a point
  69.    wt: 5:   5 Jumps and absence of unlimited error control
  70.    wt: 5:   4 Numerical properties
  71.    wt: 5:   3 Decimal insights for limits continuity convergence
  72.    wt: 5:   2 Algebraic codification
  73.    wt: 5:   1 Numerical introduction
  74.    wt: 4:   2 Computation Rules Evaluation
  75.    wt: 3:   31 basic secant cosecant cotangent trig identities
  76.    wt: 3:   30 unit circle calculation of six trigonometric functions
  77.    wt: 3:   17E Trig Formulas for dot and cross Products
  78.    wt: 3:   17A The complex number valued trig function cis
  79.    wt: 3:   Unit Circle Development of Trigonometry
  80.    wt: 3:   Right Triangle and Unit Circle Trigonometry
  81.    wt: 3:   7 Trignometric Ratios Unit Circle
  82.    wt: 3:   6 Trigonometry Sines of Supplementary Angles
  83.    wt: 3:   5 Trigonometric Ratios For Tangent and Special Triangles
  84.    wt: 3:   4 Trigonometric Ratios For Two Special Triangles
  85.    wt: 3:   3 Trigonometric Ratios sine and cosine
  86.    wt: 3:   Why Trigonometry the whyslopes view
  87.    wt: 3:   Right Triangle and Unit Circle Trigonometry
  88.    wt: 3:   7 Decimals Multiplication Methods Examples
  89.    wt: 3:   5 Areas of Rectangles Revisited
  90.    wt: 3:   4 Fraction Operations Axiomatic Development
  91.    wt: 3:   3 Inequalities Algebraically
  92.    wt: 3:   2 Fraction Operations Physical Development
  93.    wt: 3:   1 Decimals Modular and Remainder Arithmetic
  94.    wt: 3:   3 Proportionality Examples
  95.    wt: 3:   1 Equivalent Computation Rules
  96.    wt: 3:   5 Independent versus Dependent Variables
  97.    wt: 3:   4 Changing Letters
  98.    wt: 3:   3 Geometric Formulas and Function Notation
  99.    wt: 3:   1 Formulas Dependence and Function Notation
  100.    wt: 3:   4 GE III Animated Examples
  101.    wt: 3:   1 GE Substitution four examples
  102.    wt: 3:   4 Four Examples Fractional Coefficients
  103.    wt: 3:   3 Four Examples
  104.    wt: 3:   2 Three Examples
  105.    wt: 3:   9 Three Examples
  106.    wt: 3:   7 Two Examples
  107.    wt: 3:   6 Three Examples
  108.    wt: 3:   5 Three Examples
  109.    wt: 3:   4 Two Examples
  110.    wt: 3:   3 Two Examples
  111.    wt: 3:   2 Three Examples
  112.    wt: 2:   3 Natural Logarithms and Exponentials Basic Properties
  113.    wt: 2:   1 Calculator Starter Exercises
  114.    wt: 2:   16 cotangent function Definition Graph and Inverse
  115.    wt: 2:   15 cosecant function Definition Graph and Inverse
  116.    wt: 2:   14 secant function Definition Graph and Inverse
  117.    wt: 2:   13 cosecant function Definition Graph and Inverse
  118.    wt: 2:   12 motivation for term arctan
  119.    wt: 2:   11 arctan left inverse of tangent Graph
  120.    wt: 2:   10 arctan left inverse of tangent Definition
  121.    wt: 2:   9 motivation for name arcsin
  122.    wt: 2:   8 arcsin left inverse of sine Graph
  123.    wt: 2:   7 arcsin left inverse of sine Definition
  124.    wt: 2:   6 Graph of arccos function
  125.    wt: 2:   5 Swapping Coordinates is a reflection
  126.    wt: 2:   4 possible motivation for term arccos
  127.    wt: 2:   3 Left Inverse of cosine arccos definition
  128.    wt: 2:   2 cosine function more properties
  129.    wt: 2:   1 cosine function properties
  130.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  131.    wt: 2:   17 tangent function angle sum formulas
  132.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  133.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  134.    wt: 2:   33 sines and cosines of 2A 3A 4A 5A
  135.    wt: 2:   32 seven rows of pascals triangle
  136.    wt: 2:   29 secant cosecant and cotangent for acute angles
  137.    wt: 2:   28 Expressing products of sines cosines as sums
  138.    wt: 2:   27 Logarithmic use of products of sines and cosines
  139.    wt: 2:   26 Formulas for products of sines and cosines
  140.    wt: 2:   25 tangent double angle formula Slope connection
  141.    wt: 2:   24 tangent Angle Difference Formula
