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