The soft-question tag has no wiki summary.
1
vote
1answer
43 views
Two weird proofs about continuity in normed vector spaces
I am reading a pair of "proofs" that a friend sent to me. I really don't understand some passages, so I hope someone could help me. The questions are the following
First Question. The result to be ...
4
votes
3answers
216 views
Can the Bourbaki series be used profitably by undergraduates?
Can the Bourbaki series be used profitably by undergraduates and high school students?Are we the target audience? I came across the N.Bourbaki texts while surfing the internet(I have not had the ...
23
votes
1answer
318 views
What remains in student's mind
I'm a first year graduate student of mathematics and I have an important question.
I like studying math and when I attend, a course I try to study in the best way possible, with different textbooks ...
8
votes
6answers
190 views
What would be a good outdoor maths puzzle for children?
I have to find an interesting activity for some 11-year-olds moving to high school this year. It is supposed to take about 30-45 minutes, and I thought of having a mathematical theme. I can make a ...
8
votes
1answer
208 views
Stacks in arithmetic geometry [closed]
Stacks, of varying kinds, appear in algebraic geometry whenever we have moduli problems, most famously the stacks of (marked) curves. But these seem to be to be very geometric in motivation, so I was ...
0
votes
1answer
83 views
Study two different fields concurrently?
I am a newly admitted PhD student. When I applied for this program, I stated several research interests in my SOP. In the end, I am assigned with a supervisor whose research interests overlap with ...
3
votes
3answers
220 views
Main branches of mathematics
Can anybody please show me main branches and subbranches of mathematics and statistic sciences in a hierarchical form? I am not a mathematician and I often in my research see a lot of new ...
6
votes
4answers
244 views
Extracurricular ideas for UK GCSE level maths student
My daughter is 15 years old and enjoys her maths classes (perhaps only because her maths homework takes her the least amount of time).
Until now I have managed to introduce her to subject matter ...
2
votes
1answer
88 views
How much connection is there between Commutative Algebra and Algebraic Topology?
How much connection is there between Commutative Algebra and Algebraic Topology?
I am looking for general highlights, not complex details.
5
votes
3answers
207 views
How to deal with the temporary nature of my knowledge?
I'm a self-learner trying to learn Math while enrolled in a wrong major (Humanities). I have gone through the many amazing questions and answers here (& elsewhere, including Prof. Tao's blogs) ...
5
votes
3answers
109 views
How come in statistics there is very little justification for the formulas used and proofs are almost nonexistent [closed]
I don't understand why people accept certain formulas in statistics without a mathematical proof style argument. You see this a lot in statistics textbooks and unfortunately this spills over with the ...
12
votes
1answer
192 views
+150
Why are modular lattices important?
A lattice $(L,\leq)$ is said to be modular when $$(\forall a,b\in L) x \leq b \implies x \vee (a \wedge b) = (x \vee a) \wedge b,$$ where $\vee$ is the join operation, and $\wedge$ is the meet ...
2
votes
0answers
41 views
What is good about simple Lie algebras?
Recently I've been reading Naive Lie Theory by John Stillwell. In the book our aim usually concerns finding whether Lie algebras or Lie groups are simple.
I wonder what beautiful properties does a ...
1
vote
0answers
33 views
Gibbs Sampling versus General Cases
Suppose we are given a prior distribution about an unknown parameter $\pi(\theta)$. Also we are given $f(x_{1}, \dots, x_n|\theta)$. We want to find $\pi(\theta|x_1, \dots, x_n)$. Now ...
3
votes
3answers
147 views
The Importance Of Good Teachers and Guidance In the Academics
I'm a first year student for a math degree. I'm very curious on how good students overcome their bad teachers in the journey of learning and grasping the courses material fully, all in the pressure of ...
0
votes
1answer
44 views
Is the study of algebraic curve is techniquely equal to the advanced division of analytic geometry, if not, what is the difference?
Is the study of algebraic curve is techniquely equal to the advanced division of analytic geometry, if not, what is the difference?
And what is other branch of advanced analytic geometry called?
in ...
0
votes
0answers
9 views
How to relate interval estimators with preservation & reflection of convexity?
