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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
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What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

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  1.    wt: 6:   Advanced Calculus Volume 3 Appendices/
  2.    wt: 3:   13 Vectors/
  3.    wt: 3:   3 Cartesian and Polar Coordinates/
  4.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  5.    wt: 3:   Volume 3 Why Slopes A Calculus Intro Etc/
  6.    wt: 2:   3 Quadratics Geometrically/
  7.    wt: 2:   6 Trigonometry first steps/
  8.    wt: 2:   1 Maps Plans Measurement/
  9.    wt: 2:   3 Prime Factorization Skills/
  10.    wt: 2:   12 Webvideo Lessons on Area and Volume Calculation/
  11.    wt: 2:   4 Lessons on Using Derivatives/
  12.    wt: 2:   38 Lessons on Calculating Derivatives/
  13.    wt: 2:   13 Lessons on Limits and Continuity/
  14.    wt: 1:   LAMP Lean Applied Mathematics Program/
  15.    wt: 1:   Volume 1A Regles et modeles/
  16.    wt: 1:   15 Arc or Inverse Trigonometric Function/
  17.    wt: 1:   14 Degrees to Radians and Radians to Degrees/
  18.    wt: 1:   12 Function Translating and Rescaling/
  19.    wt: 1:   11 Parallel Straight Lines and Transversals/
  20.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  21.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  22.    wt: 1:   8 Unit Circle Trigonometry/
  23.    wt: 1:   7 Complex Numbers/
  24.    wt: 1:   5 What is Similarity/
  25.    wt: 1:   4 Lines and Slopes Take 1/
  26.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  27.    wt: 1:   Geometry maps plans trigonometry vectors/
  28.    wt: 1:   Step 4 Gaussian Elimination/
  29.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  30.    wt: 1:   Step 1 Stick diagram and fractions/
  31.    wt: 1:   3 Solving Linear Equations/
  32.    wt: 1:   C Decimal Multiplication Methods/
  33.    wt: 1:   5 Lessons on Integration/
  34.    wt: 1:   70 Calculus Starter Lessons/
  35.    wt: 1:   Volume 2 Three Skills For Algebra/
  36.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  37.    wt: 1:   Volume 1A Pattern Based Reason/
  38.    wt: 1:   Volume 1 Elements of Reason/
  39.    wt: 1:   Work and Study Tips/
  40.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

220 matches:

  1.    wt: 3:   33 sines and cosines of 2A 3A 4A 5A
  2.    wt: 3:   3 More on Groups of 3 Multi Digit Place Value
  3.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  4.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  5.    wt: 2:   32 seven rows of pascals triangle
  6.    wt: 2:   11 Triangle Inequality
  7.    wt: 2:   3 Isometry of Triangles Congruence
  8.    wt: 2:   3 Lengths and Areas on Maps and Plans
  9.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  10.    wt: 2:   3 Triangle Area Formula Example
  11.    wt: 2:   3 signed coordinates for maps and planes
  12.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  13.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  14.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  15.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  16.    wt: 2:   A Related Material in Volume 3
  17.    wt: 2:   A Related lessons in Volume 3
  18.    wt: 2:   33 Chain Rule Real Player video examples
  19.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  20.    wt: 2:   Fall 1983 Calculus Appetizer
  21.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  22.    wt: 1:   Skills Chapter 5 Calculus
  23.    wt: 1:   Skills Chapter 3 Algebra
  24.    wt: 1:   3 Euclidean Geometry Leanly
  25.    wt: 1:   Maps Plans Drawings
  26.    wt: 1:   teaching tips
  27.    wt: 1:   05 13 OldSiteEntrancePage
  28.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  29.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  30.    wt: 1:   3 Energy Power Heat08
  31.    wt: 1:   C Energy Power03
  32.    wt: 1:   E Wire Resistance Calculation03
  33.    wt: 1:   3 Like resistors in parallel
  34.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  35.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  36.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  37.    wt: 1:   23 Modularized Skill Development Modularized Rigor
  38.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  39.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  40.    wt: 1:   16 Secondary Mathematics Tips
  41.    wt: 1:   13 Addition and Addition Tables
  42.    wt: 1:   3 Preparing for Science Studies
  43.    wt: 1:   Ages 3 plus to 4 plus
  44.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  45.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  46.    wt: 1:   sign monoticity analysis example 3
  47.    wt: 1:   23 Inverse Functions
  48.    wt: 1:   13 From one to one to many to one
  49.    wt: 1:   3 Formula or function graphing exercise
  50.    wt: 1:   3 quadratics factoring by inspection
  51.    wt: 1:   Quadratics in 10 steps
  52.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  53.    wt: 1:   3 Polynomials Multiplication Addition
  54.    wt: 1:   13 cosecant function Definition Graph and Inverse
  55.    wt: 1:   3 Left Inverse of cosine arccos definition
  56.    wt: 1:   7 Radian Measures in special Triangles
  57.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  58.    wt: 1:   13 Velocity Vectors in Physics
  59.    wt: 1:   3 Navigation with Arrows or Vectors
  60.    wt: 1:   3 graphing y=f(x c) plus K
  61.    wt: 1:   Triangle Angles Sum To 180 Degrees
  62.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  63.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  64.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  65.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  66.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  67.    wt: 1:   31 basic secant cosecant cotangent trig identities
  68.    wt: 1:   30 unit circle calculation of six trigonometric functions
  69.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  70.    wt: 1:   16 Right Triangle Complementary Angle Relations
  71.    wt: 1:   13 Graph of tangent function many periods
  72.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  73.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  74.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  75.    wt: 1:   13 Trig Formulas for dot and cross Products
  76.    wt: 1:   3 Addition Properties
  77.    wt: 1:   8 Triangles Cascade Problem Solving
  78.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  79.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  80.    wt: 1:   3 Trigonometric Ratios sine and cosine
