Possible Duplicate: What's an intuitive way to think about the determinant? I just learned the basics of matrices. Then I came across the magical formula $$\det(AB)=\det(A)\det(B)$$ I understand the proof, but I don’t really understand why it is true. It seems that we are too lucky. The first step is to prove that $\det(EA)=\det(E)\det(A)$ for […]

While this may seem very subjective — and, admittedly, my own dislike of L’Hôpital’s rule is not entirely devoid of subjectivity — I am looking here for argumented, factual answers. From what I understand, students in the United States, when learning calculus and limits, are provided with and encouraged to use L’Hôpital’s rule very early […]

So I am looking at some math stuff and I start looking at the abc-conjecture. Naturally I run into the name Mochizuki and so start trying to see what he did. Well, he is starting look like another Galois. Frankly it was getting frustrating … the lack of information. It seems like no one understands […]

Historians widely report that l’Hopital’s 1696 book Analyse des Infiniment Petits pour l’Intelligence des Lignes Courbes contains a questionable premise expressed by an equation of type $x+dx=x$ (sometimes written as $y+dy=y$ as in Laugwitz 1997). I used to believe this until I looked in l’Hopital’s book and did not find any such equation. What I […]

It’s often said that the Lebesgue integral is superior to the Riemann integral because it satisfies nicer properties, for instance things like $$\lim_{n\to\infty} \int f_n = \int \lim_{n\to\infty} f_n$$ But if in the course of a problem we’re blocked by the fact that our (Riemann) integrals aren’t satsifying some mathematical property, how could it possibly […]

Many arguments about the foundations or philosophy of mathematics centre on the question of whether or not there exist objects or entities (such as certain sets) which are not “finite”. (For instance, Doron Zeilberger, although he is fond of April Fool jokes, does not seem to be joking here, or here.) For such arguments to […]

this is my first time on stack exchange and I am seeking advice for my future studies. Some background first; I am a undergraduate student pursuing a degree in mathematics and I hope to pursue graduate level studies and eventually be a professor. I have taken math classes through calculus I and I am looking […]

This question already has an answer here: Does mathematics become circular at the bottom? What is at the bottom of mathematics? [duplicate] 8 answers

This is an EDIT version of my original question: Recently I’ve been interested in the history of the Theory of Equations. The thing is that I learned about this mathematician named John Colson, he published a very interesting paper: Aequationum Cubicarum & Biquadraticarum, tum Analytica, tum Geometrica & Mechanica, Resolutio Universalis in the Philosophical Transactions, […]

I have taken real analysis, but never learned Fourier analysis. What is a good book to get started? I’m not sure the Stein book would be good.

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