Questions related to the teaching and learning of mathematics.

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0answers
42 views

Are variables the same in pure mathematics??? [on hold]

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
votes
1answer
27 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 ...
0
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0answers
20 views

Transforming a calculation into a formula

The figure below shows a way to calculate IT governance performance: I would like to transform step 3 to a formula. Let's say that question 1 is depicted as Q1 and question 2 as Q2. Does the ...
3
votes
1answer
63 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
13 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
votes
1answer
28 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
votes
1answer
60 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
13 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 ...
0
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1answer
51 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. ...
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0answers
33 views

Does anyone know a good maths book to read? [closed]

I'm doing a major in mathematics and want to get a head start. What are good books to read at this level?
0
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0answers
21 views

Using differential equations vs general solutions

I was looking at Newton's Cooling Law with a student when he asked me why, for this particular case, do we use the ODE and not just the general solution to analyse data. I couldn't come up with an ...
10
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2answers
774 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
votes
2answers
47 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
25 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
204 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
votes
3answers
81 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 ...
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0answers
17 views

divide amount spent equally

Me and my friend needs to divide the amount spent equally. He brought food worth of 20 dollars and I brought worth of 130 dollars. Now I need to divide this money equally so that we both spend equal ...
3
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0answers
83 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 ...
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votes
3answers
89 views

Trouble Understanding Large Number [closed]

Alright so I want to know how large this number actually is. I understand that ten to the power of ten is ten billion. What do you do when there is a power and then another power? How large is the ...
15
votes
3answers
215 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
25 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 ...
1
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2answers
80 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
votes
3answers
62 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
52 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 ...
1
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1answer
39 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
77 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
38 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
votes
2answers
83 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 ...
6
votes
1answer
106 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 ...
21
votes
6answers
1k 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
69 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
65 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
votes
0answers
36 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
52 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
vote
3answers
152 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
votes
4answers
210 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 ...
0
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0answers
27 views

Maths C Proving fibonacci sequence (induction)

Given the recurrence relation of the Fibonacci sequence: F(n) = F(n-1) + F(n-2) Knowing that F(1) = 1 and F(2) = 1, solve for x, name the two solutions as $x_1$ and $x_2$. The particular values ...
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1answer
56 views

using induction to prove that the formula for finding the n-th term of the Fibonacci sequence is: [duplicate]

May someone help me? I am trying to use induction to prove that the formula for finding the $n^{th}$ term of the Fibonacci sequence is: ...
2
votes
1answer
136 views

Math enthusiast wants to learn math

I'm an english major with a vivid interest in mathematics,I've read and enjoyed What Is Mathematics? by Courant and Robbins (does this count as some background?),and I've decided to begin a serious ...
3
votes
2answers
82 views

Prove withoui calculus: the integral of 1/x is logarithmic

It was known in the 17th century that the function $$ t \mapsto \int_{1}^{t} \frac{dx}{x} $$ is logarithmic: a geometric sequence in the domain produces an arithmetic sequence in the codomain. This ...
2
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1answer
32 views

Computing of the Gamma Function

I have stumbled upon Gamma functions when dealing with Gamma distributions on my studies with basic statistics. However, I have not understood how its computation expands factorials to real and ...
4
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3answers
122 views

(translated)Russian mathematics books?

Most russian mathematician(generally) are known to do and teach mathematics in a very original manner,they do in a very intuitive yet rigorous way, with/through wonderful connection to physics. ...
1
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1answer
185 views

Gilbert Strang's books on calculus and linear algebra?Are they for math majors?

I would to know what are the best resources to use to teach and learn elementary subjects (calculus,linear algebra),I remember when learning calculus, I used Spivak's book which had wonderful ...
0
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1answer
22 views

Can i calculate velocity at a point P without using calculus in this case

I actually wanted to understand calculus. And read many a times, that concept of differentiation is about splitting the path into infinitesimally small divisions. In most cases the such division is ...
1
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4answers
89 views

Explaining multiplication of fractions

The best way I've been able to describe multiplication is as $$ a\times b = \sum^a_{i=1} b$$ But my definition does not account for things such as $2.99792458\times8.987551787$ and ...
2
votes
1answer
77 views

Teaching the Concept of Infinity to Children.

I was recently out with the family and we left it up to the children where we ate lunch (11 and 9 years old). They couldn't agree and were going back and forth calling each other names. This ...
0
votes
2answers
31 views

Alternative to using greater than operator for comparing numbers on a number line

The sign greater than "$>$" represents the quantity of one number more than another number. However the same sign is used to know the direction of a number on the numberline ( with respect to an ...
10
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3answers
338 views

A question from an engineering undergraduate

My question primarily concerns the necessary transition from an undergraduate program in electrical engineering to graduate program in applied mathematics or pure mathematics. I'm an electrical ...
6
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1answer
258 views

Where does the “Visual Multiplication” technique originate from?

There is a geometric technique to perform multiplication of numbers. But as the internet goes, it is hard to figure out who deserves the credit. What I've heard is A mayan technique From Vedic ...