  142.    wt: 2:   23 sine and cosine of 180 plus 22.5 degrees
  143.    wt: 2:   22 sine of 22.5 degrees via half angle formulas
  144.    wt: 2:   21 sine and cosine Half Angle Formulas
  145.    wt: 2:   20 sine and cosine Double Angle Formulas
  146.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  147.    wt: 2:   18 sum of sinusoidal waves as a single wave
  148.    wt: 2:   17G Pythagorean Theorem Converse
  149.    wt: 2:   17F Law of cosines
  150.    wt: 2:   17D cis formulas for sine cosines and tangent
  151.    wt: 2:   17C sine and cosine double triple angle formulas
  152.    wt: 2:   17B sine cosine Angle Sum Formulas via cis
  153.    wt: 2:   16 Right Triangle Complementary Angle Relations
  154.    wt: 2:   15 sine cosine Complementary Angle Relations
  155.    wt: 2:   14 cosine even and sine and tangent are odd
  156.    wt: 2:   13 Graph of tangent function many periods
  157.    wt: 2:   12 Graph of tangent function for one period
  158.    wt: 2:   11 tangent function undefined when terminal side vertical
  159.    wt: 2:   10 Graphs of sines and cosines many periods
  160.    wt: 2:   9 Graphs of sine and cosine over one period
  161.    wt: 2:   8 period of tangent function
  162.    wt: 2:   7 period of sine and cosine
  163.    wt: 2:   6 sines and cosines for reference angle 30 degrees
  164.    wt: 2:   5 sines and cosines for reference angle 60 degrees
  165.    wt: 2:   4 sines and cosines for reference angle 45 degrees
  166.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  167.    wt: 2:   2 Quadrant I reference Angles
  168.    wt: 2:   1 Unit Points Reflections Rotations
  169.    wt: 2:   21 Logarithms Powers and Exponentials
  170.    wt: 2:   13 Trig Formulas for dot and cross Products
  171.    wt: 2:   9 The complex number valued trig function cis
  172.    wt: 2:   8 Unit Circle Development of Trigonometry
  173.    wt: 2:   8 Triangles Cascade Problem Solving
  174.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  175.    wt: 2:   1 Angle Measurement with Degrees
  176.    wt: 2:   12 Links Lessons elsewhere
  177.    wt: 2:   PS C Similarity Use Recognize it in Trigonometry
  178.    wt: 2:   6 Ruler and compass Angle Bisection
  179.    wt: 2:   A Measurement with Ruler Proper Use
  180.    wt: 2:   musings do not puiblish real numbers
  181.    wt: 2:   A Modular and Remainder Arithmetic
  182.    wt: 2:   A Signed Number Arithmetic Review
  183.    wt: 2:   26 More Less Greater Than Comparison
  184.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  185.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  186.    wt: 2:   23 Distributive Law Two Derivations
  187.    wt: 2:   22 Multiplication of Signed Numbers
  188.    wt: 2:   21 Addition of Multiples of a Single Vector
  189.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  190.    wt: 2:   19 Signed Multiples of Vectors
  191.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  192.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  193.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  194.    wt: 2:   15 Head to Tails in place Addition Associative
  195.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  196.    wt: 2:   13 Arrows and Vectors in a Plane
  197.    wt: 2:   12 Real Numbers Line Signed Coordinates
  198.    wt: 2:   11 Signed Number Addition and Addition Properties
  199.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  200.    wt: 2:   9 Division with Digits after Decimal Point
  201.    wt: 2:   8 Division and Mulplication of Compound Fractions
  202.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  203.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  204.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  205.    wt: 2:   4 Location of Point in Decimal Addition
  206.    wt: 2:   3 Location of Point in Decimal Multiplication
  207.    wt: 2:   2 Counting Digits in Decimal Multiplication
  208.    wt: 2:   1 Fractions with Finite Decimal Expansions
  209.    wt: 2:   E Long Division Methods more
  210.    wt: 2:   D Long Division Methods
  211.    wt: 2:   C Three Decimal Subtraction Methods
