What Is Modern Algebra and How Does It Differ from Calculus?

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Hey everyone,

I'm looking at taking Modern Algebra next semester. Could someone tell me what its all about? How does it differ from Calculus?

Also, on a scale from 1 - 10, personally how hard is it (assuming Calculus II is a 5)?

Thanks!
 
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Can't you find a syllabus? This is probably a better question for the Academic Guidance forum. If it's what is often called 'Abstract Algebra' (group theory etc.) then it's not much like Calc II. Whether it's harder or not depends completely on your skills. There's not information in a numerical rating.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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