Tagged Questions

Questions related to the teaching and learning of mathematics.

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0
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0answers
41 views

Is the field of Algebraic Topology still an active field of research?

I have been studying some Algebraic Topology in my free time, and I began to wonder whether it was still an active field of research? If not, what are some of the most active research fields nowadays. ...
1
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3answers
34 views

A silly question about potential functions

Why have physicists had the idea to define a potential function of a gradient vector field $\vec F$ to be a function $g$ such that $\vec F=-\nabla g$? What changes if we don't put the negative sign? I ...
4
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0answers
53 views

How can I retain the mathematics that I've supposedly learnt?

So my question simply is "What is the best method to make sure you retain what you have learnt?" Okay so I've tried learning mathematics up to where I should be at in the past. Every time though I ...
3
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1answer
59 views

Definition of a function and the notation $f:A\to B$.

In some textbooks on analysis, I have encountered a definition of function/mapping that distinguishes the terminology mapping on $A$ to $B$ and mapping from $A$ to $B$; the first one refers to a ...
17
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5answers
373 views

Big list of serious but fun “unusual” books

I would like to have some suggestions about serious (that is, with good mathematical content) but fun books that cover topics (or propose problems) in "recreational mathematics"; in any other field ...
4
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1answer
28 views

continues function statement in real analysis [closed]

I ran into a challenge, i read following sentence in one note. anyone could describe or prove it for me? F is a continues function at point $ x_0 \Leftrightarrow (x_n \to x_0 \Rightarrow ...
0
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2answers
53 views

Is this correct - confused in this riddle - where does the one rupee come from…? [closed]

I have 50 rupees, and spending like this and where does that ONE rupee come from.... am right or wrong ??????
0
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0answers
22 views

Is this correct? A snail climbs up a 20 metre wall. [duplicate]

A snail climbs up a 20 metre wall. Every hour it climbs up 5 metres then slides back 3 metres. How long does it take the snail to climb up the wall. My solution: By 16 m, the snail would have taken 8 ...
20
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7answers
2k views

Very *mathematical* general physics book

I am searching for a book to study physics. So far, I've been suggested Resnick, Halliday, Krane, Physics, but it doesn't seem to be very suited for a math major. Can you suggest some more ...
0
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1answer
23 views

The normal plane to a path

PROBLEM: Let $\vec x(t)$ be a path with $\vec x'$x $\vec x'' \ne 0$ and suppose that there is a point $\vec x_0$ that lies on every normal plane to $\vec x$. Show that the image of $\vec x$ lies on a ...
4
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2answers
88 views

What intuition stands behind implicit differentiation

I'm trying to undestand implicit differentation Let's take as a an example equation y^2 + x^2 = 1 1. How i think about how the equation works I think the function as : if x changes then the y term ...
1
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0answers
24 views

Which functions could be discussed in a calculus course?

In a typical calculus course, students are exposed to many functions. Some have their origin in a field of study, while others are simply combinations of polynomials, trig functions, exponentials, and ...
6
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1answer
100 views

Is the actual learning of a course done in second reading?

I am now a graduate student. When I was an undergraduate, I would mostly study on my own directly from the books, and not concentrate much on lectures. Also, since I was a pretty good student, I would ...
1
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1answer
112 views

What does mean the exact value of derivative

i'm starting my calculus's journey and i have a question. What does mean the exact value of a derivative Take an easy example we have a derivative of $f(x)=x^2$, that is $f'(x)=2x$. Someone would ...
5
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1answer
92 views

The Use of Sound in Mathematics. [closed]

I'm not sure that this question is appropriate here. There's a good chance it's too opinion-based. If that's the case, I'm sorry. I was sat in a research seminar recently and wondered whether it'd be ...
1
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2answers
67 views

Path to 3d Mathematics programming, where to start?

