Questions related to the teaching and learning of mathematics.

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0
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1answer
125 views

How to re-learn math: books or websites?

To re-learn math, both websites and books provide visual content (text and some of them shows illustrations). So are websites an alternative to books (content quality-wise)? My goal is to re-learn ...
3
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0answers
442 views

Can I get a PhD in Stochastic Analysis given this limited background?

General advice on PhD apps welcome Given my limited background in stochastic analysis and other information (below), can I apply for a PhD with stochastic analysis for my dissertation topic? 1/4 I ...
4
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0answers
77 views

Asperger's and math [closed]

I am 19, recently diagnosed with Asperger's syndrome. Question to anyone here who has AS: Has your AS helped you or held you back while learning math? If so, in what ways?
1
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1answer
43 views

Beyond calculating just as an exercise, are there any other reasons to calculate an indefinite integral?

Calculus textbooks often have us calculate indefinite integrals as exercises. However, beyond calculating just as an exercise, are there any other reasons to calculate an indefinite integral?
1
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1answer
59 views

Fundamental Counting Principle

How many four-digit numbers can be formed from the set $\{ 0, 1, 2, 3,\ldots , 10 \}$ if zero cannot be the first digit and the given conditions are to be satisfied Repetitions are allowed and the ...
6
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0answers
226 views

Most efficient way to learn mathematics

So there's a lot of advice on how to learn mathematics most efficiently, and it mostly revolves around doing problems, asking questions, and considering all possible generalizations. However, I was ...
3
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2answers
64 views

Problem-Solving and other things in mathematics relations? [closed]

Problem-Solving and the standard curriculum in typical undergrad mathematics seems to be on different levels of difficulty. IN undergrad math, you learn new concepts and try some problems. However, ...
6
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1answer
147 views

math.stackexchange has so many good mathematicians, were you all good at maths since school? [closed]

I'm afraid this question will be kicked out but I have to ask this. Were you all mathematicians brilliant and had good maths brain since you were kid? I was very bad in maths when I was in grade 8 ...
0
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2answers
69 views

What do you suggest I do to prepare? Thanks In advance!

Firstly, I'm in the military stationed overseas and I don't have access to a calculus class except online. My query is whether you think Calculus is something that can be studied by someone who has ...
2
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3answers
61 views

Undergraduate summer activities in the US or Europe?

I a currently a college freshman and I would like to do something math-related in the summer. I will have taken all of the basic courses except for analysis and set theory by the end of the summer ...
3
votes
1answer
48 views

Are there word problems without an evident unknown? [closed]

I teach secondary school maths. I appreciate the expressive precision in which word problems are couched. The unknown is usually stated in question tags at the end. I want to know if this is always ...
4
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1answer
67 views

Does performance in math competitions accurately reflect natural aptitude in mathematics? [closed]

Many great and respected mathematicians have won accolades in math (ex: IMO), does that necessarily mean that these competitions reflect one's potential to be a great mathematician?
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2answers
33 views

Given $A \subseteq \mathbf{Z}$ and $x\in \mathbf{Z}$, we say that $x$ is $A$-mirrored if and only if $−x\in A$. We also define…

Sorry if this question seems kind of long but I am confused for part C. My proof for part C that $M_a$ is closed under addition is as follows: The set $M_a$ is closed. Let $x$ be in $M_a$ and ...
0
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1answer
69 views

Phi, The Greek Letter, and It's Use in Mathematics

In the following inequality (1+c)/(a+b) ≤ φ How do I say it in English? I think that I should say, "The ratio of the sum of 1 and c to the sum of a and b is less than or equal to phi." Is the ...
2
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1answer
74 views

Show $\left|{\frac{z_1-z_2}{1-z_1 \overline{z_2}}}\right| < 1$ if $|z_1| <1$ and $|z_2| < 1$

Show $$\left|{\frac{z_1-z_2}{1-z_1 \overline{z_2}}}\right| < 1$$ if $|z_1| <1$ and $|z_2| < 1$ Consider: $$\left|{\frac{z_1-z_2}{1-z_1 \overline{z_2}}}\right|^2$$ ...
0
votes
3answers
114 views

Meaning of Math Symbols

What is the best way to learn the meaning of the math symbols beyond the alphabet or the cardinal numbers? I understand some ϵ>0 means epsilon is greater than zero ∃δ>0 means there exists delta ...
5
votes
1answer
260 views

Why do we put absolute brackets for ln?