  212.    wt: 2:   B Decimal Comparison and Subtraction
  213.    wt: 2:   A Decimal Addition Columm Methods
  214.    wt: 2:   8 Column Multiplication Methods in General
  215.    wt: 2:   6 Column Methods for Decimal Multiplication
  216.    wt: 2:   5 Distributive Law for Whole Numbers
  217.    wt: 2:   4 Commutative Law Groups Counting Form
  218.    wt: 2:   3 Multiplicative Counting Skills Principles
  219.    wt: 2:   2 Combing Counts Addition Skills and Principles
  220.    wt: 2:   1 The Counting Origins of Numbers
  221.    wt: 2:   5 Proportionality in Equivalent Fractions
  222.    wt: 2:   4 Rates Ratios and Proporitionality
  223.    wt: 2:   2 Algebraic View
  224.    wt: 2:   1 What is Proportionality
  225.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  226.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  227.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  228.    wt: 2:   6 Compound Interest Forward and Backwards
  229.    wt: 2:   5 Triangle Area Formula Backwards
  230.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  231.    wt: 2:   3 Linear Equation Literal Solution More
  232.    wt: 2:   2 Linear Equation Literal Solution
  233.    wt: 2:   1 Changing Calculations
  234.    wt: 2:   6 Equations and Systems Equivalent or Implied
  235.    wt: 2:   5 Equality in Algebra
  236.    wt: 2:   4 Subtraction and Division Axioms
  237.    wt: 2:   3 Product Axioms Two Forms
  238.    wt: 2:   2 Addition and Multiplication Axioms
  239.    wt: 2:   5 Greater More Less Than Signs in General
  240.    wt: 2:   4 Comparison of Negative Numbers
  241.    wt: 2:   3 More and Less Than with Unlike Signs
  242.    wt: 2:   2 More and Less Than for Counts and Measures
  243.    wt: 2:   1 Real Numbers Comparison
  244.    wt: 2:   16 Real Numbers Comparison
  245.    wt: 2:   15 Real Number Division
  246.    wt: 2:   14 Real Number Multiplication
  247.    wt: 2:   13 Real Number Subtraction
  248.    wt: 2:   12 Real Number Additive Inverses or Negatives
  249.    wt: 2:   11 Real Number Addition
  250.    wt: 2:   10 Real Number Lengths and Signs
  251.    wt: 2:   9 Coordinates for Regions in Space
  252.    wt: 2:   8 Coordinates for Maps and Planes
  253.    wt: 2:   7 Real Numbers as Line Cordinates
  254.    wt: 2:   6 Unsigned Real Numbers
  255.    wt: 2:   5 Rational Numbers More
  256.    wt: 2:   4 Rational Numbers
  257.    wt: 2:   3 Fractions
  258.    wt: 2:   2 Integers
  259.    wt: 2:   1 Whole and Natural Numbers
  260.    wt: 2:   More Exercises
  261.    wt: 2:   Simple Exercises
  262.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  263.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  264.    wt: 2:   3 GE III Equation Addition and Multiplication
  265.    wt: 2:   2 GE II Comparison
  266.    wt: 2:   4 Solving a triangular system exercise
  267.    wt: 2:   3 Solving triangular system example
  268.    wt: 2:   2 Essentially one exercises three with solution
  269.    wt: 2:   1 Essentially One Unknown
  270.    wt: 2:   6 Algebraic Solution Example
  271.    wt: 2:   5 Algebraic Solutions Introduction
  272.    wt: 2:   1 Proper Equal Sign Usage
  273.    wt: 2:   Skill Development Notes
  274.    wt: 2:   10 One Example
  275.    wt: 2:   8 One Example
  276.    wt: 2:   Using Letters for Physical Quantities
  277.    wt: 2:   Formula Usage Show Work Format
  278.    wt: 2:   13 Naming Identifying Formulas with Words
  279.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  280.    wt: 2:   11 Volume of Sphere
  281.    wt: 2:   10 Volume of Pyramid
  282.    wt: 2:   9 Volume of Cone
  283.    wt: 2:   8 Compound Interest Formula Evaluation
  284.    wt: 2:   7 Compound Interest Formula Introduction
  285.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  286.    wt: 2:   5 Box Volume Formula Example
  287.    wt: 2:   4 Circle Area Formula Example
  288.    wt: 2:   3 Triangle Area Formula Example
  289.    wt: 2:   2 Another Rectangle Area Formula Example
  290.    wt: 2:   1 Written work formats for developing and showing skill