  81.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  82.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  83.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  84.    wt: 1:   12 Triangles Similarity More Problems
  85.    wt: 1:   11 Triangle Similarity Missing Side Problem
  86.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  87.    wt: 1:   9 Similarity of Triangles Usual Criteria
  88.    wt: 1:   8 Similarity of Triangles and Polygons
  89.    wt: 1:   3 Similarity by Design with coordinates
  90.    wt: 1:   3 Slope product for perpendicular lines
  91.    wt: 1:   13 Pythagorean spatial distance formulas
  92.    wt: 1:   3 Rectangular Coordinates Review
  93.    wt: 1:   PS H Distributive Law For Complex Numbers
  94.    wt: 1:   PS G Rotation Distributes over Addition
  95.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  96.    wt: 1:   PS E Multiplication with Polar Coordinates
  97.    wt: 1:   PS D Addition with Cartesian Coordinates
  98.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  99.    wt: 1:   PS B Parallelogram Construction Methods
  100.    wt: 1:   PS A Kite Construction Methods
  101.    wt: 1:   19 Right Triangle Similarity
  102.    wt: 1:   18 Triangle Similarity Take 1
  103.    wt: 1:   17 Right Bisectors of Triangle Sides
  104.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  105.    wt: 1:   13 Angle Side Angle Failure
  106.    wt: 1:   11 Triangle Construction Fails
  107.    wt: 1:   8 Isoceles Triangles
  108.    wt: 1:   2 Correspondence between Triangles
  109.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  110.    wt: 1:   6 Figuring with Maps Not to Scale
  111.    wt: 1:   4 Angles on Maps Plans drawn to scale
  112.    wt: 1:   23 Distributive Law Two Derivations
  113.    wt: 1:   13 Arrows and Vectors in a Plane
  114.    wt: 1:   3 Location of Point in Decimal Multiplication
  115.    wt: 1:   4 Commutative Law Groups Counting Form
  116.    wt: 1:   3 Multiplicative Counting Skills Principles
  117.    wt: 1:   3 Inequalities Algebraically
  118.    wt: 1:   3 Proportionality Examples
  119.    wt: 1:   5 Triangle Area Formula Backwards
  120.    wt: 1:   3 Linear Equation Literal Solution More
  121.    wt: 1:   3 Product Axioms Two Forms
  122.    wt: 1:   3 More and Less Than with Unlike Signs
  123.    wt: 1:   13 Real Number Subtraction
  124.    wt: 1:   8 Coordinates for Maps and Planes
  125.    wt: 1:   3 Fractions
  126.    wt: 1:   3 Geometric Formulas and Function Notation
  127.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  128.    wt: 1:   3 GE III Equation Addition and Multiplication
  129.    wt: 1:   3 Solving triangular system example
  130.    wt: 1:   3 Four Examples
  131.    wt: 1:   3 Two Examples
  132.    wt: 1:   13 Naming Identifying Formulas with Words
  133.    wt: 1:   11 Volume of Sphere
  134.    wt: 1:   10 Volume of Pyramid
  135.    wt: 1:   9 Volume of Cone
  136.    wt: 1:   5 Box Volume Formula Example
  137.    wt: 1:   3 Counting with Sets etc
  138.    wt: 1:   3 Adding Words To Arithmetic
  139.    wt: 1:   3 Comparison of Negative Numbers
  140.    wt: 1:   3 Properties of Square Roots with example
  141.    wt: 1:   13 GCD from given Prime Factorization
  142.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  143.    wt: 1:   3 Counting with Tables and Trees II
  144.    wt: 1:   3 Multiplying Units and Numbers
  145.    wt: 1:   13 Fraction Comparison Algebraic View
  146.    wt: 1:   3 Unit fraction of a fraction
  147.    wt: 1:   13 Subtraction with Additive Inverse
  148.    wt: 1:   3 Adding Movements with same direction
  149.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  150.    wt: 1:   26 Divisibility by 2 3 5 Example
  151.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  152.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  153.    wt: 1:   23 Remainder Arithmetic Modulo 2
  154.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  155.    wt: 1:   21 Remainder Arithmetic Modulo 3
  156.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  157.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  158.    wt: 1:   13 video Factors of 24 using prime
  159.    wt: 1:   10 video Prime Factorization upto 23 squared
  160.    wt: 1:   3 video Primes and Composites from 9 times table
  161.    wt: 1:   Long Division forwards and backwards Example 3
  162.    wt: 1:   3 Division Single Digit Divisor Example
  163.    wt: 1:   3 More One Digit Multipliers
  164.    wt: 1:   1 Why 3 times 5 gives 15
  165.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  166.    wt: 1:   3. How to add with decimals A sans conversions
  167.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  168.    wt: 1:   013 Travel Time Tables
  169.    wt: 1:   3 Units and Lengths of Time
  170.    wt: 1:   Example 2 volume of a cone
  171.    wt: 1:   Example 1 volume of a pyramid
  172.    wt: 1:   Volume of Solid by Cross Sections Lesson
  173.    wt: 1:   Example 3
  174.    wt: 1:   3 Two Chain Rule Method Exercises
  175.    wt: 1:   3 Second derivative test
  176.    wt: 1:   38 Formulas and derivatives for powers and roots
  177.    wt: 1:   36 Cube root derivative animated
  178.    wt: 1:   34 Derivative of exponential function
  179.    wt: 1:   31 Derivatives of inverse functions
  180.    wt: 1:   30Chain Rule A Proof
  181.    wt: 1:   23 Chain Rule in general
  182.    wt: 1:   15 sine and cosine derivatives 3rd step
  183.    wt: 1:   13 sine and cosine derivatives 1st step
  184.    wt: 1:   3 Motivation for Limit Definition Take 2
  185.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  186.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  187.    wt: 1:   5 Jumps and absence of unlimited error control
  188.    wt: 1:   3 Decimal insights for limits continuity convergence
  189.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  190.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  191.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  192.    wt: 1:   G.3 Constant Difference Theorem Proof
  193.    wt: 1:   F.3 Intermediate Value Theorem
  194.    wt: 1:   C Triangle Inequalities
  195.    wt: 1:   B3 Bolzano Weierstrass Theorem
  196.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  197.    wt: 1:   Chapter 23 Links To Trigonometry
  198.    wt: 1:   Chapter 13. Acceleration
  199.    wt: 1:   Chapter 9 About First Courses in Calculus
  200.    wt: 1:   Chapter 3. Slope Sign Analysis
  201.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  202.    wt: 1:   Chapter 31 Direct and Indirect Reason
  203.    wt: 1:   Chapter 30 Truth Tables
  204.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  205.    wt: 1:   Chapter 23. Notation For Sums
