Appetizers and Lessons for Mathematics and Reason 
www.whyslopes.com        (missing links in the exposition of both)   ( Français)  
What does it mean to use a formula forwards and backwards

 Logic mastery is key to easing or avoiding learning difficulties in work & studies. 

Online Volumes (Book Orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3 .Why.Slopes.&
.More.Math.1995

Links To Tutoring Services

Parents:-Help. your. child. or. teen.study

Site  Math Folders

1. Arithmetic Flash Video Lessons  11-2008
2.  Algebra Videos (to appear)
3.-Fractions-Rates-Proportns-Units-2006
4.  Algebra, Odds & Ends, HS level-2001
5. 
Solving Linear Equations  04-2005
6.-Euclidean-Geometry/Complex No.s 
7.  Analytic Geometry/Functions 2006
8.  Number Theory. 2006-7
9.  Complex Numbers More 2001. 
 
10  Exponents, Radicals & logs. 2008
11. Calculus  2005

12. Real  Analysis 1995
13. Electric Circuits Etc  2007
How-TOs/ Reference - 08- 2008
1. Arithmetic
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus

Entrance Level


Adopt whyslopes.com/search/  for internet searches. 

Pages for Students

Proper notation & format 
makes the hard easier.

Pages For Teachers

Show a student how to learn and that helps one. Show a teacher or  tutor how to make skills and concepts easier for students and that helps many. 

Miscellaneous

Your IP Address  & how to use it

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

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.

YOU are better than YOU think. Show yourself  how:

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Take greater  charge of your work or studies: Read like a lawyer for better work & study skills, but do not take everything literally.

In particular, two logic puzzles  are keys to site content, and to greater work and study skills.  See if  you agree.

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Help Me Learn/Teach;

  1. Algebra
    words before symbols - direct & indirect use of formula, numerical versus algebraic solutions - what is a variable (more words)
  2. Arithmetic
    -new Arithmetic Folder
    - 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
  1. Functions - introduction
    hindsight - composition aka
    substitution
    -
  2. Geometry, Euclidean - Correspondence of trianglesTriangle construction,  duplication & Isometry - Failure of ASA & the // line postulate - angle sum in triangles -// grams - Triangle Similarity
  3. Geometry- Analytic - functions, polynomials, complex numbers, unit circle trigonometry
  4. Logic
    - First Steps -
    Symbols in Logic -
     Occurrence & Truth Tables - Indirect Reason -Indirect Reason More
  5. Proportionality
    - Definition - Direct & Indirect Use - Numerical versus Algebraic Solutions
  6. Real Analysis
    - Decimal View of concepts and of proofs
  7. Rules &Patterns in Science, Technology & Society - Pattern Based Reason
  8. Mathematical Reasoning, empirical, inductive or deductive
  9. Units
    - in rates & slopes & (?) derivatives
    - in ratios & proportions - slopes & rates included
  10. Complex Numbers & Vectors & Trig
    trig expression for dot & cross - cosine law

Books by other authors 

  • Mathematics from the Birth of Numbers, 1996, 950+, by the late Jan Gullberg, is an excellence resource forpupils and instructor in college and the upper years of secondary schools. ISBN 0-393-04002-X.  The book is a work of love by its author, one that I would highly recommend as gift for any one with a strong interest in learning or teaching mathematics. 

  • The VNR Concise Encyclopedia of Mathematics by W. Gellert, H. Küstner, M. Hellwich & H. Kästner, Van Nostrand Reinhold Company, 1975 (or 1977). ISBN: 0-442-22646-2 (hard cover) and ISBN:0-442-22647-0 (paperback). Copy right held by a corporation whose sense of public service does not exist or is insufficient to put this work back in print.  Used copies available.
  • Collin's Dictionary of Mathematics - Undergraduates and high school instructors may find it useful.. ISBN 0-00-710295-X  My copy was found in the McGill U. Bookstore for 24 $CDN.  www.collins.co.uk

More recommendations for public and private libraries with links to Amazon

Review

Calculus with Analytic Geometry, Denis Zill, Here is another well-written calculus book. A colleague of mine like it so much that he provided feedback to the author to help remove typos. Copies should be in every college library. Here is a good reference for a first course or two in calculus. 
Calculus of One and Several Variables. Einar Hille and Satunino L. Salas. Here is or was a good reference for calculus - an easier read than most. Copies should be in every college library.
Mathematics from the Birth of Numbers, Jan Gullerg. This is a work of love by the author with help from his family.  This hardcopy has over a 1004 pages, all beautifully typeset.  The word beautiful when applied to this work is an understatement. I recommend it to all high school and college instructors and tutors, and college level students in math, science or engineering. High school and college libraries should, no must, add this work to their collections.
Every high school and college library should have a hardcopy of this work. If only used copies are available, get a used one and rebind it. This work is a must. 
Mathematics for the Non-Mathematician. Morris Kline is one of my favorite authors. A recent acquisition. Prerequisite: A first or further course in calculus. My review to come. I am still reading it. 
Mathematical Thought from Ancient to Modern Times, Volumes I to III,  by Morris Kline.  All college and university libraries should have this work and its companion.  

Prerequisite: An undergraduate degree in Mathematics with a strong interest in the logic of mathematics.

Mathematics, the Loss of Certainty. Morris, Kline; Hardcover. Mathematics may be the queen of science and logic, but the certainty we once held or aspired to in this subject is not absolute.

Prerequisite: An undergraduate degree in Mathematics with a strong interest in the logic of mathematics.

Calculus, Lipman Bers, Here is a rare and beautiful calculus book which dared in the 1960s mention decimals in the representation of real numbers. Elements of this work should return to the calculus curriculum. Copies should be in every college library.
Principles of Real Analysis, Walter Rudin.   Here is a good reference for advanced students in mathematics, physics and electrical engineering.   

Prerequisite: Two or three courses in calculus. 

Introduction to Topology. Bert Mendolson. As a undergraduate, I found the introduction to topology in real analysis too hard for my liking.  This work (if I remember correctly) clarified matters - made them simpler. 

Co-requisite: A first course in real analysis. 

Advanced Calculus, Loomis and Sternberg. Here is a Banach space approach to advance calculus.  See treatment of chain-rule via linear approximation and a careful use of little o and big O asymptotic behaviors.  Out of Print.  Used copies may be available.  This work includes the proofs normally omitted in first courses in calculus. 

Co-requisite: A first course in real analysis. 

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