I would like to know the order in which mathematics should be learned.
For example to get from arithmetic to the highest math, what path
would you take? I would like some well written documents, and
especially links to some good books on the subject.

In other words I want a "map" or "learners guide" for a prolonged
study of mathematics.  I understand that the maths can branch out in
many different directions.  But that is exactly what confuses me.  I
would like a "map" of each path and its ultimate destination.  I would
like to know which "road to travel" to get to each destination.   I
know that this can be rather complicated, and I am sure there are many
roads to travel... So some good books on the subject would be ideal. 
(I am surprised that I have such a hard time finding books on this
subject!)  If there are any well written documents on the subject,
that couldnt hurt either.

---

Request for Question Clarification by alienintelligence-ga on 09 Aug 2002 14:33 PDT

Hi jmcgraw...

Have you already contacted several
universities and colleges for info
on their math curricula? 

Most have very specific paths for
doctorate routes in applied math
and similar degrees. That should
serve for a good map.

When you mention the "highest math",
what is YOUR idea of the highest.
Almost every field of math study,
has some pinnacle that could be
considered equivalent to another.

Are you interested in chemistry
math, physics math, accounting 
math and space math, also?

Anything in High School and 
before will be severely limited
by an individual school's policies
for prerequisite courses. A
"Satellite Math/Sciences School"
would be preferred and once again
their idea of the path might be
individual to them. Regional
expectations are also varied 
according to state. 

let us know
-AI

---

Clarification of Question by jmcgraw-ga on 09 Aug 2002 16:35 PDT

To answer your second question, I don’t know what the highest form of
math would be...   This is partly what I am curious about.  I am not
looking specifically at one field (physics, chemistry, etc), but would
like to learn which types of maths are used in which fields.

  I think you have taken the impression that I am looking for a path
to take in school.  This is not really the case. (Although it may be
in the future)  I am not looking for a list of prerequisites in a
legalistic sense...  (Like you said, different schools may vary)  But
am more curious in reading a survey of the different fields of
mathematics: a summary of each field, how they are connected, what
their orders of complexity are, and how one type of mathematics relies
on another type.  (For example, you would need algebra to understand
trigonometry, but you really wouldn’t even need arithmetic to
understand Euclidean geometry... Even though in a school they may
require basic math as a prerequisite to geometry)

  I know this is all very broad, and you cant really answer a specific
question. That’s why I think a book might be my best bet.  However
I've searched and cant find one.  I did find "Mathematics: From the
Birth of Number" by Jan Gullberg.  But it is more of a history of
math, and gets a lot more technical than I really want.

  And to answer your question about contacting Universities and
colleges, no I haven’t.  But I will give it a look.

Good Day,jmcgraw-ga 


I. Regardless of age, entry into the world of mathematics should be
one of joy, not pain.  In a world of few absolutes, mathematics is the
purest of pursuits and offers the excitement of constant discovery. 
Boundless curiosity is the key and the road to mathematical excellence
is bricked slowly and methodically so that this path will never need
repairs.  In awe of my brother
who handled the plumbing for large projects involving miles of piping
and the other assorted things needed for that project, he dismissed
the complexity by saying, "It's just one pipe at a time.  Do it right
and the whole thing will work."  This is also mathematics. Each of its
disciplines, done right, will accumulate and leave you a master.
Do you need to be a genius? or a mathematically gifted person?  If
that were so, we would have very few math teachers and tutors in the
world.  Most mathematicians find their niche because they love it, not
because they were born savants.  As Professor Freedman states in her
website,
"Consider math a foreign language --  it must be practiced".  Reading
Chapter One of a basic German language book is a grand accomplishment,
but I realize it would not allow me to wander around Bavaria with
complete fluency. That chapter was a brick on my road to the mastery
of German.  The same can be said of mathematics or any other
discipline.  Patience and above all, love it.  "Talk" mathematics as
Professor Freedman suggests.

