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
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school. See Site Map

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.

Home << Search

[1] [2] [3] [4]

Key Word Search

Folder Search

21 matches:

  1.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  2.    wt: 2:   7 Complex Numbers/
  3.    wt: 1:   LAMP Lean Applied Mathematics Program/
  4.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  5.    wt: 1:   Mathematics Education Essays/
  6.    wt: 1:   Volume 1A Regles et modeles/
  7.    wt: 1:   Mathematics Skills Year by Year/
  8.    wt: 1:   B Real Numbers Extrinsic Development/
  9.    wt: 1:   5 Real Numbers/
  10.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  11.    wt: 1:   8 Arithmetic with Signed Numbers/
  12.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  13.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  14.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  15.    wt: 1:   Volume 2 Three Skills For Algebra/
  16.    wt: 1:   Volume 1A Pattern Based Reason/
  17.    wt: 1:   Volume 1 Elements of Reason/
  18.    wt: 1:   Mathematics 506 Lessons/
  19.    wt: 1:   Secondary Mathematics A Practical Approach/
  20.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  21.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

136 matches:

  1.    wt: 2:   E LAMP Introduction Modern Mathematics
  2.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  3.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  4.    wt: 2:   mathematics curriculum shifts
  5.    wt: 2:   04 29 New Mathematics Curriculum
  6.    wt: 2:   need for a mixed mathematics curriculum
  7.    wt: 2:   Leaner mathematics curriculum
  8.    wt: 2:   20 N th Roots of Complex Numbers
  9.    wt: 2:   2 Complex Numbers made easier we hope
  10.    wt: 2:   7 Complex Numbers Appetizer
  11.    wt: 2:   PS H Distributive Law For Complex Numbers
  12.    wt: 2:   Chapter 22 Complex Numbers
  13.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  14.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  15.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  16.    wt: 1:   J LAMP Introduction Extrinsic Origins
  17.    wt: 1:   I LAMP Introduction Study Habits
  18.    wt: 1:   H LAMP Introduction Instructional Concepts
  19.    wt: 1:   G LAMP Introduction Problem Solving Skills
  20.    wt: 1:   F LAMP Introduction Prerequisites
  21.    wt: 1:   A Introduction Objectives
  22.    wt: 1:   Ramblings Extrinsic numbers theory
  23.    wt: 1:   Ramblings Introduction Algebra Essay
  24.    wt: 1:   Skills Chapter 0 Introduction
  25.    wt: 1:   11 pure mathematics
  26.    wt: 1:   2 arithmetic with signed numbers
  27.    wt: 1:   1 arithmetic with unsigned numbers
  28.    wt: 1:   key notes and themes
  29.    wt: 1:   Mathematics Education Professors
  30.    wt: 1:   mathematics in context
  31.    wt: 1:   Secondary Three Mathematics
  32.    wt: 1:   Secondary Two Mathematics
  33.    wt: 1:   Secondary One Mathematics
  34.    wt: 1:   three goals for Mathematics Education
  35.    wt: 1:   02 20 mathematics education references
  36.    wt: 1:   three aims for mathematics students
  37.    wt: 1:   mathematics instruction in general
  38.    wt: 1:   Education in mathematics science and technology
  39.    wt: 1:   three kinds of reason in mathematics
  40.    wt: 1:   words for mathematics instructor
  41.    wt: 1:   chapitre 01 00 Introduction
  42.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  43.    wt: 1:   22 Student Centered Highschool Mathematics
  44.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  45.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  46.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  47.    wt: 1:   18 Primary School Mathematics
  48.    wt: 1:   16 Secondary Mathematics Tips
  49.    wt: 1:   12 Goals and Objectives For Mathematics
  50.    wt: 1:   4 Function notation in and beyond mathematics
  51.    wt: 1:   1 Geometric Introduction of Function Notation
  52.    wt: 1:   Introduction Reading Guide
  53.    wt: 1:   8 Notes for instructors or tutors
  54.    wt: 1:   1 Degrees and Radians Introduction
  55.    wt: 1:   12 From Applied To Pure Mathematics
