For questions that don't admit a definitive answer but still are relevant to this site. Please be specific about what you are after.

learn more… | top users | synonyms

2
votes
0answers
48 views

Why has no body retypeset Ladyzhenskaya et al's “Linear and quasi-linear equations of parabolic type”? [closed]

The book "Linear and quasi-linear equations of parabolic type" is one of the ugliest books I have ever seen in my life. The fonts are awful, the notation is difficult to understand and recall and the ...
1
vote
2answers
77 views

Why are all non-polynomial functions are basically exponents?

There's paucity of really "original" functions in Math. Aside from power functions/ polynomials, really the only other function widely used is exponential. For example, $\log$ is simply inverse of ...
6
votes
4answers
653 views

The role of 'arbitrary' in proofs

Generally, when one is going to prove a result regarding a set of elements, they begin their proof with those first few pleasing words: "Suppose...is an arbitrary element in..." My question is, why ...
6
votes
1answer
74 views

Follow up to Pinter's abstract algebra

I wanted to learn abstract algebra this summer so I bought Pinter's A book of Abstract Algebra. I was planning on reading it over the course of the summer, but just finished the last problem of its ...
2
votes
0answers
25 views

Are there high performance computing applications for symbolic integration?

Currently there are a number of applications for numerical integration in applied mathematics and physics. Many of these are integral transforms (often Fourier or Laplace), or solving definite ...
2
votes
1answer
100 views

Most dificult concepts in mathematics [closed]

(Sorry, last soft question!) Borwien, in The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike, (probably quite rightly) says of the Riemann Hypothesis, that No layman has ever ...
46
votes
46answers
4k views

What was the book that opened your mind to the beauty of mathematics?

Of course, I am generalising here. It may have been a teacher, a theorem, self pursuit, discussions with family / friends / colleagues, etc. that opened your mind to the beauty of mathematics. But ...
2
votes
1answer
42 views

Varying definitions of symmetric and selfadjoint operators

There seems to be some disagreement (at least when consulting textbooks), what constitutes a symmetric operator and what constitutes a selfadjoint operator (of course, only the unbounded case is of ...
0
votes
0answers
39 views

Infinite-Order Duals?

Let $X$ be a Banach space. Then, $X^*$ is the Banach space of all bounded linear functionals on $X$, $X^{**}$ is the Banach space of all bounded linear functionals on $X^*$ $[\ldots]$ $X^{(n)}$ is ...
0
votes
1answer
46 views

Trying to translate the paper “COHOMOLOGIE ET GROUPE DE STEINBERG RELATIFS” by J P Loday J Alg (54) 178, 1978

I am trying to translate the paper "COHOMOLOGIE ET GROUPE DE STEINBERG RELATIFS" by J P Loday J Alg (54) 178, 1978 using google traslator. In section 1, he writes Un morphisme d’extensions relatives ...
0
votes
3answers
54 views

Name of quantity that is not invariant, but only changes in one direction

How do you call a quantity that is not an invariant, but only changes in one direction during the process? Example: The degree of the polynomials go down when Euclidean division is applied, so the ...
1
vote
1answer
38 views

Anyone worked with this particular orthogonal matrix

In my recent studies of quaternions, the following orthogonal matrix has come up. For example, it is related to the matrix representation of quaternion multiplication. Has anyone seen it come up in ...
52
votes
3answers
5k views

Mathematical research of Pokémon

In competitive Pokémon-play, two players pick a team of six Pokémon out of the 718 available. These are picked independently, that is, player $A$ is unaware of player $B$'s choice of Pokémon. Some ...
6
votes
1answer
106 views

Are there categorifications of prime or irreducible elements (of a ring, say)?

