The Mathematics Autodidact’s Aid (2005) [pdf]
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Re: The Mathematics Autodidact’s Aid (2005) [pdf]
#2I've also found these to be helpful:
The Language and Grammar of Mathematics, from The Princeton Companion to Mathematics, by James Gowers: http://press.princeton.edu/chapters/gowers/gowers_I_2.pdf
Reading Mathematics, by John Hamal Hubbard: http://www.math.cornell.edu/~hubbard/readingmath.pdf
Re: The Mathematics Autodidact’s Aid (2005) [pdf]
#3[deleted]
Re: The Mathematics Autodidact’s Aid (2005) [pdf]
#4I've also found these to be helpful: The Language and Grammar of Mathematics, from The Princeton Companion to Mathematics, by James Gowers: http://press.princeton.edu/chapters/gowers/gowers_I_2.pdf Reading Mathematics, by John Hamal Hubbard: http://www.math.cornell.edu/~hubbard/readingmath.pdf
Great read, thanks for the links
Re: The Mathematics Autodidact’s Aid (2005) [pdf]
#5maybe i am just stupid, but I find that many texts in mathematics like to skip over details, or I get stuck because there is an ambiguity in the text and there is no one to ask about it.. What do we do in this kind of situation?
Re: The Mathematics Autodidact’s Aid (2005) [pdf]
#6In the area of numerical analysis, I'd recommend works by LeVeque and Trefethen.
Re: The Mathematics Autodidact’s Aid (2005) [pdf]
#7maybe i am just stupid, but I find that many texts in mathematics like to skip over details, or I get stuck because there is an ambiguity in the text and there is no one to ask about it.. What do we do in this kind of situation?
Oh the dreaded "details left as an exercise." Personally, if I can't fill in details readily myself, I use Google or "just take there word for it" and hope it doesn't bite me later.
Re: The Mathematics Autodidact’s Aid (2005) [pdf]
#8maybe i am just stupid, but I find that many texts in mathematics like to skip over details, or I get stuck because there is an ambiguity in the text and there is no one to ask about it.. What do we do in this kind of situation?
One approach is to look at a few different but overlapping primers on the same matter and do the exercises. If one treatment doesn't click, another might. And for well-known subjects, topics are often covered in roughly the same order. Maybe not for graduate classes, not sure, but linear algebra, set theory, group theory, analysis it's generally the case.
Unless you can afford a tutor to teach it several different ways until it clicks, which is functionally similar.
Re: The Mathematics Autodidact’s Aid (2005) [pdf]
#9I enjoy a mathematics textbook as much as the next person, but what annoys me is the lack of solutions to the problems in so many of the books I've skimmed outside of classes.
Re: The Mathematics Autodidact’s Aid (2005) [pdf]
#10I enjoy a mathematics textbook as much as the next person, but what annoys me is the lack of solutions to the problems in so many of the books I've skimmed outside of classes.
I prefer solutions to some, but not all problems. Being able to independently and confidently verify your own solutions is an important skill to develop.