[gordontd]

 WellSpyder, on 2011-February-08, 03:49, said:

Reminded me of some advice I heard once from a Professor of Mathematics (http://www.maths.qmu...w/inaugtext.pdf)

I feel a bit like that about restricted choice

[Free]

 Winstonm, on 2011-February-06, 12:52, said:

A little later, we were introduced to the fascination of multiplication and division, and were shown how these activities were nothing more than shortcuts for addition and subtraction, that 2x2 was really like saying 2+2, and that 2x3 was really the same as 2+2+2.

~snip~

It was on the test. (-2)x(-3). Simple, that was the same as saying (-2)+(-2)+(-2). I proudly wrote down my answer: -6.

(-2)+(-2)+(-2) = (-2)x3. This is not the same as (-2)x(-3)... Pretty basic

[Free]

Let me tell you something: everything you've ever known about math is wrong. 1 + 1 = ??? Wrong, 1 + 1 = 1, not 2!

Suppose A = B = 1.

multiply with A

A*A = A*B

multiply with -1

-(A*A) = -(A*B )

add B*B

B*B - A*A = B*B - A*B

rearrange

(B-A)*(B+A) = (B-A)*B

divide by (B-A)

(B-A)/(B-A) * (B+A) = B

B + A = B

1 + 1 = 1

[gwnn]

it is perfect nonsense to say that

2x3 is the same as 2+2+2.

two times three = three, taken two times.

2x3=3+3=6

[gwnn]

obviously 1+1=1, in Boolean logic. but 1 xor 1=0, which has always made more sense to me.

[gwnn]

 Free, on 2011-February-08, 04:55, said:

divide by (B-A)

does not compute
does not compute
does not compute

[Winstonm]

Quote

Pretty basic

does not compute
does not compute
does not compute

[mike777]

The one scene in the movie "A Beautiful Mind" that stuck with me was where Russell Crowe hated to teach; he just hated it. He thought his students were a waste of his time.

--

In studying for (one level out of 3) my CFA exam I remember meeting a math prof who said the exam was really tough he had studied for 6 weeks. I had studied for almost a year 7 days aweek...Math guys are really good.

[kenberg]

 mike777, on 2011-February-08, 20:58, said:

The one scene in the movie "A Beautiful Mind" that stuck with me was where Russell Crowe hated to teach; he just hated it. He thought his students were a waste of his time.

--

In studying for (one level out of 3) my CFA exam I remember meeting a math prof who said the exam was really tough he had studied for 6 weeks. I had studied for almost a year 7 days aweek...Math guys are really good.

Yeah, and our social skills are really top stuff also.


When I was a grad student one of my fellow students would frequently approach me with the question "Do you know how dumb I am?" He would then continue "I didn't even know..." and then download everything he had learned in the last day or so.

Basically I like my fellow mathematicians but they can be odd. My wife recently noted that one of the guys that we have known for the 16 years that we have been married recently actually referred to her as "Becky" rather than "She".

[Winstonm]

Math is to Winston as sober is to curling.

[mike777]

fwiw as a student in high school I just remember how easy math was once you get it and how bad the teacher was in teaching it.

This seems even more true in college.

The teachers knew the subject but they did not know how to teach it. Which leads me in a circle back to how much they really knew the subject.


Lets teach transfers. You are an expert in transfers. Now teach it.

--


As far as the teachers I guess at the univ of chicago the saying was...we teach to the future nobel prize winners...we care less about the rest.

---


I fully grant many students could care less.

[kenberg]

Mathematicians don't get Nobel prizes. Unless they can convince someone they are economists or something. They can get a Fields medal.

[kenberg]

Quote

fwiw as a student in high school I just remember how easy math was once you get it and how bad the teacher was in teaching it.

This seems even more true in college.

The teachers knew the subject but they did not know how to teach it. Which leads me in a circle back to how much they really knew the subject.