  56.    wt: 1:   Vector and Complex Number Applet
  57.    wt: 1:   17A The complex number valued trig function cis
  58.    wt: 1:   9 The complex number valued trig function cis
  59.    wt: 1:   6 Field Properties of Complex Number
  60.    wt: 1:   Appetizer A Complex Number Applet
  61.    wt: 1:   musings do not puiblish real numbers
  62.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  63.    wt: 1:   22 Multiplication of Signed Numbers
  64.    wt: 1:   12 Real Numbers Line Signed Coordinates
  65.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  66.    wt: 1:   5 Distributive Law for Whole Numbers
  67.    wt: 1:   1 The Counting Origins of Numbers
  68.    wt: 1:   4 Comparison of Negative Numbers
  69.    wt: 1:   1 Real Numbers Comparison
  70.    wt: 1:   16 Real Numbers Comparison
  71.    wt: 1:   7 Real Numbers as Line Cordinates
  72.    wt: 1:   6 Unsigned Real Numbers
  73.    wt: 1:   5 Rational Numbers More
  74.    wt: 1:   4 Rational Numbers
  75.    wt: 1:   1 Whole and Natural Numbers
  76.    wt: 1:   5 Algebraic Solutions Introduction
  77.    wt: 1:   Skill Development Notes
  78.    wt: 1:   11 Volume of Sphere
  79.    wt: 1:   10 Volume of Pyramid
  80.    wt: 1:   9 Volume of Cone
  81.    wt: 1:   7 Compound Interest Formula Introduction
  82.    wt: 1:   5 Box Volume Formula Example
  83.    wt: 1:   8 Sets of Numbers
  84.    wt: 1:   5 Talking about Numbers and Quantities
  85.    wt: 1:   4 A Brief Story of numbers and algebra
  86.    wt: 1:   3 Comparison of Negative Numbers
  87.    wt: 1:   1 Squares and Square Roots Introduction
  88.    wt: 1:   1 Least Common Multiples LCM Introduction
  89.    wt: 1:   11 What are real lengths and numbers
  90.    wt: 1:   10 dividing signed numbers
  91.    wt: 1:   9 subtracting signed numbers
  92.    wt: 1:   8 multiplying signed numbers
  93.    wt: 1:   6 adding signed numbers
  94.    wt: 1:   5 lengths and signs of numbers
  95.    wt: 1:   2 signed and unsigned numbers as coordinates
  96.    wt: 1:   3 Multiplying Units and Numbers
  97.    wt: 1:   22 Complex Compound Fractions
  98.    wt: 1:   9 Improper Fractions and Mixed Numbers
  99.    wt: 1:   6 Multiplication of Mixed Numbers
  100.    wt: 1:   8 Multiplication by Signed Numbers Integers
  101.    wt: 1:   6 Multiplication by Natural Numbers
  102.    wt: 1:   7 Calculator Usage Notes and Cautions
  103.    wt: 1:   4 video Prime Factorization Introduction
  104.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  105.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  106.    wt: 1:   Quick history of numbers and algebra
  107.    wt: 1:   011 Division of Time Intervals By Numbers
  108.    wt: 1:   Example 2 volume of a cone
  109.    wt: 1:   Example 1 volume of a pyramid
  110.    wt: 1:   Volume of Solid by Cross Sections Lesson
  111.    wt: 1:   A Related Material in Volume 3
  112.    wt: 1:   A Related lessons in Volume 3
  113.    wt: 1:   18 Chain Rule Introduction
  114.    wt: 1:   1 Numerical introduction
  115.    wt: 1:   A1. Introduction
  116.    wt: 1:   Chapter 1.Introduction
  117.    wt: 1:   Appendix E. How To Study Mathematics and Why
  118.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  119.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  120.    wt: 1:   Postscript B Mathematics Education References
  121.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  122.    wt: 1:   Chapter 2 For and Against Mathematics
  123.    wt: 1:   Chapter 1 Introduction
  124.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  125.    wt: 1:   Chapter 1 Introduction
  126.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  127.    wt: 1:   R Why Learn Mathematics Skills
  128.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  129.    wt: 1:   O On Learning Mathematics and Science
  130.    wt: 1:   N Mathematics Prepare for College Studies
  131.    wt: 1:   Helping the Blind in Logic and Mathematics
  132.    wt: 1:   Mathematics Education References
  133.    wt: 1:   Mathematics Education References
  134.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  135.    wt: 1:   Implementation Notes
  136.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

