For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.

learn more… | top users | synonyms

1
vote
1answer
70 views

What is a good book to learn all of precalculus?

I need a no-fluff book with great exposition on precalculus. It should cover up intermediate algebra, trigonometry and anything else needed to get a strong preparation for Spivak's Calculus. It ...
0
votes
1answer
93 views

Applications of $p_{n+2}+p_{n+1} \le p_1p_2…p_n , \forall n >2$?

Let $p_n$ denote the $n$-th prime number ; I know that $p_{n+2}+p_{n+1} \le p_1p_2...p_n , \forall n >2$ . I am looking for some applications of it , for example I know one application of it ...
4
votes
1answer
114 views

Algebraic geometry papers for beginners

What are some papers/books suitable for a beginning graduate student interested in algebraic geometry? I have taken commutative algebra and a classical algebraic geometry class, but I have no other ...
2
votes
1answer
59 views

What is a good book to learn all of prealgebra?

I am an old man trying to learn mathematics, starting off with prealgebra and need a good comprehensive book for it. The book should NOT contain annoying images like in most American textbooks or ...
40
votes
14answers
3k views

What are “instantaneous” rates of change, really?

This is driving me crazy, I'm literally losing sleep over it, please help me resolve this confusion. Here's how I see it (please read the following if you can, because I address a lot of arguments ...
0
votes
0answers
27 views

Prerequisite for algebraic topology?

I'm a math undergraduate and taking undergraduate algebraic topology next semester. I didn't take topology and algebra but studied little of them. I studied some part of group theory for algebra and ...
3
votes
3answers
47 views

Equation of a … 3D object???

(Stupid question...) Well we can represent a point as something like $P(a,b,c)$ We can represent a line as $\dfrac{x-a}{p}=\dfrac{x-b}{q}=\dfrac{x-c}{r}$ We can also represent a plane as ...
0
votes
0answers
9 views

Precise statement of Gersho's conjecture

Here is the Gersho's conjecture from his paper "Asymptotically optiaml block qunatization" "For $N$ sufficiently large the optimal(distortion-minimizing) quantizer for a random vector uniformly ...
2
votes
0answers
27 views

Geometric Interpretation of Determinant of Transpose

Below are two well-known statements regarding the determinant function: When $A$ is a square matrix, $\det(A)$ is the signed volume of the parallelepiped whose edges are columns of $A$. When $A$ is ...
4
votes
1answer
70 views

Introductions to Ehresmann connections and Chern-Simons forms

I am looking for introductory texts on Ehresmann connections and Chern-Simons forms. I seek detailed, hands-on presentation. Please, recommend sources that employ a differential forms approach rather ...
0
votes
0answers
24 views

What exactly is Applied Analysis

I hope this question is not irrelavant for this site, and if so I would like to apologize in advance. I have seen the applied analysis as a research field in some applied mathematics programs and ...
0
votes
1answer
53 views

How to download the Latex file of an article from arXiv.org?

It is a non-mathematical question . Mathstackexchange is a not a right place to ask this question but I don't have any other choice. Any help will be appreciated. $\bf{Question:}$ How to download ...
3
votes
1answer
48 views

How did the ancient Greeks discover formulas for volume and surface area?

How did the ancient Greeks discover formulas for volume and surface area of different objects, e.g. of a sphere? They did not know about integrals, so there must another way?
2
votes
0answers
42 views

Topological issues in large deviation principle

Let $X$ be a topological space, let $B_X$ be its Borel $\sigma$-algebra, and let $B$ be the completion of $B_X$. We say that the family of probability measures $\mu_\epsilon$ defined on $(X,B)$ ...
3
votes
0answers
31 views

Minimum Knowledges to precisely calculate PDEs (integral equations)

Basically all I want to do is to calculate (or prove) precisely equations such as $$ \frac{1}{n\alpha(n)r^{n-1}}\int_{\partial B(x,r)} u(y) dS(y) = \frac{1}{n\alpha(n)} \int_{\partial B(x,r)} ...
1
vote
0answers
22 views

How to find an optimal solution for a missing player in a double-elimination tournament

Say that you have a double elimination tournament consisting of four teams with 2 players. Each of those teams of partners could be: (A,B), (C,D), (E,F), and (G,H), where A is B's partner, C is D's ...
5
votes
4answers
911 views

