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1d
revised Calculus II Function Construction
Original tag incorrect
1d
answered Find the three roots of $z^3 = -i$ in the form $a+ib$.
1d
comment Books for difficult quantitative aptitute and logical reasoning questions.
There are some interesting word problems scattered throughout Horatio Nelson Robinson's A Theoretical and Practical Treatise on Algebra (1859). Also, the 1890s and 1900s decades of American Mathematical Monthly are freely available and some of the problems in their problems section might be what you want (look at the problems in the Arithmetic and in the Algebra categories).
Apr
15
revised Taking the limit of $\infty - \infty.$ How can I arrange it to work?
parentheses seemed needed
Apr
15
comment Taking the limit of $\infty - \infty.$ How can I arrange it to work?
Hint: Rewrite as $\frac{e^{1/x} - 1}{1/x}$ (factor out $x,$ then move the $x$ to the denominator) and then consider the variable change $u = 1/x$ (with $u \rightarrow 0^{+}.)$
Apr
14
comment Books for difficult quantitative aptitute and logical reasoning questions.
I think Difficult unsolved questions does not correctly express what you intended to express, but if you think otherwise, then you should look at the Millennium Problems.
Apr
14
comment Recommendations for textbooks covering these parts of mathematics?
I think neji is looking for books at the middle to advanced undergraduate level (presumably after the calculus sequence, ODEs, and elementary linear algebra), given the use of "modern" and "abstract" algebra.
Apr
14
comment Monograph about periodic representations of numbers in non-integer bases
I don't know much about this topic, but I made some comments and gave some references that might be of use in this 5 July 2002 sci.math post. Also, try googling "multiplicatively independent" bases‌​.
Apr
10
revised Geometric meaning of Cauchy functional equation
Added an additional reference, a reference that is in English and relatively recent.
Apr
2
comment Generalization of a class of sets
Possibly relevant: For each extensive, monotone function there exists a closure operator that preserves the closed sets and The lattice of closed subsets of an algebraic closure operator is an algebraic lattice and MONOTONE SET FUNCTIONS, FIXED POINTS, AND CECH CLOSURE FUNCTIONS
Mar
27
revised Good book on Lebesgue Theory
"Lebesgue" mispelling corrected in title
Mar
27
comment Typos in Hoffman and Kunze
One thing you can try is to look for a well-used university library copy and flip through the pages to see what corrections might be penciled in.
Mar
26
comment Prove that if A is a countable set, and is a subset of R, then there exists a real number x such that A intersect A + x is disjoint.
Hint: If $a = a' + x,$ then $a - a' = x.$ Think about what you can say about the set of all "$a - a'$" numbers.
Mar
26
answered General term of monotonic-decreasing, positive series goes to $0$ quicker than $1/n\log n$?
Mar
20
comment Leibniz's theorem to find nth derivatives
@A Googler: I just checked and didn't have a problem getting it from google-books. Maybe you have to have a google account? Anyway, I downloaded it to see how big the file is, and it's 10.3 MB, which is within what I think I'm able to send by email where I'm at (it's certainly within what Yahoo mail lets you send, but I have additional constraints), so if you want a copy, send me an email to my Yahoo email (at my math stackexchange profile) and I'll send you the .pdf file.
Mar
20
comment What topics should I study to understand this document?
Regarding your question about "those books", I'm not even sure you have the background for them (assuming you only have had ODE and Calculus 3), except maybe the linear algebra texts. If you really want to stick with this, the best thing I can think of right now is to get a copy of C. H. Edwards' Advanced calculus of several variables and Wendell H Fleming's Functions of Several Variables, and try to quickly work your way through both books (they're very similar, so doing both should help if you're mostly studying this by yourself). Maybe try skipping ahead to relevant parts, also.
Mar
19
comment What topics should I study to understand this document?
For whatever it might be worth, in my opinion the listed prerequisites for the course this handout is for -- Calculus, Linear Algebra, Numerical Analysis -- don't come anywhere near to giving someone the needed background for that handout, unless "calculus" means advanced calculus (preferably something like Loomis/Sternberg), "linear algebra" means Hoffman/Kunze or Halmos level, and "numerical analysis" means something that involves functional analysis stuff.
Mar
18
comment Which of the following sets are dense in $C[0,1]$
For #2 one can also observe that any sufficiently small neighborhood of the constant function $f(x) = 42$ has empty intersection with the set under consideration. In fact, the 2nd example not only fails to be dense, but there are balls having arbitrarily large diameter that have empty intersection with the set.
Mar
18
comment How can we solve integration for fractions including $x^5$ and $x^7+1$?
Because $x^7 + 1$ is not factorable with real-radical coefficients, any "standard expression" for this is going to involve coefficients that either make use of complex numbers or trigonometric evaluations. But if you want to pursue the matter, see the appropriate references in my answer at Solving this integral?‌​.
Mar
18
answered Graph the function $f(x) = \frac{9}{14}x^\frac{1}{3}(x^2 - 7)$ by finding all critical points and inflection points.