451 matches:

  1.    wt: 8:   Chapter 4 Complex Numbers and Why Slopes
  2.    wt: 7:   Postscript B Mathematics Education References
  3.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  4.    wt: 7:   Chapter 2 For and Against Mathematics
  5.    wt: 7:   Chapter 1 Introduction
  6.    wt: 6:   Annotated Links to Material Elsehwere
  7.    wt: 6:   Postscript A Three Remarks
  8.    wt: 6:   Chapter 12 Four Phases
  9.    wt: 6:   Chapter 11 Elementary Instruction
  10.    wt: 6:   Chapter 10 Transition
  11.    wt: 6:   Chapter 9 The Two Ends
  12.    wt: 6:   Chapter 8 Modern Instruction
  13.    wt: 6:   Chapter 7 Two Treatments of Geometry
  14.    wt: 6:   Chapter 5 Four References
  15.    wt: 6:   Chapter 3 Algebra Difficulties
  16.    wt: 6:   Foreword
  17.    wt: 4:   20 N th Roots of Complex Numbers
  18.    wt: 4:   2 Complex Numbers made easier we hope
  19.    wt: 3:   E LAMP Introduction Modern Mathematics
  20.    wt: 3:   C LAMP Introduction Culture in Mathematics Education
  21.    wt: 3:   B LAMP Introduction Curriculum Development Standards
  22.    wt: 3:   mathematics curriculum shifts
  23.    wt: 3:   04 29 New Mathematics Curriculum
  24.    wt: 3:   need for a mixed mathematics curriculum
  25.    wt: 3:   Leaner mathematics curriculum
  26.    wt: 3:   9 The complex number valued trig function cis
  27.    wt: 3:   6 Field Properties of Complex Number
  28.    wt: 3:   Appetizer A Complex Number Applet
  29.    wt: 3:   Chapter 22 Complex Numbers
  30.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  31.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  32.    wt: 2:   J LAMP Introduction Extrinsic Origins
  33.    wt: 2:   I LAMP Introduction Study Habits
  34.    wt: 2:   H LAMP Introduction Instructional Concepts
  35.    wt: 2:   G LAMP Introduction Problem Solving Skills
  36.    wt: 2:   F LAMP Introduction Prerequisites
  37.    wt: 2:   A Introduction Objectives
  38.    wt: 2:   Ramblings Extrinsic numbers theory
  39.    wt: 2:   Ramblings Introduction Algebra Essay
  40.    wt: 2:   Skills Chapter 0 Introduction
  41.    wt: 2:   11 pure mathematics
  42.    wt: 2:   2 arithmetic with signed numbers
  43.    wt: 2:   1 arithmetic with unsigned numbers
  44.    wt: 2:   key notes and themes
  45.    wt: 2:   Mathematics Education Professors
  46.    wt: 2:   mathematics in context
  47.    wt: 2:   Secondary Three Mathematics
  48.    wt: 2:   Secondary Two Mathematics
  49.    wt: 2:   Secondary One Mathematics
  50.    wt: 2:   three goals for Mathematics Education
  51.    wt: 2:   02 20 mathematics education references
  52.    wt: 2:   three aims for mathematics students
  53.    wt: 2:   mathematics instruction in general
  54.    wt: 2:   Education in mathematics science and technology
  55.    wt: 2:   three kinds of reason in mathematics
  56.    wt: 2:   words for mathematics instructor
  57.    wt: 2:   chapitre 01 00 Introduction
  58.    wt: 2:   21 Logarithms Powers and Exponentials
  59.    wt: 2:   19 N th Roots of Unity
  60.    wt: 2:   18 Sixth Roots of Unity
  61.    wt: 2:   17 Cube Roots of unity
  62.    wt: 2:   16 References and Originality Question
  63.    wt: 2:   15 Pythagorean Theorem Converse
  64.    wt: 2:   14 Law of cosines
  65.    wt: 2:   13 Trig Formulas for dot and cross Products
  66.    wt: 2:   12 cis formulas for sine cosines and tangent
  67.    wt: 2:   11 sine and cosine double triple angle formulas
  68.    wt: 2:   10 sine cosine Angle Sum Formulas via cis
  69.    wt: 2:   8 Unit Circle Development of Trigonometry
  70.    wt: 2:   7 Second Way to Calculate Products
  71.    wt: 2:   5 An Easy Proof of the Distributive Law
  72.    wt: 2:   4 Multiplication Properties
  73.    wt: 2:   3 Addition Properties
  74.    wt: 2:   1 Rectangular Polar Coordinates Review
  75.    wt: 2:   7 Complex Numbers Appetizer
  76.    wt: 2:   PS H Distributive Law For Complex Numbers
  77.    wt: 2:   musings do not puiblish real numbers
