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10
votes
5answers
1k views

What is the best way to think about partial derivatives?

I'm looking for a good visual way to think about partial derivatives (and slopes and tangent lines of partial derivatives) since this concept is very new for me and a little counter intuitive. SO ...
0
votes
1answer
130 views

Meaning of differentiability

Could anyone give an intuitive idea of the meaning of differentiability in general in any dimension and any space?
3
votes
0answers
104 views

What is the most relavant math for statistics students?

As they say "the more math you learn the better". Unfortunately, I did not have a lot of mathematical training in my undergraduate. Now I am doing a master in mathematics, mainly to make up some ...
1
vote
2answers
144 views

Why do we use “if” in the definitions instead of “if and only if”? [duplicate]

I often write my notes as logical statements and constantly wonder why people use only the "if" direction in the definitions instead of the "if and only if". Consider: "A homomorphism $\phi$ is said ...
18
votes
2answers
2k views

The Gamma function and the Pi function

I have been studying differential equation, in particular special functions. Euler's Gamma function, and Gauss's Pi function are essentially the same, differing only by an offset of one unit. for ...
1
vote
1answer
140 views

Is it good that I feel embarrassed when I can't find solution to a problem? [closed]

Is it good that I feel embarrassed when I can't find solution to a problem and then I have to check the solution manual?
0
votes
2answers
140 views

General questions about theorems and laws

I have doubts about the construction of mathematical elements. There are proofs, that are proven using other theorems (corollaries) and/or axioms or definitions, such as Fermat's Last Theorem, the ...
1
vote
0answers
79 views

(Actual) applications of basic differential and integral methods

If this isn't the place, I apologize: At the end of my calculus class, we asked the students (among other things) what some applications of calculus methods are. Disappointingly, many focused on the ...
6
votes
2answers
861 views

Philosophy of a Mathematician.

Introduction I don't study Mathematics at university, and probably I don't have any chances to have a little understanding of what mathematics in all its aspects. But I love to find structures and ...
11
votes
6answers
540 views

How to explain that proof is important

I don't know if this is the right place to post this or not, but I will go ahead anyway (sorry if it ain't the right place) Yesterday I was discussing a particular theorem of geometry with my brother ...
14
votes
2answers
626 views

Pro Mathematicians: how familiar have you remained with the material covered throughout your undergrad? (Outside your field)

Outside of your field of research / application, how much of your undergrad education have you retained? Thought experiment: How would you fare today if handed old exams from your introductory ...
8
votes
3answers
162 views

What to look for in a proof?

I am a physics undergrad, wishing to pursue a PhD in Math. I am mostly self taught in the typical math undergrad curriculum. I am looking for more input, in ways I can improve my mathematical ...
2
votes
2answers
117 views

OOP and category theory, any connections?

Are there any historical connections between OOP (object oriented programming) and category theory? Could you provide some references (not necessarily historical) that link the two? I finally got ...
6
votes
3answers
857 views

How to stay academically active during a Mathematics Gap Year?

This year I started at the University of Cambridge to study Maths. I was very unfortunate to contract a serious infection early on in the term, and as a reult it has been mutually decided between ...
4
votes
4answers
343 views

The set of all things. A thing itself?

If the universe is the set of all things. Does it contain itself? In other words is it a thing itself? I know its a stupid question, but it really grinds my gears. Thanks! Edit 8.12 Okey, someone ...
5
votes
5answers
268 views

Why isn't there a fixed procedure to find the integral of a function? [duplicate]

Since the integration of a function is the opposite of a the derivative of a function, and there are clear steps to follow when we want to find the derivative of a function, I thought there would be ...
2
votes
2answers
587 views

What programming languages are used in (chaotic) dynamical systems and nonlinear phenomena research?

I'm currently considering pursuing postgraduate studies in the field of chaos/dynamical systems/nonlinear phenomena, and was wondering whether there are particular programming languages that are ...
4
votes
1answer
58 views

What are some strategies to come up with exercises?

