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4
votes
1answer
32 views

A reason for the value of $\int_{0}^{1}\log{(x)}\log{(1-x)}\,\mathrm{d}x$

In this .pdf document, which is just a list of Putnam-style undergraduate-level problems from various sources, the third question is as I have stated it below (up to a change of notation). ...
0
votes
0answers
33 views

Good algebra book to cover these topics?

I will be studying two algebra modules next year and I am looking for a comprehensive book that will cover both of them, however due to having very minmal exprience with algebra I am looking for your ...
0
votes
3answers
72 views

How would you explain Functional Integration to an 8 year old?

I get the definition of the Functional Integral, but what heuristic interpretations are available to better understand the integral? For instance, what motivates the definition? How is it related to ...
0
votes
1answer
41 views

What are some easier papers/books I can read? [on hold]

I'm trying to improve my ability in reading mathematics papers. My field is more related to biological sciences, but there are a lot of interesting papers I'd like to read that use more mathematical ...
5
votes
1answer
37 views

Does it matter if you use big $L$ or little $l$ when talking about $L$-norms?

I was reading a post on Quora regarding the application of "$l_1$", "$l_2$" norms for convex linear programming when I became very confused at which $L$-norm the posters are actually referring to. I ...
2
votes
3answers
68 views

Fun logic puzzles to teach logic/proof-writing to students

Forgive me if this is too soft of a question, but I am looking for some fun, quick, and interesting logic puzzles to give to my students. I'm teaching an honors calculus course, and this will be their ...
2
votes
1answer
54 views

Intuition for Burnside's Lemma (aka Cauchy-Frobenius Lemma)

Here is the theorem: Lemma: Let a group $G$ act on a set $S$. Define $\text{Fix}(g)$ as the set of all elements in $S$ fixed by $g$ under this group action. Then the number of distinct orbits of ...
0
votes
0answers
29 views

In what ways would a course on convex optimization be useful in game theory?

From talking to several other people in the past, and referencing Quora, it seems that convex optimization is really a tiny subset of game theory in that it only models the behavior of one single ...
2
votes
3answers
61 views

How do mathematician make sense of “outcome” and “events” in probability?

One of the biggest challenge for me to understand probability is to make sense of this concept of outcomes and events. To put it plainly, it just doesn't feel like mathematics anymore when we talk ...
5
votes
1answer
40 views

Stating the induction hypothesis

I would like to ask about the best way to state the induction hypothesis in a proof by induction. Just to use a concrete example, suppose I wanted to prove that $n!\ge 2^{n-1}$ for every positive ...
-1
votes
1answer
14 views

Zeitz's ACoPS vs Larson's PSTP

Which of the following books is better to prepare for a mathematical competition at the undergraduate level? The art and craft of problem solving (ACoPS) or Problem solving through problems (PSTP). ...
1
vote
2answers
41 views

How to document solutions for future use? [on hold]

I'm taking courses of math at university level, it's kind of the equivalent of master degree in mathematics, I'm from Argentina. The way to learn mth in my university is this: We attend lectures, we ...
-8
votes
0answers
50 views

Magic of the number $2000+15$ [on hold]

What is the most clever way of getting the number $2015$ using only addition, subtraction, and multiplication?
4
votes
3answers
64 views

Motivations for Hyperbolic Geometry

Why would one study hyperbolic geometry? I am only aware of the motivation where you give axioms for elementary euclidean geometry and then start to wonder wether the parallel axiom is necessary. You ...
2
votes
0answers
63 views

Struggling to stay at current course.

Disclaimer: I'd like to say I've been a member of this site for over a year, so I know this may be a nonstandard question, however, for personal reasons, I'd like to keep this anonymous. I'm a second ...
1
vote
3answers
66 views

Acronyms and words as variables and in mathematical notation

I am unsure if this question is warranted. Often mathematical symbols and objects are represented by a single character, e.g. variables are most often single characters like $x$, and often to ...
0
votes
0answers
24 views

About Carl Meyer's matrix analysis

I have taught some part of it to myself when i was an engineering student. but now i changed my major to the pure math so now i am studying math as an undergraduate student. i thought the book is ...
2
votes
1answer
31 views

$f(x)$ be the characteristic polynomial of a matrix $A \in M_n(\mathbb R)$ ; then is it true that $f(1)=1+\operatorname{trace}(A)+O(\|A\|^2)$?