Professor Freedman's Math Help 

Ten Ways To Reduce Math Anxiety

1. Overcome negative self-talk.
2. Ask questions.
3. Consider math a foreign language -- it must be practiced.
4. Don't rely on memorization to study mathematics.
5. READ your math text.
6. Study math according to YOUR LEARNING STYLE. 
7. Get help the same day you don't understand.
8. Be relaxed and comfortable while studying math.
9. "TALK" mathematics.
10. Develop responsibility for your own successes and failures. 

http://www.mathpower.com/

***********************************************
II. You can start by framing the Mathematical Bill of Rights as listed
by Angela Davis at her website.  A wonderful way to start your studies
each day. She includes "I have the right to NOT understand."  Yes. 
That is where we must all begin, and we build our understanding in our
own way...in our own style because we are all unique.
http://www.mathpower.com/billrght.htm
***********************************************
III. The day comes when you have the text you need. The proper study
environment. Then what?
You might consider the best way to approach that text.
Dartmouth offers some useful suggestions:

How to Read Your Texts: The SQ3R Method of Reading

One commonly used approach to reading, which works well for texts, is
the Survey, Question,

Read, Review and Recite (SQ3R) Method. 
The main steps are as follows:

Survey - before you read, scan the titles, headings, pictures and
chapter summaries
Question - actively ask yourself questions as you read such as, what
are the key topics in this

section/chapter? 
Read - read for comprehension, locate concepts and facts, record and
reduce information in the margins
Review - practice and rehearse the main concepts, reflect on key
learnings, anticipate exam questions
Recite - transfer information to long term memory 

A nice plan for the conquest of that math textbook!
By the way, there is a nice download dealing with "The Reading
Environment" that is especially needed in the study of math.... "Where
you read is a very important aspect of how you read. Be sure that you
read in a place that is quiet, has good lighting and allows you to
stay alert."
http://www.dartmouth.edu/admin/acskills/success/reading.html
***************************************************
IV. Shall we start with the wonderful world of Mathematics on the Web?
There are many useful, playful, enlightening, encouraging, detailed
websites that will be your friend in the study of mathematics.
There will be textbooks in your pursuit, but there is much to be
gathered from the Internet.

A. Comprehensive Sites
(http://www.math.utah.edu/~aroberts/resources.html#Comp)

	1.http://www.mathforum.org/ The Math Forum
	2.http://www.uen.org/ Utah Education Center
	   Great lesson plans for teachers and students here.  This is a
great guide for your study of mathematics. Skip any areas that you do
not need. Each grade is a separate webpage with valuable information.
 
 Mathematics - Kindergarten [1993] 
 
 Mathematics - 1st Grade [1993] 
 
 Mathematics - 2nd Grade [1993] 
 
 Mathematics - 3rd Grade [1993] 
 
 Mathematics - 4th Grade [1993] 
 
 Mathematics - 5th Grade [1993] 
 
 Mathematics - 6th Grade [1993] 
 
 Mathematics - 7th Grade [1995] 
 
 Mathematics - Prealgebra [1995] 
 
 Mathematics - Elementary Algebra [1995] 
 
 Mathematics - Geometry [1995] 
 
 Mathematics - Intermediate Algebra [1995] 
 
 Mathematics - Advanced Mathematics [1995] 
 
 Mathematics - Calculus [1995] 
 
 Mathematics - Applied Mathematics I [1995] 
 
 Mathematics - Applied Mathematics II [1995] 
 
http://www.uen.org/core/math/index.html 


	3.http://archives.math.utk.edu/ Mathematics Archives
Another grand site.  Each category is a separate webpage.  You may
visit this site and decide that you don't need textbooks immediately.
Tap into the "Arithmetic" site and discover the playfulness in
learning math.  Nice graphics!

Abstract Algebra
Algebra
Analysis
Applied Mathematics
Arithmetic
Art & Music
Calculus
Cellular Automata
Combinatorics
Complex Analysis
Computational Geometry
Computational Science
Computer Algebra / Cryptology
Genetic Algorithms
Differential Geometry
Discrete Mathematics
Dynamical Systems
Fluid Dynamics
Fourier Analysis & Wavelets
Fractals
Geometry
History of Mathematics
Industrial Mathematics
Linear and Matrix Algebra
Linear & Nonlinear Programming
Logic & Set Theory
Mathematics Education
Mathematical Biology
Miscellaneous
Multivariable Calculus
Nonlinear Dynamics
Number Theory
Numerical Analysis
Ordinary Differential Equations
Partial Differential Equations
Pre-Calculus
Probability Theory
Statistics
Topology
Trigonometry
http://archives.math.utk.edu/topics/arithmetic.html    

	4.http://www.math.utah.edu/~aroberts/resources.html#Comp  Resources
for Teaching Mathematics. Do visit this site.  There are many more
websites listed here...an overwhelming, delightful mess of them!

