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Math notes to take you from one year of college calculus to grad student level

math.ucr.edu

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Re: Math notes to take you from one year of college calculus to grad student level

#51

Post by atondwal »

This is extrordanarily good. For a similar, but more in depth covering of the same material I reccomend

[Osborne --- Advanced Mathematical Techniques: for Scientists and Engineers](http://www.amazon.com/Advanced-Mathematical-Techniques-Scien...)

and for a much more indepth, but less pedagogically useful (more of a reference) [Arfken --- Mathematical Methods for Physicists, Seventh Edition: A Comprehensive Guide](http://www.amazon.com/Mathematical-Methods-Physicists-Sevent...)

In addition anything by Penrose tends to target a lay audience, but quickly build up formalism and cover concepts interesting to even practicing physicists.

Re: Math notes to take you from one year of college calculus to grad student level

#52

Post by hdivider »

SandB0x wrote: post #28

I'm surprised by the excitement at every piece of teaching material or set of course notes posted here. Free textbooks and PDF notes have been around for years, especially for mathematical topics. This PDF won't do the work for you, and you can't skim-read this kind of material. To properly understand an area of mathematics then you need to put a significant amount of time and effort into working through the text, an…

Almost complete agreement here. There seems to be a 'shortcut mentality' among some hackers - the idea being that if you are faced with a difficult subject, begin with the assumption that standard learning material is padded with lots of useless filler material, and hence conclude you can save time by going for the more summarised stuff.

I think this is not generally a bad strategy in many subjects (business comes to mind), but mathematics is different. There really is no 'royal road' to any subset of it. There are shortcuts, sometimes, but every shortcut you take (with the exception of clever mathematical tricks, which count as solid learning here) deprives you of the opportunity to make a small but significant improvement to your logical problem-solving apparatus.

And that is probably a greater waste of time than anything else: shallow learning. Again, this is possibly not a bad strategy in many subjects, but again mathematics is not one of those.

Re: Math notes to take you from one year of college calculus to grad student level

#53

Post by dmcdougall_ »

olympus wrote: post #44
dmcdougall_ wrote: post #6

Earlier quoted context omitted.

Admittedly, I stopped before then when I saw the poor mathematics rendering. For some reason unbeknownst to me, the equations appear cramped and difficult to read.

I'm pretty sure I know the guy that wrote this (seriously, how many physicists named Alex Alaniz are there?), and he can't have LaTeX on his work computer because of some really dumb rules. So I don't blame him for it being an exported Word document because a LaTeX version would have meant doing this all at home instead of his spare time at work.

I don't blame him. Instead, I just didn't read it.

Re: Math notes to take you from one year of college calculus to grad student level

#54

Post by npsimons »

Confusion wrote: post #49
SandB0x wrote: post #28

I'm surprised by the excitement at every piece of teaching material or set of course notes posted here. Free textbooks and PDF notes have been around for years, especially for mathematical topics. This PDF won't do the work for you, and you can't skim-read this kind of material. To properly understand an area of mathematics then you need to put a significant amount of time and effort into working through the text, an…

if you really wanted to learn this material you would have started already. People change.

> People change.

People can change; most won't. While I, like you, take issue with the fatalistic statement of "you would have started already" (how young a person would the GP say this to? 30? 25? 18?), there is a grain of truth to it. Most people, even if they want to, won't get much out of this. Not that I'd like to discourage anyone.

Re: Math notes to take you from one year of college calculus to grad student level

#55

Post by npsimons »

SandB0x wrote: post #28

I'm surprised by the excitement at every piece of teaching material or set of course notes posted here. Free textbooks and PDF notes have been around for years, especially for mathematical topics. This PDF won't do the work for you, and you can't skim-read this kind of material. To properly understand an area of mathematics then you need to put a significant amount of time and effort into working through the text, an…

probably not as good as a well written textbook with careful examples and exercises

Name one. While I agree that this document (probably) won't compensate for a more complete education, including textbooks, the truth of the matter is that most textbooks (even many highly regarded ones) are horrible for learning on one's own. Rigorous and sound, yes, but many are bad for pedagogy, and even worse for self-teaching. A good majority are muddled and unclear to the layman, with not a very good "big picture" or "here's why it's done this way" approach. Just look at the K&R C article from the other day.

