HIP, HIP, HIP, Hooray
YOU are better than YOU think. Show yourself  how:
  

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 Logic chapters 1 to 5  re- appear not in sequence, as is or longer,  in  Volume 1A,  Pattern Based Reason, Bon Appetite.

Logic Mastery
 Amazing, Amusing, Amorous,  Delicious, Delightful, Edifying, Strengthening Elixir. 
It eases work & learning difficulties Makes the hard easier. Opens eyes. Leads to greater precision.
in reading and
writing

Logic mastery makes the hard, easier. Logic mastery  leads to better, stronger and richer comprehension.  Logic mastery  improves reading and writing.  Logic mastery ease learning difficulties.  Logic mastery gives a headstart.  In sum, logic mastery  will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.

After logic,   (a) continue reading Three Skills for Algebra, chapters 8 to 14  and do so alongside site area on solving liinear2007 Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes  & More Math, chapters 2 to 6;

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What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts.

Try the Twiddla Whiteboard. In principle, it  allows to people to draw and chat together online on a copy of this webpage or a clean sheet. The chat may be via text or audio.  Visit www.twiddla.com to set up whiteboards to work with the webpage of your choice.

For online automated help in senior high school maths & calculus, visit  quickmath.com  For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com  With  overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck.

See too Online Books in Many Fields by Many Authors, a Penn State University Library catalogue.

Subjects Besides Mathematics

1. Biology Links:  Human Anatomy and Physiology, Animal Biology,  Google > Biology > Tutorials. Virtual Lab Covering High School/College Material

2. Chemistry Links: Mr. F High School Help Page Google > Chemistry HomeWork Pages.

3. Robyn's Physics Links: Physics Joy Wagon The Physics Classroom Physics Flashlets Simple Harmonic Motion Development of the SHM formula for pendulums Animation of harmonic graphs comparing x,v,and a 

4. More Physics Links: Introduction to Physics - Elementary. Guelph, Physics Tutorials .Google > Physics > Tutorials. 

5. Science Experiments: Google > Science > Educational Resources > Experiment; 

6. Google Directory - Kids and Teens School Time English
   
7. Google Directory - Kids and Teens School Time Foreign Languages French.
   
8. Holmen High School Recommended Websites in and out of mathematics.
   
9. Strategic Studies. K12_resources
   
10. Exambot website in British Columbia (from some colleges that want you) offer reference material (definitions and such), problem sets or exams, and worked answers for them.. Perhaps the best to start is with  its help page, and then take some time to explore it.  It looks good.
    

Logic and Critical Thinking 

1. Course Syllabus, PHIL 200 - Logic, Longview Community College
2. Symbolic Logic Notes
3. Real World Reasoning - Pointers to essay and fallacies (false reasoning).
4. Mission Critical, an interactive tutorial for critical thinking, in which you will be introduced to basic concepts through text and exercises.
5. Resources for Critical Thinking
6. Guide to Philosophy on the Net
7. Medieval Theories of Practical Reason - Part of the Stanford Encyclopedia of Philosophy, almost a digression from it.
8. Persuasion - Methods of.
9. Fairness and Accuracy in Reporting

Arithmetic with whole numbers and fractions

Skill and confidence in arithmetic and beyond  in mathematics comes from taking steps or using rules, one at a time and one after another, to arrive at conclusion. Knowing that an error in one step of a calculation or chain of reason makes all that follows suspect or wrong is the first sign of intelligence.

1. Fractions leads to another site with an excellent review.
2. Scientific Notation - An explanation with links to three further sites. This explanation is located at mathmol
3. Defense Acquisition Center, Subway Map Covers (1) Basic Arithmetic, Exponents and Logarithms, Equations, Series, Self-Test; and (2) Elementary Calculus, Functions, Domains & Ranges, Intercepts, Limits, Graphing functions, Derivatives, Integrals, self-test. Looks very good.
4. AAA Math:  goal is to illustrate and provide free, online, interactive arithmetic exercises and problems.  It contains a series of basic math lessons which are intended to be a resource that can be used by math students in formal elementary education math classes, home schooling or elsewhere.
5. Edhelper.com  offers automatically generated question sheets in arithmetic and beyond (Grades 1 to 9 or 12) with answers  Comment: Best for gifted students, teachers or tutors.
6. Top Study MATH Link  Visit here for Math Games and Interactive Multiplication Tables with Ollie the Space Alien. (Cute)
7. Fractions- A huge list of webpages covering arithmetic with fractions and even decimals. From the Math Forum.
8. How Mathematics (maths) appears in chocolate making - from Cadbury in the UK.  Simple questions and answers. Visit with a young students with a knowledge of fractions, decimals and percents.