  78.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  79.    wt: 2:   22 Multiplication of Signed Numbers
  80.    wt: 2:   12 Real Numbers Line Signed Coordinates
  81.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  82.    wt: 2:   16 Real Numbers Comparison
  83.    wt: 2:   7 Real Numbers as Line Cordinates
  84.    wt: 2:   6 Unsigned Real Numbers
  85.    wt: 2:   5 Rational Numbers More
  86.    wt: 2:   4 Rational Numbers
  87.    wt: 2:   1 Whole and Natural Numbers
  88.    wt: 2:   3 Comparison of Negative Numbers
  89.    wt: 2:   11 What are real lengths and numbers
  90.    wt: 2:   10 dividing signed numbers
  91.    wt: 2:   9 subtracting signed numbers
  92.    wt: 2:   8 multiplying signed numbers
  93.    wt: 2:   6 adding signed numbers
  94.    wt: 2:   5 lengths and signs of numbers
  95.    wt: 2:   2 signed and unsigned numbers as coordinates
  96.    wt: 2:   Example 2 volume of a cone
  97.    wt: 2:   Example 1 volume of a pyramid
  98.    wt: 2:   Volume of Solid by Cross Sections Lesson
  99.    wt: 2:   A1. Introduction
  100.    wt: 2:   Chapter 1.Introduction
  101.    wt: 2:   Appendix E. How To Study Mathematics and Why
  102.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  103.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  104.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  105.    wt: 2:   Chapter 1 Introduction
  106.    wt: 2:   Helping the Blind in Logic and Mathematics
  107.    wt: 2:   Mathematics Education References
  108.    wt: 2:   Mathematics Education References
  109.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  110.    wt: 2:   Implementation Notes
  111.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  112.    wt: 1:   Appendix 2 primary school Arithmetic 01
  113.    wt: 1:   Appendix 1 primary and preschool mathematic
  114.    wt: 1:   K LAMP Musings Science Education
  115.    wt: 1:   Skills Chapter 5 Calculus
  116.    wt: 1:   Skills Chapter 4 Logic
  117.    wt: 1:   Skills Chapter 3 Algebra
  118.    wt: 1:   Skills Chapter 2 Geometry
  119.    wt: 1:   Skills Chapter 1 Arithmetic
  120.    wt: 1:   10 statistics
  121.    wt: 1:   9 combinatorics probability sets
  122.    wt: 1:   8 analytic geometry etc
  123.    wt: 1:   7 logic review and decimals an odd combination
  124.    wt: 1:   6 polynomials etc
  125.    wt: 1:   5 logarithms and exponentials etc
  126.    wt: 1:   4 algebra
  127.    wt: 1:   3 Euclidean Geometry Leanly
  128.    wt: 1:   What is POMME
  129.    wt: 1:   why bother
  130.    wt: 1:   which way to go
  131.    wt: 1:   website reviews
  132.    wt: 1:   three goals to set for students
  133.    wt: 1:   Teach the teachers plus goals
  134.    wt: 1:   permissions for teachers
  135.    wt: 1:   Math Ed if it must be short make it lean effective
  136.    wt: 1:   Applied Maths Program14092009 POMME variant
  137.    wt: 1:   activities for students
  138.    wt: 1:   links Education Resources online
  139.    wt: 1:   site origins
  140.    wt: 1:   site eurekas
  141.    wt: 1:   About site lesson plans
  142.    wt: 1:   teacher certification
  143.    wt: 1:   modern education
  144.    wt: 1:   learning takes time
  145.    wt: 1:   grouping students according to ability
  146.    wt: 1:   what should be learnt and When
  147.    wt: 1:   Postscript 2007 01 10
  148.    wt: 1:   Education Reform Inconsistencies
  149.    wt: 1:   five decades make a difference
  150.    wt: 1:   Maps Plans Drawings
  151.    wt: 1:   how letters appear
  152.    wt: 1:   talk the algebra talk
  153.    wt: 1:   three difficulties
  154.    wt: 1:   teaching tips
  155.    wt: 1:   What to Tell Students
  156.    wt: 1:   geometric implications for algebra
  157.    wt: 1:   teaching tutoring algebraic reason
  158.    wt: 1:   Lessening Algebra Difficulties
  159.    wt: 1:   the trouble with algebra
  160.    wt: 1:   05 13 OldSiteEntrancePage
  161.    wt: 1:   04 25 when to stop or suspend mathemat
  162.    wt: 1:   02 21 words for teachers