  206.    wt: 1:   Chapter 13. Second Reading Guide
  207.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  208.    wt: 1:   Chapter 3 Chains of Reason
  209.    wt: 1:   Chapter 3 Algebra Difficulties
  210.    wt: 1:   Chapter 23 Truth Tables
  211.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  212.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  213.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  214.    wt: 1:   Chapter 3 Algebra Starter Lessons
  215.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  216.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  217.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  218.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  219.    wt: 1:   More Algebra and Slope based Calculus Preview
  220.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

723 matches:

  1.    wt: 8:   G.2 Lipshitz Conditions Integration Calculus Reform
  2.    wt: 8:   B3 Bolzano Weierstrass Theorem
  3.    wt: 7:   G.1 First Fundamental Theorem of Calculus
  4.    wt: 7:   G.6 Bounded Derivatives implies Lipshitz Continuity
  5.    wt: 7:   G.4 Lipschitz Continuity implies EquiContinuity
  6.    wt: 7:   G.3 Constant Difference Theorem Proof
  7.    wt: 7:   F.5a Equicontinuity Theorems
  8.    wt: 7:   F.3 Intermediate Value Theorem
  9.    wt: 7:   C Triangle Inequalities
  10.    wt: 7:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  11.    wt: 6:   Postscript One Sided and Intermediate Value Theorems
  12.    wt: 6:   G.5 Motions With Bounded Velocities
  13.    wt: 6:   G.2 Differentiable Functions Mean Value Theorem
  14.    wt: 6:   G.1 Differentiable Functions Rolles Theorem
  15.    wt: 6:   F.5b Extreme Value Theorem
  16.    wt: 6:   F.4 Finite Covering Theorem
  17.    wt: 6:   F.2 Closed Range Theorem
  18.    wt: 6:   F.1 What Functions are Continuous
  19.    wt: 6:   E2 Algebraic Properties of Limits
  20.    wt: 6:   E1 Error Control Inequalities
  21.    wt: 6:   D2 Limits of Monotone Sequences
  22.    wt: 6:   D1 Sets and Sequences GLBs and LGBs
  23.    wt: 6:   B1 Pigeon Hole Principles from combinatorics
  24.    wt: 6:   PostScript For and Against Decimal Perspectives
  25.    wt: 6:   A1. Introduction
  26.    wt: 5:   13 Velocity Vectors in Physics
  27.    wt: 5:   3 Navigation with Arrows or Vectors
  28.    wt: 5:   34 sines and cosines of 2A 3A 4A 5A
  29.    wt: 5:   33 sines and cosines of 2A 3A 4A 5A
  30.    wt: 5:   13 Pythagorean spatial distance formulas
  31.    wt: 5:   11 Triangle Inequality
  32.    wt: 5:   3 Rectangular Coordinates Review
  33.    wt: 5:   3 Solving triangular system example
  34.    wt: 5:   Chapter 23 Links To Trigonometry
  35.    wt: 5:   Chapter 13. Acceleration
  36.    wt: 5:   Chapter 3. Slope Sign Analysis
  37.    wt: 5:   Fall 1983 Calculus Appetizer
  38.    wt: 4:   35 sines and cosines of 2A 3A 4A 5A
  39.    wt: 4:   32 seven rows of pascals triangle
  40.    wt: 4:   3 Isometry of Triangles Congruence
  41.    wt: 4:   3 Lengths and Areas on Maps and Plans
  42.    wt: 4:   3 Gaussian Elimination 3 unknowns first example
  43.    wt: 4:   13 video Factors of 24 using prime
  44.    wt: 4:   3 video Primes and Composites from 9 times table
  45.    wt: 4:   3 More on Groups of 3 Multi Digit Place Value
  46.    wt: 4:   Example 3
  47.    wt: 4:   A Related lessons in Volume 3
  48.    wt: 4:   33 Chain Rule Real Player video examples
  49.    wt: 4:   31 Derivatives of inverse functions
  50.    wt: 4:   Chapter 9 About First Courses in Calculus
  51.    wt: 3:   Skills Chapter 3 Algebra
  52.    wt: 3:   3 quadratics factoring by inspection
  53.    wt: 3:   Quadratics in 10 steps
  54.    wt: 3:   3 Circle Arclengh Proportional to Central Angle
  55.    wt: 3:   A Global Time and Navigation
  56.    wt: 3:   15 Dot and Cross Product
  57.    wt: 3:   14 Why Scalar Multiplication Distributes Physical Argument
  58.    wt: 3:   12 From Applied To Pure Mathematics
  59.    wt: 3:   11 Component Method
  60.    wt: 3:   10 Parallelogram Addition Method
  61.    wt: 3:   9 Head to Tail Coordinate View
  62.    wt: 3:   8 Parallel Vectors
  63.    wt: 3:   7 Coordinate Addition and Scalar Multiplication
  64.    wt: 3:   6 Vectors with Coordinates
  65.    wt: 3:   5 Head To Tail Arrow Addition
  66.    wt: 3:   4 Resultant of a Sum of Movements
  67.    wt: 3:   2 Signed Coordinates
  68.    wt: 3:   1 Unsigned Coordinates
  69.    wt: 3:   Vector and Complex Number Applet
  70.    wt: 3:   13 Straight Lines Finding Equations from 2 points
  71.    wt: 3:   12 Straight Lines Graphing mx plus b
  72.    wt: 3:   31 basic secant cosecant cotangent trig identities
  73.    wt: 3:   6 sines and cosines for reference angle 30 degrees
  74.    wt: 3:   13 Trig Formulas for dot and cross Products
  75.    wt: 3:   3 Addition Properties
  76.    wt: 3:   8 Triangles Cascade Problem Solving
  77.    wt: 3:   5 Trigonometric Ratios For Tangent and Special Triangles
  78.    wt: 3:   4 Trigonometric Ratios For Two Special Triangles
  79.    wt: 3:   3 Trigonometric Ratios sine and cosine
  80.    wt: 3:   2 Similar Triangles Equality of Corresponding Side Ratios
  81.    wt: 3:   Right Triangle and Unit Circle Trigonometry
  82.    wt: 3:   13 Navigation Location from Angles to 2 Landmarks
  83.    wt: 3:   3 Similarity by Design with coordinates
  84.    wt: 3:   3 Slope product for perpendicular lines
  85.    wt: 3:   12 Spatial Coordinates
  86.    wt: 3:   10 Pythagorean plane distance formula
  87.    wt: 3:   9 Pythagorean Theorem Chinese Square Proof
  88.    wt: 3:   8 Distance Between Points on a Line
  89.    wt: 3:   7 Complex Numbers Appetizer
  90.    wt: 3:   6 Polar Multiplication and Rotation
  91.    wt: 3:   5 Cartesian Addition and Translation
  92.    wt: 3:   4 Polar Coordinates to and from
  93.    wt: 3:   2 Cartesian Coordinates with signs
  94.    wt: 3:   1 Cartesian Coordinates sans signs
  95.    wt: 3:   PS C Similarity Use Recognize it in Trigonometry
  96.    wt: 3:   13 Angle Side Angle Failure
  97.    wt: 3:   8 More Use of Maps Not Drawn to Scale
  98.    wt: 3:   6 Figuring with Maps Not to Scale
  99.    wt: 3:   4 Angles on Maps Plans drawn to scale
  100.    wt: 3:   3 GE III Equation Addition and Multiplication
  101.    wt: 3:   4 Solving a triangular system exercise
  102.    wt: 3:   2 Essentially one exercises three with solution
  103.    wt: 3:   1 Essentially One Unknown
  104.    wt: 3:   3 Four Examples
  105.    wt: 3:   3 Two Examples
  106.    wt: 3:   10 video Prime Factorization upto 23 squared
  107.    wt: 3:   3 More One Digit Multipliers
  108.    wt: 3:   Example 2 volume of a cone
