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5
votes
2answers
48 views

How do I determine if I should submit a sequence of numbers to the OEIS?

When I search a sequence in the OEIS and it's not there, it gives me a message saying "If your sequence is of general interest, please submit it using the form provided and it will (probably) be added ...
1
vote
1answer
165 views

Gilbert Strang's books on calculus and linear algebra?Are they for math majors?

I would to know what are the best resources to use to teach and learn elementary subjects (calculus,linear algebra),I remember when learning calculus, I used Spivak's book which had wonderful ...
5
votes
1answer
169 views

Why do we care about simple groups rather than indecomposable groups?

A first thing that we do to analyze something is "divide and conqur." So it is natural to consider simple groups. In the same way, it appears to be natural to consider indecomposable groups. However, ...
1
vote
2answers
119 views

Three-valued logic as foundation

Isn't it more natural to use Three-valued logic(false-true-unknown) as the foundation of mathematics? It is a better model for natural languages. And it also can model sentences like the lair paradox ...
1
vote
1answer
57 views

Is there anything we can add to the present Euclidean Geometry?

I did not study the detail history of Euclid. As far as I know, the geometry starts from a few postulates and keeps on expanding (through theorems developing) to the present state. Even with these ...
1
vote
1answer
63 views

where can I get math book reviews?

The only two freely available choices are maa.org and zbmath.org ,where can get other mathematical book reviews? any one?
43
votes
7answers
5k views

What is the oldest open problem in geometry?

Geometry is one of the oldest branches of mathematics, and many famous problems have been proposed and solved in its long history. What I would like to know is: What is the oldest open problem in ...
0
votes
1answer
33 views

How do the existence and $L^p$ integrability of weak derivative affect the smoothness of Sobolev functions?

In the definition of Sobolev spaces, let us say the space $W^{1,p}(\Omega)$, where $\Omega$ is an open subset of $\mathbb{R}^n$. What contributes more to the smoothness of a function $f$: 1-The fact ...
6
votes
3answers
132 views

Algorithm for multiplying numbers

Background Today I had to explain to some kid how to multiply numbers with multiple digits in them. Then I recalled, that some other day I answered this question describing one of the numerous ...
4
votes
1answer
80 views

Who are some blind or otherwise disabled mathematicians who have made important contributions to mathematics?

Two prominent mathematicians who were disabled in ways which would have made it difficult to work were Lev Pontryagin and Solomon Lefschetz. Pontryagin was blind as a result of a stove explosion at ...
0
votes
0answers
34 views

Reference: Fields of characteristic p

I am interested in learning more about fields of characteristic $p\neq 0$. Does anyone know of a good reference that covers the basics of this topic and possibly galois theory over fields of prime ...
2
votes
1answer
61 views

Starting with ring theory

Can anyone suggest a book on rings explaining concepts using visual diagrams, similar to the one visual group theory book by Nathan Carter for groups.The problem with me is that after reading that ...
2
votes
2answers
115 views

Set of sequences -roots of unity

Consider $G_n$ as the multiplicative cyclic group given by the $n^{th}$ roots of unity. $$G_n = \left\{ e^{ 2ik\pi/n} \mid 1\leq k \leq n \right\}$$ Now construct a sequence from each $G_n$ by ...
3
votes
0answers
61 views

Attemping Qualifying Exam Problems — and failing

My question is concerning learning strategy. I can solve the majority of the exercises in a typical graduate mathematics textbook like, say, Dummit/Foote's Abstract Algebra. To supplement my education ...
1
vote
0answers
41 views

Most important results from pure math in applied probability?