  163.    wt: 1:   standards for course material
  164.    wt: 1:   Operational Viewpoint to Value
  165.    wt: 1:   formal or informal peer review
  166.    wt: 1:   Theory of Knowledge
  167.    wt: 1:   Different Kinds of Reasoning in maths
  168.    wt: 1:   cultivating intelligence
  169.    wt: 1:   Four ways to improve education reform
  170.    wt: 1:   How to be a better instructor
  171.    wt: 1:   Motivation and Context Problem
  172.    wt: 1:   Prequel In For A Penny In For A Pound
  173.    wt: 1:   education an empirical art
  174.    wt: 1:   fairness and inductive principles for instruction
  175.    wt: 1:   chapitre 12 00 les iles et division
  176.    wt: 1:   chapitre 07 01 principle D induction mathematique
  177.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  178.    wt: 1:   chapitre 06 00 Chaines de la raison
  179.    wt: 1:   chapitre 05 00 Deception
  180.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  181.    wt: 1:   chapitre 04 09 Regles accidentelles
  182.    wt: 1:   chapitre 04 08 Limitations et benefices
  183.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  184.    wt: 1:   chapitre 04 06 engagements
  185.    wt: 1:   chapitre 04 05 Implication versus suggestion
  186.    wt: 1:   chapitre 04 04 Parlons de la logique
  187.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  188.    wt: 1:   chapitre 04 02 Deuxieme enigme
  189.    wt: 1:   chapitre 04 01 Premiere enigme
  190.    wt: 1:   chapitre 04 00 Les regles d implication
  191.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  192.    wt: 1:   chapitre 02 00 La Communication des idees
  193.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  194.    wt: 1:   22 Student Centered Highschool Mathematics
  195.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  196.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  197.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  198.    wt: 1:   18 Primary School Mathematics
  199.    wt: 1:   16 Secondary Mathematics Tips
  200.    wt: 1:   12 Goals and Objectives For Mathematics
  201.    wt: 1:   Ages 12 to 14 Skills with take home value
  202.    wt: 1:   Ages 12 to 14 Geometry
  203.    wt: 1:   Ages 12 to 14 Arithmetic
  204.    wt: 1:   Ages 10 to 12 Geometry
  205.    wt: 1:   Ages 10 to 12 Arithmetic
  206.    wt: 1:   Ages 9 to 10
  207.    wt: 1:   Ages 8 to 9
  208.    wt: 1:   Ages 7 to 8
  209.    wt: 1:   Ages 6 to 7
  210.    wt: 1:   Ages 4 plus to 5 plus
  211.    wt: 1:   Ages 3 plus to 4 plus
  212.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  213.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  214.    wt: 1:   4 Function notation in and beyond mathematics
  215.    wt: 1:   1 Geometric Introduction of Function Notation
  216.    wt: 1:   Introduction Reading Guide
  217.    wt: 1:   8 Notes for instructors or tutors
  218.    wt: 1:   1 Degrees and Radians Introduction
  219.    wt: 1:   12 From Applied To Pure Mathematics
  220.    wt: 1:   Vector and Complex Number Applet
  221.    wt: 1:   17A The complex number valued trig function cis
  222.    wt: 1:   A Modular and Remainder Arithmetic
  223.    wt: 1:   A Signed Number Arithmetic Review
  224.    wt: 1:   26 More Less Greater Than Comparison
  225.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  226.    wt: 1:   23 Distributive Law Two Derivations
  227.    wt: 1:   21 Addition of Multiples of a Single Vector
  228.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  229.    wt: 1:   19 Signed Multiples of Vectors
  230.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  231.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  232.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  233.    wt: 1:   15 Head to Tails in place Addition Associative
  234.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  235.    wt: 1:   13 Arrows and Vectors in a Plane
  236.    wt: 1:   11 Signed Number Addition and Addition Properties
  237.    wt: 1:   9 Division with Digits after Decimal Point