Algebra

1. Numerical Applet graphing a parabolas when a parabola is given by y=ax2+bx+c or y = a(x-h)2+k with buttons allowing you to change coefficients. See how changes in coefficients in one representation changes the coefficients in another.

2. For Novices:  Defense Acquisition Center, Subway Map Covers (1) Basic Arithmetic, Exponents and Logarithms, Equations, Series, Self-Test; and (2) Elementary Calculus, Functions, Domains & Ranges, Intercepts, Limits, Graphing functions, Derivatives, Integrals, self-test. Looks very good.

3. The Basic Algebra, Math 152A Home Page : Lecture Notes: Real Numbers and Definitions] [Linear Equations and Inequalities] [Exponents and Polynomials] [Functions and Graphs].  See the problems sets as well. This is good work.

4. Math Abundance offers a good collection of  advanced lessons and problem sets - material put online to advance mathematics education by J. C.

5. Dave's Math Tables - A cross section of high school/college mathematics.

6. Word Problems For Students: Grade Five Grade Six Grade Seven Grade Eight Grade Nine Grade Ten Grade Eleven Grade Twelve from a St Xavier Francis University math page.

7. SOS Math  offers lesson on Algebra | Trigonometry | Calculus | Differential Equations
   Complex Variables | Matrix Algebra | Tables
8. SOS Math also offer quizzes (multiple choice) on Intermediate Algebra Mathematics for Social Sciences I  Mathematics for Social Sciences II Pre-Calculus I  Pre-Calculus II  Calculus  Differential Equations. After answering, right or wrong, you may retreat or advance to the next question.
9. Sample Math 101 Test Problems from Washington State U. A student can feel mathematically ready to attend College if he or she can get at least 33 out of the 36 problems correct.
10. Exactly how is math used in technology? Do not forget drawing reading and following maps and plans in construction and navigation. Outside of technology,  consumer math involves savings, investments, loans, mortgages, credit cards, stocks, bonds, pension plans +  price calculations by weight, area, volume, etc. All applications involve arithmetic. Some involve algebra, geometry, trig and calculus for the presentation or justification of formulas. Would you trust a formula if you have not seen a justification for it?
11. Calculating and Predicting Your Grades in a course.
12. What Good is Mathematics?  - Several Simple Examples. Skip the first.
13. From Think Quest: Function Basics and Simple Graphing. Find in interactive math onlines. Neat page
14. From Think Quest: Many Kinds of functions (periodic, odd, even, etc.) Find in interactive math online. Neat page.
15. Percentages From Jenny Olive, author of Maths, Student Survival Guide for science and engineering students.
16. Middle School Math. A collection of links for students or teachers.

Purple Math (Arithmetic, Geometry, Algebra)

Purplemath modules (algebra lessons)  give practical tips, hints, and examples, and point out common mistakes.  They are cross-referenced to each other, to help you find related material.   Purple math material in algebra complements this site.

Still More Algebra Lessons Elsewhere.