Can I do research just because I am able to? [closed]

I hesitated to ask this question since it may not relevant to this website, but I saw a question of same category here but still I couldn't find some answer .. (EDIT - while despite that question, my ...
2
votes
1answer
35 views

Exam questions on sobolev spaces, sobolev embedding [closed]

Hi I am doing some preparation for research in nonlinear PDE. I have almost finished reading the chapter of sobolev spaces and want some questions to test my understanding on various important ...
1
vote
2answers
81 views

How to explain linear algebra to someone who knows nothing about it? [closed]

A friend recently looked at a little blurb about some guy who had studied infinite sets and linear algebra. The friend asked me something along the lines of, "What is linear algebra anyway?". I was ...
2
votes
2answers
146 views

Why is math so difficult for me? [closed]

I'm an aspiring software engineer and currenly in college for computer science. For some reason, no matter what I try, math is so unbearably difficult and indecipherable until I design a program for ...
1
vote
0answers
38 views

Is there a rigorous mathematical definition of “trivial”?

I have heard the words "trivial" and "non-trivial" a lot in reference to all sorts of mathematics. To give you an idea of what I mean, consider the following differential equation: ...
1
vote
3answers
47 views

About $0!=1$ and $a^0=1$ as cases of empty product.

Some useful ''conventions'' as $0!=1$ or $a^0=1$ are particular cases of an empty product, i.e. a product between elements of the empty set. I know that such product is defined as a convention by: $$ ...
1
vote
0answers
46 views

Application of Morse Inequalities

I am an undergraduate student interested in morse theory. I understand, that the morse inequalities provide an lower bound for the number of critical points morse functions on a manifold can take. One ...
8
votes
1answer
161 views

Reference Request: what are some books on mathematics you can read without pencil and paper

I am going overseas for the summer, I need a book or two so I can learn about mathematics (overviews, engineering applications, history, connection with other branches of science) without actually ...
7
votes
1answer
220 views

Shortcuts for long, frequently used sentences [closed]

I was sitting on my laptop, reading a document where the term "WLOG" appeared. I liked how people realized that this is a frequently used, bothersome to write sentence, and made up that term as a ...
19
votes
11answers
1k views

What are some results that shook the foundations of one or more fields of mathematics? [closed]

An example would be the proof that $\sqrt{2}$ is not rational, which was a violation of some fundamental assumptions that mathematicians at the time made about numbers. Another would be Russell's ...
1
vote
1answer
57 views

Website for Mathematics enigmas?

I seek some website just for the pleasure of solving mathematics enigmas. I know this website : Brilliant.org I just want to know if you know some others good sites ! Thank you
1
vote
0answers
33 views

Relation between Extensions and self-Extensions!

This should be considered as very general question regarding the extension group $Ext^i _A (R,S)$, in particular where $i=1$, for $R$ and $S$, a pair of given objects in an abelian category $A$. For ...
0
votes
0answers
37 views

Which are the most (used/powerful/recurring) theorems in a real analysis course?

We all know that take a real analysis course is traumatic for a large ammount of people (me included). There are many theorems to understand, much more relationships and a huge ammount of ...
0
votes
0answers
35 views

What are the desired questions that should to be in SM (stackexchangemath)? [migrated]

According to many questions posted in SM ,I see that SM give a high importance for the related questions to Real analysis and number theory and contests where "MO" give a high importance to ...
2
votes
0answers
65 views

I am uncertain as how to best check my work in a way conducive to learning. [closed]

I am currently learning calculus for the first time by self-studying Stewart's early transcendentals. When I have completed a problem, I find several alluring options for checking my work. I can check ...
1
vote
0answers
180 views

Can you identify this book?

I am looking for a very conceptual book on analysis to recommend it to one of my juniors. I have a book in my mind which I once read during my UG days in my college library on one fine morning, a book ...
2
votes
1answer
48 views

What is the need to define so many forms of equation of a straight line?

When I study maths, I try to understand why the mathematicians brought out this concept or what usefulness they might have seen in the concept that they worked upon. So when I started with straight ...
3
votes
0answers
51 views

Are there concepts in nonstandard analysis that is useful for a introductory calculus student to know?

