Self made mathematician

[JDrozen]

I'm an aspiring high schooler who wants to be a self study in math. Can you
suggest the literature where I can begin?

[Stephen J. Herschkorn]

JDrozen wrote:

>I'm an aspiring high schooler who wants to be a self study in math. Can you
>suggest the literature where I can begin?
>

From another recent post:

Me:

> Courant and Robbins, What is Mathematics?
> Stewart, Concepts of Modern Mathematics
>
> The latter is a particularly gentlle introduction. Unfortunately, it
> does not give suggestions for further reading, but you can always look
> for that on the Internet (e.g., by asking here.)
>
> Go to amazon.com or your local well-stocked bookstore to look for
> similar books.
>
> Also possibly of interest to you:
> Davis and Hersh, The Mathematical Experience
> Newman, ed., The World of Mathematics: to peruse, not to read cover
> to cover.

I also suspect you will find
Lehman, CH. College Algebra. New York: Wiley, 1962.
very enlightening. If you cannot find that particular text, other
"college algebra" texts from around the same time will be similar.
(Later texts are dumbed-down.)

--
Stephen J. Herschkorn sjher...@netscape.net
Math Tutor on the Internet and in Central New Jersey and Manhattan

[quasi]

I would start with problem solving.

Here are some great books with an emphasis on challenge problems. Some
of these are out of print, but you can probably borrow many of them
from a library

Contest Problem Book No 1: Annual High School Mathematics Examinations
1950-1960
by Charles Salkind

One Hundred Problems in Elementary Mathematics
by Hugo Steinhaus

Five Hundred Mathematical Challenges
by Barbeau / Klamkin / Moser

Tomorrow's math; unsolved problems for the amateur
by C. Stanley Ogilvy

250 problems in elementary number theory
by Waclaw Sierpinski

A selection of problems in the theory of numbers
by Waclaw Sierpinski

Analytic Inequalities
by Nicholas D. Kazarinoff

quasi

[gwl...@nukove.com]

Try to get a copy of "Journey Through Genius" by Durham. A thoroughly
readable book (and funny at times) that takes you on a tour from the
ancient Greeks, who hid the fifth perfect solid because it didn't fit
their views) up thru Cantor's work. You can skip parts that are tricky
(I have never negotiated my way thru Heron's formula for the area of a
triangle based only on the length of the sides (no knowledge of the
height is needed).

I've had a PhD for nearly 30 years and find the book very interesting.
If I still though I'd use the book in a senior seminar - it's that
good. Try to get a used copy on amazon.com

Good luck!

Gordon
PhD 1976 UMass
"Compact Transitive Isometry Groups"

[gwl...@nukove.com]

Please read "taught" for "though" in the second paragraph, and the
author's name is Dunham not Durham. Sorry.

[gwl...@nukove.com]

I meant to say "taught" towards the end "If I still taught..."

[A Aitken]

Stephen J. Herschkorn wrote:
> JDrozen wrote:
>
> >I'm an aspiring high schooler who wants to be a self study in math. Can you
> >suggest the literature where I can begin?
> >
>
> From another recent post:
>
> Me:
>
> > Courant and Robbins, What is Mathematics?
> > Stewart, Concepts of Modern Mathematics
> >
> > The latter is a particularly gentlle introduction. Unfortunately, it
> > does not give suggestions for further reading, but you can always look
> > for that on the Internet (e.g., by asking here.)
> >
> > Go to amazon.com or your local well-stocked bookstore to look for
> > similar books.
> >
> > Also possibly of interest to you:
> > Davis and Hersh, The Mathematical Experience
> > Newman, ed., The World of Mathematics: to peruse, not to read cover
> > to cover.
>
>
> I also suspect you will find
> Lehman, CH. College Algebra. New York: Wiley, 1962.
> very enlightening. If you cannot find that particular text, other
> "college algebra" texts from around the same time will be similar.
> (Later texts are dumbed-down.)
>

I second this recommendation. Very good pre-univ algebra book.

