Appetizers and Lessons for Mathematics & Reason Français: 26 pages
A 1100+ page site with math-free logic chapters and wordy algebra chapters.
For comprehension, study site chapters and steps. Go beyond rote learning.

Logic mastery strengthens comprehension and so improves home, work & study abilities .
 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 14+: 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
Forewords + leading chapters give original reasons, still valid, for site content & growth.

Site Review: Mathphobics, this site may ease your fears of the subject, perhaps even help you njoy it. ... unintimidating, sometimes funny and very clear. ... . Read all. Continue with Volume 2, Three Skill for Algebra.

Site Review. Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation ... Read all. See site books as well.

Teachers & Tutors: Site material uniquely explains common troubles in terms of steps too large or missing. Plus, this December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 may focus on skills with actual or potential local 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.

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28 matches:

  1.    wt: 8:   2 Natural Logarithms Exponentials Powers Roots/
  2.    wt: 3:   10 Examples of Algebraic Reasoning/
  3.    wt: 2:   5 Factored Polynomial Sign Analysis Examples/
  4.    wt: 2:   4 Functions/
  5.    wt: 2:   3 Quadratics Geometrically/
  6.    wt: 2:   1 Five Polynomial Operations/
  7.    wt: 2:   More Algebra/
  8.    wt: 2:   A Origins of Counting and Figuring Methods/
  9.    wt: 2:   8 Unifying Theme For Algebra/
  10.    wt: 2:   Step 2 Algebraic solutions for one unknown/
  11.    wt: 2:   1 Working With Sets/
  12.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  13.    wt: 1:   B Real Numbers Extrinsic Development/
  14.    wt: 1:   9 Proportionality Backwards and Forwards/
  15.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  16.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  17.    wt: 1:   5 Real Numbers/
  18.    wt: 1:   4 Computation Rules and Function Notation/
  19.    wt: 1:   Step 4 Gaussian Elimination/
  20.    wt: 1:   Step 3 Easy systems in 2 or more unknowns/
  21.    wt: 1:   Step 1 Stick diagram and fractions/
  22.    wt: 1:   3 Solving Linear Equations/
  23.    wt: 1:   2 Formula Forward Use Evaluation/
  24.    wt: 1:   Algebra Starter Lessons/
  25.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  26.    wt: 1:   11 Squares and Square Roots/
  27.    wt: 1:   Volume 2 Three Skills For Algebra/
  28.    wt: 1:   Volume 1 Elements of Reason/

Web Page Search

223 matches:

  1.    wt: 3:   3 Natural Logarithms and Exponentials Basic Properties
  2.    wt: 3:   27 Logarithmic use of products of sines and cosines
  3.    wt: 3:   21 Logarithms Powers and Exponentials
  4.    wt: 3:   Chapter 24 Logarithms Powers and Exponentials
  5.    wt: 3:   Chapter 19. Exponentials and Natural Logarithms
  6.    wt: 2:   5 logarithms and exponentials etc
  7.    wt: 2:   2 Algebraic use of function notation
  8.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  9.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  10.    wt: 2:   5 Natural Logarithm Calculator Exercises
  11.    wt: 2:   10 arctan left inverse of tangent Definition
  12.    wt: 2:   7 arcsin left inverse of sine Definition
  13.    wt: 2:   3 Left Inverse of cosine arccos definition
  14.    wt: 2:   4 Resultant of a Sum of Movements
  15.    wt: 2:   20 N th Roots of Complex Numbers
  16.    wt: 2:   19 N th Roots of Unity
  17.    wt: 2:   18 Sixth Roots of Unity
  18.    wt: 2:   17 Cube Roots of unity
  19.    wt: 2:   5 An Easy Proof of the Distributive Law
  20.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  21.    wt: 2:   5 Algebraic View of Slopes
  22.    wt: 2:   21 Addition of Multiples of a Single Vector
  23.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  24.    wt: 2:   4 A Brief Story of numbers and algebra
  25.    wt: 2:   3 Properties of Square Roots with example
  26.    wt: 2:   C Counting Areas with Powers of Ten
  27.    wt: 2:   B Powers of Ten
  28.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  29.    wt: 2:   Quick history of numbers and algebra
  30.    wt: 2:   38 Formulas and derivatives for powers and roots
  31.    wt: 2:   17 Derivatives of quotients of sine and cosine
  32.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  33.    wt: 2:   E2 Algebraic Properties of Limits
  34.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  35.    wt: 1:   Ramblings Introduction Algebra Essay
  36.    wt: 1:   Skills Chapter 3 Algebra
  37.    wt: 1:   4 algebra
  38.    wt: 1:   Mathematics Education Professors
  39.    wt: 1:   talk the algebra talk
  40.    wt: 1:   geometric implications for algebra
  41.    wt: 1:   teaching tutoring algebraic reason
  42.    wt: 1:   Lessening Algebra Difficulties
  43.    wt: 1:   the trouble with algebra
  44.    wt: 1:   Theory of Knowledge
