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3
votes
1answer
81 views

Real analysis with a non-standard topology

I have recently undertaken a self study of topology and am using Munkres Topology 2nd edition as the primary text. My background(theoretical chemistry & physics) is almost entirely void of any ...
0
votes
0answers
23 views

How to find out convergence of sequence of functions in short time.

I was studying about sequence of functions and about uniform and pointwise convergence of these series. To prove or disprove the convergence of sequence of functions we have several methods like by ...
0
votes
1answer
44 views

Writing a chain of implications in English

How to write a theorem of the form $A\Rightarrow B\Rightarrow C\Rightarrow D$ where every $A$, $B$, $C$, $D$ are formulated with words (English) rather than with formulas? One idea: The next item of ...
1
vote
1answer
52 views

What are the problems that you tried to find their solutions and you did not know that it is impossible?

Tell us your story about Mathematics. Have you dream one day to do a big contribution in Mathematics because you are curious and love challenges. What are things that you tried to prove which then ...
1
vote
3answers
126 views

Which course is best to take after calculus, linear algebra, and real analysis?

During my first year at university I took our honors versions of multivariable calculus and linear algebra (which was very abstract) as well as an introductory real analysis course focusing on ...
0
votes
8answers
108 views

Soft question about the square root

I got to thinking about the square root the other day, and there's this thing that bugs me in the back of my mind. As far as I know, $\sqrt{4}$ is unambiguously $2$, and nothing else, as the square ...
19
votes
6answers
832 views

Category-theoretic description of the real numbers

The familiar number sets $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$ all have "natural constructions", which indicate, why they are mathematically interesting. For example, equipping $\mathbb{N}$ with ...
8
votes
3answers
1k views

Is it bad to keep aside Lang's Algebra in graduate school?

Question is as it is stated in title. I will be joining for PhD program in this July 2014. I am interested in working in Algebra/Algebraic Geometry/Algebraic Number Theory. I tried to learn algebra ...
4
votes
0answers
46 views

Name for a body that can be completely described using its silhouettes

I'm shooting blind over here because I have no background in this field of mathematics. I assume that if you have a body (in $\mathbb{R}^3$), you can call it convex if any segment from one point ...
2
votes
2answers
118 views

Applications of groups, rings and modules in life [closed]

I have read calculus. Now I'm reading algebra. What is the application of groups, rings and modules in life? When we study derivations we know several applications. What about groups, rings and ...
1
vote
0answers
65 views

Things you've believed for a long time were true, but are false in reality [duplicate]

Do you have any things (mathematical statements, statements about mathematics) you've believed for a long time were true, but now with enough mathematical knowledge you realize were wrong? For ...
2
votes
5answers
130 views

Is $0$ the midpoint of $(-\infty,+\infty)$?

Is $0$ the midpoint of $(-\infty,+\infty)$? Intuitively, I'd think so, and trying to refine my intuition as to why I'd think so, I would say that this is the case because there is a one-to-one ...
0
votes
1answer
28 views

Books and/or online resources on solving problems.

What are some good resources(online, books) that teach you how to tackle difficult and ugly problems in higher math arranged by subjects(analysis, topology, ODEs, groups etc) or topics(polynomials, ...
0
votes
0answers
53 views

can't even solve a single question

I have a test 2 days after and am preparing for it. When trigo was being taught in class I was quite interested and solved questions in few minutes but now I am struggling to solve those questions ...
0
votes
1answer
58 views

Starting Calculus with a weak foundation in Pre-Calculus

I am struggling in Pre-Calc mathematics, and I want to know is it ok if I start Calculus I with a weak foundation in Pre-calculus mathematics? I understand the general gist of limits, function ...
0
votes
1answer
47 views

good lecture series for complex analysis?

I was wondering if i could teach myself complex analysis. Any good lecture series out there on the internet available for free (preferably)? One that would be suitable for an undergraduate student?
2
votes
2answers
68 views

Low Level Books on Conjectures/Famous Problems

I am currently an undergraduate math/CS major with coursework done in Linear Algebra, Vector Calculus (that covered a significant amount of Real 1 material), Discrete Math, and about to take courses ...
1
vote
2answers
67 views

What do people mean by “(this piece of maths) is hard/difficult”?

Sometimes when I talk to my maths professors, they would say "this piece of maths (e.g. differential geometry) is hard". What do they exactly mean by "hard" (difficult) - when clearly they're the ...
2
votes
1answer
65 views

How do you use reference books?

Reference books at the research levels often does not include any problem or exercise. While you can't read these books like novels(you normally need to work on other sheet of paper), I'm just ...
2
votes
3answers
321 views

What languages to learn for maths?

For people with "hands-on" experience in mathematical research, what languages are the most beneficial to learn? I know that many graduate programs require some degree of non-native lingual ...
0
votes
1answer
28 views

Evolution of Relations

In Frege, one finds relations treated as predicates in complex terms. However, modern set theory appears to treat them as two-place relation. Is this correct? If so, when did this shift occur and to ...
0
votes
1answer
25 views

contact point and point of intersection

I am just unable to understand the definitions of contact point and point of intersection.My doubts can be summed up into the following two questions : 1) Suppose $f(x)=x^2$ and $g(x)=0$ are two ...
1
vote
1answer
90 views

Path to Differential Geometry

What do I need to learn to start on the rigorous study of differential geometry? I'm about to start my 3rd undergrad year at school, and have taken Cal 1-3, Linear Algebra, Elementary Number Theory, ...
2
votes
4answers
82 views

How does one explain basic probability theory to a layman?

I have recently been involved in a number of discussions with people with little or no background in mathematics when we considered a problem of the following shape. A random event is going to ...
1
vote
0answers
32 views

Less Terse alternative to Advanced Calculus by Folland.

I am currently in an advanced calculus class in university. We use Advanced Calculus by Folland. When I try to follow along the book I find that it is not verbose enough, and has too few examples. I ...
8
votes
3answers
522 views

What level of rigour is expected in Real Analysis?

I fail to find a duplicate. I am wondering what level of rigour is needed in a typical undergraduate course in Real Analysis. To clarify my question, I provide an exercise from Rudin and my proposed ...
1
vote
1answer
45 views

How can I know which theorem to use to prove another one?

In class this year a part of what we do is re learning theorems etc from previous years, but a more rigorous way. However, when I suggest a way to prove those theorems/properties/..., I often get an ...
5
votes
0answers
69 views

Relations between definite integrals not having a known closed form

Are there any known cases, when there are two (or more) definite integrals, none of them having any known closed-form expression on its own, but there is still a non-trivial$^\dagger$ elementary ...
4
votes
1answer
74 views

Is the exclusion of uncountable additivity a drawback of Lebesgue measure?

A friend and I were having a discussion about Lebesgue measure. I attempted to be profound by making the following points: Analytic geometry has been a fantastic tool, but the concept of ...
9
votes
2answers
238 views

Why is a straight line the shortest distance between two points?

The first application I was shown of the calculus of variations was proving that the shortest distance between two points is a straight line. Define a functional measuring the length of a curve ...
2
votes
0answers
49 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
75 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
27 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
102 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
43 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
39 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
86 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
71 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
66 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
273 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 ...