  291.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  292.    wt: 2:   9 Sets in Probability and Statistics
  293.    wt: 2:   8 Sets of Numbers
  294.    wt: 2:   7 Cautious or Safe Set Construction
  295.    wt: 2:   6 Power Set Notation
  296.    wt: 2:   5 Product Builder Notation
  297.    wt: 2:   4 Subset Builder Notation
  298.    wt: 2:   3 Counting with Sets etc
  299.    wt: 2:   2 Venn Diagrams
  300.    wt: 2:   1 Finite Sets
  301.    wt: 2:   6 Three Notions of What is a Variable
  302.    wt: 2:   5 Talking about Numbers and Quantities
  303.    wt: 2:   4 A Brief Story of numbers and algebra
  304.    wt: 2:   3 Adding Words To Arithmetic
  305.    wt: 2:   2 What is a Variable
  306.    wt: 2:   1 Three Skills For Algebra
  307.    wt: 2:   About Folder Contents
  308.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  309.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  310.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  311.    wt: 2:   Chapter 24 Logarithms Powers and Exponentials
  312.    wt: 2:   Chapter 23 Links To Trigonometry
  313.    wt: 2:   Chapter 19. Exponentials and Natural Logarithms
  314.    wt: 2:   Chapter 9 About First Courses in Calculus
  315.    wt: 2:   Fall 1983 Calculus Appetizer
  316.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  317.    wt: 2:   Chapter 3 Algebra Starter Lessons
  318.    wt: 1:   Skills Chapter 5 Calculus
  319.    wt: 1:   5 logarithms and exponentials etc
  320.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  321.    wt: 1:   chapitre 06 00 Chaines de la raison
  322.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  323.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  324.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  325.    wt: 1:   sign monoticity analysis example 4
  326.    wt: 1:   sign monoticity analysis example 3
  327.    wt: 1:   sign monoticity analysis example 2
  328.    wt: 1:   sign monoticity analysis example 1
  329.    wt: 1:   19 Horizontal line rule and method
  330.    wt: 1:   18 Vertical Line Rule and Method
  331.    wt: 1:   11 Growth and Decay in Biology
  332.    wt: 1:   10 Exponential Growth and Decay Models
  333.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  334.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  335.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  336.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  337.    wt: 1:   5 Natural Logarithm Calculator Exercises
  338.    wt: 1:   2 Square Root Simplification a prequel
  339.    wt: 1:   7 Links Lessons Elsewhere
  340.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  341.    wt: 1:   9 Summary Degrees to Radians and back
  342.    wt: 1:   8 Radian Measures of Common Angles
  343.    wt: 1:   7 Radian Measures in special Triangles
  344.    wt: 1:   6 Radian Measure to Degrees
  345.    wt: 1:   5 Degrees to Radian Measure
  346.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  347.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  348.    wt: 1:   2 Radian Measure Numerical Value of one degree
  349.    wt: 1:   1 Degrees and Radians Introduction
  350.    wt: 1:   A Global Time and Navigation
  351.    wt: 1:   15 Dot and Cross Product
  352.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  353.    wt: 1:   13 Velocity Vectors in Physics
  354.    wt: 1:   12 From Applied To Pure Mathematics
  355.    wt: 1:   11 Component Method
  356.    wt: 1:   10 Parallelogram Addition Method
  357.    wt: 1:   9 Head to Tail Coordinate View
  358.    wt: 1:   8 Parallel Vectors
  359.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  360.    wt: 1:   6 Vectors with Coordinates
  361.    wt: 1:   5 Head To Tail Arrow Addition
  362.    wt: 1:   4 Resultant of a Sum of Movements
  363.    wt: 1:   3 Navigation with Arrows or Vectors
  364.    wt: 1:   2 Signed Coordinates
  365.    wt: 1:   1 Unsigned Coordinates
  366.    wt: 1:   Vector and Complex Number Applet
  367.    wt: 1:   4 graphing y=Asin(x c)
  368.    wt: 1:   3 graphing y=f(x c) plus K