  45.    wt: 1:   Different Kinds of Reasoning in maths
  46.    wt: 1:   three kinds of reason in mathematics
  47.    wt: 1:   deux definitions pour variable
  48.    wt: 1:   E Kirchoffs Second Law
  49.    wt: 1:   D Kirchoff First Law
  50.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  51.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  52.    wt: 1:   8 The Effect of Negative Remarks
  53.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  54.    wt: 1:   26 Function definitions done and coming
  55.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  56.    wt: 1:   15 Sign analysis of functions
  57.    wt: 1:   8 Set view of relations and functions
  58.    wt: 1:   1 Geometric Introduction of Function Notation
  59.    wt: 1:   8 quadratics backward use of various formulas
  60.    wt: 1:   4 quadratics difference of two squares
  61.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  62.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  63.    wt: 1:   Rewriting algebraic substitution as function substitutions
  64.    wt: 1:   16 cotangent function Definition Graph and Inverse
  65.    wt: 1:   15 cosecant function Definition Graph and Inverse
  66.    wt: 1:   14 secant function Definition Graph and Inverse
  67.    wt: 1:   13 cosecant function Definition Graph and Inverse
  68.    wt: 1:   11 arctan left inverse of tangent Graph
  69.    wt: 1:   8 arcsin left inverse of sine Graph
  70.    wt: 1:   6 Graph of arccos function
  71.    wt: 1:   8 Radian Measures of Common Angles
  72.    wt: 1:   2 Radian Measure Numerical Value of one degree
  73.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  74.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  75.    wt: 1:   Straight Lines Intersection of
  76.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  77.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  78.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  79.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  80.    wt: 1:   32 seven rows of pascals triangle
  81.    wt: 1:   30 unit circle calculation of six trigonometric functions
  82.    wt: 1:   28 Expressing products of sines cosines as sums
  83.    wt: 1:   26 Formulas for products of sines and cosines
  84.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  85.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  86.    wt: 1:   18 sum of sinusoidal waves as a single wave
  87.    wt: 1:   17F Law of cosines
  88.    wt: 1:   13 Graph of tangent function many periods
  89.    wt: 1:   12 Graph of tangent function for one period
  90.    wt: 1:   10 Graphs of sines and cosines many periods
  91.    wt: 1:   9 Graphs of sine and cosine over one period
  92.    wt: 1:   8 period of tangent function
  93.    wt: 1:   7 period of sine and cosine
  94.    wt: 1:   Unit Circle Development of Trigonometry
  95.    wt: 1:   14 Law of cosines
  96.    wt: 1:   8 Unit Circle Development of Trigonometry
  97.    wt: 1:   6 Field Properties of Complex Number
  98.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  99.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  100.    wt: 1:   9 Similarity of Triangles Usual Criteria
  101.    wt: 1:   8 Similarity of Triangles and Polygons
  102.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  103.    wt: 1:   4 Similarity Definition with Coordinate
  104.    wt: 1:   1 Early Concept of Like or Similar Shapes
  105.    wt: 1:   10 Midpoint of [a b] and [b a]
  106.    wt: 1:   6 Intersection of lines by solving linear systems
  107.    wt: 1:   1 Numerical view of lines and their equations
  108.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  109.    wt: 1:   17 Right Bisectors of Triangle Sides
  110.    wt: 1:   9 Construction of a right bisector
  111.    wt: 1:   3 Isometry of Triangles Congruence
  112.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  113.    wt: 1:   22 Multiplication of Signed Numbers
  114.    wt: 1:   19 Signed Multiples of Vectors
  115.    wt: 1:   8 Division and Mulplication of Compound Fractions
  116.    wt: 1:   4 Location of Point in Decimal Addition
  117.    wt: 1:   3 Location of Point in Decimal Multiplication
  118.    wt: 1:   1 The Counting Origins of Numbers
  119.    wt: 1:   5 Areas of Rectangles Revisited
  120.    wt: 1:   3 Inequalities Algebraically
  121.    wt: 1:   2 Algebraic View
  122.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  123.    wt: 1:   5 Equality in Algebra
  124.    wt: 1:   4 Comparison of Negative Numbers
  125.    wt: 1:   1 Whole and Natural Numbers
  126.    wt: 1:   6 Algebraic Solution Example
  127.    wt: 1:   5 Algebraic Solutions Introduction
  128.    wt: 1:   11 Volume of Sphere
  129.    wt: 1:   10 Volume of Pyramid
  130.    wt: 1:   9 Volume of Cone
  131.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  132.    wt: 1:   8 Sets of Numbers
  133.    wt: 1:   6 Three Notions of What is a Variable
  134.    wt: 1:   1 Three Skills For Algebra
