For questions related to the teaching and learning of mathematics. Note that Mathematics Educators StackExchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

learn more… | top users | synonyms (3)

-1
votes
4answers
39 views

Particles that are distinguishable and indistiguishable at the same time

Thinking about a question and my answer to it and another question I asked earlier. I've come up with the following problem: Consider two otherwise very similar marbles, a red one and a blue one. Let ...
0
votes
1answer
38 views

In Novice Terms, How Does an Ordered Pair Relate to a Database Row (Tuple)?

Im putting a technical presentation for an interview (topic I chose). I am researching real-time data streaming. I am familiar with what an ordered pair is as it pertains to a graph i.e (x, y) ...
0
votes
1answer
78 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
votes
2answers
466 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
votes
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
votes
1answer
104 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
votes
1answer
41 views

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

Consider the group $\mathbb{Z}^{\ast}_p$ where $p = 8631907183416457710036142986950248939902071925468562052182263723074665 2812723253836453003270766004614328295206393288529828311628415785652726 ...
0
votes
0answers
251 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 ...
0
votes
0answers
49 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 ...
1
vote
1answer
119 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
votes
0answers
22 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
votes
3answers
111 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
votes
2answers
97 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
votes
1answer
100 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
votes
1answer
139 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
votes
0answers
552 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
votes
0answers
83 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
44 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
vote
4answers
88 views

What is not the second derivative of a parametric equation?

1142004    Consider the parametric equations $x=f(t)$ and $y=g(t)$. To "find" $\frac{d^2y}{dx^2}$, there are three ways to go: (1) the correct one, that is, ...
1
vote
1answer
62 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
votes
1answer
338 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
votes
2answers
66 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
votes
1answer
154 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
votes
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 ...
6
votes
1answer
148 views

Help with diagram chasing

Given the diagram $\require{AMScd}$ \begin{CD} 0 @>>> A @>f>> B @>g>> C @>>> 0 \\ @. @V\alpha VV \#@V\beta V V\# @VV\gamma V @. \\ 0 @>>> {A'} ...
2
votes
3answers
68 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
49 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
votes
1answer
68 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?
3
votes
0answers
72 views

A good way to explain $\varepsilon$-$\delta$ for chemistry / biology students?

I feel like I have a pretty good way to talk about $\varepsilon$-$\delta$ to physics and engineering students (and possibly students in comp sci). But I am not very sure what I can do for chemistry ...
0
votes
2answers
44 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
votes
1answer
75 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
votes
1answer
75 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: $$\left|{\frac{z_1-z_2}{1-z_1 \overline{z_2}}}\right|^2$$ ...
1
vote
1answer
119 views

Why are Fourier series important?

Are there any real life applications of Fourier series? Are there examples of Fourier series which have an impact on students learning this topic. I have found the normal suspects of examples in this ...
3
votes
1answer
40 views

Find a set of minimal natural axioms, from which we construct $\mathbb{Z}$.

I am interested in this question for teaching two very different kind of students. The first (less important to me) is students in their first year in the university. I wish to construct ...
1
vote
0answers
76 views

Intuition behind the link between coding theory and group theory

I am trying to find an easy link between group theory and coding theory. The usual path that most of the texts follow is that they present introductory material on groups, fields, rings, etc., and ...
0
votes
3answers
141 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
282 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
vote
1answer
63 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
votes
2answers
52 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 ...
1
vote
0answers
39 views

Proper usage for term, addend, factor, multiplicand, expression, formula

The definitions and usage of the following words seem to vary, depending on the source text: term addend factor multiplicand expression formula The words are being used in the context of ...
0
votes
1answer
86 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
vote
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
votes
0answers
93 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
vote
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 ...
-6
votes
3answers
92 views

Why does the author prefer function names after arguments?

As you can see above, the author prefers to write functions after elements, which is contrary to the century old practice of writing arguments after the functions. I wonder why he does that? Is ...
108
votes
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
120 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
vote
0answers
42 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
76 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
300 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 ...