B. Initial search on www.altavista.com was simply "mathematics"
+studies. Try this and you will discover enough great material in
mathematics for ten lifetimes!

IV.http://www.singaporemath.com/ Singapore Mathematics Books

No. I don't expect you to go to Singapore or to import their
textbooks. Singapore's math students lead the world in mathematics
testing. This assemblage of the books they use for each grade is
perfect for review, so that you can walk into your library or
bookstore with an understanding of exactly the textbook you will need
for you current stage of mathematics study.

By the way, I buy all my math textbooks from Half Price bookstores. 
They have a wide selection of inexpensive current used math books.  I
have acquired the usual Statistics, Algebra, Geometry,Trigonometry and
Calculus books here. Yes. I love math and I tutor it freely in the
local high schools.  My reward?  That bright wonderful look in a
students face when "he gets it!"..when the concepts sinks in his mind
forever, never to be released!

This is a good place to stop, but I do hope you continue to contact me
through Google, not for a couple of bucks, but as a source of help to
you as you move along that digital highway.

Brad-ga

---

Clarification of Answer by brad-ga on 10 Aug 2002 16:04 PDT

Hi jmcgraw-ga,

I am glad you found what you needed, but my answer was not suitable to
your needs and there is no need to be out on this.  Just request a
refund from Google and they will reverse it.

By the way, if you ever get interested in Calculus, a nice read is A
Tour of the Calculus by David Berlinski.

Don't forget your refund.  If you're not satisfied, I'm not happy with
my research.

Brad-ga

The question was not answered.  Details were provided on a broader
matter that were not directly related to my question.  I have found
the answer by other means and no longer need the question to be
researched.  The researcher, Brad, also recommended that I request a
refund.

My question was not really answered, although some of the sites
recommended are useful.  I was asking for a description of the forms
of maths, and how they are all related.  This was not answered.  I did
not ask for a guide on study resources.

http://mathworld.wolfram.com/

Eric Weisstein's World of Mathematics (MathWorldTM) is the web's most
complete mathematical resource, assembled over more than a decade by
internet encyclopedist Eric W. Weisstein with assistance from the
mathematics and internet communities.
MathWorld is a comprehensive and interactive mathematics encyclopedia
intended for students, educators, math enthusiasts, and researchers.
Like the vibrant and constantly evolving discipline of mathematics,
this site is continuously updated to include new material and
incorporate new discoveries.

Although it is often difficult to find explanations for technical
subjects that are both clear and accessible, this website bridges the
gap by placing an interlinked framework of mathematical exposition and
illustrative examples at the fingertips of every internet user.

If you find MathWorld useful, you may also be interested in the
author's ScienceWorld site, which contains topically similar material
about astronomy, scientific biography, chemistry, and physics, and the
authors encyclopedias under development, which contain information on
scientific books, music theory, and the Game of Life cellular
automatan.

MathWorld is hosted and sponsored by Wolfram Research, Inc., makers of
Mathematica, the world's most powerful and flexible software package
for doing mathematics.
(the above is a long quote from their "about" page)
http://mathworld.wolfram.com/about.html

Brad:

  I'm sorry, but I did not ask for a guide on how to study math.  And
even though I specifically mentioned it, you did not recommend one
book.

  I have been searching and have finally found some books that look
hopeful.
Concepts of Modern Mathematics by Ian Stewart, From here to Infinity
by Ian Stewart, and "What Is Mathematics?" by Richard Courant and Ian
Stewart.

  Although I apreciate your attempt, you did not really zero in on my
question. I have finally succeeded in finding the books on my own, so
I do not think further help will be needed.

Ulu:

  Thanks!  That is one great site!

QUOTE>By the way, if you ever get interested in Calculus, a nice read is A
QUOTE>Tour of the Calculus by David Berlinski.

Brad,

  Thanks, I will remember that.