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7
votes
3answers
1k views

What is the prerequisite knowledge for learning Galois theory?

What is the prerequisite knowledge for learning Galois theory? I don't know what a ring is.
1
vote
3answers
553 views

Looking for philosophical subject for my Bachelor Thesis

In may 2013 I have to write a Bachelor Thesis for my bachelor Mathematics. I prefer to choose a subject which involves philosophy. At the same time I have the feeling that my university wants me to ...
9
votes
8answers
746 views

“How I wish I could calculate pi” analogs…

You might know the mnemonic for $\pi$ in the title or even this more elaborated one: Sir, I bear a rhyme excelling In mystic force, and magic spelling Celestial sprites elucidate All my own ...
5
votes
2answers
269 views

How does one best balance learning from a “problem based book” with supplementary material?

We all know that when learning math, one has to do more than just simply read - one must try to solve problems and work actively with the material. Many books try to force the reader to participate ...
14
votes
3answers
1k views

Explaining what real math is to a high school student

I think, after reading through some of the questions here and their answers, that there are many people here who share my opinion on high school mathematics that it's quite different from "real ...
20
votes
6answers
1k views

How to read letters such as $\mathbb A$, $\mathbb B$, etc., or $\mathfrak A$, $\mathfrak B$, etc.?

This is a soft question. We can read the letters $\bf A$, $\bf B$, etc. as bold A, bold B, etc. We can read the letters $\textit{A}$, $\textit{B}$, etc. as italic A, italic B, etc. We can read the ...
10
votes
2answers
579 views

Category Theory with and without Objects

Slight Motivation: In Mac Lane and Freyd's books (the latter being a reprint of an older book called "Abelian Categories") they note that instead of defining any Objects in a category we may define an ...
4
votes
1answer
327 views

why algebraic structures?

According to wikipedia, an algebraic structure is an arbitrary set with one or more finitary operations defined on it. From a model theory perspective, I understand this definition as: structure with ...
2
votes
1answer
115 views

Finding his own path [closed]

I am a graduate student in major mathematics and now the time has come to choose a "specialization" (I have to choose 3 between 4 subjects). I like algebra a lot and I am also interested in ...
18
votes
1answer
571 views

How do you manage your “pedanticism”?

After I took my first analysis course and learned how to be truly "pedantic," I have always been having a dilemma of balancing myself between being "detailed" and "intuitive". I would like to ask how ...
13
votes
1answer
594 views

Does every closed curve contain the vertices of a square?

This is the question on Futility Closet Is there really no answer?
4
votes
2answers
100 views

Why saying that “$x$ is an indeterminate real number” is misleading?

I'm reading: Behnke's Fundamentals of Mathematics, Vol.1 On page 23, he says: In order to indicate that a variable $x$ has the real numbers for its range, mathematicians often say that $x$ is ...
3
votes
0answers
107 views

A few questions about nonabelian cohomology of finite groups.

I apologize in advance if these questions are broad or basic. I tried to read about them at the Wikipedia, but everything is written in the language of category theory, in which I have had no formal ...
5
votes
1answer
361 views

Academic failure [closed]

I'm an undergrad student majoring in maths in my next semester. Up until the current semester I was able to get very good grades in almost every course and I had a grade average which I think would be ...
12
votes
1answer
881 views

What is the expected mathematical repertoire of a Ph.D. program applicant?

I am an undergraduate (currently a sophomore) studying to prepare for applying to a Ph.D. program in mathematics. I have thus far structured my course selection upon the advice of a friend I met ...
4
votes
3answers
817 views

How can One Generalize a Result?

Suppose we are trying to generalize some result, for example, a well known theorem or some theory. The generalization must improve the result in some way. What are the best tactics to do this? Let me ...
1
vote
1answer
158 views

Intuition Regarding Homotopic Spaces

I am just starting to do some algebraic topology (very basic stuff) so have obviously just been introduced to the notion of homotopys, contractible spaces and homotopic spaces. It's this last one that ...
12
votes
2answers
343 views

When does “pairwise” strengthen and when does it weaken?

