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Comment by timwaagh | Hacker News Reader

math bsc here. In my opinion there is no reason to want such a thing. why? because mathematics is the most academic of degrees. you will want to build relationships with professors so you have a chance for a career in academia. it is also extremely difficult and you will want to team up with other students for assignments and the like. the study load is very high and without any community to support you, you are very likely to quit (which happens to one-third of first year students even on-campus at my alma mater).

if you just want to learn a bit on your free time, buying books is much cheaper. studying math for a degree is more than 40 hours a week. i can give a few suggestions if you like.

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Sure - Please suggest. I have been buying books (the likes of Apostol, Spivak, Artin) and doing self study. The typical pattern is start solving the problems and I get stuck with tough ones. And I hardly go past the third chapter of all the books that I had bought because of this.

What areas of mathematics are you interested in learning about? I would also pick up Principles of Mathematical Analysis by Rudin.

Being unable to solve some tough problems is entirely normal - there is only a handful of people gifted enough to go though a mathematics curriculum, getting 100% on all their assignments, working in isolation. I certainly didn't! Having been a TA in upper-level math courses, many/most of the students averaged 80% on homeworks which were certainly NOT made up of entirely tough problems - and they probably worked together quite a bit, and had teachers to ask for help if they want. So don't get frustrated if you get stuck regularly, just move on, then come back later in a couple of weeks when you're reviewing and try again. If you're still stuck, go to an online forum to ask for a hint, or you don't have to feel guilty about skipping some of the hardest problems entirely.

Two book suggestions:

Strichartz - The way of analysis. MUCH more user friendly than the standard analysis texts. The book is filled with long paragraphs if english sentences explaining what your are doing, and why you are doing it (if you can imagine a mathematics book committing that sin!).

Pressley - Elementary Differential Geometry. The appeal of this book is that it teaches only the more concrete classical formulation of the theory, so you don't have to confront tensors and n-dimensional abstractions at first, and also that it provides outlined solutions to every problem in the text!

Armstrong - Groups and Symmetry is accessible. Munkres - Topology also doable. Vector Calculus by Marsden/Tromba was my intro calculus book however im not sure if calculus is ever going to be very interesting. not a bad book though.

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