  109.    wt: 3:   Example 1 volume of a pyramid
  110.    wt: 3:   Volume of Solid by Cross Sections Lesson
  111.    wt: 3:   Example 4 with x function of y
  112.    wt: 3:   Example 2
  113.    wt: 3:   Example 1
  114.    wt: 3:   A Related Material in Volume 3
  115.    wt: 3:   3 Second derivative test
  116.    wt: 3:   2 Second derivative test prequel
  117.    wt: 3:   38 Formulas and derivatives for powers and roots
  118.    wt: 3:   36 Cube root derivative animated
  119.    wt: 3:   34 Derivative of exponential function
  120.    wt: 3:   30Chain Rule A Proof
  121.    wt: 3:   23 Chain Rule in general
  122.    wt: 3:   22 Chain Rule for polynomials
  123.    wt: 3:   15 sine and cosine derivatives 3rd step
  124.    wt: 3:   13 sine and cosine derivatives 1st step
  125.    wt: 3:   12 Quotient rule examples
  126.    wt: 3:   5 Product Rule
  127.    wt: 3:   3 Motivation for Limit Definition Take 2
  128.    wt: 3:   1 Fall 1983 Why Slopes Appetizer
  129.    wt: 3:   13 Limits with Parameters and Derivatives Take II
  130.    wt: 3:   5 Jumps and absence of unlimited error control
  131.    wt: 3:   4 Numerical properties
  132.    wt: 3:   3 Decimal insights for limits continuity convergence
  133.    wt: 3:   Postscript Pythagorean Theorem yet another proof
  134.    wt: 3:   Chapter 24 Logarithms Powers and Exponentials
  135.    wt: 3:   Chapter 22 Complex Numbers
  136.    wt: 3:   Chapter 21 Arrow Addition
  137.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  138.    wt: 3:   Chapter 19. Exponentials and Natural Logarithms
  139.    wt: 3:   Chapter 18. Slopes Areas Integration
  140.    wt: 3:   Chapter 17. Area Approximation
  141.    wt: 3:   Chapter 16. Velocity Approximation
  142.    wt: 3:   Chapter 15. Slope Approximation
  143.    wt: 3:   Chapter 15. Algebraic Evaluation of Limits
  144.    wt: 3:   Chapter 14 Limits and Continuity with and sans Decimals
  145.    wt: 3:   Chapter 12. Units and Slopes
  146.    wt: 3:   Chapter 11. Graphing Slope versus Position
  147.    wt: 3:   Chapter 10 Slopes and Units
  148.    wt: 3:   Chapter 8. Slope Interpretation
  149.    wt: 3:   Chapter 7 Slopes and Velocity
  150.    wt: 3:   Chapter 6. Slopes and Vertical Shifts
  151.    wt: 3:   Chapter 5. Slope Sign Tests
  152.    wt: 3:   Chapter 4. More Slope Sign Analysis
  153.    wt: 3:   Chapter 2. Slopes and Ski Trails
  154.    wt: 3:   Chapter 1.Introduction
  155.    wt: 3:   Foreword
  156.    wt: 3:   Chapter 31 Direct and Indirect Reason
  157.    wt: 3:   Chapter 30 Truth Tables
  158.    wt: 3:   Chapter 23. Notation For Sums
  159.    wt: 3:   Chapter 13. Second Reading Guide
  160.    wt: 3:   Chapter 3 Chains of Reason
  161.    wt: 3:   Chapter 3 Algebra Difficulties
  162.    wt: 3:   Chapter 23 Truth Tables
  163.    wt: 3:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  164.    wt: 3:   Chapter 3 What is in chapters 4 to 8
  165.    wt: 3:   More Algebra and Slope based Calculus Preview
  166.    wt: 3:   Systematic Algebra Skill Development Missing Links
  167.    wt: 3:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  168.    wt: 2:   Skills Chapter 5 Calculus
  169.    wt: 2:   Ramblings Extrinsic numbers theory
  170.    wt: 2:   Ramblings Introduction Algebra Essay
  171.    wt: 2:   3 Euclidean Geometry Leanly
  172.    wt: 2:   Education Reform Inconsistencies
  173.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  174.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  175.    wt: 2:   C Energy Power03
  176.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  177.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  178.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  179.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  180.    wt: 2:   13 Addition and Addition Tables
  181.    wt: 2:   3 Preparing for Science Studies
  182.    wt: 2:   Ages 3 plus to 4 plus
  183.    wt: 2:   sign monoticity analysis example 3
  184.    wt: 2:   23 Inverse Functions
  185.    wt: 2:   13 From one to one to many to one
  186.    wt: 2:   3 Formula or function graphing exercise
  187.    wt: 2:   A Quadratics Summary
  188.    wt: 2:   10 quadratic exercises
  189.    wt: 2:   9 quadratics physical and further context
  190.    wt: 2:   8 quadratics backward use of various formulas
  191.    wt: 2:   7 quadratic formulla derivation
  192.    wt: 2:   6 quadratics numerical approach
  193.    wt: 2:   5 quadratics completing the square
  194.    wt: 2:   4 quadratics difference of two squares
  195.    wt: 2:   2 quadratics graphing in general
  196.    wt: 2:   1 quadratics graphing exercises
  197.    wt: 2:   3 Natural Logarithms and Exponentials Basic Properties
  198.    wt: 2:   13 cosecant function Definition Graph and Inverse
  199.    wt: 2:   3 Left Inverse of cosine arccos definition
  200.    wt: 2:   7 Radian Measures in special Triangles
  201.    wt: 2:   3 graphing y=f(x c) plus K
  202.    wt: 2:   Triangle Angles Sum To 180 Degrees
  203.    wt: 2:   Parallel Lines and Alternating Corresponding Angles
  204.    wt: 2:   Construction Methods and Criteria for Isometric and Similar Triangles
  205.    wt: 2:   SAS Method For Isometric Or Proportional Triangle Construction
  206.    wt: 2:   Analytic View of Triangle Construction or Line Instersection More
  207.    wt: 2:   Straight Lines Intersection of
  208.    wt: 2:   14 Straight Lines Equations General Case
  209.    wt: 2:   11 Straight Lines Graphing y=mx
  210.    wt: 2:   10 Straight Lines through Origin Equations More
  211.    wt: 2:   9 Straight Lines through Origin Equations
  212.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  213.    wt: 2:   30 unit circle calculation of six trigonometric functions
  214.    wt: 2:   24 tangent Angle Difference Formula
  215.    wt: 2:   23 sine and cosine of 180 plus 22.5 degrees
  216.    wt: 2:   16 Right Triangle Complementary Angle Relations
  217.    wt: 2:   15 sine cosine Complementary Angle Relations
  218.    wt: 2:   13 Graph of tangent function many periods
  219.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  220.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  221.    wt: 2:   7 Trignometric Ratios Unit Circle
  222.    wt: 2:   6 Trigonometry Sines of Supplementary Angles
  223.    wt: 2:   1 Angle Measurement with Degrees
  224.    wt: 2:   Why Trigonometry the whyslopes view
  225.    wt: 2:   12 Triangles Similarity More Problems
  226.    wt: 2:   11 Triangle Similarity Missing Side Problem
  227.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  228.    wt: 2:   9 Similarity of Triangles Usual Criteria
  229.    wt: 2:   8 Similarity of Triangles and Polygons