Like many programming books, there are mathematics books which do not provide exercises. Although similar in theory, how can I come up with exercises that will help illuminate a subject? The ...
14
votes
3answers
288 views

definite and indefinite sums and integrals

It just occurred to me that I tend to think of integrals primarily as indefinite integrals and sums primarily as definite sums. That is, when I see a definite integral, my first approach at solving it ...
1
vote
2answers
118 views

Nice notation for projection maps

Let $X\times Y$ be a product of two object of a category, and consider the natural projections $$ X\times Y \to X \quad\text{ and }\quad X\times Y \to Y. $$ Usually I denote them by $\pi_X$ and ...
0
votes
2answers
87 views

Need a head-start for new topics in maths [closed]

I am a maths enthusiast ( but from electrical engineering background ) . In my college I had two math courses on differential and integral calculus and I had choosen an elective in complex-analysis . ...
4
votes
1answer
1k views

Real Analysis and Statistics

What level of real analysis do you think is desirable for the study of statistics? I know that for many statisticians with applied focus, rigorous mathematics tend to give them a headache and I am ...
7
votes
1answer
184 views

What is a good communication platform, which supports something like TeX-code?

I moved away and am now planning to communicate with a friend over the internet and talk about mathematical subjects (e.g. via Skype). However the text blocks like "\int_G\omega..." in a chat window ...
0
votes
1answer
135 views

Can anyone recommend books for self learning calculus which focus on developing understanding?

I am trying to learn a little basic mathematics by myself with help from a few books and this site. So far I have read 3 excellent books: Algebra, Trigonometry and Method of Coordinates by Gelfand et ...
2
votes
2answers
97 views

Show these approximations of $\cos$, $\sin$ and $\tan$ are exact.

A while back I was looking for an approximation to $\cos(x)$ and I constructed a polynomial with zeros in the same places as the first few zeros of $cos(x)$: $$c_n(x) = \frac{\prod_{i=1}^n ...
16
votes
2answers
3k views

Learning Mathematics using only audio.

Are there any mathematics audio books or other audio sources for learning mathematics. I ask this because I make about 1 hour from my house to the school and staring at a screen on the car makes me ...
2
votes
1answer
94 views

Can axioms of the Euclidean space be proven in the Real space?

I'm not a mathematical logic student so my question can be naïve. I'm thinking if we identify $\Bbb{E}^2$ with $\Bbb{R}^2$( as a normed space with the Euclidean norm), Then can we prove all Euclidean ...
18
votes
5answers
760 views

Are all good mathematicians fluent in computational aspects of mathematics

I am in first year at college. I like studying Abstract Algebra from Michael Artin's book and Calculus from Apostol's books. However, I didn't get very good in computing things like ...
6
votes
2answers
156 views

In algebraic geometry, why do we use $\mathbb C$ instead of the algebraic closure of $\mathbb Q$?

In algebraic geometry, why do we use $\mathbb C$ instead of the algebraic closure of $\mathbb Q$? What properties of algebraic varieties use the topological completeness of our field? I'd be ...
1
vote
0answers
52 views

Background required for Computational Geometry

I am hoping to enroll in Computational Geometry course this spring. This was the textbook used for the course in the past. I am trying to figure out if I have required math background for this ...
6
votes
1answer
122 views

Books/Articles/Journals about pedagogy and the experience of teaching

I'm going to be a teaching assistant and I'm currently looking for books/reviewed articles/journals written by mathematicians or people who taught mathematics (at a university level) about pedagogy ...
4
votes
1answer
782 views

Good book for logic self-study

I know a similar question has already been asked, but can anyone suggest a good book on mathematical logic that includes answers to exercises? I am looking for something that is conducive to ...
6
votes
6answers
2k views

What is the purpose of the limit?

I haven't taken Calculas yet, but I see the use of limit (approaching zero or infinity) in other classes such as physics. I just wanted some intuitive explanation of the limit. I was thinking that ...
0
votes
2answers
77 views

Mapping Normal distribution to a new bounded distribution.

