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Topic: Is logic part of mathematics - or is mathematics part of logic?
Replies: 32   Last Post: Jul 7, 2013 9:03 PM

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Louis Talman

Posts: 4,461
Registered: 12/27/05
Re: Is logic part of mathematics - or is mathematics part of logic?
Posted: Jul 5, 2013 11:47 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Fri, 05 Jul 2013 17:41:04 -0600, Robert Hansen <bob@rsccore.com> wrote:

> Some, well, mainly Lou, have questioned my hypothesis that there has
> been a decline. Although, I think he means a decline in student ability,
> not a decline in the quality of mathematics education. I recall being
> exposed to so many derivations in my classes and producing many of them
> myself. Those are mostly gone today.


I was graduated from high school in 1962; derivations, and "producing them
myself" were gone by then---if they'd ever been there in the first place.
They were in the textbooks, but the "teachers" ignored them. The closest
I ever came to derivation in trigonometry was working trig identities
using the standard identities---which we never bothered to derive. Only
two or three of the fifteen us were any good at that---and the "teacher"
handle us by calling on us to present the solutions to the hard ones. In
so doing, he got us to think about those hard ones while not having to
think about them himself.

I see no reason to suppose that my high school was much different from
most others. Certainly the students in my college calculus courses, in
1962-3 and 1963-4, gave no indication of having anything in their
backgrounds much deeper than what I had.

It wasn't until I took my first calculus course as a freshman in college
that I encountered real concern about proofs and derivations. I was
fortunate in that my professors there made proofs and derivations about
half of their calculus sequence---all four semesters of it. And they
examined us on those proofs and derivations, not only in the calculus
sequence, but in the junior and senior comprehensive exams all math majors
had to pass in order to be graduated. (Many of my colleagues during that
first calculus sequence would not have agreed that any of this
proof-and-derivation business was "fortunate"; a substantial fraction of
them show themselves to be completely at sea at that business.)

So, yes. I do question your hypothesis that there has been a decline, and
I do mean a decline in the quality of mathematics education.

- --Louis A. Talman
Department of Mathematical and Computer Sciences
Metropolitan State University of Denver

<http://rowdy.msudenver.edu/~talmanl>


Date Subject Author
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Clyde Greeno
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/4/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Louis Talman
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of
logic?
Wayne Bishop
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/7/13
Read Re: Is logic part of mathematics - or is mathematics part of
logic?
Wayne Bishop
7/7/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of
logic?
Wayne Bishop
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Joe Niederberger
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Louis Talman
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/6/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Louis Talman
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Jonathan Crabtree
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
Robert Hansen
7/7/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy
7/5/13
Read Re: Is logic part of mathematics - or is mathematics part of logic?
GS Chandy

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