Can anyone provide me a source to learn algebraic number theory via solving problems which has solutions available too?
I'm not too sure whether this is the right place to ask this (and please correct me if it is not), but I'm currently studying a course in Algebraic Number Theory and would like to be pointed in the direction of any solved problems that can assist in learning.  I have the book Problems in Algebraic Number Theory by Murty and Esmonde, which is particularly good, but are there any further sources (inc. online) available that do a similar job?   It is so often frustrating to be presented with an extensive list of practice questions, many of which form part of the exposition of the material (as in Number Fields by Marcus for example) and then to have no real way of knowing whether any solution you generate is correct and has not made any oversights.   MSE is undoubtedly a good place to verify any answers and clear up issues, but question limits and the impracticality of going online every time a solution seems suspect (or the question is computational and lacks any result to check against) form a barrier.  I suppose any ANT textbook that has an accompanying solutions manual or online published solutions is what I have in mind. Or failing that, links to institutions running a course in ANT with answers to homework exercises.  Thanks in advance.
Several ways to prove that $\sum\limits^\infty_{n=1}\left(1-\frac1{\sqrt{n}}\right)^n$ converges Gravatar links on "Filtered Questions" page are not HTTPS Does light reflect if incident at exactly the critical angle? A lot of textbooks and exam boards claim that light incident at exactly the critical angle is transmitted along the media boundary (i.e. at right-angles to the normal), but this seems to violate the principle of reversibility in classical physics.  How would a photon or ray travelling in the reverse direction "know" when to enter the higher refracting medium?  It can't know, so I conclude that such light is simply reflected?  Is this correct? Aware abbreviating those commands need not always be helpful, I would like to know how to abbreviate them? 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