Preservation and reflection of properties are categorical notions but really should be more widely appreciated throughout STEMs (science, technology, engineering, mathematics), for example closely ...
0
votes
1answer
27 views
Importance Sampling
Suppose $p(x)$ approximates the density of interest $q(x)$. Then $$\int f(x) q(x) = \int f(x) \left(\frac{q(x)}{p(x)} \right) p(x) \ dx = E_{p(x)} f(x) \left(\frac{q(x)}{p(x)} \right)$$
Why don't the ...
1
vote
1answer
39 views
What is the utility in writing pdfs in terms of their kernel?
Consider the normal distribution. We know that $$p(x| \mu, \sigma^2) = \frac{1}{\sqrt{2 \pi \sigma^{2}}} e^{-\frac{(x-\mu)^{2}}{2 \sigma^{2}}} $$
The kernel is $$ p(x| \mu, \sigma^{2}) \propto ...
13
votes
1answer
322 views
What did Gauss think about infinity?
I have someone who is begging for a conversation with me about infinity. He thinks that Cantor got it wrong, and suggested to me that Gauss did not really believe in infinity, and would not have ...
7
votes
8answers
322 views
Where to begin with foundations of mathematics
I would like to know more about the foundations of mathematics, but I can't really figure out where it all starts. If I look in a book on axiomatic set theory, then it seems to be assumed that one ...
4
votes
1answer
119 views
Independent undergraduate research — what to do?
I hope this question is within the scope of this website. I am currently a rising senior, and need to decide on a topic for my independent undergraduate research/thesis. I was hoping to get some ...
9
votes
8answers
943 views
What math should a programmer know?
I am an application programmer focussing on Line Of Business (LOB) applications. I am from non-mathematics and non-CS background. What mathematics should I learn which help me improve my programming ...
5
votes
3answers
206 views
Is there a branch of mathematics that requires the existence of sets that contain themselves?
I notice that Russell's paradox, Burali-Forti's paradox, and even Cantor's paradox, all depend on our tolerance of sets that contain themselves (at one level of depth or another). Thus, I was thinking ...
1
vote
1answer
60 views
Is there a theory that extend real analysis to functions maps into other algebraic structure?
I am studying real analysis now, reading Rudin's book Real and Complex Analysis. One thing confused me is when talking about measurable functions, we assume the function to be, from an abstract space ...
3
votes
0answers
62 views
Status of PL topology
I'm starting to learn about geometric topology and manifold theory. I know that there are three big important categories of manifolds: topological, smooth and PL. But I'm seeing that while topological ...
11
votes
4answers
577 views
Importance of rigor
I always have a hard time explaining the importance of rigor to my friends who are not mathematically minded. A lot of past mathematicians develop the foundations of today's mathematics without going ...
17
votes
2answers
241 views
Which results depend on the irrationality of $\pi$?
Recently the following uninteresting clock picture was posted by one of my non-mathematically inclined friends to my facebook wall, saying that it was funny and possibly thinking that I would find it ...
2
votes
2answers
125 views
How much algebra is there in Noncommutative Geometry?
My Professor of Homological Algebra got me into some Hochschild (co)homology and then suggested to continue with formally smooth algebras, noncommutative differential forms and so forth.
Now, my ...
2
votes
5answers
119 views
Simple applications of complex numbers
I've been helping a high school student with his complex number homework (algebra, de Moivre's formula, etc.), and we came across the question of the "usefulness" of "imaginary" numbers - If there ...
3
votes
1answer
41 views
Varieties given by non-algebraic equations
In algebraic geometry one (mostly) studies varieties given by polynomial equations.
Such equations define algebraic varieties and there are many "dictionaries" available.
For example, the category ...
5
votes
3answers
237 views
What does it really mean for something to be “trivial”?
I see this word a lot when I read about mathematics. Is this meant to be another way of saying "obvious" or "easy"? What if it's actually wrong? It's like when I see "the rest is left as an exercise ...
1
vote
0answers
81 views
I'm interested in different meanings of “normal”~ [closed]
Possible Duplicate:
What is it to be normal?
I've learned in algebra class that
"normal" means a linear operator is commutative with its adjoint;
also we say that $H$ is a normal ...
4
votes
4answers
212 views
What are special functions for?