I'm taking a course next semester at my university on applied probability (with relevance to signal and information theory). Although the nature of probability is mostly problem solving and applying ...
10
votes
3answers
330 views

A question from an engineering undergraduate

My question primarily concerns the necessary transition from an undergraduate program in electrical engineering to graduate program in applied mathematics or pure mathematics. I'm an electrical ...
2
votes
2answers
67 views

square root solutions

Is there a specific rule to get square root of any non-negative number?. The main reason why I'm asking this is that my maths teacher told me there is only one solution can be contained for any ...
2
votes
0answers
45 views

Path-independent contour integrals and how to define them

If a contour $C$ is parameterized by $z(t): [a, b] \to \mathbb{C}$, then we define $$ \int_C f(z) \, dz= \int_a^b f(z(t)) \, z'(t) \, dt.$$ If the contour integral on the left side is equal to some ...
1
vote
1answer
78 views

How to make a good definiton

The reason why I come up this idea may due to Banach–Tarski paradox. The process we make a definition may consist of several steps. First step is that we observe a phenomenon. Second is to make a ...
9
votes
3answers
218 views

Applications of advanced number theory to other areas of math

In a recent conversation with a friend, I was discussing the fact that out of all of the fields of math, number theory seems to be among those that apply ideas from a large number of different fields. ...
7
votes
1answer
100 views

Derivation of Schrödinger's equation

I recall a famous quote of the late physicist Richard Feynman: Where did we get that from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger. This ...
2
votes
1answer
131 views

What if 'proof by contradiction' is not a valid method of proof?

I've just been reading this question about the existence (or lack thereof) of contradictions in maths. I've been wondering: What if 'proof by contradiction' is not a valid method to (dis)prove a ...
5
votes
4answers
197 views

Studying mathematics: Is proving things yourself worth the time?

When studying mathematics, is proving things yourself (before reading the proof given in the text) worth the time? This approach takes significantly longer than simply trying to follow along, but you ...
2
votes
0answers
25 views

Have any authors suggested mathematics-wide prefixes for “missing a quotient” and/or “missing an identity”?

The prefixes in the following terms both mean: "missing the obvious quotient by the obvious equivalence relation." seminorm pseudometric Similarly, the prefixes in the following terms both mean: ...
12
votes
5answers
756 views

In what ways has physics spurred the invention of new mathematical tools?

I came across this comment: Mathematical rigor is not a criterion that physicists have for evaluating their theories. From a mathematical perspective, the non-rigorous theories are far more ...
4
votes
1answer
109 views

How do you write an integral and why

A. Year 1 Calculus Student Approach $$ F(x) = \int f(x') dx\, $$ B. Random math paper you find online approach $$ F(x) = \int dx f(x') \, $$ C. Spivak $$ F(x) = \int f(x) \, $$ D. ??? (Edit) ...
1
vote
0answers
24 views

Research scopes in Computational Geometry

I have taken a short a course on Computational Geometry and at present I want to do some research works of my own. Can anybody tell me about the research scopes on it? I mean, what are the active ...
2
votes
0answers
53 views

Interesting examples of switching limit and integral

We learn many theorems regarding the relationship of limit and integral (Dominated/ Monotone Convergence, Fatou, Semicontinuity of norms, etc...). As I'm working on my research, I find that I often ...
3
votes
3answers
429 views

Math Olympiads: Hard work or talent? [closed]

I have a question regarding Math Olympiads. I always asked myself if Math Olympiads need natural intelligence or rigorous hard work (or both) in order to reach levels such as the IMO. I always hear ...
3
votes
1answer
59 views

Actuarial Science or Financial Mathematics?

I’m a second year undergraduate student of Actuarial Science that equally loves finance and pure mathematics. I only knew of Actuarial Science as a career that suited best these two requirements ...
0
votes
0answers
51 views

Alternatives to the notation $\|x\|$ for the norm of $x$?

For aesthetic reasons, I don't like the notation $\|x\|$ for the norm of $x$. Have any alternatives been proposed?
5
votes
1answer
84 views

What math have I missed as an Engineeering graduate? [closed]

To explain, I have a Master's in Engineering from a well known university. We did a wide variety of mathematical topics, vector calc, perturbation methods, numerical methods, linear algebra, discrete ...
4
votes
2answers
86 views

Probability of Sum of Independent Events Exceeding a Value

Suppose I have $n$ random number generators. Once an hour, on the hour, each one generates a random real number $x_k$ such that $0 \le x_k \lt \infty$. Each generator produces its values according to ...
1
vote
1answer
136 views

Comparing $\pi^e$ and $e^\pi$

Comparing $\pi^{e}$ and $e^{\pi}$ I read the answer there but I didn't understand one thing. How I should know to put $\dfrac{π}e-1$ instead of $x$? If I had this question on a test, I had no idea ...
1
vote
2answers
32 views

What does “symbolically tractable” mean?