+++++++++++++++
Andre Aitken

[G. A. Edgar]

In article <1137453488....@g14g2000cwa.googlegroups.com>,
<gwl...@nukove.com> wrote:

> Try to get a copy of "Journey Through Genius" by Durham.

you mean Dunham

> A thoroughly
> readable book (and funny at times) that takes you on a tour from the
> ancient Greeks, who hid the fifth perfect solid because it didn't fit
> their views) up thru Cantor's work. You can skip parts that are tricky
> (I have never negotiated my way thru Heron's formula for the area of a
> triangle based only on the length of the sides (no knowledge of the
> height is needed).
>
> I've had a PhD for nearly 30 years and find the book very interesting.
> If I still though I'd use the book in a senior seminar - it's that
> good. Try to get a used copy on amazon.com

Or why not get a new copy for $10.17 ??

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/

[JDrozen]

Thank you for your recommendations.

[conesetter]

JDrozen wrote:
> Thank you for your recommendations.

Best to think of topics first then books which cover them. If you
learn Peano's arithmetic, linear algebra, Boolean algebra and analysis
you will then be able to move on to anything else in mathematics.
Regarding books, older ones are usually easier to read than modern ones
which tend to be more abstract.

[gwl...@nukove.com]

He's a high school student - the cheaper the better!

[gwl...@nukove.com]

Dunham has a second book that is a little easier to read (I suspect
you'll have no problem with most of "Journey Through Genius"). It is
titled "The Mathematical Universe" and he goes A thru Z thru great
results.

BTW not all mathematical conjectures need be intractable except to
experts. Recently Fermat's "Last Theorm" was solved by Andrew Wiles at
the Institute at Princeton. You may have read about it. You probably
are familiar with the Pythagorean Theorem. For a right triangle

H^2 = S1^2 + S2^2

Where H is the hypoteneuse and S1 and S2 are the lengths of the side.
Familiar example: 3-4-5 because 5^2 =3^2+4^2 (here the "^2" means
square the number, that is 5^2 =5*5 = 25).

Fermat conjectured, for example, that H^3 = S1^3 + S2^3 and in fact H^N
= S1^N + S2^N have no integer solutions for H, S1 and S2. He curiously
wrote in the margin of a document "I have a simple solution but not the
room to write it down..." This conjecture had many false "proofs". I
believe there is a place in the "standard" approach where a certain
assumption that seems fine is wrong.

After centuries, Wiles closeted himself at Princeton for seven years
and then gave a famous talk where at the end he simply said "...and
that establishes Fermat's Last Theorem." It took a good solid year for
specialists to go through his proof - there were a few glitches of no
real importance - and unlike some fields of "science" it such as social
science it is now considered a proven fact.

It is said that Wiles, in his quest, created a body of mathematics that
will keep mathematicians busy for 300 years!

But here's an even easier one to state. Goldbach was a rich man during
the heyday of math a couple centuries ago. He fancied himself a
mathematician but never did much except fund others and bask in their
success. He conjectured that any even integer may be written as the
sum of two prime numbers. Examples:

10 = 3 + 7 (and 5 + 5)

30 = 13 + 17

and so on.

While this has been established by computers for even integers into the
billions, no one has come close to a proof! The utility of a positive
is questionable!

Feel free to e-mail me at gordon.XXXlukXXXesh @nukXXXove.XXXcom

taking out the X's and the space.

Meanwhile, do a google on "twin primes".

Good luck!

Gordon

[david bandel]

"- there were a few glitches of no
real importance -"

yeah.. that's not even true. there was a major hole and he had to
modify his approach significantly to get a working proof. it took
another great insight before he was ready to unveil the corrected
version.

how about saying "there was a glitch or two beyond the scope of this
explanation"

troll.

[gwl...@nukove.com]

Hey, I don't have a clue as to how the proof proceeded but at the time
"glitch" was used and I knew it took a year to fix ir, which is minor
when the proof took a couple centuries, or in the modern era decades
(some Japanese folks had a major hand in it years ago).