Chapter 5 Mathematics of Finance

• 5.1 Simple Interest
• 5.2 Compound Interest
• 5.3 Annuities, Loans, and Bonds
• You're the Expert--Saving for College

On-Line Resources for Chapter 5

• Chapter Summary | Chapter True/False Quiz | Chapter Excel Tutorials

Math Tools for Chapter 5

• Time Value of Money Utility

Online Algebra Review Tutorials

• A.1 Real Numbers - On-line tutorial for Section A.1
• A.2 Exponents and Radicals On-line tutorial for Section A.2
• A.3 Multiplying and Factoring Algebraic Equations On-line tutorial for Section A.3
• A.4 Rational Expressions On-line tutorial for Section A.4
• A.5 Solving Polynomial Equations On-line tutorial for Section A.5

Interactive Mathematics, local & away

[Top] [First Steps in Mathematics and Logic] [Why Learn Some Mathematics] [Logic and Critical Thinking ] [Arithmetic] [More Algebra] [Geometry] [Complex Numbers and Trig] [Interactive Math]   [Calculus and Real Analysis] [Mathematics Instruction]

1. Try the local Complex Number Applet to see how to add or  multiply points and vectors  in the Cartesian or Complex Number  plane
2. Automatic Calculus Derivatives and Integrals - Many worked examples with free evaluation of derivatives and polynomial operations, plus password access for a price to evaluation of integrals. Special notation required to enter your problems. Step by step solutions!

3. The Integrator - free evaluation of integrals 

4. Online questions covering sets, coordinates, algebra, trig and calculus from Maths Online  (Answers multiple choice, drag and drop)
5. The best inlinks to the Mathematica Web Server Home Page are given by Math Links and Tools Page at Maths Online. Links give tools for common calculation in algebra, geometry, trig and calculus.
6. On-Line Tutorials (with interactive questions) for or from three books Finite Mathematics, Applied Calculus Finite Mathematics & Applied Calculus, by Stefan Waner and Steven R. Costenoble,
7. Science > Math > Education > Java Applets Dozens of Applets.

Favorites from the work of  Tom Leathrum (precalculus to calculus)

Mathlets: Java^TM Applets for Math Explorations

Clicking on an example in most of the following pages  will enter the coefficients  in the applet.

1. Numerical Applet graphing a parabolas in both standard form, y=a(x-h)²+k, and general form, y=ax²+bx+c with buttons allowing you to change coefficients. See how changes in coefficients in one representation changes the coefficients in another. 

2. Numerical Applet that graphs a polynomial given its roots. 

3. Numerical Applet that Graphs a periodic function of the form y=A sin(Bx+C)+D, showing transformations corresponding to changing the values of the coefficients.

4. Numerical Applet Parametric Paths (3-D Graphing). Graphs a path in three dimensions specified parametrically, as x=f(t), y=g(t), and z=h(t), with parameter t. 

Complex Numbers and Trigonometry

1. Hot (New August 3, 2001)   Webpages Complex Numbers and  Distributive Law for Complex Numbers  offer a quick way to understand and explain complex numbers and trigonometry  Is there is a quicker way to explain  trig and complex numbers, etc?

2. Applied Calculus Everything - more online text on or for books by Stefan Waner and Steven R. Costenoble, Covers Calculus and Some Trig.

3. Trig without Tears - Basic ideas plus the cis(iA) = exp(i A) approach to trigonometry. Best explored after a knowledge of complex numbers and the Pythagorean theorem.

4. Trigonometry from SOS Math

5. Complex Numbers from SOS Math

6. The Exambot website in British Columbia offer reference material (definitions and such), problems and answers to them in trig, calculus and physics. Perhaps the best to start is with  its help page. See it is web links.

Geometry

1. Top Study Geometry:  Seven Interactive (step by steps) online proofs of (1) vertically opposite angles are equal, (2) Sum of angles in a triangle = 180 degrees (3) equality of angles at base of an isosceles triangle ..
2. TopStudy More Geometry More Seven More Interactive (step by steps) online proofs
3. Top Study MATH Link  Visit here for Arc, Area and Volume Calculation (Mensuration) formulas
4. Working with Vectors - From Jenny Olive, author of Maths, Student Survival Guide for science and engineering students.

Calculus and Real Analysis

1. For Novices:  Defense Acquisition Center, Subway Map Covers (1) Basic Arithmetic, Exponents and Logarithms, Equations, Series, Self-Test; and (2) Elementary Calculus, Functions, Domains & Ranges, Intercepts, Limits, Graphing functions, Derivatives, Integrals, self-test. Looks very good.