  369.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  370.    wt: 1:   1 graphing y=f(x a)
  371.    wt: 1:   Parallel Lines and Parallel Transversals
  372.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  373.    wt: 1:   Triangle Angles Sum To 180 Degrees
  374.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  375.    wt: 1:   Parallel Lines and Interior Angles
  376.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  377.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  378.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  379.    wt: 1:   Straight Lines ASA Intersection Study More
  380.    wt: 1:   Straight Lines ASA Intersection Study
  381.    wt: 1:   Straight Lines Instersection Solving Equations
  382.    wt: 1:   Straight Lines Intersection of
  383.    wt: 1:   C Straight Lines Slope from Coordinates
  384.    wt: 1:   B Straight Line Slope Scaling Properties More
  385.    wt: 1:   A Straight Line Slope Scaling Properties
  386.    wt: 1:   14 Straight Lines Equations General Case
  387.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  388.    wt: 1:   12 Straight Lines Graphing mx plus b
  389.    wt: 1:   11 Straight Lines Graphing y=mx
  390.    wt: 1:   10 Straight Lines through Origin Equations More
  391.    wt: 1:   9 Straight Lines through Origin Equations
  392.    wt: 1:   8 Straight Lines Equation for vertical
  393.    wt: 1:   7 Tangent Function is odd on this domain
  394.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  395.    wt: 1:   5 Tangent Function Graph
  396.    wt: 1:   4 Tangent Function Properties
  397.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  398.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  399.    wt: 1:   1 Straight Lines Slope Concept
  400.    wt: 1:   20 N th Roots of Complex Numbers
  401.    wt: 1:   19 N th Roots of Unity
  402.    wt: 1:   18 Sixth Roots of Unity
  403.    wt: 1:   17 Cube Roots of unity
  404.    wt: 1:   16 References and Originality Question
  405.    wt: 1:   15 Pythagorean Theorem Converse
  406.    wt: 1:   14 Law of cosines
  407.    wt: 1:   12 cis formulas for sine cosines and tangent
  408.    wt: 1:   11 sine and cosine double triple angle formulas
  409.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  410.    wt: 1:   7 Second Way to Calculate Products
  411.    wt: 1:   6 Field Properties of Complex Number
  412.    wt: 1:   5 An Easy Proof of the Distributive Law
  413.    wt: 1:   4 Multiplication Properties
  414.    wt: 1:   3 Addition Properties
  415.    wt: 1:   2 Complex Numbers made easier we hope
  416.    wt: 1:   1 Rectangular Polar Coordinates Review
  417.    wt: 1:   Appetizer A Complex Number Applet
  418.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  419.    wt: 1:   12 Triangles Similarity More Problems
  420.    wt: 1:   11 Triangle Similarity Missing Side Problem
  421.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  422.    wt: 1:   9 Similarity of Triangles Usual Criteria
  423.    wt: 1:   8 Similarity of Triangles and Polygons
  424.    wt: 1:   7 Translations Rotations Reflections Dilatations
  425.    wt: 1:   6 Geometric Diagrams in Class
  426.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  427.    wt: 1:   4 Similarity Definition with Coordinate
  428.    wt: 1:   3 Similarity by Design with coordinates
  429.    wt: 1:   2 Similarity By Design
  430.    wt: 1:   1 Early Concept of Like or Similar Shapes
  431.    wt: 1:   Four Simple Exercises
  432.    wt: 1:   11 A Partial Summary
  433.    wt: 1:   10 Midpoint of [a b] and [b a]
  434.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  435.    wt: 1:   8 Mid Point Formula
  436.    wt: 1:   7 Exercises to test skill and concept mastery
  437.    wt: 1:   6 Intersection of lines by solving linear systems
  438.    wt: 1:   5 Algebraic View of Slopes
  439.    wt: 1:   4 Equations for lines three forms
  440.    wt: 1:   3 Slope product for perpendicular lines
  441.    wt: 1:   2 point slope equation for a line
  442.    wt: 1:   1 Numerical view of lines and their equations
