Recent content by mathwonk

Here is a link to a beautiful and eloquent talk given recently by a friend of mine, Michael Comenetz, containing the gentlest and clearest possible introduction to Galois theory, amazingly aimed at "anyone", i.e. essentially no background at all assumed by the reader, (well, maybe high school...

In terms of quality of exposition versus price, there can perhaps be nothing to match the great, but succinct and theoretical, treatment from 1942 by Emil Artin, (Mike's father), (ed. and supplem. by Arthur Milgram) , available for $7.39 at amazon! Artin throws in a complete elementary...

The good news is: once one appreciates the need for a Riemann sum type definition of a complex path integral, it is possible then to use antiderivatives to evaluate them. I.e. once a path is parametrized, one pulls the integral back to the real parameter interval, and uses the usual real...

real Calculus comes before complex calculus. And when learning real calculus, the topics that will be especially useful in complex calculus are power series and path integration. It helps also to focus on the actual definition of the Riemann integral as approximated by sums. We have a bad...

As to the breadth of Galois' research, the third part of his testamentary letter, on integrals, displays keen insight into basic questions on abelian integrals, later clarified by Riemann, in particular the division of differentials into first, second, and third kind, according to the nature of...

In my case, "I am older than dirt" seems more accurate, (or for purists, perhaps "I am older than dirt is"?) But probably both make the point.

@Hornbein: they give us the syllabus, and the criterion for passing, and then they tell us we cannot fail the number of students who actually would fail by those criteria, even if those students do not attend either class or office hours, nor turn in homework. It poses a difficult challenge.

Feel free to ignore, as I am interpreting this question more generally as "should we teach in college things that students should have learned earlier?, i.e. should prerequisites matter?" My take: For most of my 40 year career as a college math professor, I proceeded somewhat as follows...

Ok, going down same rabbit hole as Edwards, trying to explain Galois in modern terms, in particular, why the table at the bottom of page 916 of the linked AMS Notices article, which is on page 116-117, of Neumann, does display the Galois group of the equation g whose roots are a,b,c…...

I have spent some time pondering the first part of the translation of Galois' "first memoir" by Neumann, roughly pages 107-117 in Neumann's, The mathematical writings of Evariste Galois, from the European Mathematical Union, and comparing it to H. Edwards AMS Notices exposition. I confess I...

the difference between someone who understands Galois theory and the rest of us is illustrated by this simple question: when asked why the sum of a complex number and its conjugate is real, I say because (a+bi) + (a-bi) = 2a which is real; and why the product is also real: well, (a+bi)((a-bi) =...

wouldn't an AI bot have more perfect grammar?

Please forgive me for reminding you that it is much easier to make a list than it is to read profitably through that list. In my opinion, the books on your list would require many years of hard study for a very bright focused person to actually master. Moreover, I doubt if anyone I know has...

It is true that OP has not checked simple connectedness. However, although the theorem stated specifies simply connected, all that is really needed is for the set D not to contain a path that winds around the point p, which I take to be the meaning of the OP's requirement that the set not...

The natural logarithm is by definition any analytic function defined on a (connected) open set U not including 0, and (right-) inverse to the exponential function. (I.e. such that exp(Ln(z)) = z for all z in U.) Such inverses do not exist on open sets which include a loop that goes around the...