2. OJK's Precalculus Page ( Linear & Quadratics Polynomial Functions  Inequalities Functions Exponents & Logs Analytic Geometry Trig Functions Trig Equations, Apps Triangle Trig Trig Formulas Polar & Complex # Sequences & Series Limits, Rat Functions Intro to Calculus Basic Calculus Quizaroos Puzzles Random Riddles Scientific Calculator Graphing Calculator Student Found Links Algebra II Quizaroos Homework Help)  Looks good - navigation difficult.  Added March 27th, 2005

3. Applied Calculus Everything - more online text and interactive quizzes, etc, on or for books by Stefan Waner and Steven R. Costenoble, Covers Calculus and Some Trig. Recommended.

4. Automatic Calculus Derivatives and Integrals - Many worked examples with free evaluation of derivatives and polynomial operations, plus password access for a price  to evaluation of integrals. Special notation required to enter your problems. Solutions shown step by step. 

5. The Integrator - free evaluation of integrals 

6. The Dobson Files - Exercises for Calculus I & II
7. Calculus from SOS Math
8. For calculus I, II and III tests,  visit Robert. Seely's Course Materials Page.& see his study aids. In 1975, Robert & I volunteered to help with the math department at McGill U setup an mathematics display for a university open house.  On being offered our help, the full professor in charge abandoned his responsibility in this project and left it to us. That abandonment was the start of my interest in mathematics education.
9. Hot Items: The Exambot website in British Columbia (from some colleges that want you) offer reference material (definitions and such), problem sets or exams, and worked answers for them.. Perhaps the best to start is with  its help page, and then take some time to explore it.  It looks good.
   

If you are student of analysis, look at the introduction to complex numbers,  sines, cosines and exponential functions in W. Rudin's Principles of Mathematical Analysis to see how all can be defined in a diagram free way, with no use of Euclidean Geometry.

Explore CyberCalc  (Michele Williams, T. J. Willis, & Ed Bogucz) with or besides the following links. The combination appears good. 

Links to Their CyberCalc directory with the following sections.. Hint: Use the next buttons in each section and subsection for navigation.

Now you are asking "What is this CyberCalc thing all about, anyway?" ...  briefly it is to help students learn (at present) first semester calculus. It has a Concept Reviewer and an Interactive Quizzer. Once you have found this document, your personal exploration into making calculus less confusing may begin at your own pace. So, go to it! I hope you have at least a little bit of fun in the process, and I'd like to hear what you think of the environment...most of all, do you find it helpful???  Quote from above authors. 

Chapter 1: Review of Needed Topics

• 1.1 Graphing with Coordinates in the Plane
• 1.2 Slope and Line Equations
• 1.3 Functions and Graphs
• 1.4 Trigonometry Review
• 1.5 Absolute Value

Chapter 2: Limits and Continuity

• 2.1 Limits
• 2.2 Limits at Infinity
• 2.3 A Trigonometric Limit
• 2.4 Continuous Functions
• 2.5 Formal Definition of Limits

Chapter 3: Derivatives

• 3.1 Tangent Lines and The Derivative
• 3.2 Rules of Differentiation
• 3.3 Rates of Change
• 3.4 Derivatives of Trigonometric Functions
• 3.5 The Chain Rule
• 3.6 Implicit Differentiation

The above introduces calculus. Read it after or besides the key lessons here.

See Karl's Calculus Tutor Table of Contents.for the same material, plus more on differentiation and integration.

Mathematics Instruction

1. Ten Commandments for Mathematics Teachers

Still More Links Etc

Recent Additions

1. Math Comics or Cartoons, not all friendly to the discipline.
2. Links courtesy of the Department of Science and Mathematics Education at the University of Melbourne in Australia. 
3. Links to Scholarly Societies Web Page -- from the University of Waterloo Library.