  443.    wt: 1:   What is and is not here
  444.    wt: 1:   13 Pythagorean spatial distance formulas
  445.    wt: 1:   12 Spatial Coordinates
  446.    wt: 1:   11 Triangle Inequality
  447.    wt: 1:   10 Pythagorean plane distance formula
  448.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  449.    wt: 1:   8 Distance Between Points on a Line
  450.    wt: 1:   7 Complex Numbers Appetizer
  451.    wt: 1:   6 Polar Multiplication and Rotation
  452.    wt: 1:   5 Cartesian Addition and Translation
  453.    wt: 1:   4 Polar Coordinates to and from
  454.    wt: 1:   3 Rectangular Coordinates Review
  455.    wt: 1:   2 Cartesian Coordinates with signs
  456.    wt: 1:   1 Cartesian Coordinates sans signs
  457.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  458.    wt: 1:   PS H Distributive Law For Complex Numbers
  459.    wt: 1:   PS G Rotation Distributes over Addition
  460.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  461.    wt: 1:   PS E Multiplication with Polar Coordinates
  462.    wt: 1:   PS D Addition with Cartesian Coordinates
  463.    wt: 1:   PS B Parallelogram Construction Methods
  464.    wt: 1:   PS A Kite Construction Methods
  465.    wt: 1:   21 Parallelograms
  466.    wt: 1:   19 Right Triangle Similarity
  467.    wt: 1:   18 Triangle Similarity Take 1
  468.    wt: 1:   17 Right Bisectors of Triangle Sides
  469.    wt: 1:   16 Angles Subtended By Chords and Diameters
  470.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  471.    wt: 1:   14 Parallel Lines Postulate
  472.    wt: 1:   13 Angle Side Angle Failure
  473.    wt: 1:   12 Side Angle Side Failure
  474.    wt: 1:   11 Triangle Construction Fails
  475.    wt: 1:   10 Dropping a perpendicular to line
  476.    wt: 1:   9 Construction of a right bisector
  477.    wt: 1:   8 Isoceles Triangles
  478.    wt: 1:   7 Angle Side Angle
  479.    wt: 1:   5 Side Angle Side
  480.    wt: 1:   4 Side Side Side
  481.    wt: 1:   3 Isometry of Triangles Congruence
  482.    wt: 1:   2 Correspondence between Triangles
  483.    wt: 1:   1 Initial Concepts and Terms
  484.    wt: 1:   Short Course on Euclidean Geometry
  485.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  486.    wt: 1:   6 Figuring with Maps Not to Scale
  487.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  488.    wt: 1:   4 Angles on Maps Plans drawn to scale
  489.    wt: 1:   3 Lengths and Areas on Maps and Plans
  490.    wt: 1:   2 Measuring Area Directly
  491.    wt: 1:   1 Length Measurement
  492.    wt: 1:   About Folder Contents
  493.    wt: 1:   3 Properties of Square Roots with example
  494.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  495.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  496.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  497.    wt: 1:   4 Counting with Trees Product Rule Take I
  498.    wt: 1:   D Remainders Modulo 11 Pair Rule
  499.    wt: 1:   12 Adding Integers More Examples
  500.    wt: 1:   11 Adding Integers Formulas and Examples
  501.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  502.    wt: 1:   26 Divisibility by 2 3 5 Example
  503.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  504.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  505.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  506.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  507.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  508.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  509.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  510.    wt: 1:   11 Efficient Square Rule Use
  511.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  512.    wt: 1:   5 Prime Factorization and a Square Rule
  513.    wt: 1:   1 Divsion Physical Examples
  514.    wt: 1:   Subtraction with J Conversions Example
  515.    wt: 1:   2 Subtraction Easy Case Examples
  516.    wt: 1:   5. How to add decimals C. Examples
  517.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  518.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  519.    wt: 1:   G.5 Motions With Bounded Velocities