I'm very sorry if this is a duplicate in any way or is otherwise a stupid question. I've looked around (for quite a while) but . . . no luck. There's a categorification of what it means to be an ...
5
votes
1answer
84 views

What background is required to understand Random Matrix Theory

I would like to be able to understand RMT but after "reading" many articles I have found that I have a limited capacity. I just see complicated equations. I guess I know linear algebra, classical ...
3
votes
0answers
70 views

Pythagorean like theorem for general spaces

There are laws, for example Pythagorean theorem, for calculating distance of two points, say $d(a,b)$, using third point and knowing $d(a,c)$ and $d(c,b)$ in vector spaces. My question is that for ...
0
votes
1answer
64 views

having great difficulty in understanding long math problems ! any advices !!! please

I'm not an English origin I'm good at direct math exercises But I'm having great difficulty in understanding long math problems Such as described below Which contains many sentences and many terms ...
1
vote
2answers
95 views

Abstract Objects in Logic

I am confused on the concept of extensionality versus intensionality. When we say 2<3 is True, we say that 2<3 can be demonstrated by a mathematical proof. So, according to mathematical logic, ...
1
vote
3answers
272 views

About Zeno's paradox and its answers

I read this question How can Zeno's dichotomy paradox be disproved using mathematics? . The first (ie the one on the top) answer uses the fact that $\sum\limits_{n=1}^\infty\frac{1}{2^n}=1$, ...
0
votes
1answer
70 views

Where should I go for translations of mathematical texts?

I am currently trying to read Applications algébriques de la cohomologie de groupes. II: théorie des algèbres simples by J-P. Serre. It is very hard for me to read this article since I'm not a native ...
0
votes
2answers
109 views

List of Advanced Math Text Books with answers

Can anybody please recommend a list of Advanced Mathematics Books for physics that can be used for self study. Most importantly they must have answers for odd or even problems. I have a big list of ...
3
votes
0answers
63 views

Is Courant's Introduction to Calculus and Analysis still up-to-date?

I just found this marvelous book and I think that it's the best book in this category, but I'm worried that it is not up-to-date. I've heard that Hardy's A Course of Pure Mathematics has some switched ...
9
votes
3answers
255 views

Book series like AMS' Student Mathematical Library?

I had the joy of discovering AMS' Student Mathematical Library book series today, and I have been pleasantly surprised by how enticing some of the titles seem: exciting and expositionary, a perfect ...
10
votes
0answers
466 views

Is there any formal definition or reasonably good heuristic for mathematical 'interestingness?' [closed]

One of the projects I'd like to work on over the next several years in my spare time is a first order theorem prover similar to Prover9 to attack some of the TPTP problems, and it occurs to me that ...
14
votes
3answers
324 views

Book ref. request: “…starting from a mathematically amorphous problem and combining ideas from sources to produce new mathematics…”

I couldn't find Charles Radin's Miles of Tiles at the local university library or the public library, and cannot afford its Amazon price right now. Thus, while sorely disappointed for the moment, I ...
2
votes
1answer
34 views

Can you interpolate a function $f: \mathbb{R} \rightarrow \mathbb{R}^2$ piecewise (by two interpolations)?

I am currently trying to improve on-line handwriting recognition. On-line means in this case that I have the information how the symbols are written as a list of $n$ tuples of coordinates $(x(t_i), ...
0
votes
0answers
52 views

Difference between isomorphisms, deformations, diffeomorphisms and homeomorphis,s

I am learning about complex algebraic varieties and have encountered several equivalence relations: isomorphism, birational, deformation equivalent, diffeomorphic and homeomorphic. I consider all of ...
1
vote
1answer
61 views

Concerning a specific family of recursive sequences

There is a family of recursive sequences that I came up with: $$a_n=\text{sum of factors less than $a_{n-1}$ of } a_{n-1}, a_0\in\mathbb{N}$$ First question: Has it been studied before? Here are ...
1
vote
1answer
73 views

Book: Functional Calculus

Is there a good book that investigates in detail the various kinds of functional calculus? I'm having now some knowledge about unbounded operators and integration but I would like to understand ...
42
votes
7answers
5k views

What is integration by parts, really?

Integration by parts comes up a lot - for instance, it appears in the definition of a weak derivative / distributional derivative, or as a tool that one can use to turn information about higher ...
3
votes
1answer
56 views

Is there a reason that sine substitution is preferred to cosine substitution?

When integrating by trigonometric substitution that has $\sqrt{a^2-x^2}$ in the integrand, the general recommended approach is to make the substitution $x = a \sin\theta$, and this substitution is the ...
5
votes
0answers
161 views

Propper algorithm to integrate ODE's numerically.