When writing out the final answer in $\ln$ form, why is it necessary to put absolute brackets? How does it affect the answer? I have this answer of $-3\ln|\frac{3+\sqrt{9-x^2}}{x}|$, but why does it ...
1
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1answer
61 views

What class would this be covered in?

Would the material in this section of a wikipedia article be covered in a standard course on Differential Geometry, or should I look elsewhere to learn those sorts of things? Specifically, topics like ...
0
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2answers
49 views

Evaluate a function along a complex curve

Well, I don't know this question is appropriate but I really need to understand it. So, please help me. In the book Love and Math, The heart of hidden reality of Edward Frenkel, chapter 15, he said ...
0
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1answer
66 views

Choosing a Project Topic.

I am a undergraduate student and recently i have been assigned to project (one of courses). But i have to choose my own topic. I want to work in the field of ...
1
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1answer
31 views

Where can I find simple integration problems (and other computational exercises) involving special functions?

Working lots of computational exercises in my pre-calculus and calculus classes has given me a great deal of intuition in dealing with elementary functions. Thanks to these years of practice, I can ...
4
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0answers
91 views

A future in mathematics [closed]

I am a Junior in high school right now, trying to figure out what to do next mathematically. I have familiarity with real analysis (Baby Rudin, and also a bit on the gauge integral), complex analysis ...
1
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1answer
43 views

Which is a better definition of a parabola?

Based from reading Math books I have this question, hope you can help me Sirs/Madams Which is a better definition of a simplified parabola A locus of an equation $Cy^2+Dx=0$ or $Ax^2+Ey=0$. (In ...
4
votes
2answers
389 views

An example of a great explanation or freely accessible article on a math concept [closed]

Question: Give an example of a great explanation or freely accessible article on a math concept (suitable at the undergraduate or lower level), and explain why you think it is great. Possible ...
108
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44answers
13k views

What's your favorite proof accessible to a general audience? [closed]

What math statement with proof do you find most beautiful and elegant, where such is accessible to a general audience, meaning you could state, prove, and explain it to a general audience in ...
2
votes
2answers
103 views

What is the most appropriate book for teaching, not the content but skills of mathematics

Hello Everyone I am a high school student currently doing Extension 1 Mathematics at my school. I am currently looking for a high quality mathematics book. Although I am not looking for a book, like ...
1
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0answers
40 views

Obtain distribution of mid-range in uniform

I want to obtain distribution of mid-range, $(x_{(1)} + x_{(n)})/2$, of an uniform(a, b) random variable. One can use the following transformation. $M = \frac{X_{(1)} + X_{(n)}}{2}$ and $W = ...
5
votes
0answers
71 views

Algorithm for finding “fact families”

My friend's 3rd grader encountered the following question regarding "fact families" on her math homework: I was in 3rd grade sometime in the 1980s, so I don't believe I ever encountered this term ...
4
votes
3answers
297 views

What things should one know in order to enjoy their undergraduate degree? [closed]

From looking at undergraduate mathematics programmes it's quite apparent that mathematics degrees are demanding, one could even say the work load is grueling. However I'm certain that there are ...
3
votes
5answers
227 views

Does taking courses in mathematics give any help for mathematical logic?

I'm undergraduate student of philosophy department and I think I'll major in mathematical logic. For studying mathematical logic, I thought studying math lectures would give help to logic. So I ...
3
votes
1answer
84 views

Math or Physics

I'm a Master Math Student And I'm very interested in Some fields in Physics Like Cosmology. I even Considered Changing my field and Apply for physics(Cosmology) but wasn't really possible (my ...
2
votes
3answers
132 views

Why do some accept zero as a natural number but others don't? [duplicate]

I have had many teachers who have told me that zero is a natural number but then there is those teachers who say its not. why is that ?
-1
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0answers
28 views

question on Stieltjes-Lebesgue Measure [closed]

I began learning Real Analysis last year and always couldn't find someone to answer my questions till I found this site recently. Hope can find some answer here :) And...BTW, how to display LaTeX ...
0
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1answer
66 views

Which topics in maths should I know before I dive into programming for image processing?