  230.    wt: 2:   6 Geometric Diagrams in Class
  231.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  232.    wt: 2:   PS H Distributive Law For Complex Numbers
  233.    wt: 2:   PS G Rotation Distributes over Addition
  234.    wt: 2:   PS F Scalar Multiplication Distributes over Addition
  235.    wt: 2:   PS E Multiplication with Polar Coordinates
  236.    wt: 2:   PS D Addition with Cartesian Coordinates
  237.    wt: 2:   PS B Parallelogram Construction Methods
  238.    wt: 2:   PS A Kite Construction Methods
  239.    wt: 2:   19 Right Triangle Similarity
  240.    wt: 2:   18 Triangle Similarity Take 1
  241.    wt: 2:   17 Right Bisectors of Triangle Sides
  242.    wt: 2:   15 Triangle Angle Sum is 180 degrees
  243.    wt: 2:   11 Triangle Construction Fails
  244.    wt: 2:   8 Isoceles Triangles
  245.    wt: 2:   2 Correspondence between Triangles
  246.    wt: 2:   A Measurement with Ruler Proper Use
  247.    wt: 2:   5 Drawing to Scale Avoids Angle Distortions
  248.    wt: 2:   2 Measuring Area Directly
  249.    wt: 2:   1 Length Measurement
  250.    wt: 2:   23 Distributive Law Two Derivations
  251.    wt: 2:   3 Multiplicative Counting Skills Principles
  252.    wt: 2:   3 Proportionality Examples
  253.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  254.    wt: 2:   3 Triangle Area Formula Example
  255.    wt: 2:   3 Comparison of Negative Numbers
  256.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  257.    wt: 2:   3 signed coordinates for maps and planes
  258.    wt: 2:   3 Unit fraction of a fraction
  259.    wt: 2:   3 Adding Movements with same direction
  260.    wt: 2:   13 Remainder Arithmetic Modulo 5 Example
  261.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  262.    wt: 2:   20 Uniqueness of Prime Factorization
  263.    wt: 2:   19 video Prime Factorization Unique
  264.    wt: 2:   18 video Count Factors given Prime Factorization
  265.    wt: 2:   17 Identify and Count Factors using Primes
  266.    wt: 2:   16 video Factors of 980 using prime
  267.    wt: 2:   15 video Factors of 20 using Prime Factorization
  268.    wt: 2:   14 video Factors of 24 Take II
  269.    wt: 2:   12 LCD GCD and LCM using Primes
  270.    wt: 2:   11 Efficient Square Rule Use
  271.    wt: 2:   9 video Prime Factorization upto 19 squared
  272.    wt: 2:   8 video Prime Factorization upto 19
  273.    wt: 2:   7 Calculator Usage Notes and Cautions
  274.    wt: 2:   6 Sieve of Eratosthenes and Square Rule
  275.    wt: 2:   5 Prime Factorization and a Square Rule
  276.    wt: 2:   4 video Prime Factorization Introduction
  277.    wt: 2:   2 Prime and Composites less than 16
  278.    wt: 2:   1 video how Products are bigger than factor
  279.    wt: 2:   3 Division Single Digit Divisor Example
  280.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  281.    wt: 2:   1 Why 3 times 5 gives 15
  282.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  283.    wt: 2:   3. How to add with decimals A sans conversions
  284.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  285.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  286.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  287.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  288.    wt: 2:   Example 1. Area Between x and x squared
  289.    wt: 2:   Area Between Crossing Curves Lesson Take 2
  290.    wt: 2:   Area Between Crossing Curves Lesson Take 1
  291.    wt: 2:   Area Between Curves Lesson Take 2
  292.    wt: 2:   Area Between Curves Lesson Take 1
  293.    wt: 2:   Summary
  294.    wt: 2:   3 Two Chain Rule Method Exercises
  295.    wt: 2:   4 Second derivative test exercise example
  296.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  297.    wt: 2:   A Chain Rule Real Player video examples
  298.    wt: 2:   29 Chain Rule Optional Reading
  299.    wt: 2:   28 Chain Rule Preparation for a Proof
  300.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  301.    wt: 2:   26 Chain Rule Recognising outer inner functions
  302.    wt: 2:   25 Chain Rule Animated Examples Continued
  303.    wt: 2:   24 Chain Rule Animated Examples
  304.    wt: 2:   21 Chain Rule for powers
  305.    wt: 2:   20 Chain Rule for Pulley Systems
  306.    wt: 2:   19 Chain Rule for linear functions
  307.    wt: 2:   18 Chain Rule Introduction
  308.    wt: 2:   17 Derivatives of quotients of sine and cosine
  309.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  310.    wt: 2:   14 sine and cosine derivatives 2nd step
  311.    wt: 2:   11 Quotient rule
  312.    wt: 2:   10 Power rule for negative integers
  313.    wt: 2:   9 Reciprocal rule
  314.    wt: 2:   8 Differentiation of polynomials
  315.    wt: 2:   7 Animated Differentiation Examples
  316.    wt: 2:   6 Power rule from product rule
  317.    wt: 2:   4 Sum Rule
  318.    wt: 2:   2 Motivation for Limit Definition Take 1
  319.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  320.    wt: 2:   11 Limits at infinity Three Examples
  321.    wt: 2:   10 Three one sided limits with infinite values
  322.    wt: 2:   9 Limits Continuity and Composition
  323.    wt: 2:   8 Four Animated Examples
  324.    wt: 2:   7 Evaluation by immediate or delayed substitution
  325.    wt: 2:   6 Continuity at a point
  326.    wt: 2:   2 Algebraic codification
  327.    wt: 2:   1 Numerical introduction
  328.    wt: 2:   Appendix C. How to Read
  329.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  330.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  331.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  332.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  333.    wt: 2:   Postscript A Three Remarks
  334.    wt: 2:   M Words to extend arithmetic
  335.    wt: 2:   C. Domino effect of being careful
  336.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  337.    wt: 2:   Chapter 3 Algebra Starter Lessons
  338.    wt: 2:   3 Telling Tracking Time Temporal and More Place Sense
  339.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  340.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  341.    wt: 2:   Implementation Notes
  342.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  343.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  344.    wt: 1:   Appendix 2 primary school Arithmetic 01
  345.    wt: 1:   Appendix 1 primary and preschool mathematic
  346.    wt: 1:   K LAMP Musings Science Education
  347.    wt: 1:   J LAMP Introduction Extrinsic Origins
  348.    wt: 1:   I LAMP Introduction Study Habits
  349.    wt: 1:   H LAMP Introduction Instructional Concepts
  350.    wt: 1:   G LAMP Introduction Problem Solving Skills