  135.    wt: 1:   3 Comparison of Negative Numbers
  136.    wt: 1:   5 Square Roots with primes more still
  137.    wt: 1:   4 Square Roots with primes more
  138.    wt: 1:   2 Square Roots with Prime
  139.    wt: 1:   1 Squares and Square Roots Introduction
  140.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  141.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  142.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  143.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  144.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  145.    wt: 1:   4 LCM of 8 and 10 via Prime
  146.    wt: 1:   5 lengths and signs of numbers
  147.    wt: 1:   6 Simplification of Fractions with Units
  148.    wt: 1:   13 Fraction Comparison Algebraic View
  149.    wt: 1:   11 Simplification an Algebraic View
  150.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  151.    wt: 1:   6 Multiplication Algebraically Take II
  152.    wt: 1:   3 Unit fraction of a fraction
  153.    wt: 1:   6 Multiplication by Natural Numbers
  154.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  155.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  156.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  157.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  158.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  159.    wt: 1:   20 Uniqueness of Prime Factorization
  160.    wt: 1:   16 video Factors of 980 using prime
  161.    wt: 1:   15 video Factors of 20 using Prime Factorization
  162.    wt: 1:   14 video Factors of 24 Take II
  163.    wt: 1:   13 video Factors of 24 using prime
  164.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  165.    wt: 1:   8 Subtraction with Units of Measure
  166.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  167.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  168.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  169.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  170.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  171.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  172.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  173.    wt: 1:   012 Division of Time Intervals by Time Intervals
  174.    wt: 1:   011 Division of Time Intervals By Numbers
  175.    wt: 1:   010 Repeated Addition of Time Intervals
  176.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  177.    wt: 1:   8 Addition of Time Intervals via subtotaling
  178.    wt: 1:   7 Addition of Time Intervals
  179.    wt: 1:   4 Mixing and Changing Units of Time
  180.    wt: 1:   3 Units and Lengths of Time
  181.    wt: 1:   1 Intro of Kids To Time Date Skills
  182.    wt: 1:   Example 2 volume of a cone
  183.    wt: 1:   Example 1 volume of a pyramid
  184.    wt: 1:   Volume of Solid by Cross Sections Lesson
  185.    wt: 1:   Example 4 with x function of y
  186.    wt: 1:   34 Derivative of exponential function
  187.    wt: 1:   31 Derivatives of inverse functions
  188.    wt: 1:   30Chain Rule A Proof
  189.    wt: 1:   28 Chain Rule Preparation for a Proof
  190.    wt: 1:   21 Chain Rule for powers
  191.    wt: 1:   8 Differentiation of polynomials
  192.    wt: 1:   3 Motivation for Limit Definition Take 2
  193.    wt: 1:   2 Motivation for Limit Definition Take 1
  194.    wt: 1:   5 Jumps and absence of unlimited error control
  195.    wt: 1:   2 Algebraic codification
  196.    wt: 1:   .H1 First Fundamental Theorem of Calculus
  197.    wt: 1:   G.3 Constant Difference Theorem Proof
  198.    wt: 1:   D2 Limits of Monotone Sequences
  199.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  200.    wt: 1:   Chapter 18. Rules for Algebra
  201.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  202.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  203.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  204.    wt: 1:   Chapter 8 Three Skills For Algebra
  205.    wt: 1:   Chapter 6 Change of Language
  206.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  207.    wt: 1:   Chapter 4 Longer Chains of Reason
  208.    wt: 1:   Chapter 3 Chains of Reason
  209.    wt: 1:   Chapter 7 Two Treatments of Geometry
  210.    wt: 1:   Chapter 3 Algebra Difficulties
  211.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  212.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  213.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  214.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  215.    wt: 1:   Chapter 8 Change of Language
  216.    wt: 1:   Chapter 7 Longer Chains of Reason
  217.    wt: 1:   Chapter 6 Chains of Reason
  218.    wt: 1:   S Adding words to algebra
  219.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  220.    wt: 1:   C. Domino effect of being careful
  221.    wt: 1:   B. Domino effect of errors
  222.    wt: 1:   More Algebra and Slope based Calculus Preview
  223.    wt: 1:   Systematic Algebra Skill Development Missing Links

Extended Search

461 matches:

  1.    wt: 9:   9 Formulas for Real Exponents with Logarithms