Studying calculus I became aware that nonstandard analysis had some methods that that made the concept of infinitesimal concrete, so that $dx$ actually made sense Can someone elaborate on this ...
-1
votes
0answers
49 views

Which has greater powers: $0$ or $\infty$? [duplicate]

Okay, I know that this may seem silly, but please try to clear my doubts. The question is, that which 'term' has more powers. If we multiply $\infty$ and $0$, what do we get. I know that infinity is ...
0
votes
0answers
10 views

Any difference in factoring product of two large regular primes or two large (same magnitude) irregular primes?

an RSA-like situation: If one multiplies two 300 digit regular primes to form a product, and another multiplies two 300 digit irregular prime to form a product, is there any way that a factorization ...
3
votes
1answer
32 views

Is there a mathematical distinction between “on” and “in”?

Is there any difference if I said a function on an interval or a function in an interval? or a vector field on a manifold versus a vector field in a manifold? The main reason is because some online ...
5
votes
1answer
84 views

Ideas for basic application of homotopy theory to homological algebra?

I'm taking a first course in homological algebra. As a project, the lecturer suggested each student find a topic, presentable in an hour, relating to the material studied in the course. The material ...
5
votes
0answers
61 views

What Constitutes a Pattern

Mathematics is often referred to as the "study of patterns." What I'm wondering is whether there is somehow a technical way to describe a pattern. For the length of this question let's assume that ...
2
votes
1answer
79 views

A categorical approach to algebraic geometry

I learned Algebraic Geometry in a geometrical viewpoint, e.g. Hartshorne's book. But I want to learn algebraic geometry categorically, for examples, i) Sheafification $\mathcal{F}^+$ of a presheaf ...
0
votes
0answers
26 views

What is the Laplace Transform? [duplicate]

What is the Laplace transform? I understand how to do it (taken differential equations), but my professor just kinda told us to accept that $ F(s) = \int_0^\infty e^{-st}f(t)dt $ is gospel and to ...
0
votes
1answer
32 views

Are there undescribable mathematical objects when we represent them as drawings?

It was argued at "Are there mathematical objects that have been proved to exist but cannot be described in words?" that there are mathematical objects that we can't describe in words because there are ...
1
vote
0answers
34 views

Exotic applications of Hilbert spaces?

So my final exam for an introductory course on Hilbert spaces is just a weeks away. I enjoyed the course, we covered the theory in enough detail to illustrate its richness and elegance. I'm aware of ...
8
votes
0answers
71 views

How to explain the topic of Fourier transform interactively? [closed]

This is a soft question . In the walk-in for the lectureship, I have decided to give demo lecture on the topic of Fourier transform. The principal of the institution ask me to take lecture ...
14
votes
6answers
1k views

How to think of a set?

I am doing self study for the last two months on functional analysis. As I get a bit used to the terms like space, topology, manifold, etc, etc, I realized that everything is defined in terms of set. ...
-6
votes
3answers
126 views

What is the significance of stuff like the “Pigeonhole Principle”? [closed]

Pigeonhole Principle if n items are put into m containers, with n > m, then at least one container must contain more than one item src I thoroughly read What is your favorite application of the ...
7
votes
0answers
145 views

Work of Ted Kaczynski

I hope this question is not too crazy sounding, but I was wondering if anyone is familiar with the work of Ted Kaczynski (or even has cited/used it before). After reading in Lars Ahlfors' Complex ...
3
votes
2answers
40 views

Intersections between a function and its Taylor polynomial

Suppose $D \subset \mathbb{R}$ is open, $f : D \to \mathbb{R}$ is a smooth (not necessarily real analytic) function, $x_0 \in D$, and $T_n$ is the degree $n$ Taylor polynomial of $f$ centered at ...
2
votes
3answers
93 views

How do I figure out my math aspirations? [closed]

I am really confused. Here's my present situation: I'm 18. I am about to start a computer science degree this August--going there only coz my parents want me to. I know most teachers for undergrads ...
21
votes
4answers
2k views

How can you show Godel's incompleteness theorem using mathematical symbols?

I want to get this as a tattoo as I love the role maths plays in the universe and the idea that the farthest reaches of what we can ever know, fall short of the limits of what is true, even in ...