I am a student who wants to start out with programming for Image processing but as I do not have a good mathematical background(I haven't studied A-level Maths) I would like to know what are the ...
2
votes
3answers
130 views

Prove “the length of the arc is proportional to the central angle subtended”

Depending on individuals’ experiences, the following might not (and hope not) happen to you. However, it did happen to some (including me). When I first studied the topic on “central angle + arc ...
1
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0answers
49 views

Understanding mathematical syntax in SO(3) - Part II

In a paper I found in internet there is a relation about mapping a matrix into a vector and viceversa. One question has been already kindly answered here, but since I'm new to this kind of syntax I ...
1
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1answer
42 views

Help for understanding a vectorial equation found in a paper.

Trying to implement a code for the algorithm described in this paper I found something not very clear to me that leads me to misunderstand the whole concept. To calculate the vector $\vec{b_{3d}}$ ...
0
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1answer
89 views

Which topology textbook has the greatest amount of ancillary support available on the Internet?

I'm considering to begin upon the study of topology and am wondering which book would the best option. I've even started reading Munkres and G. F. Simmons, but the problem is neither book has any ...
0
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1answer
54 views

Understanding mathematical syntax in SO(3)

In this paper, pp. 2, I found the following differential equation system and a statement: There are two things not clear to me: the hat map symbol seems to make mathematical symbolics shorter and ...
90
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17answers
7k views

What parts of a pure mathematics undergraduate curriculum have been discovered since 1964?

What parts of an undergraduate curriculum in pure mathematics have been discovered since, say, 1964? (I'm choosing this because it's 50 years ago). Pure mathematics textbooks from before 1964 seem to ...
20
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2answers
528 views

Collections of undergraduate research projects

I would like to compile a "big list" of undergraduate research projects in the following areas of mathematics: calculus; analysis; abstract algebra; linear algebra; number theory; geometry; ...
1
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2answers
89 views

Let $\{a_n\}_{n=1}^\infty$ be an infinite sequence. Does there exist an infinite series whose partial sums is $\{a_n\}_{n=1}^\infty$?

Definition: By an Infinite Sequence of real numbers, we shall mean any real valued function whose domain is the set of all positive integers. Definition: By an Infinite Series of real numbers, we ...
2
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1answer
148 views

Natural progression in a curriculum for self-study of analysis

Would you list what is a natural and effective progression to self-study topics in analysis in order to gain a broad knowledge of the enormous corpus of knowledge that modern analysis involves. As a ...
2
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2answers
269 views

I want to learn math from zero

I finished high school 2 years ago and now I'm stuck in a university in Turkey. I am interested in learning precalculus, discrete mathematics, physics and chemistry. Question: I need to learn math ...
4
votes
2answers
221 views

Solving min-max optimization problems in original ways (that is, avoiding the frenzy of differentiation)

As I see from the students I'm tutoring, once faced with a min-max problem, the average student is taken by the frenzy of differentiation. I would like to show that sometimes it is better to use ...
0
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2answers
26 views

Is it correct to define variables and functions that are more than one character?

Most of the time (at least at my high school student level), we are using variables such as a, b or $\theta$, and functions such as f, g etc... But would it be possible to use multiple characters ? ...
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2answers
38 views

components of a vector

If I have the angle between two vectors and , I have the components (x,y,z) of the first vector ( xi + yj + zk) how can I know the components (x,y,z) of of the second vector ?
2
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3answers
159 views

Education problem - what to do ? Very intriguing problem [closed]

I really love maths, I see some people complaining of being afraid of maths, or finding it difficult to have motivation to do maths and I can't understand them. Since I'm blinded by my love of maths; ...
17
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4answers
2k views

Why do we need to learn Set Theory?

I was planning to write some article for the Mathematics magazine of our college and it occurred to me that it will be a good idea to write about the impact and importance of Set Theory. I plan ...
9
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3answers
320 views

Examples of useful, insightful, and interesting hand-waving [closed]

It seems to me that some hand-waving (by which I mean some arguments that aim at giving some form of intuition on the problem even at expenses of complete rigour [and not mnemonics for high-schoolers ...