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Dear MathOverflow community,

In about a year, I think I will be starting my undergraduate studies at a Dutch university. I have decided to study mathematics. I'm not really sure why, but I'm fascinated with this subject. I think William Dunham's book 'Journey through Genius ' has launched this endless fascination.

I can't wait another whole year, however, following the regular school-curriculum and not learning anything like the things Dunham describes in his book. Our mathematics-book at school is a very 'calculus-orientated' one, I think. I don't think it's 'boring', but it's not a lot of fun either, compared to the evalutation of $\zeta(2)$, for example. Which is why I took up a 'job' as as a tutor for younger children to help them pass examinations. I wanted to make money (I've gathered about 300 euros so far) to buy some new math-books. I have already decided to buy the book ' Introductory Mathematics: Algebra and Analysis' which should provide me with some knowledge on the basics of Linear Algebra, Algebra, Set Theory and Sequences and Series. But what should I read next? What books should I buy with this amount of money in order to acquire a firm mathematical basis? And in what order? (The money isn't that much of a problem, though, I think my father will provide me with some extra money if I can convince him it's a really good book). Should I buy separate books on Linear Algebra, Algebra and a calculus book, like most university web-pages suggest their future students to buy?

Notice that it's important for me that the books are self-contained, i.e. they should be good self-study books. I don't mind problems in the books, either, as long as the books contain (at least a reasonable portion) of the answers (or a website where I can look some answers up).

I'm not asking for the $quickest$ quickest way to be able to acquire mathematical knowledge at (graduate)-university level, but the $best$ best way, as Terence Tao once commented (on his blog): "Mathematics is not a sprint, but a marathon".

Last but not least I'd like to add that I'm especially interested in infinite series. A lot of people have recommended me Hardy's book '$\textit{Divergent Series}$Divergent Series' (because of the questions I ask) but I don't think I posess the necessary prerequisite knowledge to be able to understand its content. I'd like to understand it, however!

4 improved formatting

Dear MathOverflow community,

In about a year, I think I will be starting my undergraduate studies at a Dutch university. I have decided to study mathematics. I'm not really sure why, but I'm fascinated with this subject. I think William Dunham's book 'Journey through Genius ' has launched this endless fascination.

I can't wait another whole year, however, following the regular school-curriculum and not learning anything like the things Dunham describes in his book. Our mathematics-book at school is a very 'calculus-orientated' one, I think. I don't think it's 'boring', but it's not a lot of fun either, compared to the evalutation of $\zeta(2)$, for example. Which is why I took up a 'job' as as a tutor for younger children to help them pass examinations. I wanted to make money (I've gathered about 300 euros so far) to buy some new math-books. I have already decided to buy the book ' Introductory Mathematics: Algebra and Analysis' which should provide me with some knowledge on the basics of Linear Algebra, Algebra, Set Theory and Sequences and Series. But what should I read next? What books should I buy with this amount of money in order to acquire a firm mathematical basis? And in what order? (The money isn't that much of a problem, though, I think my father will provide me with some extra money if I can convince him it's a really good book). Should I buy separate books on Linear Algebra, Algebra and a calculus book, like most university web-pages suggest their future students to buy?

Notice that it's important for me that the books are self-contained, i.e. they should be good self-study books. I don't mind problems in the books, either, as long as the books contain (at least a reasonable portion) of the answers (or a website where I can look some answers up).

I'm not asking for the $quickest$ way to be able to acquire mathematical knowledge at (graduate)-university level, but the $best$ way, as Terence Tao once commented (on his blog): "Mathematics is not a sprint, but a marathon".

Last but not least I'd like to add that I'm especially interested in infinite series. A lot of people have recommended me Hardy's book '$\textit{Divergent Series}$' (because of the questions I ask) but I don't think I posess the necessary prerequisite knowledge to be able to understand its content. I'd like to understand it, however!

3 deleted 1 characters in body; edited tags

Dear Math-Overflow MathOverflow community,

In about a year, I think I will be starting my undergraduate studies at a Dutch university. I have decided to study mathematics. I'm not really sure why, but I'm fascinated with this subject. I think William Dunham's book 'Journey through Genius ' has launched this endless fascination.

I can't wait another whole year, however, following the regular school-curriculum and not learning anything like the things Dunham describes in his book. Our mathematics-book at school is a very 'calculus-orientated' one, I think. I don't think it's 'boring', but it's not a lot of fun either, compared to the evalutation of $\zeta(2)$, for example. Which is why I took up a 'job' as as a tutor for younger children to help them pass examinations. I wanted to make money (I've gathered about 300 euros so far) to buy some new math-books. I have already decided to buy the book ' Introductory Mathematics: Algebra and Analysis' which should provide me with some knowledge on the basics of Linear Algebra, Algebra, Set Theory and Sequences and Series. But what should I read next? What books should I buy with this amount of money in order to acquire a firm mathematical basis? And in what order? (The money isn't that much of a problem, though, I think my father will provide me with some extra money if I can convince him it's a really good book). Should I buy separate books on Linear Algebra, Algebra and a calculus book, like most university web-pages suggest their future students to buy?

Notice that it's important for me that the books are self-contained, i.e. they should be good self-study books. I don't mind problems in the books, either, as long as the books contain (at least a reasonable portion) of the answers (or a website where I can look some answers up).

I'm not asking for the $quickest$ way to acquire mathematical knowledge at (graduate)-university level, but the $best$ way, as Terence Tao once commented (on his blog): "Mathematics is not a sprint, but a marathon".

Last but not least I'd like to add that I'm especially interested in infinite series. A lot of people have recommended me Hardy's book '$\textit{Divergent Series}$' (because of the questions I ask) but I don't think I posess the necessary prerequisite knowledge to be able to understand its content. I'd like to understand it, however!

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