Studying Mathematics Thread

[Reltzik]

..... grumblegrumblethatsnotcheatingYOUREcheatinggrumblegrumble....

I'm pretty sure the only thing that constitutes as cheating would be to actually use a protractor to measure the angles.

Or using trig. The problem says not to use trig.

[GrandizerII]

Well, I had a quick look at it to see if I could mentally figure some shit out on the go. But still not seeing anything yet.

Just waiting for the weekends now, and hopefully I'll finally get to more drawing.

[Fireball]

I'll readily admit that I flogged the first one for about half an hour.  Then it was "AHA!", but really more like "FFS". One thing about this sort of learning experience is that next time, you'll knock it right down. I've not done a problem like this in far too long.

[Reltzik]

I'll readily admit that I flogged the first one for about half an hour.  Then it was "AHA!", but really more like "FFS". One thing about this sort of learning experience is that next time, you'll knock it right down. I've not done a problem like this in far too long.

Yeah, math skills turn to rust if you don't use them. It's been way too long since I did basic geometry.

[Aliza]

I'll readily admit that I flogged the first one for about half an hour.  Then it was "AHA!", but really more like "FFS". One thing about this sort of learning experience is that next time, you'll knock it right down. I've not done a problem like this in far too long.

Yeah, math skills turn to rust if you don't use them.  It's been way too long since I did basic geometry.

I was just thinking that today! I was asked to find the inverse of (i 3). Five years ago, it would have been no sweat. Today, I really couldn't figure it out and then I realized that my professor's answer key reads -i and my calculator reads i.

I haven't touched this stuff in years.  

[Kernel Sohcahtoa]

I'm most likely going to get back into elementary number theory, as I encountered basic number theory in my study of abstract algebra. Prior to beginning my abstract algebra self-study in early July,  I studied divisibility and primes, which IMO, were very interesting.  In particular, I enjoyed the proof of the fundamental theorem of arithmetic.  Hence, I'm looking forward to learning/getting underneath this material again.

[Fireball]

I'm most likely going to get back into elementary number theory, as I encountered basic number theory in my study of abstract algebra. Prior to beginning my abstract algebra self-study in early July,  I studied divisibility and primes, which IMO, were very interesting.  In particular, I enjoyed the proof of the fundamental theorem of arithmetic.  Hence, I'm looking forward to learning/getting underneath this material again.

I have Oysteen Ore's book on Number Theory. A friend of mine who also has it was astonished that one of the mathematicians in it solved a Diophantine problem that had (if memory serves me correct) 1260 solutions. He was astonished that the guy had figured it out, as it was done in Arabic and not the Hindu-derived integers. I probably have some of the details wrong, it's been a long time. He went ahead and wrote some FORTRAN code and discovered that there were two more solutions! He then contacted Donald Knuth, who wrote some code in C and came up with the same answer. I have the paper somewhere in my stuff, which may be in storage. But I did find the book, so I can flip through it soon and see if I can find the problem. I worked my way through that book about 15 years or more ago.

[polymath257]

I'm most likely going to get back into elementary number theory, as I encountered basic number theory in my study of abstract algebra. Prior to beginning my abstract algebra self-study in early July,  I studied divisibility and primes, which IMO, were very interesting.  In particular, I enjoyed the proof of the fundamental theorem of arithmetic.  Hence, I'm looking forward to learning/getting underneath this material again.

I might suggest learning about Principle Ideal Domains (PIDs). There is a version of the Fundamental Theorem of Arithmetic in that generality, which includes polynomials in one variable. Polynomials in more than one variable are not PIDs, but do also have an analog. They are Unique Factorization Domains (UFDs).

[GrandizerII]

Ok, I'm about to give up on those geometry problems I linked to a few pages ago here. But let me try doing the first problem in stages first and get feedback along the way here.

This stage is very easy, but let me know if I made any calculation errors here:

https://pasteboard.co/HKpm2E7.png

I see a 60 degree angle in one of the smaller triangles. Maybe if I force an equilateral triangle in there, will that lead me somewhere? Also, the main triangle is isosceles. Hmmmmmm ... ... ...

[Fireball]

Ok, I'm about to give up on those geometry problems I linked to a few pages ago here. But let me try doing the first problem in stages first and get feedback along the way here.

This stage is very easy, but let me know if I made any calculation errors here:

https://pasteboard.co/HKpm2E7.png

No mistakes there.