This might read like duplicate of this question https://math.stackexchange.com/search?q=where+to+start However since that one wasn't answered, and I have a more specific problem in regards to ...
1
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1answer
66 views

Proof of big-O notation

Prove the following: If f is a polynomial of degree $d$, then $f(n)=O(n^{d})$. For every $d \in N, n^{d} = O(e^{n})$ Intuitively, it makes sense to me that for the first one, growth order depends ...
0
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0answers
30 views

Prerequisites for learning 'computer mathematics'.

O.K. I know basic arithmetic and nothing else. I want to be able to implement the algorithms in Knuth's 'The Art of Computer Programming'. I have my own curriculum for the programming aspect. I need ...
-5
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1answer
107 views

Are variables the same in pure mathematics??? [closed]

my question is In pure mathematics, $x$ always $=x$ $x = x$, the variables are abstract. In modelling, $t$ could mean the time that has elapsed since you started a machine for example. Or ...
2
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1answer
37 views

Vectors and polyhedra: a surprising fact

Given a $n$-faced polyhedron, associate to each face an outward-pointing normal vector with length equal to the area of that face. Show that the sum of these $n$ vectors is zero. I've already proved ...
4
votes
1answer
103 views

How important is the “prestige” of your university for undergraduate mathematics?

I go to a university in Canada. It's not really considered a top university (it is one of the best universities in the province but is ranked really low nationally). I study mathematics here and ...
0
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1answer
18 views

I am looking for a book designed for self teaching applied/engineering mathematics. Can someone help me find a few?

I have used Shaum's differential equations. Are there others that I could use that are designed for self-study?
2
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1answer
50 views

Solve a problem using vectors

The purpose of this problem is to use vectors to show that the medians of a triangle all meet at a point. First, I have to show that $P$ (see the picture below) must lie two-thirds of the way from $B$ ...
2
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1answer
68 views

How useful is Web Development to a Mathematician?

I'd like to ask for a career advice here if that's ok. I've graduated as an engineer in 2010 and recently got offered a place on the Computation Mathematics program in a university in the UK, entry in ...
0
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0answers
22 views

Partial fractions and Hermit reduction?

According to the late Manuel Bronstein in his "Symbolic Integration Tutorial" (ISSAC 98), and available here, the partial fraction algorithm "should not be used in practice, yet it remains the method ...
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2answers
84 views

Pure Mathematics to Actuarial Science.

I did my undergraduate in pure mathematics and recently after a three year break I decided to get a master's degree in Actuarial Science. I am in the second week of classes and I feel completely lost. ...
10
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2answers
808 views

Success in maths (soft question)

I would really like to hear from any professional mathematicians who didn't just sail through their university education. If one looks at the pages of many of today's mathematicians, one finds that ...
5
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2answers
65 views

Intuitive characterization of the graph of a twice differentiable function

In high school textbooks, the following characterizations are often found: A function is continuous if its graph can be drawn without lifting the pencil. and A function is differentiable if ...
0
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1answer
26 views

How to calculate how much to add so that buying 1 expensive item is better than 10 cheap items

I am trying to make a shop for self learning but i have a small hiccup! I have this list of items that has a USD value assigned to it. But I want to make it so if they buy a "100 GB/s" it should be ...
5
votes
1answer
316 views

A question about a mathematical analysis book

I am a newcomer to Analysis. All knowledge I know about "Analysis" are differentials,limit and integration (basically, what we have been taught in high school) I am studying Principles of ...
2
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3answers
118 views

Fun proofs for layperson?

I'm not quite sure whether this question belongs here, because it has no definite answer. But I'll give it a shot. If any of the mods objects, then I will, of course, respectfully delete this ...
3
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0answers
94 views

Why is there no collection about all mathematical theorems and open questions?

I really would like to have a giant math collection which is sorted according to the Mathematics Subject Classification, but with more then 3 levels, and it should contain all known theorems and also ...
16
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3answers
260 views

Is$\frac{\sqrt{a}}{\sqrt{b}}$ the same as $\sqrt{\frac{a}{b}}$?

