Ask HN: Independent Math Study • Hacker News Board

Re: Ask HN: Independent Math Study

#11

Post by jknupp » Sun, Jul 19, 2009, 7:03 AM UTC

TriinT wrote: post #9

mark-t wrote: post #7

To be honest, calculus isn't that important for mathematicians, but if you want to study mathematics seriously, I'd suggest picking up a rigorous text like Rudin's or Apostol's. It will be difficult. You'll have to read most of it several times. That's perfectly fine; the point is that it will help you learn to think like a mathematician does. Now, on the other hand, linear algebra is almost universally important and…

I would claim that Calculus isn't that important for engineers / scientists / programmers either. Real Analysis is important if one needs to understand thing deeper. In the real world, problems can't be solved analytically... and many of the tools one learns in Calculus are kind of useless. I think Linear Algebra is much, much more important than Calculus. Linear Algebra is the arithmetic of higher mathematics, like…

>In the real world, problems can't be solved analytically...

Your other suggestions notwithstanding, you and I live in a very different "real world" my fried.

Re: Ask HN: Independent Math Study

#12

Post by mark-t » Sun, Jul 19, 2009, 7:30 AM UTC

aneesh wrote: post #8

mark-t wrote: post #7

To be honest, calculus isn't that important for mathematicians, but if you want to study mathematics seriously, I'd suggest picking up a rigorous text like Rudin's or Apostol's. It will be difficult. You'll have to read most of it several times. That's perfectly fine; the point is that it will help you learn to think like a mathematician does. Now, on the other hand, linear algebra is almost universally important and…

Saying the Putnam is a next step from AMC12 problems is like saying the NBA is a next step from pickup basketball with friends in middle school! There are people who can do Putnam problems for fun, but those people generally know who they are already.

Putnam problems are not considerably harder than AIME problems, and AIME is definitely the next step from AMC12. Anybody who can solve a few AIME problems can certainly solve A1 on the Putnam of almost every year.

Re: Ask HN: Independent Math Study

#13

Post by jibiki » Sun, Jul 19, 2009, 7:32 AM UTC

mark-t wrote: post #7

To be honest, calculus isn't that important for mathematicians, but if you want to study mathematics seriously, I'd suggest picking up a rigorous text like Rudin's or Apostol's. It will be difficult. You'll have to read most of it several times. That's perfectly fine; the point is that it will help you learn to think like a mathematician does. Now, on the other hand, linear algebra is almost universally important and…

> calculus isn't that important for mathematicians

That's a joke, right?

Re: Ask HN: Independent Math Study

#14

Post by wheels » Sun, Jul 19, 2009, 7:36 AM UTC

I've learned a lot of math that's beyond the scope of what I had in college. I usually find that it works best when it's on the way to something that I'm trying to do or understand. I never really tried to learn math for the sake of math -- I wanted to understand quantum computing algorithms, recommender systems and graph clustering -- and had to fill in the gaps so that the papers in the fields made sense.

Re: Ask HN: Independent Math Study

#15

Post by streblo » Sun, Jul 19, 2009, 7:38 AM UTC

You should take a look at a book called The Road to Reality by Roger Penrose. While it's geared more towards physics, this book has proven to me to be the most enlightening mathematics text I've ever read. Admittedly I'm only about 10 chapters in - it's a very dense book, and you'd do well to go through it slowly. But, if you're interested in math, this book will blow your mind.

http://www.amazon.com/Road-Reality-Complete-Guide-Universe/d...

Re: Ask HN: Independent Math Study

#16

Post by TriinT » Sun, Jul 19, 2009, 7:40 AM UTC

jknupp wrote: post #11

TriinT wrote: post #9

Earlier quoted context omitted.

I would claim that Calculus isn't that important for engineers / scientists / programmers either. Real Analysis is important if one needs to understand thing deeper. In the real world, problems can't be solved analytically... and many of the tools one learns in Calculus are kind of useless. I think Linear Algebra is much, much more important than Calculus. Linear Algebra is the arithmetic of higher mathematics, like…

>In the real world, problems can't be solved analytically... Your other suggestions notwithstanding, you and I live in a very different "real world" my fried.