  2.    wt: 9:   8 Formulas for Fractional Exponents with Logarithms
  3.    wt: 8:   11 Growth and Decay in Biology
  4.    wt: 8:   10 Exponential Growth and Decay Models
  5.    wt: 8:   2 Square Root Simplification a prequel
  6.    wt: 8:   1 Calculator Starter Exercises
  7.    wt: 4:   2 Algebraic use of function notation
  8.    wt: 4:   5 Areas of Rectangles Revisited
  9.    wt: 4:   3 Inequalities Algebraically
  10.    wt: 4:   1 Decimals Modular and Remainder Arithmetic
  11.    wt: 3:   26 Function definitions done and coming
  12.    wt: 3:   21 Graphs of functions given by Horizontal Line Method
  13.    wt: 3:   15 Sign analysis of functions
  14.    wt: 3:   8 Set view of relations and functions
  15.    wt: 3:   1 Geometric Introduction of Function Notation
  16.    wt: 3:   8 quadratics backward use of various formulas
  17.    wt: 3:   4 quadratics difference of two squares
  18.    wt: 3:   Rewriting algebraic substitution as function substitutions
  19.    wt: 3:   7 arcsin left inverse of sine Definition
  20.    wt: 3:   3 Left Inverse of cosine arccos definition
  21.    wt: 3:   27 Logarithmic use of products of sines and cosines
  22.    wt: 3:   21 Logarithms Powers and Exponentials
  23.    wt: 3:   21 Addition of Multiples of a Single Vector
  24.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  25.    wt: 3:   1 The Counting Origins of Numbers
  26.    wt: 3:   4 Fraction Operations Axiomatic Development
  27.    wt: 3:   2 Fraction Operations Physical Development
  28.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  29.    wt: 3:   1 Changing Calculations
  30.    wt: 3:   1 Whole and Natural Numbers
  31.    wt: 3:   6 Algebraic Solution Example
  32.    wt: 3:   5 Algebraic Solutions Introduction
  33.    wt: 3:   11 Volume of Sphere
  34.    wt: 3:   10 Volume of Pyramid
  35.    wt: 3:   10 Set View of Wordy Extensions To Arithmetic
  36.    wt: 3:   8 Sets of Numbers
  37.    wt: 3:   1 Finite Sets
  38.    wt: 3:   4 A Brief Story of numbers and algebra
  39.    wt: 3:   3 Properties of Square Roots with example
  40.    wt: 3:   Chapter 24 Logarithms Powers and Exponentials
  41.    wt: 3:   Chapter 19. Exponentials and Natural Logarithms
  42.    wt: 2:   5 logarithms and exponentials etc
  43.    wt: 2:   sign monoticity analysis example 4
  44.    wt: 2:   sign monoticity analysis example 3
  45.    wt: 2:   sign monoticity analysis example 2
  46.    wt: 2:   sign monoticity analysis example 1
  47.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  48.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  49.    wt: 2:   23 Inverse Functions
  50.    wt: 2:   22 Square Root function graphically
  51.    wt: 2:   20 Interchanging coordinates a reflection
  52.    wt: 2:   19 Horizontal line rule and method
  53.    wt: 2:   18 Vertical Line Rule and Method
  54.    wt: 2:   17 Function maxima minima and their location
  55.    wt: 2:   16 Increasing or decreasing on intervals
  56.    wt: 2:   14 Surjections Injections Bijections
  57.    wt: 2:   13 From one to one to many to one
  58.    wt: 2:   12 Function Domain Recognition Exercises
  59.    wt: 2:   11 Function Domain Range Source and Targets
  60.    wt: 2:   10 Interval Notation
  61.    wt: 2:   9 Set theory term relation possible origins
  62.    wt: 2:   7 Functions with finite domains
  63.    wt: 2:   6 Set Existence Formation and Notation
  64.    wt: 2:   5 Function notation for geometric transformations
  65.    wt: 2:   4 Function notation in and beyond mathematics
  66.    wt: 2:   3 Formula or function graphing exercise
  67.    wt: 2:   Introduction Reading Guide
  68.    wt: 2:   A Quadratics Summary
  69.    wt: 2:   10 quadratic exercises
  70.    wt: 2:   9 quadratics physical and further context
  71.    wt: 2:   7 quadratic formulla derivation
  72.    wt: 2:   6 quadratics numerical approach
  73.    wt: 2:   5 quadratics completing the square
  74.    wt: 2:   3 quadratics factoring by inspection
  75.    wt: 2:   2 quadratics graphing in general
  76.    wt: 2:   1 quadratics graphing exercises
  77.    wt: 2:   Quadratics in 10 steps
  78.    wt: 2:   8 Notes for instructors or tutors
  79.    wt: 2:   7 Links Lessons Elsewhere
  80.    wt: 2:   6 Polynomial Operations and Equivalent Computation Rules
  81.    wt: 2:   5 Polynomials Long division Nonlinear divisor
  82.    wt: 2:   4 Polynomials Long division linear divisor
  83.    wt: 2:   3 Polynomials Multiplication Addition
  84.    wt: 2:   2 Column Multiplication Method
  85.    wt: 2:   1 Polynomials Distributive Law
  86.    wt: 2:   10 arctan left inverse of tangent Definition
  87.    wt: 2:   8 arcsin left inverse of sine Graph
  88.    wt: 2:   6 Graph of arccos function
  89.    wt: 2:   4 Resultant of a Sum of Movements
  90.    wt: 2:   Analytic View of Triangle Construction or Line Instersection More
  91.    wt: 2:   Straight Lines Intersection of
  92.    wt: 2:   20 N th Roots of Complex Numbers