  238.    wt: 1:   8 Division and Mulplication of Compound Fractions
  239.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  240.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  241.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  242.    wt: 1:   4 Location of Point in Decimal Addition
  243.    wt: 1:   3 Location of Point in Decimal Multiplication
  244.    wt: 1:   2 Counting Digits in Decimal Multiplication
  245.    wt: 1:   1 Fractions with Finite Decimal Expansions
  246.    wt: 1:   5 Distributive Law for Whole Numbers
  247.    wt: 1:   1 The Counting Origins of Numbers
  248.    wt: 1:   4 Comparison of Negative Numbers
  249.    wt: 1:   1 Real Numbers Comparison
  250.    wt: 1:   15 Real Number Division
  251.    wt: 1:   14 Real Number Multiplication
  252.    wt: 1:   13 Real Number Subtraction
  253.    wt: 1:   12 Real Number Additive Inverses or Negatives
  254.    wt: 1:   11 Real Number Addition
  255.    wt: 1:   10 Real Number Lengths and Signs
  256.    wt: 1:   9 Coordinates for Regions in Space
  257.    wt: 1:   8 Coordinates for Maps and Planes
  258.    wt: 1:   3 Fractions
  259.    wt: 1:   2 Integers
  260.    wt: 1:   5 Algebraic Solutions Introduction
  261.    wt: 1:   Skill Development Notes
  262.    wt: 1:   11 Volume of Sphere
  263.    wt: 1:   10 Volume of Pyramid
  264.    wt: 1:   9 Volume of Cone
  265.    wt: 1:   7 Compound Interest Formula Introduction
  266.    wt: 1:   5 Box Volume Formula Example
  267.    wt: 1:   8 Sets of Numbers
  268.    wt: 1:   5 Talking about Numbers and Quantities
  269.    wt: 1:   4 A Brief Story of numbers and algebra
  270.    wt: 1:   4 Greater More Less Than Signs in General
  271.    wt: 1:   2 More and Less Than with Unlike Signs
  272.    wt: 1:   1 More and Less Than for Counts and Measures
  273.    wt: 1:   1 Squares and Square Roots Introduction
  274.    wt: 1:   1 Least Common Multiples LCM Introduction
  275.    wt: 1:   7 negative and additive inverse
  276.    wt: 1:   4 signed coordinates for regions in space
  277.    wt: 1:   3 signed coordinates for maps and planes
  278.    wt: 1:   3 Multiplying Units and Numbers
  279.    wt: 1:   22 Complex Compound Fractions
  280.    wt: 1:   9 Improper Fractions and Mixed Numbers
  281.    wt: 1:   6 Multiplication of Mixed Numbers
  282.    wt: 1:   8 Multiplication by Signed Numbers Integers
  283.    wt: 1:   6 Multiplication by Natural Numbers
  284.    wt: 1:   7 Calculator Usage Notes and Cautions
  285.    wt: 1:   4 video Prime Factorization Introduction
  286.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  287.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  288.    wt: 1:   Quick history of numbers and algebra
  289.    wt: 1:   011 Division of Time Intervals By Numbers
  290.    wt: 1:   Example 1. Area Between x and x squared
  291.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  292.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  293.    wt: 1:   Example 4 with x function of y
  294.    wt: 1:   Example 3
  295.    wt: 1:   Example 2
  296.    wt: 1:   Example 1
  297.    wt: 1:   Area Between Curves Lesson Take 2
  298.    wt: 1:   Area Between Curves Lesson Take 1
  299.    wt: 1:   Summary
  300.    wt: 1:   A Related Material in Volume 3
  301.    wt: 1:   A Related lessons in Volume 3
  302.    wt: 1:   18 Chain Rule Introduction
  303.    wt: 1:   1 Numerical introduction
  304.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  305.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  306.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  307.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  308.    wt: 1:   G.5 Motions With Bounded Velocities
  309.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  310.    wt: 1:   G.3 Constant Difference Theorem Proof
  311.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  312.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  313.    wt: 1:   F.5b Extreme Value Theorem
