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3

Back in my student days I found that: Studying my favorite subjects could be done in almost any setting, regardless of distractions. But to study less favorite subjects I had to be a a quiet place with no distractions. This was in the Olden Days when I did not have distractions like an iPhone in my pocket that went with me everywhere. Believe it or not: ...


2

Do you think you will enjoy learning calculus on manifolds? I think there is a lot to appreciate there, and it opens the doors to a lot of beautiful mathematics and physics(differential geometry, differential topology, general relativity, de Rham cohomology, Hodge theory, etc). You can mostly get by in calculus on manifolds with just Riemannian integration. ...


3

It sounds to me like you need exposure to mathematical topics beyond what is covered in an undergraduate math major. Here's one recommendation: Fuks, Dmitrij Borisovič, and Serge Tabachnikov. Mathematical Omnibus: Thirty Lectures on Classic Mathematics. American Mathematical Soc., 2007.        There are similar collections, but this one is both broad and ...


2

Given you seem to have zero exposure to this material, I would just look for a reasonable undergrad text. I would avoid classes "for business" or the like (although really they are way better than nothing!) I would also be a little careful about asking for "mathematical statistics". Some people may interpret that as asking for a hyper ...


6

(I had tried to add a clarifying comment to @AlexanderWoo's good answer, but it was mysteriously deleted.) My point was, and is, that it is not constructive to think of "proofs" as a thing separate from normal human discussion of things. Rather, proofs are really explanations, or discussions that persuade. There is no magic formula, and "proof&...


3

I have that book. It's actually a very easy gentle book. I think easier than the medium difficulty calculus books or ODE books (not Spivak) that I have. I don't think you'd have any issues self studying it. Note, that it only has answers for 50% of the exercises, but the amount of exercises is vast (and like I said, the content is easy). So I think you ...


10

This is a text for an "introduction to proofs" course. It might not be well-known outside mathematical circles, because mathematics educators don't like to advertise this fact, but, outside of fairly selective universities, most students taking such courses fail to learn the material despite earning a passing grade. The majority of students never ...


5

The text says it is designed for a 14-week semester. With an instructor, we could guess that means 3 hours a week of class and 6 hours a week of additional work ( = 126 hours?). I cannot say whether someone without an instructor could do it in that time, or could do it at all. That will vary greatly depending on the student.


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