Let $f(x)$ be the characteristic polynomial of a matrix $A \in M_n(\mathbb R)$; then is it true that $f(1)=1+\operatorname{trace}(A)+O(\|A\|^2)$ ? I need a proof if it is true ; or any modification ...
2
votes
0answers
62 views

Measuring the set-theoretical complexity of sets/spaces encountered in general analysis

In analysis, it is common to encounter subsets of $\mathbb R$ (or even $\mathbb R^n$) which appear to be "well-behaved", especially with regard to properties like being measurable, compactness, etc. ...
2
votes
1answer
49 views

Can anyone please help to clarify the sentences “ into a fat tail part in L2 plus a fat body part in L1.”

In the link https://en.wikipedia.org/wiki/Fourier_transform#On_Lp_spaces what does this sentences mean: into a fat tail part in L2 plus a fat body part in L1? Would anyone please help?
5
votes
3answers
452 views

What is the pre-requisite knowledge for generating my own integer sequence?

I've recently come across the On-Line Encyclopedia of Integer Sequences and I'm completely fascinated by it; something about how easy integers are to grasp and yet how complex the sequences are. I ...
1
vote
2answers
73 views

Conceptual differences between the notations $\int_{a}^{b}f$ and $\int_{[a,b]}f$

Let $[a,b] \subset \mathbb{R}$ and let $f: [a,b] \to \mathbb{R}$ be continuous. Then $f$ is Riemann-integrable. What are the conceptual differences between the two notations $\int_{a}^{b}f$ and ...
2
votes
4answers
111 views

Is $i^i$ mathematically valid? [duplicate]

WARNING: SLIGHT NSFW http://www.smbc-comics.com/index.php?db=comics&id=2934#comic Uhh...guys, mathematically speaking, how accurate is this comic. From what I remember in High School $$a^b= ...
3
votes
0answers
76 views

May Algebraic Geometry be appropriate for me? [closed]

I am a student of Mathematics who have to choose its area of specialization. I am trying to obtain as more information as possible, by asking a lot of questions to more experienced people, trying to ...
7
votes
1answer
112 views

What is $\varphi(0)$? [duplicate]

$\varphi$ is Euler's totient function. My question is: When/if $\varphi$ is defined at $0$, what is it usually defined as? Is there a "most natural" or more commonly accepted definition of ...
4
votes
0answers
97 views

Why I can't use Latex editor? [closed]

I cant use latex editor because I need 10 reputation, so what should I do?
1
vote
0answers
41 views

Can we have different methods to estimate elements from Lp spaces?

Sorry if my question is vague. Consider I have some time samples and it is known to be summation of sinusoidal. Problem is to estimates the frequencies. Generally, Fast Fourier transform (FFT) is the ...
6
votes
2answers
244 views

What is the interest of duality in algebra, and in general in mathematics?

Before to ask my question I precise I'm a chemist, I ask this question because it makes me crazy to don't understand something I learnt in school. So I had two years ago a small chapter about ...
0
votes
3answers
25 views

Quick and simple funtamental question about sets

Please feel free not to read this its just a prelude: Ok I am sorry for making this question since as far as I can tell the level of the other questions here is higher by far compared to mine, but I ...
0
votes
0answers
22 views

Does a ratio of PDFs have any usable meaning?

I'm calculating the probability that a standard Brownian motion path will cross a boundary. I have $A$ and $B$ representing the PDFs for the Brownian motion going above a boundary function $a$ and ...
0
votes
0answers
23 views

Why can't the pseudosphere be completed in $R^3$?

Without appealing to Hilbert's theorem on the non-embeddability of complete hyperbolic surfaces in $R^3$, is there a way to "see" that one can't extend the pseudosphere / surface of revolution of a ...
0
votes
0answers
23 views

What does a functional integral evaluation look like?

I've read the Wikipedia page on functional integration, but it really isn't very easy to understand. There don't seem to be any online videos on the subject either. In addition, when I search online, ...
1
vote
1answer
37 views

Generalizations of Inverse Function Theorem

A beautiful exercise in Guilleman and Pollack asks us to show the following generalization of the Inverse Function Theorem: Suppose $f: M \to N$ is a map of smooth manifolds, and $Z$ is a ...
4
votes
1answer
51 views

Is there an English version of Johann Bernoulli's integral calculus lectures?

