Re: ~ Proper sequence of mathematics to learn

From: Herman Rubin (hrubin_at_odds.stat.purdue.edu)
Date: 07/29/04 

Date: 29 Jul 2004 14:17:45 -0500

In article <a88af92f.0407261049.640846ec@posting.google.com>,
David Bandel <dwb1729@yahoo.com> wrote:
>"Klueless" <klueless@worldnet.att.net> wrote in message news:<HT8Nc.329166$Gx4.252060@bgtnsc04-news.ops.worldnet.att.net>...
>> "Adam" <addam@rogers.com> wrote in message news:3l8Nc.106$zyJ1.8@news04.bloor.is.net.cable.rogers.com...
>> > I'd appreciate any additions or changes to the material/order of study
>> > 1) Set theory + proofs
>> > 2) Group theory
>> > 3) Linear Algebra
>> > 4) Single-variable calculus
>> > 5) Multi-variable calculus
>> > 6) Ordinary differential equations
>> > 7) Partial differential equations
>> > 8) Calculus with complex number

>> Calculus (4) & (5) first. Then group theory (4)
>> --or abstract algebra, which includes group theory.
>> The rest in any order, except PDE after ODE. Analysis,
>> such as Rudin's Principles of Mathematical Analysis,
>> is part of the basic foundation.

>> Algebra
>> Geometry
>> Trigonometry
>> Advanced Math
>> Calculus
>> Abstract Algebra Analysis
>> <======== Everything Else ===========>

>first learn ur plusses and minuses then times and divides, then the
>x's and y's then the circles and then derivatives and squigglies then
>equations of derivatives... then donughts and football playing areas
>and learn some of the prime numbers too

Learn it from the most abstract approach you can in each area.

Start with the purely linguistic use of variables for
ANYTHING, and then try to understand logic, which
includes the restricted predicate calculus used for
proofs by more than 99% of mathematicians, and then
in some order, the integers, set theory, other number
systems, abstract algebra. The foundations of analysis
should if possible precede calculus, which does not need
geometry, although this is a good idea if done as in
Euclid, or a modernized version. The foundations of
analysis should be, if possible, presented in such a
way as not to interfere with later learning abstract
point-set topology.

Learning special cases, unless necessary, usually makes
learning more general situations more difficult, as it
puts in unlearning. Learning how to calculate is very
often useful, but rarely adds much to concepts. From
the attempts to teach teachers, and students who go to
college having the usual cookbook arithmetic, algebra,
geometry, etc., without proofs and emphasizing getting
answers, is worse than useless. 

-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558
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