  93.    wt: 2:   19 N th Roots of Unity
  94.    wt: 2:   18 Sixth Roots of Unity
  95.    wt: 2:   17 Cube Roots of unity
  96.    wt: 2:   5 An Easy Proof of the Distributive Law
  97.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  98.    wt: 2:   10 Midpoint of [a b] and [b a]
  99.    wt: 2:   5 Algebraic View of Slopes
  100.    wt: 2:   22 Multiplication of Signed Numbers
  101.    wt: 2:   19 Signed Multiples of Vectors
  102.    wt: 2:   8 Division and Mulplication of Compound Fractions
  103.    wt: 2:   4 Location of Point in Decimal Addition
  104.    wt: 2:   3 Location of Point in Decimal Multiplication
  105.    wt: 2:   E Long Division Methods more
  106.    wt: 2:   D Long Division Methods
  107.    wt: 2:   C Three Decimal Subtraction Methods
  108.    wt: 2:   B Decimal Comparison and Subtraction
  109.    wt: 2:   A Decimal Addition Columm Methods
  110.    wt: 2:   8 Column Multiplication Methods in General
  111.    wt: 2:   7 Decimals Multiplication Methods Examples
  112.    wt: 2:   6 Column Methods for Decimal Multiplication
  113.    wt: 2:   5 Distributive Law for Whole Numbers
  114.    wt: 2:   4 Commutative Law Groups Counting Form
  115.    wt: 2:   3 Multiplicative Counting Skills Principles
  116.    wt: 2:   2 Combing Counts Addition Skills and Principles
  117.    wt: 2:   2 Algebraic View
  118.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  119.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  120.    wt: 2:   6 Compound Interest Forward and Backwards
  121.    wt: 2:   5 Triangle Area Formula Backwards
  122.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  123.    wt: 2:   3 Linear Equation Literal Solution More
  124.    wt: 2:   2 Linear Equation Literal Solution
  125.    wt: 2:   5 Equality in Algebra
  126.    wt: 2:   1 Equivalent Computation Rules
  127.    wt: 2:   4 Comparison of Negative Numbers
  128.    wt: 2:   1 Real Numbers Comparison
  129.    wt: 2:   4 Four Examples Fractional Coefficients
  130.    wt: 2:   3 Four Examples
  131.    wt: 2:   2 Three Examples
  132.    wt: 2:   1 Proper Equal Sign Usage
  133.    wt: 2:   10 One Example
  134.    wt: 2:   Using Letters for Physical Quantities
  135.    wt: 2:   13 Naming Identifying Formulas with Words
  136.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  137.    wt: 2:   9 Volume of Cone
  138.    wt: 2:   1 Written work formats for developing and showing skill
  139.    wt: 2:   9 Sets in Probability and Statistics
  140.    wt: 2:   7 Cautious or Safe Set Construction
  141.    wt: 2:   6 Power Set Notation
  142.    wt: 2:   5 Product Builder Notation
  143.    wt: 2:   4 Subset Builder Notation
  144.    wt: 2:   3 Counting with Sets etc
  145.    wt: 2:   2 Venn Diagrams
  146.    wt: 2:   6 Three Notions of What is a Variable
  147.    wt: 2:   1 Three Skills For Algebra
  148.    wt: 2:   3 Comparison of Negative Numbers
  149.    wt: 2:   5 Square Roots with primes more still
  150.    wt: 2:   4 Square Roots with primes more
  151.    wt: 2:   2 Square Roots with Prime
  152.    wt: 2:   1 Squares and Square Roots Introduction
  153.    wt: 2:   C Counting Areas with Powers of Ten
  154.    wt: 2:   B Powers of Ten
  155.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  156.    wt: 2:   Quick history of numbers and algebra
  157.    wt: 2:   012 Division of Time Intervals by Time Intervals
  158.    wt: 2:   011 Division of Time Intervals By Numbers
  159.    wt: 2:   010 Repeated Addition of Time Intervals
  160.    wt: 2:   1 Intro of Kids To Time Date Skills
  161.    wt: 2:   38 Formulas and derivatives for powers and roots
  162.    wt: 2:   17 Derivatives of quotients of sine and cosine
  163.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  164.    wt: 2:   E2 Algebraic Properties of Limits
  165.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  166.    wt: 2:   Chapter 18. Rules for Algebra
  167.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  168.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  169.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  170.    wt: 2:   Chapter 8 Three Skills For Algebra
  171.    wt: 2:   Chapter 6 Change of Language
  172.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  173.    wt: 2:   Chapter 4 Longer Chains of Reason
  174.    wt: 2:   Chapter 3 Chains of Reason
  175.    wt: 1:   Ramblings Introduction Algebra Essay
  176.    wt: 1:   Skills Chapter 3 Algebra
  177.    wt: 1:   4 algebra
  178.    wt: 1:   1 arithmetic with unsigned numbers
  179.    wt: 1:   Mathematics Education Professors
  180.    wt: 1:   talk the algebra talk
  181.    wt: 1:   geometric implications for algebra
  182.    wt: 1:   teaching tutoring algebraic reason
  183.    wt: 1:   Lessening Algebra Difficulties
  184.    wt: 1:   the trouble with algebra
  185.    wt: 1:   Theory of Knowledge
  186.    wt: 1:   Different Kinds of Reasoning in maths
  187.    wt: 1:   three kinds of reason in mathematics
  188.    wt: 1:   deux definitions pour variable