Re: Math notes to take you from one year of college calculus to grad student level

#56

Post by spacemanaki »

npsimons wrote: post #55
SandB0x wrote: post #28

I'm surprised by the excitement at every piece of teaching material or set of course notes posted here. Free textbooks and PDF notes have been around for years, especially for mathematical topics. This PDF won't do the work for you, and you can't skim-read this kind of material. To properly understand an area of mathematics then you need to put a significant amount of time and effort into working through the text, an…

probably not as good as a well written textbook with careful examples and exercises Name one. While I agree that this document (probably) won't compensate for a more complete education, including textbooks, the truth of the matter is that most textbooks (even many highly regarded ones) are horrible for learning on one's own. Rigorous and sound, yes, but many are bad for pedagogy, and even worse for self-teaching. A g…

Gilbert Strang's Linear Algebra textbook is designed to be useful to the self-learner, and I think the latest edition was revised after MIT's OCW was a thing, so actually references all the material online, IIRC.

I've read some of it and it's quite good. His lectures are great too.

Re: Math notes to take you from one year of college calculus to grad student level

#57

Post by geoka9 »

hdivider wrote: post #52
SandB0x wrote: post #28

I'm surprised by the excitement at every piece of teaching material or set of course notes posted here. Free textbooks and PDF notes have been around for years, especially for mathematical topics. This PDF won't do the work for you, and you can't skim-read this kind of material. To properly understand an area of mathematics then you need to put a significant amount of time and effort into working through the text, an…

Almost complete agreement here. There seems to be a 'shortcut mentality' among some hackers - the idea being that if you are faced with a difficult subject, begin with the assumption that standard learning material is padded with lots of useless filler material, and hence conclude you can save time by going for the more summarised stuff. I think this is not generally a bad strategy in many subjects (business comes to…

and hence conclude you can save time by going for the more summarised stuff.

I think this is not generally a bad strategy in many subjects (business comes to mind), but mathematics is different.

I agree, math books tend to be on the terse side as they are - you wouldn't want the material to be even more terse, because you'll end up spending more time grasping it without the help the additional text may provide.

Re: Math notes to take you from one year of college calculus to grad student level

#58

Post by hcarvalhoalves »

You know what I would like? Math material that is less concise.

Some math concepts are too dense to grasp without first understanding the reasoning behind it, the axioms it's based on, real-world applications, metaphors, diagrams... heck, even the history behind the mathematician helps sometimes (e.g., knowing Newton was a theologist is relevant to understand some things about classic physics [1]). In fact, I love how earlier mathematicians were mostly multi-disciplinary scientists, and almost always philosophers. We need a new Renaissance.

[1] http://en.wikipedia.org/wiki/Isaac_Newton#Religious_views

Re: Math notes to take you from one year of college calculus to grad student level

#59

Post by gnu8 »

hcarvalhoalves wrote: post #58

You know what I would like? Math material that is less concise. Some math concepts are too dense to grasp without first understanding the reasoning behind it, the axioms it's based on, real-world applications, metaphors, diagrams... heck, even the history behind the mathematician helps sometimes (e.g., knowing Newton was a theologist is relevant to understand some things about classic physics [1]). In fact, I love ho…

That's what university is for.

~There is no royal road to mathematics~

Re: Math notes to take you from one year of college calculus to grad student level

#60

Post by baaats »

hcarvalhoalves wrote: post #58

You know what I would like? Math material that is less concise. Some math concepts are too dense to grasp without first understanding the reasoning behind it, the axioms it's based on, real-world applications, metaphors, diagrams... heck, even the history behind the mathematician helps sometimes (e.g., knowing Newton was a theologist is relevant to understand some things about classic physics [1]). In fact, I love ho…

I think what you're looking for are textbooks.
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