  351.    wt: 1:   F LAMP Introduction Prerequisites
  352.    wt: 1:   E LAMP Introduction Modern Mathematics
  353.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  354.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  355.    wt: 1:   A Introduction Objectives
  356.    wt: 1:   Skills Chapter 4 Logic
  357.    wt: 1:   Skills Chapter 2 Geometry
  358.    wt: 1:   Skills Chapter 1 Arithmetic
  359.    wt: 1:   Skills Chapter 0 Introduction
  360.    wt: 1:   permissions for teachers
  361.    wt: 1:   Math Ed if it must be short make it lean effective
  362.    wt: 1:   modern education
  363.    wt: 1:   learning takes time
  364.    wt: 1:   grouping students according to ability
  365.    wt: 1:   what should be learnt and When
  366.    wt: 1:   mathematics in context
  367.    wt: 1:   Postscript 2007 01 10
  368.    wt: 1:   five decades make a difference
  369.    wt: 1:   Maps Plans Drawings
  370.    wt: 1:   teaching tips
  371.    wt: 1:   teaching tutoring algebraic reason
  372.    wt: 1:   the trouble with algebra
  373.    wt: 1:   05 13 OldSiteEntrancePage
  374.    wt: 1:   Theory of Knowledge
  375.    wt: 1:   Different Kinds of Reasoning in maths
  376.    wt: 1:   chapitre 12 00 les iles et division
  377.    wt: 1:   chapitre 07 01 principle D induction mathematique
  378.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  379.    wt: 1:   chapitre 06 00 Chaines de la raison
  380.    wt: 1:   chapitre 05 00 Deception
  381.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  382.    wt: 1:   chapitre 04 09 Regles accidentelles
  383.    wt: 1:   chapitre 04 08 Limitations et benefices
  384.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  385.    wt: 1:   chapitre 04 06 engagements
  386.    wt: 1:   chapitre 04 05 Implication versus suggestion
  387.    wt: 1:   chapitre 04 04 Parlons de la logique
  388.    wt: 1:   chapitre 04 02 Deuxieme enigme
  389.    wt: 1:   chapitre 04 01 Premiere enigme
  390.    wt: 1:   chapitre 04 00 Les regles d implication
  391.    wt: 1:   chapitre 02 00 La Communication des idees
  392.    wt: 1:   chapitre 01 00 Introduction
  393.    wt: 1:   liens
  394.    wt: 1:   3 Energy Power Heat08
  395.    wt: 1:   E Wire Resistance Calculation03
  396.    wt: 1:   A Wire Resistance Qualitative01
  397.    wt: 1:   3 Like resistors in parallel
  398.    wt: 1:   B Electromotive force conventional current01
  399.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  400.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  401.    wt: 1:   16 Secondary Mathematics Tips
  402.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  403.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  404.    wt: 1:   3 Polynomials Multiplication Addition
  405.    wt: 1:   16 cotangent function Definition Graph and Inverse
  406.    wt: 1:   15 cosecant function Definition Graph and Inverse
  407.    wt: 1:   14 secant function Definition Graph and Inverse
  408.    wt: 1:   12 motivation for term arctan
  409.    wt: 1:   11 arctan left inverse of tangent Graph
  410.    wt: 1:   10 arctan left inverse of tangent Definition
  411.    wt: 1:   9 motivation for name arcsin
  412.    wt: 1:   8 arcsin left inverse of sine Graph
  413.    wt: 1:   7 arcsin left inverse of sine Definition
  414.    wt: 1:   6 Graph of arccos function
  415.    wt: 1:   5 Swapping Coordinates is a reflection
  416.    wt: 1:   4 possible motivation for term arccos
  417.    wt: 1:   2 cosine function more properties
  418.    wt: 1:   1 cosine function properties
  419.    wt: 1:   9 Summary Degrees to Radians and back
  420.    wt: 1:   8 Radian Measures of Common Angles
  421.    wt: 1:   6 Radian Measure to Degrees
  422.    wt: 1:   5 Degrees to Radian Measure
  423.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  424.    wt: 1:   2 Radian Measure Numerical Value of one degree
  425.    wt: 1:   1 Degrees and Radians Introduction
  426.    wt: 1:   4 graphing y=Asin(x c)
  427.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  428.    wt: 1:   1 graphing y=f(x a)
  429.    wt: 1:   Parallel Lines and Parallel Transversals
  430.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  431.    wt: 1:   Parallel Lines and Interior Angles
  432.    wt: 1:   Straight Lines ASA Intersection Study More
  433.    wt: 1:   Straight Lines ASA Intersection Study
  434.    wt: 1:   Straight Lines Instersection Solving Equations
  435.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  436.    wt: 1:   C Straight Lines Slope from Coordinates
  437.    wt: 1:   B Straight Line Slope Scaling Properties More
  438.    wt: 1:   A Straight Line Slope Scaling Properties
  439.    wt: 1:   8 Straight Lines Equation for vertical
  440.    wt: 1:   7 Tangent Function is odd on this domain
  441.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  442.    wt: 1:   5 Tangent Function Graph
  443.    wt: 1:   4 Tangent Function Properties
  444.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  445.    wt: 1:   1 Straight Lines Slope Concept
  446.    wt: 1:   17 tangent function angle sum formulas
  447.    wt: 1:   29 secant cosecant and cotangent for acute angles
  448.    wt: 1:   28 Expressing products of sines cosines as sums
  449.    wt: 1:   27 Logarithmic use of products of sines and cosines
  450.    wt: 1:   26 Formulas for products of sines and cosines
  451.    wt: 1:   25 tangent double angle formula Slope connection
  452.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  453.    wt: 1:   21 sine and cosine Half Angle Formulas
  454.    wt: 1:   20 sine and cosine Double Angle Formulas
  455.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  456.    wt: 1:   18 sum of sinusoidal waves as a single wave
  457.    wt: 1:   17G Pythagorean Theorem Converse
  458.    wt: 1:   17F Law of cosines
  459.    wt: 1:   17E Trig Formulas for dot and cross Products
  460.    wt: 1:   17D cis formulas for sine cosines and tangent
  461.    wt: 1:   17C sine and cosine double triple angle formulas
  462.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  463.    wt: 1:   17A The complex number valued trig function cis
  464.    wt: 1:   14 cosine even and sine and tangent are odd
  465.    wt: 1:   12 Graph of tangent function for one period
  466.    wt: 1:   11 tangent function undefined when terminal side vertical
  467.    wt: 1:   10 Graphs of sines and cosines many periods
  468.    wt: 1:   9 Graphs of sine and cosine over one period
  469.    wt: 1:   8 period of tangent function
  470.    wt: 1:   7 period of sine and cosine
  471.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  472.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  473.    wt: 1:   2 Quadrant I reference Angles