"Pairwise disjoint" is stronger than "disjoint"; it sometimes happens that $\displaystyle\bigcap\limits_{i\in I} A_i=\varnothing$ but for every $i,j$, or at least for some, one has $A_i \cap ...
3
votes
1answer
90 views

Presentation, Reduction and Generalization in Mathematics: The Case of Linear Algebra

Apologies for the grandiose title, but it is motivated by a serious consideration. Linear algebra, LA hereafter, is an enormously interesting area of mathematics. What's more, it is fairly ...
6
votes
0answers
120 views

Proof that there is no algebraic proof of Fundemental Theorem of Algebra [duplicate]

Possible Duplicate: Is there a purely algebraic proof of the Fundamental Theorem of Algebra? I have heard many times that there is no algebraic proof of the fundamental theorem of algebra ...
3
votes
3answers
283 views

How to do diagram chasing effectively?

I am trying to teach myself some homological algebra, and the book I am using is Aluffi's wonderful Algebra: Chapter 0, which introduces homology at the end of chapter 3. I have spent a lot of time ...
5
votes
1answer
713 views

How can I add equations to services such as Keynote or Pages in iPad?

Mathematical formulae are very poor in services such as Windows Word, Keynote, Pages -- or many times totally missing, not to speak about compability -problems. So how can I create and add formulae to ...
13
votes
8answers
1k views

What would be a good outdoor maths puzzle for children?

I have to find an interesting activity for some 11-year-olds moving to high school this year. It is supposed to take about 30-45 minutes, and I thought of having a mathematical theme. I can make a ...
3
votes
2answers
272 views

Why are only the first four alternating groups are non-simple?

I know asking for intuition in math is a generally flawed approach, but can anyone give any reason why only the first four alternating groups are non-simple?
1
vote
1answer
68 views

Interesting verification of functoriality

Functors and morphisms of functors (aka natural transformations) have become powerful tools in all areas of pure (and meanwhile also applied) mathematics. There are lots of nontrivial constructions of ...
1
vote
1answer
135 views

Book recommendation request for geometric bodies (cube, pyramid, prism etc.)

Can anyone recommend books that deal with geometric bodies (cube, pyramid, prism etc.)? I haven't been able to find any.
7
votes
3answers
736 views

Some intuitive vision on abstract algebra

I'm currently on my second year of Mathematics and first one I'm learning abstract algebra. So far it's being the most interesting subject I've seen, but I have a problem with some intuitive visions ...
9
votes
5answers
1k views

Mathematics, Philosophy and writing.

Do you know of any famous mathematicians who were also philosophers? I have heard of Descartes, Plato and Leibniz. Are there other good examples, especially more modern examples? Also welcome are ...
5
votes
4answers
231 views

I need a lot of questions for mathematics. Algebra to calculus so that I learn by solving.

One huge problem I have with learning mathematics is that I have not got enough problems to solve, with answers. Is there a resource that I can get hundreds of mathematical questions, small questions, ...
3
votes
3answers
205 views

Groups and Rings course suggestion

I am a physics undergrad, looking to explore pure maths. I apologize if this question is not appropriate for MathSE, but I couldn't resist posting it. Feel free to close it down. I haven't taken ...
-1
votes
1answer
150 views

What does it mean for a random variable to describe an experiment?

I often hear the expression, random variable (or sequence of rd's) to describes an experiment (or sequence of experiments. But that sound totally unrigorous to me: So we're given a mapping $X:\Omega ...
20
votes
1answer
740 views

Given a group $ G $, how many topological/Lie group structures does $ G $ have?

Given any abstract group $ G $, how much is known about which types of topological/Lie group structures it might have? Any abstract group $ G $ will have the structure of a discrete topological group ...
0
votes
1answer
137 views

Examples of dictionaries between two distinct fields of mathematics (or between “differents” structures of math).

I'd like to meet explicit examples of dictionaries between two distinct fields of Mathematics (or between two "different" structures of Mathematics). I'm not interested in the usual sense dictionary ...
4
votes
3answers
2k views

Does the set of all sets that contain themselves contain itself?

