Questions related to the teaching and learning of mathematics.

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1answer
68 views

Is there a Set Theory textbook which include visual explanation?

Right now I am taking a class in set theory, The professor in many cases draw a diagram,pic or anything which help you intuitionally understand the material better. What was surprised me many (at ...
8
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2answers
259 views

How to tackle the depression and frustration regarding math? [closed]

I'm a high school student and it is my last year at school. I've always loved math from the core of my heart. Last year, I prepared a lot for the National olympiad. I cleared the regionals smoothly ...
0
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0answers
16 views

Find a % chance to meet or beat a number knowing a dice's average roll

A 6 Sided Dice's average roll is 3.5. I want to roll three 6 Sided Dice and meet or beat an arbitrary number 30% of the time. How do I figure out what that arbitrary number needs to be to meet or ...
4
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1answer
101 views

Making progress in learning hard math?

I'm not a mathematician, but a computer scientist, but the following problem has puzzled me and I'm wondering how people counter it. In the last 5-6 years, I've probably read the first 5 sections of ...
0
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1answer
37 views

Find element of specific order in group of a large prime power

Consider the group $\mathbb{Z}^{\ast}_p$ where $p = 8631907183416457710036142986950248939902071925468562052182263723074665 2812723253836453003270766004614328295206393288529828311628415785652726 ...
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0answers
69 views

Importance of set theory

Currently I write an article about set theory (in German). Therefore I want to answer the question, why students need to learn something about sets. Among other reasons I have currently the following ...
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0answers
44 views

Probability (Checking if my answers are correct)

Please check if my answers are correct and please show me how to answer this using equation because I answer this question using listing method Two dice are rolled. What is the probability of ...
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1answer
51 views

Understand Logarithm of Bar values manipulation step.

Currently I am learning Logarithm , but I can't understand the manipulation of the following Highlighted step how it comes How the result come after after ...
2
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0answers
21 views

Learning Logic and Metric Spaces

I want to learn how to manipulate metric spaces. I have been reading this book about metric spaces. ...
2
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3answers
99 views

Good math books to get on with my education? [closed]

im looking for a set of good math books. Since i live in norway im going through the norwegian school system, where i choose to go whats called a electrical line. Im not gonna go to deep into the ...
0
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2answers
87 views

How to set interesting integrals

I'm teaching integration by substitution and integration by parts and I'd like to make some interesting problems. I'd like to be able to use the chain rule and the product rule to reverse engineer ...
0
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1answer
65 views

How to find the minimum value of this integral?

I am struggling to find the solution to this problem. If anyone could help to explain how to solve this problem to me, it would be really appreciated. Let $$ f(x)=-\sqrt{3}x+(1+\sqrt{3}) $$ $$ ...
0
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1answer
121 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
393 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
72 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
vote
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?
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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
186 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
62 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
142 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
67 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
60 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
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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
64 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
66 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
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3answers
92 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
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1answer
229 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
60 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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1answer
70 views

The definition of “Dhuruva Numbers” [closed]

From my readings I encountered this number called "Dhuruva Numbers" Dhuruva Numbers are defined as follows: Definition. The numbers which do not change when performing a single operation or a ...
0
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2answers
45 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
62 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
90 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
42 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
385 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 ...
106
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44answers
12k 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
93 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 ...
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0answers
36 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 = ...
4
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0answers
60 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
296 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
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5answers
220 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
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1answer
82 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
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3answers
125 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 ?
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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
60 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
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3answers
110 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 ...
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0answers
38 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
36 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 $\vec{b_{3d}}$ ...