My question is vague. I am looking for distributions that can be obtained from Normal distribution by mapping it to a bounded interval. "By mapping" I mean that a probability distribution ...
2
votes
1answer
298 views

Software for generating Cayley graphs of $\mathbb Z_n$?

Does it exist any program (for linux) which can generate a nice Cayley graph of any $\mathbb Z_n$? (If it's possible to create such a graph at all, that is.) (where perhaps $n ≤ 100$ or something ...
0
votes
2answers
91 views

Formal definition of plane

The formal definition of plane says that: A plane is a set of points such that if any two points are taken on it, all the points lying on the line joining these two points also lie on the plane. The ...
3
votes
3answers
340 views

Still struggling with proofs. [closed]

How do you construct rigorous math proofs on your own? Also how do you verify? I am finishing up my first semester of undergraduate analysis and still am struggling with writing proofs. Even though I ...
8
votes
3answers
329 views

Bedtime maths books?

Most of math books require you to copy proofs and do excersices to extract the content from them. Are there any good serious math books which require only reading and no writing? ADDED: One ...
2
votes
1answer
164 views

Understand a weird method of calculus

I see this method of calculus on youtube and my question: is this method valid? How we can understand it? Thanks.
1
vote
0answers
131 views

Applications of identity theorem to physics

Holomorphic functions have the property that they can be uniquely analytically continued to (almost) the entire complex plane. So, just by knowing how the function behaves at a teenie-weenie open disc ...
3
votes
0answers
208 views

Relationship between paradoxes in logic and geometry/topology

Though I've been reading for years, this is my first question here. Believe it or not, I've tried the search feature- apologies if this is a duplicate. The main point of this post can be summarized ...
3
votes
3answers
99 views

Why do we have $3$ Isomorphism Theorems?

This is a bit of a soft question, but I've wondered about it since being introduced to the $3$ isomorphism theorems (I'm aware of the $4^{th}$ as well, but it is not typically presented in the ...
3
votes
5answers
1k views

What is the best sequence in which to self study undergraduate mathematics?

I am currently teaching myself Mathematics at the moment, with my current focus being Pre-calculus mathematics however at some point I'll eventually reach undergrad material. As I do not have a great ...
1
vote
2answers
40 views

Easy Trig question

Easy question here. I ran across this trig identity while doing a problem: $\tan(x)\cdot\tan(y) =-1$ implies that $y = x \pm \pi/2$. Why is this?
3
votes
4answers
449 views

Stats is not maths?

How mainstream is the claim that stats is not maths? And if it's right, how many people don't agree? Given that it's all numbers, taught by maths departments and you get maths credits for it, I ...
2
votes
1answer
218 views

Explaining probability theory versus statistics

I'm not sure whether this question was asked before, but it's hard to search because of lots and lots non-descriptive titles like "statistics and probability". The context: There is an anecdote I ...
1
vote
2answers
54 views

Improper integral: $ \int_{-1}^{\infty} \frac{dx}{x^2 + \sqrt[3]{x^4 + 1}}$

Decide if the integral $$ \int_{-1}^{\infty} \frac{dx}{x^2 + \sqrt[3]{x^4 + 1}}$$ converges. I decided to write $ \int_{-1}^{\infty} \frac{dx}{x^2 + \sqrt[3]{x^4 + 1}}$ = $ \int_{-1}^{1} ...
1
vote
1answer
72 views

Why can the limit of a sequence approach a number and converge, but the limit of the series must approach $0$ to converge?

My question may not make much sense because I'm still trying to wrap my mind around infinite sequences and series. I seem to have good working knowledge of when and why to apply a certain tests for a ...
3
votes
2answers
2k views

How does one get better at real analysis proofs?

How does one proceed through a math proof in real analysis? My instructor always says make a diagram, but I am not a visual learner. It seems that whenever I write out the definition of an assumption, ...
0
votes
0answers
82 views

Nonsingular curve

I am kind of curious about the nice properties between affine nonsingular curve and projective nonsingular curve. In my feeling to define sheaf of nonsigluar curve, most of the resources are focusing ...