  474.    wt: 1:   1 Unit Points Reflections Rotations
  475.    wt: 1:   Unit Circle Development of Trigonometry
  476.    wt: 1:   21 Logarithms Powers and Exponentials
  477.    wt: 1:   20 N th Roots of Complex Numbers
  478.    wt: 1:   19 N th Roots of Unity
  479.    wt: 1:   18 Sixth Roots of Unity
  480.    wt: 1:   17 Cube Roots of unity
  481.    wt: 1:   16 References and Originality Question
  482.    wt: 1:   15 Pythagorean Theorem Converse
  483.    wt: 1:   14 Law of cosines
  484.    wt: 1:   12 cis formulas for sine cosines and tangent
  485.    wt: 1:   11 sine and cosine double triple angle formulas
  486.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  487.    wt: 1:   9 The complex number valued trig function cis
  488.    wt: 1:   8 Unit Circle Development of Trigonometry
  489.    wt: 1:   7 Second Way to Calculate Products
  490.    wt: 1:   6 Field Properties of Complex Number
  491.    wt: 1:   5 An Easy Proof of the Distributive Law
  492.    wt: 1:   4 Multiplication Properties
  493.    wt: 1:   2 Complex Numbers made easier we hope
  494.    wt: 1:   1 Rectangular Polar Coordinates Review
  495.    wt: 1:   Appetizer A Complex Number Applet
  496.    wt: 1:   7 Translations Rotations Reflections Dilatations
  497.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  498.    wt: 1:   4 Similarity Definition with Coordinate
  499.    wt: 1:   2 Similarity By Design
  500.    wt: 1:   1 Early Concept of Like or Similar Shapes
  501.    wt: 1:   Four Simple Exercises
  502.    wt: 1:   12 Links Lessons elsewhere
  503.    wt: 1:   11 A Partial Summary
  504.    wt: 1:   10 Midpoint of [a b] and [b a]
  505.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  506.    wt: 1:   8 Mid Point Formula
  507.    wt: 1:   7 Exercises to test skill and concept mastery
  508.    wt: 1:   6 Intersection of lines by solving linear systems
  509.    wt: 1:   5 Algebraic View of Slopes
  510.    wt: 1:   4 Equations for lines three forms
  511.    wt: 1:   2 point slope equation for a line
  512.    wt: 1:   1 Numerical view of lines and their equations
  513.    wt: 1:   What is and is not here
  514.    wt: 1:   21 Parallelograms
  515.    wt: 1:   16 Angles Subtended By Chords and Diameters
  516.    wt: 1:   14 Parallel Lines Postulate
  517.    wt: 1:   12 Side Angle Side Failure
  518.    wt: 1:   10 Dropping a perpendicular to line
  519.    wt: 1:   9 Construction of a right bisector
  520.    wt: 1:   7 Angle Side Angle
  521.    wt: 1:   6 Ruler and compass Angle Bisection
  522.    wt: 1:   5 Side Angle Side
  523.    wt: 1:   4 Side Side Side
  524.    wt: 1:   1 Initial Concepts and Terms
  525.    wt: 1:   Short Course on Euclidean Geometry
  526.    wt: 1:   About Folder Contents
  527.    wt: 1:   26 More Less Greater Than Comparison
  528.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  529.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  530.    wt: 1:   22 Multiplication of Signed Numbers
  531.    wt: 1:   13 Arrows and Vectors in a Plane
  532.    wt: 1:   3 Location of Point in Decimal Multiplication
  533.    wt: 1:   4 Commutative Law Groups Counting Form
  534.    wt: 1:   3 Inequalities Algebraically
  535.    wt: 1:   5 Triangle Area Formula Backwards
  536.    wt: 1:   3 Linear Equation Literal Solution More
  537.    wt: 1:   3 Product Axioms Two Forms
  538.    wt: 1:   3 More and Less Than with Unlike Signs
  539.    wt: 1:   13 Real Number Subtraction
  540.    wt: 1:   8 Coordinates for Maps and Planes
  541.    wt: 1:   3 Fractions
  542.    wt: 1:   3 Geometric Formulas and Function Notation
  543.    wt: 1:   More Exercises
  544.    wt: 1:   Simple Exercises
  545.    wt: 1:   4 GE III Animated Examples
  546.    wt: 1:   2 GE II Comparison
  547.    wt: 1:   1 GE Substitution four examples
  548.    wt: 1:   6 Algebraic Solution Example
  549.    wt: 1:   5 Algebraic Solutions Introduction
  550.    wt: 1:   4 Four Examples Fractional Coefficients
  551.    wt: 1:   2 Three Examples
  552.    wt: 1:   1 Proper Equal Sign Usage
  553.    wt: 1:   Skill Development Notes
  554.    wt: 1:   10 One Example
  555.    wt: 1:   9 Three Examples
  556.    wt: 1:   8 One Example
  557.    wt: 1:   7 Two Examples
  558.    wt: 1:   6 Three Examples
  559.    wt: 1:   5 Three Examples
  560.    wt: 1:   4 Two Examples
  561.    wt: 1:   2 Three Examples
  562.    wt: 1:   Using Letters for Physical Quantities
  563.    wt: 1:   Formula Usage Show Work Format
  564.    wt: 1:   13 Naming Identifying Formulas with Words
  565.    wt: 1:   11 Volume of Sphere
  566.    wt: 1:   10 Volume of Pyramid
  567.    wt: 1:   9 Volume of Cone
  568.    wt: 1:   5 Box Volume Formula Example
  569.    wt: 1:   3 Counting with Sets etc
  570.    wt: 1:   3 Adding Words To Arithmetic
  571.    wt: 1:   3 Properties of Square Roots with example
  572.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  573.    wt: 1:   13 GCD from given Prime Factorization
  574.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  575.    wt: 1:   2 Least Common Multiple LCM intro via list method
  576.    wt: 1:   3 Counting with Tables and Trees II
  577.    wt: 1:   3 Multiplying Units and Numbers
  578.    wt: 1:   13 Fraction Comparison Algebraic View
  579.    wt: 1:   A Associative Law Theorectical Note
  580.    wt: 1:   13 Subtraction with Additive Inverse
  581.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  582.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  583.    wt: 1:   26 Divisibility by 2 3 5 Example
  584.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  585.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  586.    wt: 1:   23 Remainder Arithmetic Modulo 2
  587.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  588.    wt: 1:   21 Remainder Arithmetic Modulo 3
  589.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  590.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  591.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  592.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  593.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  594.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  595.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  596.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  597.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  598.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  599.    wt: 1:   Long Division Backward
  600.    wt: 1:   Long Division forwards and backwards Example 3
  601.    wt: 1:   D Decimal Multiplication Methods Derived
  602.    wt: 1:   C Counting Areas with Powers of Ten