My idea is that the two functions are not the same since for the first function, the domain of the function is only non negative reals for the numerator and positive reals for the denominator. ...
0
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1answer
29 views

Finding eq of tan to the curve

I am trying to figure out how to find the eq to the tan to the curve x = cost + cos2t, y = sint + sin2t, (-1,1) I'm lost at the point where you plug in t in order to find the slope. I have the ...
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2answers
87 views

Do mathematics researchers regularly solve problems like this?

I'm not sure that this is the right exchange for this question. It asks about the possibilities of research in mathematics and computer science. Extended Background I am very interested in ...
6
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3answers
77 views

Interesting, unusual max/min problems?

So I've got to that stage of my elementary mathematics subject for engineers when we talk about differentiation and solution of max/min problems. And I'd like to entertain and engage the students ...
1
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1answer
59 views

ROI Forumla for this scenario

I couldn't come up with a proper formula for the scenario below. I'm not so good at Maths. With, $X$ - monthly gains in percentage $C$ - Initial capital $N$ - number of years $M$ - Amount ...
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1answer
44 views

Converting 16bit float to Base10 and vice versa

Hi! I have some difficulties understanding how I'm supposed to calculate this 16bit float to base10. This is something that is coming up on a test so I would be pleased to learn how this is supposed ...
0
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2answers
90 views

What are the differences between mathematics courses taken by engineering majors and by math majors? [closed]

I am curious to know what are the differences between mathematics taken by engineering students and by math majors. Let's say in terms of the approach, depth and in the topics covered. And even within ...
1
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2answers
41 views

rationalize the complex number multiplication rule

For a middle school student without previous knowledge of complex number, how do one introduce the multiplication rules of complex number? i.e., if we have two real number pairs of $(a,b)$ and ...
2
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2answers
102 views

Going Back to Grad School After Being Away from Math

I graduated with a degree in Math-Computer Science(dual degree) from a college in the US in 2012, and have been working in the Software industry ever since. From 2012 to mid 2014 I was a software ...
9
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2answers
178 views

Good Reference for Justifying (less well-known fields of) Math?

How do we as mathematicians justify the study of math to students? Or, indeed, how do we justify it to the general public? How do you justify your particular field? I'm particularly interested in ...
22
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6answers
2k views

Mathematics - The big picture

My knowledge in math sums up to several university level courses and a lot of self-study. Sometimes it feels like Mathematics is a huge subject with a lot of different areas which some of them ...
0
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0answers
85 views

The steps to becoming a Pure Mathematician

I'm a college freshmen intending to major in Mathematics. I started college with not so great grades in my calculus courses. However, I realized that to get the grades I just have to practice. I ...
0
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1answer
150 views

“Real world” applications of rational functions

I need a rational function/equation beyond the contrived d=rt and work problems typically given in beginner algebra. I am teaching such a class and would like to motivate the study of techniques for ...
2
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0answers
39 views

Equillibrium between Programming and Math Skills? [closed]

So I enjoy recreationally doing math and programming and am now at a stage where I will be pursuing them in University but I have found myself in a bit of a bind. My programming ability seems to lag ...
2
votes
2answers
55 views

Writing solutions of inequalities: $3<x$ versus $x>3$

My son wrote a solution to a number line graph as 3 < x instead of what his teacher said was the correct answer of x > 3. When he brought his paper back in to bring it up he was told that the ...
1
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3answers
160 views

Is tutor essential for success in mathematics? [closed]

Everyone in my Pre-Calc - Calc I class is failing, except the kids who go tutor. They get top percentile ranks in the class. Should I drop maths all together so I don't have to invest in a tutor? I ...
5
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4answers
254 views

What sequence should I study these topics in?

I will shortly list a series of topics that amount to what is essentially the first two years of an undergraduate degree. I'd like to know what is considered best order in which to study these ...
0
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0answers
17 views

Maths C sum and series

The quality of the waste water from a manufactory contains 500g pollution per 1OL of waste water. Each time the water passes through a filter, 18% of pollutant are removed According to NHMRC ...