Questions related to the teaching and learning of mathematics.

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0
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3answers
53 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 ...
0
votes
2answers
46 views

Show that there exists no integer $x$ such that $3x$ is congruent to 5 (modulo 6)

So far my approach was to rewrite the congruency to $5-3x=6t$ for some integer $t$. My problem is I get stuck in trying to show how $5-3x$ is never divisible by $6$.
-1
votes
1answer
64 views

Best schools for commutative algebra [on hold]

I will be applying to graduate programs this fall and I was curious which schools have the best commutative algebra groups. I know berkeley and michigan are up there, but what are others?
5
votes
1answer
183 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
55 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
1answer
56 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
votes
2answers
36 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
votes
1answer
47 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
26 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
79 views

A future in mathematics

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
38 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 ...
2
votes
2answers
301 views

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

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 ...
88
votes
41answers
11k views

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

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 ...
4
votes
0answers
50 views

Tricky question (physics) [migrated]

I know this may not be the place for this question, by stackexchange physics has banned homework questions :( A piece of hair taken from a goat has a radius of $3.1\times 10^{-5}\text{ m}$. What is ...
1
vote
2answers
50 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
23 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
votes
0answers
45 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
283 views

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

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 ...
4
votes
5answers
155 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 ...
-1
votes
1answer
76 views

factor and simplify $x^{7/8} - x^{1/8}$ [closed]

I do not know how to factor this AND simplify after I factor. I need help please and as soon as possible. I've been trying to figure it out for the past 3 hours and I don"t know how to get the answer. ...
3
votes
1answer
62 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
109 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
votes
0answers
26 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
votes
1answer
49 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
47 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
vote
0answers
30 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
vote
1answer
32 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
votes
1answer
73 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
votes
1answer
45 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 ...
86
votes
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 ...
2
votes
1answer
65 views

Popularization of mathematics: inspiring quotes (or interviews) on the fascination of mathematics

I would like to compile a big list of references to particularly inspiring interviews with important mathematicians or famous quotes on the fascination that mathematics holds for ...
13
votes
1answer
216 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
vote
2answers
81 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
votes
1answer
108 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 ...
1
vote
1answer
119 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
116 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
votes
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 ? ...
1
vote
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
votes
3answers
146 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; ...
15
votes
4answers
1k 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
votes
3answers
268 views

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

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 ...
2
votes
5answers
132 views

Is there a proof that $\int \frac {dx}{x}=\ln |x|+c$?

Is there a proof that $$\int \frac {dx}{x}= \ln|x|+c$$ for $x\neq 0$ I would be interest for any replies or any comment.
7
votes
1answer
121 views

So bad at maths sometimes I feel depressed about it [closed]

I taught myself how to count before I even learnt how to talk or read. Playing with numbers was all I did when I was young. I didn't have anyone to foster that type of passion that I believe I still ...
2
votes
2answers
40 views

Printer toner coverage

I have a printer that I used for $2$ years. First year I printed $9630$ pages, with $17\%$ ink coverage per page. Ink coverage is the percent of the page that is not white. Second year I printed ...
11
votes
6answers
236 views

Sources for mathematics outside the mathematics world

In this question I would like to ask you about material showing the uses (or occurrences) of mathematics in the everyday world. The aim is to encourage with it a group of young undergraduate ...
2
votes
1answer
147 views

Why is the axiom of choice not taught from the start to mathematics undergraduates?

I've recently discovered that the following theorems require the axiom of choice to be proven: every surjective function has a right inverse. a real-valued function that is sequentially continuous ...
0
votes
0answers
35 views

Algebra Questions-Academic

ı must solve this ı only know question 2)s' b) option is Euler's prime-generating polynomial.But ı dont know to show that,too.please help :(
1
vote
0answers
23 views

Calculate year for a provided yield

\$146.25 will yeild \$46.25 at 7.5% per annum. How to get the number of years? Answer is 6 but how do you get it? What is the formula?
3
votes
2answers
53 views

Condition of the mean value theorem

The usual formulation of the mean value theorem in a real analysis course is something like this: Let $f\colon [a,b] \to \mathbb{R}$ be continous on $[a,b]$ and differentiable on $]a,b[$. Then there ...
0
votes
1answer
70 views

Question about independent study in differential geometry for an undergraduate.

I am a senior undergraduate math and physics student applying to graduate school in math for this upcoming fall. I have had classes in: Abstract Algebra (Rings, Fields, and Groups), Point-Set ...