We always hear about the paradox of the set of all sets that don't contain themselves and whether it contains itself or not. What about the set of all sets that do contain themselves? Is that an ...
8
votes
2answers
1k views

How do you pronounce the symbol $'$ in $f'$?

I'm not a native English speaker. A quick Google search revealed the symbol's name is apostrophe, just like in French. When used in a mathematical setting, I usually call it prime, so for instance ...
1
vote
2answers
228 views

Cantor's intersection theorem and Baire Category Theorem

From an old post in math stackexchange, I read a comment which goes as follows " I like to think of Baire Category Theorem as spiced up version of Cantor's Intersection Theorem". My question -----is ...
3
votes
1answer
167 views

Prize for textbook aesthetics

When browsing through Alain Connes' textbook on Noncommutative Geometry, whose illustrations must have been conceived as true works of love, I was wondering if there is a recognized prize for ...
7
votes
1answer
680 views

Liouville's proof of the existence of transcendental numbers

The existence of transcendental numbers can be shown easily by considering the cardinality of the set of solutions to polynomials with integer cofficents and the cardinality of the real numbers. It ...
0
votes
1answer
129 views

Infinite versus unendlich and double-negation

The German term for infinite is unendlich, which transliterates as non-ending, or non-finite. This is just word-play but from a constructive point of view, is the shift from a negative to a positive ...
49
votes
6answers
3k views

Why don't analysts do category theory?

I'm a mathematics student in abstract algebra and algebraic geometry. Most of my books cover a great deal of category theory and it is an essential tool in understanding these two subjects. Recently, ...
2
votes
0answers
58 views

About “unital partial magmas after n-multifunctors”

Motivation In Haskell, there are a bunch of so-called type classes that are theoretically "alike": ...
5
votes
1answer
330 views

Galois Theory Texts

What is a very comprehensive text regarding Galois Theory? I'm about to take a course in Galois Theory this spring, and I usually like to complement my course texts with something more rigorous, ...
5
votes
3answers
227 views

In a proof that is reliant on proven theorems, does one assume the reader's familiarity with said theorems, or explicitly include their logic?

In composing a proof that is reliant on proven theorems, does one simply assume the reader's familiarity with said theorems, or does one explicitly include their logic in the new logic?
2
votes
3answers
286 views

How to say the notation $ x_{i,j}^{ k}$

$ x_{i,j}^{ k}$ May I say the following to say the above notation? x sub i j to k ? x sub i j sup(prounced like "soup") k ? (Can I say "soup" for "superscript"? Could you please show me a ...
2
votes
2answers
97 views

Indexing notation after $i$, $j$ and $k$ have been used?

If I have already used $i,j,k$ as indices, and need two more, where should I look? $l,m$?, $m$? I know from my previous questions that I can use anything I want as long as I define it, but I use $n$ ...
5
votes
3answers
223 views

Studying at home and finding good resources in Algebra

I'm a graduate student studying at home. I find that ressources in Mathematics on the web are easier and easier to find, and I am happy for that, because I like to have different points of view about ...
1
vote
2answers
222 views

Primary ideals confusion with definition

In a commutative ring, can I say An ideal $\mathfrak q$ in a ring $A$ is primary if $\mathfrak q \neq A $ and if $ xy \in \mathfrak q \Rightarrow $ either $ x \in \mathfrak q$ or $y^n \in \mathfrak ...
18
votes
6answers
834 views

Difficulty in Mathematical Writing

Lots of people (including myself) face lot of problems in tackling Mathematical Problems, which appear as if we can solve it, but then writing out a solution becomes difficult. Let us consider some ...
2
votes
0answers
126 views

DFT shift theorem generalizations?

The DFT shift theorem implies that any circular shift in the input space is equivalent to a phase change in the frequency domain, while the absolute values are preserved. $$ ...
3
votes
2answers
111 views

Useful faculty sites that provide explanations of mathematical ideas

I'm looking for resourses on undergraduate mathematics, explaining ideas behind well-known proofs, etc. What are some other sites like T. Tao's blog or T. Gowers'? I.e. ...