I have studied in a course several algorithms to integrate ODE's numerical: Runge-Kutta, Predictor-Corrector methods, Taylor... However the teacher failed to show which is the best for every ...
0
votes
0answers
29 views

General Strategy for solving mathematical problems

Lately I noticed that I am good at solving only those problems, similar to which I have encountered before. I get stuck with problems which ask for new(at least to me) mathematical reasoning. When I ...
3
votes
2answers
87 views

I want to learn math from ground-up, basic to advanced, beginner to expert

I want to learn math. I've learned math long time ago, but i hardly remember anything. I really want to relearn but have no idea where to begin. I want to learn math by reading through good books, ...
1
vote
0answers
23 views

What [precisely] is special, algebraically, about fundamental Pell solutions?

I'm asking for a list of algebraic identities which "uniquely identify" (or nearly so) the fundamental solution (or those immediately around it) of a Pell equation. As a concrete [numerical] example, ...
0
votes
0answers
24 views

Best multivariable calculus text for physics

I will soon start studying electrodynamics from griffiths electrodynamics. I tried to learn the math required from the first chapter but found that I couldn't understand it very well. So are there ...
3
votes
1answer
165 views

Too “young” for advanced mathematics?

Is it harmful to try to learn an advanced topic that is way beyond your mathematical maturity, even if you're really interested in it? Should I focus only on standard material for undergraduates and ...
0
votes
1answer
46 views

Questions about the field Business Mathematics

What interests should one have to decide to pursue a master's degree in Business Mathematics? Which subjects are related with this field? What career opportunities are there having this master's ...
8
votes
3answers
175 views

Abstract nonsense proof

What is a simple example of an "abstract nonsense" proof in category theory. For a theorem you are proving, it doesn't matter if the category or regular proof came first, it is just that the category ...
2
votes
2answers
63 views

On prime(less)ness and composite(less)ness of 1

I was sitting in my room when suddenly my cousin came and asked me, "Why is $1$ neither prime nor composite". Well ofcourse, i was never given an explaination of that in school, it was just a ...
2
votes
0answers
105 views

How mathematical theorems and concepts gain their names?

Cantor's theorem, Woodin Cardinal, Sacks Forcing and Martin's Axiom are just some of well-known theorems and concepts of mathematics which have the name of those mathematicians who introduced these ...
2
votes
1answer
50 views

“Canonical” symmetrization/skew-symmetrization/alternation of multilinear functions

Is there some precise sense in which the "alternation" functor $A$ that maps a multilinear function $f\colon M^d\to N$ to the alternating multilinear function $A(f)\colon M^d\to N$ defined by $$ ...
1
vote
0answers
73 views

How can I learn to think in probability given my background?

I have this question for some time now and I've decided to ask here. I'm a student of Physics and I'm taking a probability course. Currently I'm used to deal with Physics itself (mechanics, ...
2
votes
1answer
53 views

The term “Homotopy” was given by whom?

I want to know the names who define the term 'Homotopy' in algebraic topology in 1907. Are they Dehn and Paul Heegaard? What is the full name of Dehn? Thank you in advance.
1
vote
1answer
68 views

What defines “triviality”?

I realize the title is perhaps not the most helpful. I am aware of several uses of the word "trivial," and I'm hoping that perhaps someone can provide some further insight. 1) Trivial sub-objects, ...
2
votes
0answers
89 views

Why are large cardinal axioms actually axioms?

A cardinal is an isomorphism class in ZFC, or a representative of one. I'm not asking what the significant uses of large cardinals are, or why we would want to find them or construct them; I'm ...
3
votes
2answers
121 views

What jobs in Mathematics are always in demand, and are deeply Mathematically specialised or greatly general?

I am wondering what jobs in the field of Mathematics are (seemingly) always in demand. I am also wondering what jobs there are that are (once again seemingly) greatly Mathematically demanding in ...
2
votes
1answer
96 views

Is it worth it? [closed]

I am studying pure mathematics at university, as well as minoring in physics. I am soon to finish to BSc degree, and I am considering continuing on with studying pure mathematics. However, I do have a ...
1
vote
0answers
46 views

R. Jeffrey and the Three Prisoners

Here’s something curious, from p. 26 of the estimable Richard Jeffrey’s last, posthumously-published book, Subjective Probability: The correct (or at least orthodox) answer to this puzzle would be ...
3
votes
3answers
124 views

Can a mathematician be a multi-discipline expert?

My professor says: If you be a mathematician then you can easily learn any discipline like physics, chemistry, engineering and even medical! Is he right? I am an enthusiast of all scientific ...