  314.    wt: 1:   F.5a Equicontinuity Theorems
  315.    wt: 1:   F.4 Finite Covering Theorem
  316.    wt: 1:   F.3 Intermediate Value Theorem
  317.    wt: 1:   F.2 Closed Range Theorem
  318.    wt: 1:   F.1 What Functions are Continuous
  319.    wt: 1:   E2 Algebraic Properties of Limits
  320.    wt: 1:   E1 Error Control Inequalities
  321.    wt: 1:   D2 Limits of Monotone Sequences
  322.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  323.    wt: 1:   C Triangle Inequalities
  324.    wt: 1:   B3 Bolzano Weierstrass Theorem
  325.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  326.    wt: 1:   PostScript For and Against Decimal Perspectives
  327.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  328.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  329.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  330.    wt: 1:   Chapter 23 Links To Trigonometry
  331.    wt: 1:   Chapter 21 Arrow Addition
  332.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  333.    wt: 1:   Chapter 18. Slopes Areas Integration
  334.    wt: 1:   Chapter 17. Area Approximation
  335.    wt: 1:   Chapter 16. Velocity Approximation
  336.    wt: 1:   Chapter 15. Slope Approximation
  337.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  338.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  339.    wt: 1:   Chapter 13. Acceleration
  340.    wt: 1:   Chapter 12. Units and Slopes
  341.    wt: 1:   Chapter 11. Graphing Slope versus Position
  342.    wt: 1:   Chapter 10 Slopes and Units
  343.    wt: 1:   Chapter 9 About First Courses in Calculus
  344.    wt: 1:   Chapter 8. Slope Interpretation
  345.    wt: 1:   Chapter 7 Slopes and Velocity
  346.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  347.    wt: 1:   Chapter 5. Slope Sign Tests
  348.    wt: 1:   Chapter 4. More Slope Sign Analysis
  349.    wt: 1:   Chapter 3. Slope Sign Analysis
  350.    wt: 1:   Chapter 2. Slopes and Ski Trails
  351.    wt: 1:   Fall 1983 Calculus Appetizer
  352.    wt: 1:   Foreword
  353.    wt: 1:   Postscript More on Better Performance
  354.    wt: 1:   Postscript For Better Performance
  355.    wt: 1:   Appendix D. What to do in School and Why
  356.    wt: 1:   Appendix C. How to Read
  357.    wt: 1:   Appendix B. How To Learn
  358.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  359.    wt: 1:   Chapter 31 Direct and Indirect Reason
  360.    wt: 1:   Chapter 30 Truth Tables
  361.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  362.    wt: 1:   Chapter 28 Occurrence Tables
  363.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  364.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  365.    wt: 1:   Chapter 25. Mathematical Induction Examples
  366.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  367.    wt: 1:   Chapter 23. Notation For Sums
  368.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  369.    wt: 1:   Chapter 21. Third Reading Guide
  370.    wt: 1:   Chapter 20. Degrees and Radians
  371.    wt: 1:   Chapter 19. Functions and Sets
  372.    wt: 1:   Chapter 18. Rules for Algebra
  373.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  374.    wt: 1:   Chapter 16. Painless Theorem Proving
  375.    wt: 1:   Chapter 15. Solving Linear Equations
  376.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  377.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  378.    wt: 1:   Chapter 13. Second Reading Guide
  379.    wt: 1:   Chapter 12. Shorthand Usage Guide
  380.    wt: 1:   Chapter 11. Why Shorthand
  381.    wt: 1:   Chapter 10 Describing and Changing Calculations
  382.    wt: 1:   Postscript What is a Variable
  383.    wt: 1:   Chapter 8 Three Skills For Algebra
  384.    wt: 1:   Solutions For Arithmetic Exercises
  385.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  386.    wt: 1:   Chapter 6 Change of Language
  387.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  388.    wt: 1:   Chapter 4 Longer Chains of Reason
  389.    wt: 1:   Chapter 3 Chains of Reason