If you can solve your problems analytically, then you're either working in a blessed field, or you're working with simplistic models...

Re: Ask HN: Independent Math Study

#17

Post by albertni » Sun, Jul 19, 2009, 7:49 AM UTC

aneesh wrote: post #8

mark-t wrote: post #7

To be honest, calculus isn't that important for mathematicians, but if you want to study mathematics seriously, I'd suggest picking up a rigorous text like Rudin's or Apostol's. It will be difficult. You'll have to read most of it several times. That's perfectly fine; the point is that it will help you learn to think like a mathematician does. Now, on the other hand, linear algebra is almost universally important and…

Saying the Putnam is a next step from AMC12 problems is like saying the NBA is a next step from pickup basketball with friends in middle school! There are people who can do Putnam problems for fun, but those people generally know who they are already.

Solving problems 1-4 on each day of the Putnam with an "unlimited" amount of time is not a ridiculous expectation. Putnam's difficulty is partly due to its time format.

Re: Ask HN: Independent Math Study

#18

Post by mark-t » Sun, Jul 19, 2009, 7:55 AM UTC

jibiki wrote: post #13

mark-t wrote: post #7

To be honest, calculus isn't that important for mathematicians, but if you want to study mathematics seriously, I'd suggest picking up a rigorous text like Rudin's or Apostol's. It will be difficult. You'll have to read most of it several times. That's perfectly fine; the point is that it will help you learn to think like a mathematician does. Now, on the other hand, linear algebra is almost universally important and…

> calculus isn't that important for mathematicians That's a joke, right?

No. Many pure math classes require no (or very little) calculus. Abstract algebra, number theory, combinatorics, and graph theory certainly fall into this category. Topology does, too, depending on which area you study and what you consider calculus. Sure, there are obviously fields that do rely heavily on calculus, as well as certain branches in the above fields, but my point was that it's nowhere near universally needed. I'm a graduate student at UCSD, and I can't remember the last time I used calculus in my research.

Re: Ask HN: Independent Math Study

#19

Post by alxv » Sun, Jul 19, 2009, 8:02 AM UTC

mark-t wrote: post #7

To be honest, calculus isn't that important for mathematicians, but if you want to study mathematics seriously, I'd suggest picking up a rigorous text like Rudin's or Apostol's. It will be difficult. You'll have to read most of it several times. That's perfectly fine; the point is that it will help you learn to think like a mathematician does. Now, on the other hand, linear algebra is almost universally important and…

> I would also suggest picking up a Number Theory or Combinatorics text; they're practically useless

Useless? I dear to say that number theory is currently the most lucrative field of mathematics. Without number theory, modern day cryptography would not exist and thus everything that depends on secure communication of information would not exist. So forget about commerce over the Internet, bank wire transfers, credit cards, administrating computers remotely and, most importantly, hiding your huge porn collection from your wife.

And, combinatorics is useful for the study of algorithms. It is pretty much the foundation of computer science.

Re: Ask HN: Independent Math Study

#20

Post by mark-t » Sun, Jul 19, 2009, 8:17 AM UTC

alxv wrote: post #19

mark-t wrote: post #7

To be honest, calculus isn't that important for mathematicians, but if you want to study mathematics seriously, I'd suggest picking up a rigorous text like Rudin's or Apostol's. It will be difficult. You'll have to read most of it several times. That's perfectly fine; the point is that it will help you learn to think like a mathematician does. Now, on the other hand, linear algebra is almost universally important and…

> I would also suggest picking up a Number Theory or Combinatorics text; they're practically useless Useless? I dear to say that number theory is currently the most lucrative field of mathematics. Without number theory, modern day cryptography would not exist and thus everything that depends on secure communication of information would not exist. So forget about commerce over the Internet, bank wire transfers, credit…

I'm aware of their applications; by "practically", I meant "almost". There are certainly compelling uses for number theory and combinatorics (though I'm not convinced the study of algorithms is one of them), but they're nothing compared to calculus.