  603.    wt: 1:   B Powers of Ten
  604.    wt: 1:   A Elementary Basis for Multiplication Methods
  605.    wt: 1:   6 Multiplication Commutes Order Not Important
  606.    wt: 1:   5 Decimal Fraction Multiplication
  607.    wt: 1:   4 Two and Three Digit Multipliers
  608.    wt: 1:   2 One Digit Multipliers
  609.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  610.    wt: 1:   Video Power Notation in Decimal Expansion
  611.    wt: 1:   Subtraction Another Video Lesson
  612.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  613.    wt: 1:   Expression Evaluation how to show work
  614.    wt: 1:   013 Travel Time Tables
  615.    wt: 1:   3 Units and Lengths of Time
  616.    wt: 1:   5 Area Under Curve Exercise
  617.    wt: 1:   4 Definite Integrals Evaluation Exercises
  618.    wt: 1:   2 Indefinite Integrals Exercises
  619.    wt: 1:   1 Chain Rule in Reverse Integration Method
  620.    wt: 1:   Postscript More on Better Performance
  621.    wt: 1:   Postscript For Better Performance
  622.    wt: 1:   Appendix E. How To Study Mathematics and Why
  623.    wt: 1:   Appendix D. What to do in School and Why
  624.    wt: 1:   Appendix B. How To Learn
  625.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  626.    wt: 1:   Chapter 28 Occurrence Tables
  627.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  628.    wt: 1:   Chapter 25. Mathematical Induction Examples
  629.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  630.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  631.    wt: 1:   Chapter 21. Third Reading Guide
  632.    wt: 1:   Chapter 20. Degrees and Radians
  633.    wt: 1:   Chapter 19. Functions and Sets
  634.    wt: 1:   Chapter 18. Rules for Algebra
  635.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  636.    wt: 1:   Chapter 16. Painless Theorem Proving
  637.    wt: 1:   Chapter 15. Solving Linear Equations
  638.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  639.    wt: 1:   Chapter 12. Shorthand Usage Guide
  640.    wt: 1:   Chapter 11. Why Shorthand
  641.    wt: 1:   Chapter 10 Describing and Changing Calculations
  642.    wt: 1:   Postscript What is a Variable
  643.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  644.    wt: 1:   Chapter 8 Three Skills For Algebra
  645.    wt: 1:   Solutions For Arithmetic Exercises
  646.    wt: 1:   Chapter 6 Change of Language
  647.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  648.    wt: 1:   Chapter 4 Longer Chains of Reason
  649.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  650.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  651.    wt: 1:   Foreword
  652.    wt: 1:   Annotated Links to Material Elsehwere
  653.    wt: 1:   Postscript B Mathematics Education References
  654.    wt: 1:   Chapter 12 Four Phases
  655.    wt: 1:   Chapter 11 Elementary Instruction
  656.    wt: 1:   Chapter 10 Transition
  657.    wt: 1:   Chapter 9 The Two Ends
  658.    wt: 1:   Chapter 8 Modern Instruction
  659.    wt: 1:   Chapter 7 Two Treatments of Geometry
  660.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  661.    wt: 1:   Chapter 5 Four References
  662.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  663.    wt: 1:   Chapter 2 For and Against Mathematics
  664.    wt: 1:   Chapter 1 Introduction
  665.    wt: 1:   Foreword
  666.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  667.    wt: 1:   Postscript C Consistency as a Tool for Reason
  668.    wt: 1:   Postscript B More on Story Telling and Reason
  669.    wt: 1:   Postscript A Story Telling
  670.    wt: 1:   Chapter 24 Direct and Indirect Reason
  671.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  672.    wt: 1:   Chapter 21 Occurrence Tables
  673.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  674.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  675.    wt: 1:   Chapter 18 Sense and Knowledge
  676.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  677.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  678.    wt: 1:   Chapter 15 Objective Processes
  679.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  680.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  681.    wt: 1:   Chapter 11 Accidental Patterns
  682.    wt: 1:   Chapter 10 Responsibility
  683.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  684.    wt: 1:   Chapter 8 Change of Language
  685.    wt: 1:   Chapter 7 Longer Chains of Reason
  686.    wt: 1:   Chapter 6 Chains of Reason
  687.    wt: 1:   Chapter 5 Deception
  688.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  689.    wt: 1:   Chapter 2 Skill Development
  690.    wt: 1:   Chapter 1 Introduction
  691.    wt: 1:   Three Remarks
  692.    wt: 1:   Foreword
  693.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  694.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  695.    wt: 1:   S Adding words to algebra
  696.    wt: 1:   R Why Learn Mathematics Skills
  697.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  698.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  699.    wt: 1:   O On Learning Mathematics and Science
  700.    wt: 1:   N Mathematics Prepare for College Studies
  701.    wt: 1:   L Skills with take home value
  702.    wt: 1:   N Improving Marks on Tests and Finals
  703.    wt: 1:   J. More on written work and showing skill
  704.    wt: 1:   I. Logic and language skills
  705.    wt: 1:   H more Routine to non routine problem solving
  706.    wt: 1:   H Jigsaw puzzles and problem solving
  707.    wt: 1:   G. Written work formats for developing and showing skill
  708.    wt: 1:   F. The student teacher tutor feedback loop
  709.    wt: 1:   E. When and how to correct errors
  710.    wt: 1:   D. Check work a must with a caution
  711.    wt: 1:   B. Domino effect of errors
  712.    wt: 1:   A. Skill has to be seen to believed
  713.    wt: 1:   How to Build Skills and Confidence
  714.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  715.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  716.    wt: 1:   Helping the Blind in Logic and Mathematics
  717.    wt: 1:   Mathematics Education References
  718.    wt: 1:   Mathematics Education References
  719.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  720.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  721.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  722.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  723.    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.

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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

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