  390.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  391.    wt: 1:   Foreword
  392.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  393.    wt: 1:   Postscript C Consistency as a Tool for Reason
  394.    wt: 1:   Postscript B More on Story Telling and Reason
  395.    wt: 1:   Postscript A Story Telling
  396.    wt: 1:   Chapter 24 Direct and Indirect Reason
  397.    wt: 1:   Chapter 23 Truth Tables
  398.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  399.    wt: 1:   Chapter 21 Occurrence Tables
  400.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  401.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  402.    wt: 1:   Chapter 18 Sense and Knowledge
  403.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  404.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  405.    wt: 1:   Chapter 15 Objective Processes
  406.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  407.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  408.    wt: 1:   Chapter 11 Accidental Patterns
  409.    wt: 1:   Chapter 10 Responsibility
  410.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  411.    wt: 1:   Chapter 8 Change of Language
  412.    wt: 1:   Chapter 7 Longer Chains of Reason
  413.    wt: 1:   Chapter 6 Chains of Reason
  414.    wt: 1:   Chapter 5 Deception
  415.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  416.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  417.    wt: 1:   Chapter 2 Skill Development
  418.    wt: 1:   Three Remarks
  419.    wt: 1:   Foreword
  420.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  421.    wt: 1:   R Why Learn Mathematics Skills
  422.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  423.    wt: 1:   O On Learning Mathematics and Science
  424.    wt: 1:   N Mathematics Prepare for College Studies
  425.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  426.    wt: 1:   Chapter 8 Skipped Topics and Why
  427.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  428.    wt: 1:   Chapter 6 More Algebra and Geometry
  429.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  430.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  431.    wt: 1:   Chapter 3 Algebra Starter Lessons
  432.    wt: 1:   Chapter 2 Why Sets
  433.    wt: 1:   Chapter 1 Arithmetic
  434.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  435.    wt: 1:   7 Games and Activities for Instruction
  436.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  437.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  438.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  439.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  440.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  441.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  442.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  443.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  444.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  445.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  446.    wt: 1:   More Algebra and Slope based Calculus Preview
  447.    wt: 1:   Systematic Algebra Skill Development Missing Links
  448.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  449.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  450.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  451.    wt: 1:   Which Way To Go

Teachers & Tutors: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

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.

Return to Page Top

Home << Search

[1] [2] [3] [4]

Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
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
5. Formulas Backwards 		More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers 		Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

All trademarks and copyrights in this are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster.
The Rest © 1995-2011, by site author, Alan Selby, Ph. D., Montreal,
All Rights Reserved --- Skype or Email to contact.