  189.    wt: 1:   E Kirchoffs Second Law
  190.    wt: 1:   D Kirchoff First Law
  191.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  192.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  193.    wt: 1:   10 Ends values for work study instruction
  194.    wt: 1:   8 The Effect of Negative Remarks
  195.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  196.    wt: 1:   16 cotangent function Definition Graph and Inverse
  197.    wt: 1:   15 cosecant function Definition Graph and Inverse
  198.    wt: 1:   14 secant function Definition Graph and Inverse
  199.    wt: 1:   13 cosecant function Definition Graph and Inverse
  200.    wt: 1:   11 arctan left inverse of tangent Graph
  201.    wt: 1:   9 motivation for name arcsin
  202.    wt: 1:   5 Swapping Coordinates is a reflection
  203.    wt: 1:   4 possible motivation for term arccos
  204.    wt: 1:   2 cosine function more properties
  205.    wt: 1:   1 cosine function properties
  206.    wt: 1:   8 Radian Measures of Common Angles
  207.    wt: 1:   2 Radian Measure Numerical Value of one degree
  208.    wt: 1:   1 Degrees and Radians Introduction
  209.    wt: 1:   10 Parallelogram Addition Method
  210.    wt: 1:   1 graphing y=f(x a)
  211.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  212.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  213.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  214.    wt: 1:   Straight Lines ASA Intersection Study More
  215.    wt: 1:   Straight Lines ASA Intersection Study
  216.    wt: 1:   Straight Lines Instersection Solving Equations
  217.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  218.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  219.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  220.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  221.    wt: 1:   32 seven rows of pascals triangle
  222.    wt: 1:   30 unit circle calculation of six trigonometric functions
  223.    wt: 1:   28 Expressing products of sines cosines as sums
  224.    wt: 1:   26 Formulas for products of sines and cosines
  225.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  226.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  227.    wt: 1:   18 sum of sinusoidal waves as a single wave
  228.    wt: 1:   17F Law of cosines
  229.    wt: 1:   13 Graph of tangent function many periods
  230.    wt: 1:   12 Graph of tangent function for one period
  231.    wt: 1:   10 Graphs of sines and cosines many periods
  232.    wt: 1:   9 Graphs of sine and cosine over one period
  233.    wt: 1:   8 period of tangent function
  234.    wt: 1:   7 period of sine and cosine
  235.    wt: 1:   Unit Circle Development of Trigonometry
  236.    wt: 1:   14 Law of cosines
  237.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  238.    wt: 1:   8 Unit Circle Development of Trigonometry
  239.    wt: 1:   6 Field Properties of Complex Number
  240.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  241.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  242.    wt: 1:   9 Similarity of Triangles Usual Criteria
  243.    wt: 1:   8 Similarity of Triangles and Polygons
  244.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  245.    wt: 1:   4 Similarity Definition with Coordinate
  246.    wt: 1:   1 Early Concept of Like or Similar Shapes
  247.    wt: 1:   6 Intersection of lines by solving linear systems
  248.    wt: 1:   1 Numerical view of lines and their equations
  249.    wt: 1:   10 Pythagorean plane distance formula
  250.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  251.    wt: 1:   17 Right Bisectors of Triangle Sides
  252.    wt: 1:   10 Dropping a perpendicular to line
  253.    wt: 1:   9 Construction of a right bisector
  254.    wt: 1:   3 Isometry of Triangles Congruence
  255.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  256.    wt: 1:   1 Length Measurement
  257.    wt: 1:   musings do not puiblish real numbers
  258.    wt: 1:   A Modular and Remainder Arithmetic
  259.    wt: 1:   A Signed Number Arithmetic Review
  260.    wt: 1:   26 More Less Greater Than Comparison
  261.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  262.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  263.    wt: 1:   23 Distributive Law Two Derivations
  264.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  265.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  266.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  267.    wt: 1:   15 Head to Tails in place Addition Associative
  268.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  269.    wt: 1:   13 Arrows and Vectors in a Plane
  270.    wt: 1:   12 Real Numbers Line Signed Coordinates
  271.    wt: 1:   11 Signed Number Addition and Addition Properties
  272.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  273.    wt: 1:   9 Division with Digits after Decimal Point