Older Links:

1. The ASKERIC web site This is a link to many subjects including mathematics. Enter here and look for math link. (Resources for teachers with a gopher orientation perhaps)
2. dept.physics.upenn.edu/courses/gladney/mathphys/Contents.html This is (or was) a collection of images (diagrams, etc) illustrating calculus level ideas in physics.
3. Camel: the CAnadian Mathematical Electronic Information Service. This service may be depicted by a multi-humped camel. (If for n > 2, an n humped camel is possible, then an n+1 humped camel is also possible.)
4. Cornell Theory Center Math and Science Gateway. This Gateway is for high school students and educators, and includes links to resources in biology, chemistry, astronomy, and many other areas, in addition to math. This is another place to visit if you are interested in learning or teaching.
5. ENC-Online EisenHower Clearing House for Math and Science. They have an online Gopher collection that may be more extensive.
6. The Mathematics Page at Einet Galaxy. Einet Galaxy offers links to many www resources besides math: a guide to the web for all. 
7. Material or links for people age 3 to adult courtesy of Brendan Kehoe. The educational sites in the first link here include some of the following math links and others, not necessarily in math. The second link takes you directly to the home page of Brendan Kehoe.
8. London Mathematical Society WWW Server. Visit here to see the UK perspective on math education.
9. Mathematics Archives WWW Server. This is a huge resource for teachers. The following areas are especially of interest:
   • Collegiate Teaching Sites
   • K12 Internet Sites.
   • The Calculus Quarter of the Math Archives
10. The Swarthmore-based Math Forum (was the Geometry Forum). The following forum pages are of special interest:
    • Issues in Math Education .
    • Key Issues for the Math Community.
    • Internet Resource Collection.
    • Internet Math Providers.
    • The Math Job Market -- ouch, the market is most impolite.

    There is also a Quick Reference Tabular Guide to the forum's resources.

11. Mathematical Association of America (MAA)
12. Office for Mathematics, Science and Technology Education
13. Some where in NASA Connections to Education Resources.
14. U.S.A. National Science Teacher Associaton Web Page.
15. New Jersey Math Coalition at Rutgers University.
16. List of Math Information Servers etc. at Penn State University --- Growing. You will find here one of the largest set of pointers to mathematical institutions around the world. 
17. Standards of Learning For Virginian Public Schools. The 120K mathematics document here covers grades 1 to 11 (or is that 12).
18. World-Wide Web Virtual Library: Education has pointers to math and other subjects: a guide to the web for all.
19. Yahoo's Science Link includes a link to math (resources for teachers). Yahoo links to many others areas as well: a very selective guide to the web. 

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Three Links for Teachers:
(i) First Year High School Math - Lesson Plans with Fraction Focus (ii) Second Year High School Math - Lesson Plans with an algebra focus (iii) Algebra Lesson Plans

 

Help U Learn/ Teach

1. Algebra
   words before symbols - direct & indirect use of formula, numerical versus algebraic solutions - what is a variable (more words)
2. Arithmetic
   - exercises
   - with fractions
   - videos on primes, lcm, gcm,lcd, square roots etc
3. Calculus - geometric preview, algebraic preview,
   3 study guides,
   much more
4. Complex numbers
   -starter lesson with java applet - easy consequences  for trig & vectors in the plane
5. Education
   - Empirical Course Design & Delivery
6. Fractions
   - alone
   - by rote
   - with algebra
   - videos
7. Functions - introduction
   hindsight - composition aka
   substitution -
8. Geometry, Euclidean - Correspondence of triangles,  Triangle construciton,  duplication & Isometry - Failure of ASA & the // line postulate - angle sum in triangles -// grams - Triangle Similarity
   
9. Geometry- Analytic - functions, polynomials, complex numbers, unit circle trigonometry
10. Logic
    - First Steps -
    Symbols in Logic -
     Occurrence & Truth Tables - Indirect Reason -Indirect Reason More
11. Proportionality
    - Definition - Direct & Indirect Use - Numerical versus Algebraic Solutions
12. Real Analysis
    - Decimal View of concepts and of proofs
13. Rules &Patterns in Science, Technology & Society - Pattern Based Reason
14. Mathematical Reasoning, empirical, inductive or deductive
15. Units
    - in rates & slopes & (?) derivatives
    - in ratios & proportions - slopes & rates included
16. Complex Numbers & Vectors & Trig
    -  trig expression for dot & cross - cosine law

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