This is a very one sided treatment of "all mathematics" between college calculus and graduate level mathematics. Sounds like typical mathematical physics, which is a far cry from all mathematics, and the treatment of things like, say, topoological spaces is quite shallow. You couldn't survive a minute in a graduate level mathematics class with this treatment of topology alone.
Math notes to take you from one year of college calculus to grad student level
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Re: Math notes to take you from one year of college calculus to grad student level
#32This is a very one sided treatment of "all mathematics" between college calculus and graduate level mathematics. Sounds like typical mathematical physics, which is a far cry from all mathematics, and the treatment of things like, say, topoological spaces is quite shallow. You couldn't survive a minute in a graduate level mathematics class with this treatment of topology alone.
Re: Math notes to take you from one year of college calculus to grad student level
#33This is a very one sided treatment of "all mathematics" between college calculus and graduate level mathematics. Sounds like typical mathematical physics, which is a far cry from all mathematics, and the treatment of things like, say, topoological spaces is quite shallow. You couldn't survive a minute in a graduate level mathematics class with this treatment of topology alone.
Re: Math notes to take you from one year of college calculus to grad student level
#34I'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, then you would have started already This is pretty much the only statement i have an objection or reaction to. I simply don't understand the basis for assertions along these lines. These sorts of fatalistic proclamations are made not-infrequently in the context of programming and development as well. Its as if we feel that the only ones worthy of pursuing a given discip…
I agree with your sentiment. Sometimes we get articles on (say) the Fourier transform, with its own intuitive take on how and why it works, some visualisation and some maths. I think these articles are great. I can understand how they would spark the interest of someone who is not familiar with the maths, whatever their age.
That's not the case here. I don't think that anyone who has upvoted this has read any significant part of the document, simply because it would take months if not years to go through. It's like me posting a several-hundred page set of homemade notes on cell biology and saying "Notes to take you to medical school level biology".
Re: Math notes to take you from one year of college calculus to grad student level
#35If you're interested in this material, you may also like my LaTeX'ed lecture notes covering the last few years of my mathematics degree - mostly pure mathematics with some statistics and financial mathematics.
http://tullo.ch/2011/mathematics-lecture-notes/ for the PDFs, and https://github.com/ajtulloch/SydneyUniversityMathematicsNote... for the LaTeX source.
Re: Math notes to take you from one year of college calculus to grad student level
#36I'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, then you would have started already This is pretty much the only statement i have an objection or reaction to. I simply don't understand the basis for assertions along these lines. These sorts of fatalistic proclamations are made not-infrequently in the context of programming and development as well. Its as if we feel that the only ones worthy of pursuing a given discip…
This kind of mathematics is at a level that requires a certain amount of self-motivation, passion, desire, whatever you want to call it, to learn. It's probably something you're born with, which is why not many people pursue graduate studies in mathematics and those who do are mostly people with a real love for it. It's unlikely that at some point in your adult life you're going to suddenly develop the necessary burning desire to motivate such study on the basis of a set of notes someone posted on the internet.
Re: Math notes to take you from one year of college calculus to grad student level
#37Earlier quoted context omitted.
iconjack, you are a dead user. Time to create a new account.
What do you mean, a dead user? I was just quoting from the document, as an example of writing some might find obnoxious. Personally I find it rather entertaining.
No worries. This happens when you 'double post' a comment (usually because HN dies in mid submission) and then delete the original. The duplicate then stays grayed out making people think that your account has been hellbanned.
Re: Math notes to take you from one year of college calculus to grad student level
#38I can't stand the sans serif typesetting and cramped mathematical formulas. The tone is kind of obnoxious, too.
When he introduces group theory:
Group theory basics. It is time to note that our one-parameter symmetries are groups in the sense of modern algebra. Why? To masturbate with nomenclature as you do in an abstract algebra class? No. Because, as you will soon see, studying the group structure of a symmetry of a differential equation will have direct relevance to reducing its order to lower order, and will have direct relevance to finding some, possibly all of the solutions to the given differential equation—ordinary, partial, linear, or nonlinear. So what is a group?
I don't get the pedagogical purpose of calling what one does in an abstract algebra class "masturbating with nomenclature." I think every word in a textbook should be crafted with a pedagogical goal in mind. Making the material more light-hearted and less daunting is a valid purpose, but this tone just seems sour.
In fact, I count three uses of the word "masturbate" in the notes.
I prefer something like Richard Feynman's style, where he makes a subject accessible while still respecting the subject.
Here's a fantastic example of Feynman explaining how a computer works, using an analogy of an ever-faster filing clerk: http://www.youtube.com/watch?v=EKWGGDXe5MA
Re: Math notes to take you from one year of college calculus to grad student level
#39I found the writing style to be incredibly obnoxious and hand wavy, and really make me stop reading.
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.
When I saw that this was a word document exported as a pdf I knew this wasn't a serious text.
Re: Math notes to take you from one year of college calculus to grad student level
#40This is a very one sided treatment of "all mathematics" between college calculus and graduate level mathematics. Sounds like typical mathematical physics, which is a far cry from all mathematics, and the treatment of things like, say, topoological spaces is quite shallow. You couldn't survive a minute in a graduate level mathematics class with this treatment of topology alone.
I'm not quite sure why he always relates abstract algebra examples to ODES etc. Surely there are more motiving examples when discussing groups, esp from geometry.