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seen Sep 29 at 6:03

Sep
19
awarded  Notable Question
Sep
4
reviewed Approve group of permutation - cycles of length $n$ - order of generated group
Aug
28
reviewed Approve series for $n$-th prime number and prime counting function
Aug
27
reviewed Approve Studying the function $f(x) = x^4-6x^2$ using derivatives: minima, maxima, inflection, concavity
Aug
27
reviewed Approve Integration by parts
Aug
27
reviewed Reject Do journals that published a proof of an important theorem $T$ publish another proof of $T$?
Aug
27
awarded  Popular Question
Apr
28
comment Show a simple strategy.
Either I'm missing something or Paula can simply choose $1$ and then keep choosing the same number as Victor until they're all gone.
Apr
27
comment Suggest an Antique Math Book worth reading?
@JackM I definitely agree that the classical approach to geometry is important and should be studied by anyone learning math. However, I think a new resource discussing these foundations will do it using modern notation and presentation which is easier on modern ears (arguably even genuinely "clearer"), and fits better into later theory. Example: "A prime number is that which is measured by a unit alone." (VII.Def11)
Apr
20
revised Removing two adjacent edges so that the graph remains connected
added 1225 characters in body
Apr
20
answered Removing two adjacent edges so that the graph remains connected
Apr
18
revised How to justify this orthogonality?
edited body
Apr
17
answered How to justify this orthogonality?
Mar
25
comment Find all solutions for $7x^2 \equiv 3 \mod5$, if any.
Note that there are only $5$ numbers modulo $5$, so finding the solutions directly is always easy.
Mar
21
comment Visualizing mathematics and geometry
I've heard of mathematicians who lost their eyesight (Even at a very early age) and constructed some beautiful geometry, supposedly being able to visualize things outside of the real world with less distraction, but do you have any examples of mathematicians who were born blind (and thus never had the chance to experience vision) and contributed in geometry?
Mar
17
comment How do you find two functions $f$ and $g$ such that $f(x) \cdot g(x)=f(x)-g(x)$?
As for the identity, $$\tan^2x\sin^2x=\tan^2x-\sin^2x$$ is just $$\sin^2x=1-\cos^2x$$ multiplied by $\tan^2x$, and the latter is the Pythagorean theorem which is indeed very useful and well known.
Mar
16
comment Recursively Enumerable Languages and Turing Machines
I just looked at Wikipedia for Turing Machine, and the informal definition looks pretty good, and I would cite the Church-Turing Thesis as my "justification" for just writing the algorithm in words (precisely constructing an actual Turing machine can be long and painful). Unfortunately I don't know any more comprehensive online resources, but I recall having studied from a book called "Introduction to the Theory of Computation" by Michael Sipser.
Mar
16
comment How to detect an asymptote
You could try run the user input through some symbolic analysis program and get the "real" asymptotes, but for your program it will probably be better for you to apply some heuristic such as calling an asymptote anywhere you find the "derivative" ($\frac{\Delta y}{\Delta x}$) is larger than some threshold and the nearby values seem large.
Mar
16
comment Recursively Enumerable Languages and Turing Machines
In this case (I suppose) you can just write the algorithm out in words and ignore the inner workings of a Turing machine. The method I described above allows you to run $M$ for any finite number of steps on all possible inputs; that means that you'll eventually be able to pick out any input for which $M$ terminates in a finite number of steps. Therefore, if there are $637$ of these, the machine will find them in a finite time and be able to accept $M$.
Mar
16
comment Recursively Enumerable Languages and Turing Machines
It is, but I'm not sure you got my explanation right; to show that $L_1$ is r.e. you have to construct a Turing machine that accepts it, that is: Given a machine $M$, construct a Turing machine (that can use $M$ and the method I described above) that checks whether $M$ terminates on at least $637$ inputs.