The name of lectures of integral calculus written by Johann or Jeans Bernoulli (he is called by both names as far as I know) might be " lecciones mathematicæ de calculo integral"; I must mention that, ...
-5
votes
3answers
68 views

In the real domain, are there any theorems or definitions that state all functions are differentiable? [closed]

I want to ask about basic theory of calculus, say differentiation. We know that not every function can be integrable, but as far as I know all functions are differentiable in the real domain. My ...
0
votes
1answer
65 views

Background for Graduate Real Analysis I Class

This semester, I have signed up for a graduate Real Analysis I course (really a course in measure theory/Hilbert Spaces/Lebesgue integration) and have thus far attended two lectures. However, from ...
1
vote
2answers
52 views

Thought Provoking Reads [closed]

I apologize if the gist of this question has been covered before: I tried to find posts relating to it, but nothing I could find was asking for quite what I was looking for. I am an undergrad in ...
0
votes
0answers
37 views

Does any one have a link to Jorm Steuding's Probablistic Number Theory? [closed]

I was reading it through the browser and the link on CiteSeer died. :( I will download it this time. Thanks. Regards, -EM
1
vote
0answers
29 views

What is the terminology of the collection of all possible combinations of the element of a set?

Let me explain my question better: Suppose I have a set $(1,2,3)$. Clearly, I have 6 ways to choose some elements from it: $$ (1),(2),(3),(1,2),(1,3),(2,3) $$ and I can make a collection to ...
0
votes
1answer
65 views
+50

Soft Question: Weblinks to pages with explanation on quadratics.

I recently placed a question based on quadratics and received a few valuable answers. One of them was a comment in an answer with a link in it which I found useful. But unfortunately the webpage (of ...
0
votes
1answer
33 views

Program languages recommended for complexity theory

I am an undergraduate studying mathematics and one of my interests include complexity and computability theory. I have no experience in programming. The computability theory books I looked into didn't ...
1
vote
1answer
32 views

Where can I find “On the significance of the principle of excluded middle in mathematics, especially in function theory”?

I'm looking for L.E.J. Brouwer's article "On the significance of the principle of excluded middle in mathematics, especially in function theory". I've searched my university catalogues and every open ...
0
votes
0answers
19 views

Adding a website in bibliography. [closed]

I have taken information from this link for my project report. I want to add the website link in the "bibliography" section. But I don't know how is to cite this. Any help is appreciated. Thanks.
0
votes
2answers
74 views

What does exactly “giacche” mean here?

While translating some Italian paper with Google translator of the following sentence Gli elementi di $G_\nu $, che godono la detta proprieta, formano evidentemente gruppo e questo gruppo, giacche ...
0
votes
1answer
38 views

Are these inequalities useless for getting better estimates? If not what is needed?

Are these inequalities useless for getting better estimates? If not what is needed? My motivation for asking this question is to get a glimpse to the mind of masters that can tell if a line of ...
2
votes
1answer
71 views

Topology(meaning) [closed]

When we define Topology we say that a topology on a set(let's say X) is a collection of subsets of X having certain 3 properties. Now, here what do we actually mean by saying "topology on a set". What ...
1
vote
2answers
66 views

Notation seen in “awfully sophisticated proof…” I don't understand

I want to understand what the definition of $f_n$ given here means? I tried to seek on the net but I not succeeded. I precise I do chemistry, maths are "just" a curiosity for me. I should be glad, ...
3
votes
1answer
56 views

High School Geometry Text?

This year I will be teaching 8 hard-working home-educated teens a Geometry course. Back in 1994-1999 I worked full time as a High School educator, taking a turn teaching everything from Pre Algebra ...
0
votes
0answers
14 views

Looking for some good introductory level resources for Gibbs Sampling

In context of a course in bayesian modelling Im following, im looking for some good resources (videos, lecture slides, texts) about Gibbs sampling.
6
votes
0answers
44 views

What should I do with a paper I've translated? [migrated]

Aside from reaping the personal benefits, what should one do after translating a paper? It would be nice to offer it to others, but I assume it is a copyright violation to post it online. Sending it ...