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Ask HN: How to self-study mathematics from the undergrad through graduate level?

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Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#171

Post by oefrha »

enraged_camel wrote: post #149
forkandwait wrote: post #89

Earlier quoted context omitted.

Depending on your background, you probably don't have enough information to pick a long-term goal anyway. I am afraid that sounds curmudgeonly, but I have also seen students shoot themselves in the foot because they decided they didn't need a class for their not very well informed goals.

>>Depending on your background, you probably don't have enough information to pick a long-term goal anyway. Nah, it's totally possible for newbies to pick high-level long-term goals. This can be something like "I want to teach my computer to tell apart dogs and cats", or "I want to create a website where people can buy and sell yarn." From there, Google searches can direct someone towards concepts and various methods…

Not in math. Unless you are a mathematician, I challenge you to pick a math equivalent of "I want to create a website where people can buy and sell yarn." I’ll wait.

People just assume learning math is the same as learning everything else. That is not even remotely true.

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#172

Post by asdffdsa »

jack_h wrote: post #84
gnulinux wrote: post #61

Earlier quoted context omitted.

I strongly disagree actually. I think mathematics is the best field to self-study. There is nothing in mathematics that cannot be explained on the paper. There are many textbooks that are very good that in most universities professors won't be that good anyway. I went to UC Berkeley to study mathematics (ended up studying CS though) which is supposed to be a top department, but most of my textbooks were better teache…

As someone who did study both math and CS at university I disagree. I think there are numerous courses that can more easily be self-taught[1], mostly what one would encounter in their first ~2 years in a math degree. After that things get conceptually a lot more difficult. For me personally I didn't really need an instructor for most of my calculus courses, or ordinary differential equations, or most of the linear al…

The reality is that having a great mentor is a privilege, not a given. I don't think anyone is arguing that having a genius and brilliant teacher wouldn't help, rather that it is possible to reach an "advanced" (grad/undergrad level) understanding of mathematics without the luxury of having someone who is far more knowledgeable to turn to for help.

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#174

Post by Koshkin »

Karrot_Kream wrote: post #134
azhenley wrote: post #22

Earlier quoted context omitted.

Any suggested reading on rings and lattices? I took a lot of math classes in undergrad but was never exposed to these concepts.

Really enjoyed Algebra: Category 0. Introduces some basic Category Theory and uses it to develop the standard practice of undergrad algebra. The exercises are medium difficulty (nothing ridiculous like a Knuth or Spivak problem, but nothing breezy either) and there are enough examples in the text of proofs with enough detail to get you working on the exercise problems.

Did you mean Aluffi’s Algebra: Chapter 0? What a wonderful book.

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#175

Post by Bedon292 »

Not sure if its great for your purposes, but I like the 'No Bullshit guide to Math and Physics' at least as a reference. It might be a good place to brush up on lower level stuff before advancing to harder topics.

https://minireference.com/

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#176

Post by shriek »

Bedon292 wrote: post #175

Not sure if its great for your purposes, but I like the 'No Bullshit guide to Math and Physics' at least as a reference. It might be a good place to brush up on lower level stuff before advancing to harder topics. https://minireference.com/

Can anyone share some insight on if there has been any improvements on this since the last time it was posted here [1]? From that thread it appears that it has few misinformation there.

[1]https://news.ycombinator.com/item?id=4994367

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#177

Post by Karrot_Kream »

Koshkin wrote: post #174
Karrot_Kream wrote: post #134

Earlier quoted context omitted.

Really enjoyed Algebra: Category 0. Introduces some basic Category Theory and uses it to develop the standard practice of undergrad algebra. The exercises are medium difficulty (nothing ridiculous like a Knuth or Spivak problem, but nothing breezy either) and there are enough examples in the text of proofs with enough detail to get you working on the exercise problems.

Did you mean Aluffi’s Algebra: Chapter 0? What a wonderful book.

Sorry yes

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#178

Post by gnulinux »

asdffdsa wrote: post #172
jack_h wrote: post #84

Earlier quoted context omitted.

As someone who did study both math and CS at university I disagree. I think there are numerous courses that can more easily be self-taught[1], mostly what one would encounter in their first ~2 years in a math degree. After that things get conceptually a lot more difficult. For me personally I didn't really need an instructor for most of my calculus courses, or ordinary differential equations, or most of the linear al…

The reality is that having a great mentor is a privilege, not a given. I don't think anyone is arguing that having a genius and brilliant teacher wouldn't help, rather that it is possible to reach an "advanced" (grad/undergrad level) understanding of mathematics without the luxury of having someone who is far more knowledgeable to turn to for help.

Precisely. GP here. I didn't argue against having a great mentor. If you go to a great university you clearly have an advantage. I think it's perfectly doable to teach yourself mathematics if you study intense enough eith correct tools.

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#179

Post by gnulinux »

azhenley wrote: post #22
madhadron wrote: post #20

There's a set of basics that you will want no matter which direction you go: calculus/real analysis, linear algebra, differential equations/dynamical systems, and sets, groups, rings, and lattices. Calculus: learn to extract qualitative information about a function (it goes up here, has a maximum there, goes down there, oscillates with an increasing period, goes to this value at infinity...) and to numerically comput…

Any suggested reading on rings and lattices? I took a lot of math classes in undergrad but was never exposed to these concepts.

Dummit&Foote imho is the best undergrad algebra book.

Re: Ask HN: How to self-study mathematics from the undergrad through graduate level?

#180

Post by analog31 »

you_owe_me wrote: post #114
analog31 wrote: post #108

Earlier quoted context omitted.

From what I've observed, most engineers are glad to be done with math when they finish college. Most engineering is qualitative: Organizing and arranging things, making things fit together, and troubleshooting. Maybe 10% of engineering is quantitative, and that work often goes to the handful of people in the department who have maintained an interest in it. Some of the engineers who attract quantitative work are peop…

When you refer to engineers, do you mean actual engineers (BSc in Engineering)? or your web designer with jquery skills who calls himself engineer?

I'm referring to people with degrees in mechanical, electrical, etc., or programmers with computer science or related degrees. These are all people who got through some level of college math requirement such as calculus.

And I'm not blaming anybody -- for one thing college math is often badly taught, and there's a pervasive message that you won't use any of your math or theory after you finish your degree. And then we get them so busy with CAD and bureaucracy, that they forget a lot of their school stuff.

But anything requiring calculus or above, goes to a handful of "math people" in the department, who accept those tasks in return for avoiding the CAD and organization stuff. (I'm one of those people at my workplace, my degree is in physics).

To make it a bit harder, virtually all math these days is done with computation, which means a person has to be good at both math and programming at some level.

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