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
#2[deleted]
Re: Math notes to take you from one year of college calculus to grad student level
#3This looks great based on my quick perusal. I'd be very surprised if the notes could teach these subjects to anyone who didn't have significant prior exposure. The notes seem better suited for reviewing and contextualizing material you already know rather well. My favorite book of this type is Shafarevich's Basic Notions of Algebra.
The stated prerequisites are also more advanced than the submission title implies. At my university we didn't have a dedicated course in complex analysis until our third semester, and that was in Denmark, where students will study nothing but mathematics from day one. In the American system where even mathematics majors have a mixed course of study for their first several years, it's not unusual for rigorous complex analysis to be a final year subject. Even Harvard's infamous Math 55b second-semester honors course only treats complex analysis very superficially.
Re: Math notes to take you from one year of college calculus to grad student level
#4I found the writing style to be incredibly obnoxious and hand wavy, and really make me stop reading.
Re: Math notes to take you from one year of college calculus to grad student level
#5I found the writing style to be incredibly obnoxious and hand wavy, and really make me stop reading.
That's interesting. I guess 'obnoxious' is pretty subjective, but which part did you find 'hand-wavy'? The parts I've read have been quite rigorous.
Re: Math notes to take you from one year of college calculus to grad student level
#6I 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.
Re: Math notes to take you from one year of college calculus to grad student level
#7this is gold. thanks!
Re: Math notes to take you from one year of college calculus to grad student level
#8This looks great based on my quick perusal. I'd be very surprised if the notes could teach these subjects to anyone who didn't have significant prior exposure. The notes seem better suited for reviewing and contextualizing material you already know rather well. My favorite book of this type is Shafarevich's Basic Notions of Algebra. The stated prerequisites are also more advanced than the submission title implies. At…
I don't think it's implied that complex analysis is required for reading these notes. The author writes that he expects students will take a course on complex analysis "at some point" but as far as I can tell he doesn't do anything requiring complex analysis in these notes (e.g. every search for "complex" turns up something unrelated to complex analysis, and the word "contour" (as in contour integral) doesn't appear in the notes at all).
Re: Math notes to take you from one year of college calculus to grad student level
#9It would be wonderful to have the privilege and dedication to learn all of this.
Do you think it would be possible to construct a high level treatment that would impart a rough idea of to the layman? One that omitted all the business about finding solutions and stuck to merely tracing the structures?
I have seen that lower-level concepts like the fundamental theorem of calculus and the Fourier transform can be easily explained in a matter of minutes with the help of diagrams. It is my hunch, but I lack proof, that the same could be done for all of mathematics. Of course I have been told a few times that it would be impossible.
Re: Math notes to take you from one year of college calculus to grad student level
#10This looks great based on my quick perusal. I'd be very surprised if the notes could teach these subjects to anyone who didn't have significant prior exposure. The notes seem better suited for reviewing and contextualizing material you already know rather well. My favorite book of this type is Shafarevich's Basic Notions of Algebra. The stated prerequisites are also more advanced than the submission title implies. At…
I don't think it's implied that complex analysis is required for reading these notes. The author writes that he expects students will take a course on complex analysis "at some point" but as far as I can tell he doesn't do anything requiring complex analysis in these notes (e.g. every search for "complex" turns up something unrelated to complex analysis, and the word "contour" (as in contour integral) doesn't appear…
I'll take your word for it. In that case, the notes can't very well be said to take you to the graduate level. There's no point in skating over arguably the most beautiful and interconnected area of mathematics (by which I mean complex analysis) in an effort to get to some nominal level of mathematical advancedness.