If you read enough mathematics, you eventually come across several so-called "special functions". I'm always left wondering what on Earth these things are actually for.
We have the Euler Gamma ...
5
votes
5answers
310 views
Why do we consider prime numbers important, and what are their applications other than number theory in pure math?
Why do we consider prime numbers important, and what are their applications other than number theory in pure math? I know that Number theory is devoted to studying prime numbers, but there must be ...
2
votes
3answers
37 views
notation of distribution
I have a question:
Does $$N(0, x)$$ mean a normal distribution with mean $0$ and variance $x$? Or standard deviation $x$?
The notation seems ambiguous sometimes.
1
vote
2answers
92 views
Struggling to Bridge the Gap (to Rudin's Principles of Mathematical Analysis)
After taking an introductions to proofs course and abstract algebra, I have been trying to study from Rudin's Principles of Mathematical Analysis. Unfortunately, I still find it very very difficult to ...
7
votes
1answer
170 views
Undergrad Student Trying to Figure Out What to Study
this is my first time on stack exchange and I am seeking advice for my future studies.
Some background first; I am a undergraduate student pursuing a degree in mathematics and I hope to pursue ...
0
votes
0answers
18 views
Unbiased Estimator equal to 0
Suppose $X_1, \dots X_n \sim p(x, \theta_{true})$. Consider an unbiased estimator $\hat{\theta} = h(X)$ of $\theta$. So $E(h(X)) = \theta$. Then why does
$$\frac{1}{n} \sum_{i=1}^{n} h(x_i, \theta) = ...
3
votes
1answer
133 views
What Are R-Modules Used For?
Kind of a simple question, but what exactly are R-modules used for? Do they have any engineering applications?
EDIT:
If it helps, I'll give some more context to the question...
I am a graduate ...
0
votes
2answers
66 views
Recommendation for a precalculus textbook
I'm a high school senior interested in pursuing a major in quantitative economics, which I understand is heavily math-intensive. However, as it stands, my academic strengths are more verbal (780 on ...
6
votes
4answers
448 views
What do I need to know to understand the Riemann hypothesis
Which kinds of fields of mathematics do I have to know about in order to understand the Riemann hypothesis millenium prize problem?
0
votes
1answer
29 views
Combination Conceptual Understanding
I'm currently studying some combinatorics and I'm trying to understand combinations ${{n}\choose{r}}$ conceptually. I don't have trouble understanding permutations (n!) and r-permutations P(n,r) ...
3
votes
4answers
272 views
How to figure out the log of a number without a calculator?
I have seen people look at log (several digit number) and rattle off the first couple of digits.
I can get the value for small values (aka the popular or easy to know roots), but is there a formula. ...
5
votes
6answers
227 views
A book for self-study of matrix decompositions
I am a third year math student and I noticed that there are many uses for decomposing a matrix (I mean decompositions like SVD, LU etc').
Is there a good book for self-study of the subject ?
Note ...
3
votes
2answers
67 views
Dealing with many entities that need a symbol
What does one do when one needs a lot of symbols and one has exhausted the useful symbols of the latin and greek alphabets? (I say useful symbols because letters like iota (ι) and upsilon (υ) seem too ...
0
votes
6answers
98 views
Taking the derivative of $y = \dfrac{x}{2} + \dfrac {1}{4} \sin(2x)$
Again a simple problem that I can't seem to get the derivative of
I have $\frac{x}{2} + \frac{1}{4}\sin(2x)$
I am getting $\frac{x^2}{4} + \frac{4\sin(2x)}{16}$
This is all very wrong, and I do not ...
6
votes
3answers
218 views
Characterizations of primes
Let $\mathbb{P}$ be the primes set.
We know from Wilson's Theorem that
$$(p-1)!\equiv-1 \pmod p \iff p \in \mathbb{P}$$
What another formulas we have with an if and only if ($\iff$) statement to ...
8
votes
0answers
157 views
How do Greek mathematicians name variables?
I've always wondered how people in Greek name variables that other people use greek letters e.g. $\theta$. They use latin?
1
vote
3answers
90 views
Steps to learning Bayesian probability
Lets pretend I have no experience with statistics...
what books, in what order, will get me to the point of being able to understand Bayesian probability fastest.