  274.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  275.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  276.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  277.    wt: 1:   2 Counting Digits in Decimal Multiplication
  278.    wt: 1:   1 Fractions with Finite Decimal Expansions
  279.    wt: 1:   5 Proportionality in Equivalent Fractions
  280.    wt: 1:   4 Rates Ratios and Proporitionality
  281.    wt: 1:   3 Proportionality Examples
  282.    wt: 1:   1 What is Proportionality
  283.    wt: 1:   6 Equations and Systems Equivalent or Implied
  284.    wt: 1:   4 Subtraction and Division Axioms
  285.    wt: 1:   3 Product Axioms Two Forms
  286.    wt: 1:   2 Addition and Multiplication Axioms
  287.    wt: 1:   5 Greater More Less Than Signs in General
  288.    wt: 1:   3 More and Less Than with Unlike Signs
  289.    wt: 1:   2 More and Less Than for Counts and Measures
  290.    wt: 1:   16 Real Numbers Comparison
  291.    wt: 1:   15 Real Number Division
  292.    wt: 1:   14 Real Number Multiplication
  293.    wt: 1:   13 Real Number Subtraction
  294.    wt: 1:   12 Real Number Additive Inverses or Negatives
  295.    wt: 1:   11 Real Number Addition
  296.    wt: 1:   10 Real Number Lengths and Signs
  297.    wt: 1:   9 Coordinates for Regions in Space
  298.    wt: 1:   8 Coordinates for Maps and Planes
  299.    wt: 1:   7 Real Numbers as Line Cordinates
  300.    wt: 1:   6 Unsigned Real Numbers
  301.    wt: 1:   5 Rational Numbers More
  302.    wt: 1:   4 Rational Numbers
  303.    wt: 1:   3 Fractions
  304.    wt: 1:   2 Integers
  305.    wt: 1:   5 Independent versus Dependent Variables
  306.    wt: 1:   4 Changing Letters
  307.    wt: 1:   3 Geometric Formulas and Function Notation
  308.    wt: 1:   2 Computation Rules Evaluation
  309.    wt: 1:   1 Formulas Dependence and Function Notation
  310.    wt: 1:   More Exercises
  311.    wt: 1:   Simple Exercises
  312.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  313.    wt: 1:   4 GE III Animated Examples
  314.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  315.    wt: 1:   3 GE III Equation Addition and Multiplication
  316.    wt: 1:   2 GE II Comparison
  317.    wt: 1:   1 GE Substitution four examples
  318.    wt: 1:   4 Solving a triangular system exercise
  319.    wt: 1:   3 Solving triangular system example
  320.    wt: 1:   2 Essentially one exercises three with solution
  321.    wt: 1:   1 Essentially One Unknown
  322.    wt: 1:   Skill Development Notes
  323.    wt: 1:   9 Three Examples
  324.    wt: 1:   8 One Example
  325.    wt: 1:   7 Two Examples
  326.    wt: 1:   6 Three Examples
  327.    wt: 1:   5 Three Examples
  328.    wt: 1:   4 Two Examples
  329.    wt: 1:   3 Two Examples
  330.    wt: 1:   2 Three Examples
  331.    wt: 1:   Formula Usage Show Work Format
  332.    wt: 1:   8 Compound Interest Formula Evaluation
  333.    wt: 1:   7 Compound Interest Formula Introduction
  334.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  335.    wt: 1:   5 Box Volume Formula Example
  336.    wt: 1:   4 Circle Area Formula Example
  337.    wt: 1:   3 Triangle Area Formula Example
  338.    wt: 1:   2 Another Rectangle Area Formula Example
  339.    wt: 1:   5 Talking about Numbers and Quantities
  340.    wt: 1:   3 Adding Words To Arithmetic
  341.    wt: 1:   2 What is a Variable
  342.    wt: 1:   About Folder Contents
  343.    wt: 1:   4 Greater More Less Than Signs in General
  344.    wt: 1:   2 More and Less Than with Unlike Signs
  345.    wt: 1:   1 More and Less Than for Counts and Measures
  346.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  347.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  348.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  349.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  350.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  351.    wt: 1:   4 LCM of 8 and 10 via Prime
  352.    wt: 1:   5 lengths and signs of numbers
  353.    wt: 1:   6 Simplification of Fractions with Units
  354.    wt: 1:   13 Fraction Comparison Algebraic View
  355.    wt: 1:   11 Simplification an Algebraic View
  356.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  357.    wt: 1:   6 Multiplication Algebraically Take II
  358.    wt: 1:   3 Unit fraction of a fraction
  359.    wt: 1:   10 Integer Multiplication Formulas
  360.    wt: 1:   6 Multiplication by Natural Numbers
  361.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  362.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  363.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  364.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  365.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  366.    wt: 1:   20 Uniqueness of Prime Factorization
  367.    wt: 1:   16 video Factors of 980 using prime
  368.    wt: 1:   15 video Factors of 20 using Prime Factorization
  369.    wt: 1:   14 video Factors of 24 Take II
  370.    wt: 1:   13 video Factors of 24 using prime
  371.    wt: 1:   10 video Prime Factorization upto 23 squared