I have heard all of my life about how the really good mathematicians can't teach, and I want to respond. On occasion that may be true but mostly it's bunk. For example, Hillel Furstenberg was teaching at Minnesota when I was a grad student there. He soon moved to Hebrew University and is one of the top people in a very top level school. I had to take a required course in philosophy at the hour that he was teaching a different course, but I only got to the required course on Jewish holidays since I far preferred to listen to Furstenberg. (I got an A, philosophy not being one of your more difficult subjects.) Charlie Fefferman got his Ph.D. from Princeton when he was 20 or so, maybe 21, and soon became a professor there. He has one of these Fields medals I mentioned. He is a clear and fascinating lecturer. Steve Smale, another Fields medalist, you will get mixed opinions about but I think he is a great lecturer. He gives the key ideas without much detail, asks if anyone can see anything wrong with his argument, and if no one speaks up he moves on to the next big idea. Definitely leaves room for filling in the gaps, but the key ideas he mentions really are the key ideas. These are three of many many examples. The most obvious difference between high school and college is the depth of knowledge possessed by the person in front of the class. To each his own, but I far preferred college to high school.

[mike777]

fwiw I will grant having a "tiger mom" would have helped me in all of my subjects but esp math.

Many of us have something close to we hope mom can pay the rent mom; even today.



have heard all of my life about how the really good mathematicians can't teach

[wyman]

 mike777, on 2011-February-08, 23:58, said:

have heard all of my life about how the really good mathematicians can't teach

Mostly this is a function of social aptitude. The most knowledgeable people about an area will by-and-large be the best teachers; the problem is that there are an awful lot of socially awkward and inept people in the hard sciences.

The other thing is that good teachers make hard things appear easy. The downside of this is that the teacher appears less smart in contrast to his colleague who babbles about some seemingly impossible concept (which would be possible if the right person were explaining).

[kenberg]

There is something to this last comment. I think some colloquium speakers are terrified by the thought that someone will say that they found the talk really easy to follow.

[wyman]

 kenberg, on 2011-February-09, 12:54, said:

There is something to this last comment. I think some colloquium speakers are terrified by the thought that someone will say that they found the talk really easy to follow.

This is a huge concern when giving job talks. You don't want the audience saying "yeah, but that was kind of trivial."

[kenberg]

 wyman, on 2011-February-09, 13:01, said:

This is a huge concern when giving job talks. You don't want the audience saying "yeah, but that was kind of trivial."

A job is good, tenure is better, retirement is really where it's at.

[shyams]

 Free, on 2011-February-08, 04:55, said:

Let me tell you something: everything you've ever known about math is wrong. 1 + 1 = ??? Wrong, 1 + 1 = 1, not 2!

Suppose A = B = 1.

multiply with A

A*A = A*B

multiply with -1

-(A*A) = -(A*B )

add B*B

B*B - A*A = B*B - A*B

rearrange

(B-A)*(B+A) = (B-A)*B

divide by (B-A)

(B-A)/(B-A) * (B+A) = B

B + A = B

1 + 1 = 1

 gwnn, on 2011-February-08, 06:08, said:

does not compute
does not compute
does not compute

Here's another one -- again easy to find the flaw.

We start by saying: -20 = -20
This is the same as: 16 - 36 = 25 - 45
Add in (81/4): 16 - 36 + 81/4 = 25 - 45 + 81/4
Re-state as: (4 + 9/2)^2 = (5 + 9/2)^2
Take sq roots: 4 + 9/2 = 5 + 9/2
Eliminate 9/2 from both: 4 = 5

[BunnyGo]

 shyams, on 2011-February-09, 13:57, said:

Here's another one -- again easy to find the flaw.

We start by saying: -20 = -20
This is the same as: 16 - 36 = 25 - 45
Add in (81/4): 16 - 36 + 81/4 = 25 - 45 + 81/4
Re-state as: (4 + 9/2)^2 = (5 + 9/2)^2
Take sq roots: 4 + 9/2 = 5 + 9/2
Eliminate 9/2 from both: 4 = 5

Do the factorization wrong? I think you meant (4 - 9/2)^2 and (5 - 9/2)^2.

But the essential flaw is very cute. I hadn't seen this one presented this way before.