@D.C.theIII some friends (a professor from Ireland & family) were supposed to visit for dinner tonight, but unfortunately his wife (yet another Irish professor) fell and broke her elbow. She is in surgery today.
I went for the ride on Friday so I would have time to prep for dinner (I am relegated to cleaning duties)
Do you know any online course on real analysis. I really need that. I have never had a formal math education and somehow found myself in the middle of math problems. I would appreciate if you could give me some advice on this journey.
Being a professor I would assume he would be responsible enough to deal with all those contingencies. Not like he is a young backpacker and has to cut corners.
@D.C.theIII Because it's more basic and chapter 6 leads into chapter 8. Our semester ended with chapter 5. If there had been more time, I might have concluded with chapter 6.
I took a remedial 104 real analysis class when i started at Berkeley and found it tough. Later I looked at my high school & undergraduate math notes and found I had been exposed to exactly the same material, but clearly it had not sunk in.
Lots of the students in the Honors course I taught (based on the text) were econ majors who either double-majored in math or who wanted to do serious grad work in econ. Calculus for econ students is too watered-down a course to be of much value.
@TedShifrin THis is what led me down this path of masochism. Doing finance and said this is not rigourous enough for me....I wanted to know "how" theses black box formulas worked.....and now I'm here.......
Sure, @Samir. It has all the proofs (pretty much) and also plenty of concrete examples/computations. If you're interested in homework exercises, you pretty much need the book to get those. D.C. can whine plenty about those :P
the way i did it was fully review calculus on khan academy accompanied with Stewart's calculus and then i started doing problems here and there in Thomson et. al.'s Elementary Real Analysis, and then i started mixing it up with Spivak's Calculus which i found easier in some parts
I initially started with Salas, Hille, and Etgen's , then after some time ended up on SPivak's Calc, then Friedberg, Insel, and Spence's Linear Algebra *after having done a simpler Linear ALgebra course, and now Ted's book.
@SAMIRORUJOV Never too late. I'm also above 30, that's why I mentioned a strong sense of belief in what you're doing because there is going to be a lot of external "pressure" on what to do.
@SAMIRORUJOV no not in that sense, but i used to hang out in this chatroom and ask questions whenever something didn't make sense, and if the question was more involved i would post it on the main website
@SAMIRORUJOV What Shin suggested is how you would have to do it. You're going to have to be very self motivated because it is a long journey and won't be easy. But we are blessed with the interconnectivity of the internet and folks that are altruistic enough to help.....something that I am still captivated by
Apostol is very carefully written, but not nearly so much depth of analysis as in Spivak, and the proof exercises are nothing comparable.
Apostol does, however, do integration first. I think he did that because the students he taught at Cal Tech who had AP credit came in thinking they knew everything. ... And also because it's historically accurate and pedagogically sound.
@SAMIRORUJOV per day: 7 - 10 hrs, some are very productive some hrs are not. And of course not every day ends up being 7-10 hrs, but that's what I aim for.
My favourite analysis book is the one by Dieundonné, but I admit I only ever read like 3 chapters of it (but the chapter on differentiation is incredible)
Later volumes cover integration theory, differentiable manifolds, some differential and Riemannian geometry, some Lie groups, even a bit of differential systems.
@TedShifrin Treatise on Analysis*, but yeah the first volume was originally written separately and is usually sold with the title "foudnations of modern analysis"
we consider subgroups of $\mathbb Z^2$. consider $G_1$ generated on $(2,0), (0,3)$ and $G_2$ generated on $(2,0), (0,1)$. we consider their Z-module structure to represent the group homomorphism $G_1 \to G_2$ by a matrix. clearly $G_1 \to G_2$ is represented by a matrix with integer entries, but shouldn't there be a matrix with integer entries representing $G_2 \to G_1$?
>Dieudonné is putting together a monumental treatise which will comprise d volumes; the best estimate we know on d is 8 < d < 12, but the upper limit is not certain. So far, 6 volumes have appeared in English and 2 others in French that have not yet been translated.
I tried to clean up the setup. Could you please have a look at it? I just need to make sure that the leap from Eq.(2a) to Eq.(3) and Eq.(4) is correct.
Suppose $\mathbf{X}$ is a random binary vector over the sample space $\Omega$ such that $\mathbf{X} \sim Bernoulli(\bar{\mathbf{p}})$. As a matter of notation, suppose $f(\cdot;\bar{\mathbf{p}})$ is the joint probability mass function (pmf) of $\mathbf{X}$. By definition, such a pmf is continuous...
@shintuku You have a maximization of a multivariate function with the foc given in (Eq.2a). Then I deduced eq.3 and eq.4. Is this deduction correct or not. That is all
@shintuku We all suck at something until we give a try
Maybe do it over a fixed domain as an example such as $\mathbb{R}^3$ and see how the Langragian set up works out then you can generalize? Because the way it is typed up there is a lot of compact notation, which appears elegant, but if you're not in the field will appear confusing.
*Does there exist a pair of smooth manifolds $(M,N),$ $M\ne N$ related by an isometry $g,$ s.t. every smooth regular foliation of $M$ satisfies some differential equation on $N,$ and every smooth regular foliation of $N$ satisfies some differential equation on $M?$*
Essentially one is taking all smooth regular foliations on $M,$ restricting to the metric of $N$ which can be obtained via the isometry $g,$ and checking whether these foliations satisfy differential equations. The same process is done with foliations on $N.$