What does "symbolically tractable" mean in the following quote? "Traditional treatments of mechanics concentrate most of their effort on the extremely small class of symbolically tractable dynamical ...
3
votes
0answers
133 views

Any comments on Lax's “Calculus with Applications, 2e”

There's a new calculus book titled Calculus with Applications by Peter Lax (2nd edition of an old one). I really liked his linear algebra and functional analysis books, and I was wondering if this ...
5
votes
0answers
130 views

How do mathematicians know what is known?

How do mathematicians know that what they are researching has not been already know for 200 years? Obviously if they are researching something that is cutting edge it is not a problem, but if one is ...
59
votes
21answers
12k views

Why do we still do symbolic math?

I just read that most practical problems (algebraic equations, differential equations) do not have a symbolic solution, but only a numerical. Numerical computations, to my understanding, never deal ...
1
vote
1answer
79 views

An introduction for integral tricks.

I wonder if there's a good book or internet page introducing integral tricks? For example integration by parts, and Feynman's trick. I'm not looking for an exercise book such as "Problems in ...
30
votes
5answers
2k views

Examples of “Non-Logical Theorems” Proven by Logic

I am still an undergraduate student, and so perhaps I just haven't seen enough of the mathematical world. Question: What are some examples of mathematical logic solving open problem outside of ...
1
vote
3answers
116 views

What is subtraction?

Let $a, b \in \mathbf{R}$. It is an elementary fact that addition is a commutative binary operation on the reals, that is, $a + b \in \mathbf{R}$ and $a + b = b + a$. With the exception of ...
0
votes
1answer
57 views

Fibonacci Numbers in Nature

Supposedly the Fibonacci sequence appears naturally in nature, and my question is how, where and I guess why? I read that one way this is so is that it models the population of honey bees under ideal ...
1
vote
2answers
50 views

“Unclosure” on a set with binary operation

I was wondering if there is any usefulness to having a set that has no closure under a particular operation. For example, the set of prime numbers, $\mathbb{P}$ along with multiplication of integers ...
4
votes
0answers
52 views

Where to post a Calculus review guide?

I created a PDF document (using LaTeX) in which I wrote relevant review materials and Calculus problems for Calculus 1, 2, and 3. Is there an appropriate forum where I could try to post this to ...
2
votes
0answers
35 views

Asymmetry in definition of regular measure

In a Borel measure space $(X, \mathcal{B}, \mu)$, $\mu$ is outer regular at $E$ if \begin{equation} \mu(E) = \inf_{U \textrm{ open}} \{\mu(U): U \supseteq E\} \end{equation} and ...
1
vote
3answers
298 views

Have any one studied this binomial like coefficients before?

Consider the following identities. $\dfrac{n}{n-r}\dbinom{n-r}{r}=\dfrac{n}{r}\dbinom{n-r-1}{r-1}$ ...
3
votes
0answers
64 views

Why not defining a measure as a function on functions?

A measure $\mu$ is a function to $\left[0,\infty\right]$ on the sets belonging to a $\sigma$-algebra. Then for integrable functions $f$ the integral $\int fd\mu$ comes in, having nice properties ...
5
votes
2answers
252 views

Is there any similar math limerick?

I found this one $$\frac{(12+144+20)+\left(3 \cdot \sqrt{4}\right)}{7}+(5 \cdot 11)=9^2+0.$$ Which is : ...
7
votes
3answers
304 views

Video lectures of algebraic geometry (Hartshorne, Shafarevich, … )

I am a commutative algebra student. I wonder if there is some video lectures of algebraic geometry courses available online for free? I'd like the lectures to cover main topics of the books ...
1
vote
1answer
44 views

Alternative function definitions

If you go to the wikipedia page on the sine function or the log function you'll find a number of different definitions of these functions. I know that what defines a function are it's values, for ...