  372.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  373.    wt: 1:   10 Division by Five Long and Short Ways
  374.    wt: 1:   8 Subtraction with Units of Measure
  375.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  376.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  377.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  378.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  379.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  380.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  381.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  382.    wt: 1:   016 Numbering Occidental Calendar Days
  383.    wt: 1:   015 School and work day counting tables
  384.    wt: 1:   014 Counting Days with Calendars
  385.    wt: 1:   013 Travel Time Tables
  386.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  387.    wt: 1:   8 Addition of Time Intervals via subtotaling
  388.    wt: 1:   7 Addition of Time Intervals
  389.    wt: 1:   4 Mixing and Changing Units of Time
  390.    wt: 1:   3 Units and Lengths of Time
  391.    wt: 1:   Example 2 volume of a cone
  392.    wt: 1:   Example 1 volume of a pyramid
  393.    wt: 1:   Volume of Solid by Cross Sections Lesson
  394.    wt: 1:   Example 4 with x function of y
  395.    wt: 1:   34 Derivative of exponential function
  396.    wt: 1:   31 Derivatives of inverse functions
  397.    wt: 1:   30Chain Rule A Proof
  398.    wt: 1:   28 Chain Rule Preparation for a Proof
  399.    wt: 1:   21 Chain Rule for powers
  400.    wt: 1:   8 Differentiation of polynomials
  401.    wt: 1:   3 Motivation for Limit Definition Take 2
  402.    wt: 1:   2 Motivation for Limit Definition Take 1
  403.    wt: 1:   5 Jumps and absence of unlimited error control
  404.    wt: 1:   2 Algebraic codification
  405.    wt: 1:   .H1 First Fundamental Theorem of Calculus
  406.    wt: 1:   G.3 Constant Difference Theorem Proof
  407.    wt: 1:   D2 Limits of Monotone Sequences
  408.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  409.    wt: 1:   Postscript More on Better Performance
  410.    wt: 1:   Postscript For Better Performance
  411.    wt: 1:   Appendix E. How To Study Mathematics and Why
  412.    wt: 1:   Appendix D. What to do in School and Why
  413.    wt: 1:   Appendix C. How to Read
  414.    wt: 1:   Appendix B. How To Learn
  415.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  416.    wt: 1:   Chapter 31 Direct and Indirect Reason
  417.    wt: 1:   Chapter 30 Truth Tables
  418.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  419.    wt: 1:   Chapter 28 Occurrence Tables
  420.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  421.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  422.    wt: 1:   Chapter 25. Mathematical Induction Examples
  423.    wt: 1:   Chapter 25. Mathematical Induction Examples
  424.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  425.    wt: 1:   Chapter 23. Notation For Sums
  426.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  427.    wt: 1:   Chapter 21. Third Reading Guide
  428.    wt: 1:   Chapter 20. Degrees and Radians
  429.    wt: 1:   Chapter 19. Functions and Sets
  430.    wt: 1:   Chapter 16. Painless Theorem Proving
  431.    wt: 1:   Chapter 15. Solving Linear Equations
  432.    wt: 1:   Chapter 13. Second Reading Guide
  433.    wt: 1:   Chapter 12. Shorthand Usage Guide
  434.    wt: 1:   Chapter 11. Why Shorthand
  435.    wt: 1:   Chapter 10 Describing and Changing Calculations
  436.    wt: 1:   Postscript What is a Variable
  437.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  438.    wt: 1:   Solutions For Arithmetic Exercises
  439.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  440.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  441.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  442.    wt: 1:   Foreword
  443.    wt: 1:   Chapter 7 Two Treatments of Geometry
  444.    wt: 1:   Chapter 3 Algebra Difficulties
  445.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  446.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  447.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  448.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  449.    wt: 1:   Chapter 8 Change of Language
  450.    wt: 1:   Chapter 7 Longer Chains of Reason
  451.    wt: 1:   Chapter 6 Chains of Reason
  452.    wt: 1:   S Adding words to algebra
  453.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  454.    wt: 1:   C. Domino effect of being careful
  455.    wt: 1:   B. Domino effect of errors
  456.    wt: 1:   More Algebra and Slope based Calculus Preview
  457.    wt: 1:   Systematic Algebra Skill Development Missing Links
  458.    wt: 11:   3 Natural Logarithms and Exponentials Basic Properties
  459.    wt: 10:   7 Formulas for Roots with Logarithms Derivation
  460.    wt: 10:   6 Formulas for Even and Odd Roots with Logarithms
  461.    wt: 10:   5 Natural Logarithm Calculator Exercises

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