  520.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  521.    wt: 1:   G.3 Constant Difference Theorem Proof
  522.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  523.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  524.    wt: 1:   F.5b Extreme Value Theorem
  525.    wt: 1:   F.5a Equicontinuity Theorems
  526.    wt: 1:   F.4 Finite Covering Theorem
  527.    wt: 1:   F.3 Intermediate Value Theorem
  528.    wt: 1:   F.2 Closed Range Theorem
  529.    wt: 1:   F.1 What Functions are Continuous
  530.    wt: 1:   E2 Algebraic Properties of Limits
  531.    wt: 1:   E1 Error Control Inequalities
  532.    wt: 1:   D2 Limits of Monotone Sequences
  533.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  534.    wt: 1:   C Triangle Inequalities
  535.    wt: 1:   B3 Bolzano Weierstrass Theorem
  536.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  537.    wt: 1:   PostScript For and Against Decimal Perspectives
  538.    wt: 1:   A1. Introduction
  539.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  540.    wt: 1:   Chapter 22 Complex Numbers
  541.    wt: 1:   Chapter 21 Arrow Addition
  542.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  543.    wt: 1:   Chapter 18. Slopes Areas Integration
  544.    wt: 1:   Chapter 17. Area Approximation
  545.    wt: 1:   Chapter 16. Velocity Approximation
  546.    wt: 1:   Chapter 15. Slope Approximation
  547.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  548.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  549.    wt: 1:   Chapter 13. Acceleration
  550.    wt: 1:   Chapter 12. Units and Slopes
  551.    wt: 1:   Chapter 11. Graphing Slope versus Position
  552.    wt: 1:   Chapter 10 Slopes and Units
  553.    wt: 1:   Chapter 8. Slope Interpretation
  554.    wt: 1:   Chapter 7 Slopes and Velocity
  555.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  556.    wt: 1:   Chapter 5. Slope Sign Tests
  557.    wt: 1:   Chapter 4. More Slope Sign Analysis
  558.    wt: 1:   Chapter 3. Slope Sign Analysis
  559.    wt: 1:   Chapter 2. Slopes and Ski Trails
  560.    wt: 1:   Chapter 1.Introduction
  561.    wt: 1:   Foreword
  562.    wt: 1:   Chapter 25. Mathematical Induction Examples
  563.    wt: 1:   Chapter 18. Rules for Algebra
  564.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  565.    wt: 1:   Chapter 4 Longer Chains of Reason
  566.    wt: 1:   Chapter 3 Chains of Reason
  567.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  568.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  569.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  570.    wt: 1:   Chapter 7 Longer Chains of Reason
  571.    wt: 1:   Chapter 6 Chains of Reason
  572.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  573.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  574.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  575.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  576.    wt: 1:   More Algebra and Slope based Calculus Preview
  577.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  578.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Teachers, Tutors, Parents: Site material offers better or best practices for mathematics skill building - simpler than expected and comprehensive. Your duty is to study them alone or with help. Start now.

Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.


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Logic-Reason for all
Careful Thinking
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Responsibility
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Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
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5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity
Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
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More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
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Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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