Motivational example for complex numbers

Years ago I was introduced to complex numbers. In class we had been talking about the cubic polynomial and its solutions. At one point we saw an example where, when using the formula, one had to stop because one had to take a square root of a negative number. The teacher went ahead and expressed … Read more

Is there a math website to study math from a mathematician point of view (ie proof oriented?)

I´m a student of the University of Puebla, Mexico, and I think that we lack of exigence there so I want to study math on internet to improve my education. I have already looked sites like edX, but I can´t find a source for pure mathematicians. Can somebody bring me a high quality resource for … Read more

Difference between Logarithms of different bases

Every time i see a logarithmic function and if it so happens that i’am required to take the derivative or the integral of that particular function i get stumped and i tend to avoid that problem. What i’am saying is ddx(log10x) and ddx(lnx) are the same i.e 1x Why is that? Infact they both are … Read more

How a layperson in mathematics learn mathematics from basics to at least intermediate level?

From few weeks I have been watching videos on Mathematics and came across the mystery of prime numbers. I am no mathematician, Even I almost know nothing about this field but I don’t know I find Prime number fascinating. I have watched several other videos too like the Pascal’s triangle and few more math unproven … Read more

How important it is to learn different proofs

As one studies mathematics, how important it is to find various proofs? I mean that if one has to prove for example that conditions (i), (ii), and (iii) are equivalent then is it enough to learn to prove that (i)->(ii)->(iii)->(i) or do mathematicians also think why (ii)->(i), (i)->(iii) and (iii)->(ii)? Answer Sometimes a direct proof … Read more

Calculus for beginners

What resources for “Calculus” do you recommend for beginners; they should describe the topics in a way easy to understand? Answer Another very helpful site is http://www.khanacademy.org/. It has videos on almost any subject and they are only about 10minutes long. They are clear and easy to understand. Khan teaches the idea and does example … Read more