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.

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7
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3answers
169 views

Algebraic number theory topics for undergrads

What are some interesting topics or problems in algebraic number theory which could be presented to students in a first undergraduate algebra course (which covers some elementary number theory, ...
4
votes
3answers
277 views

Monotonous function or monotonic function

I am from a non-English speaking country. Should we say monotonous function or monotonic function?
0
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0answers
33 views

Pursuing Maths after Majoring in Engineering

I will be graduating this summer with an undergraduate degree in Mechanical Engineering. I want to pursue my interest in the field of mathematics. If anyone can provide guidance on how to go about it? ...
2
votes
1answer
143 views

Mathematics books that tell you what is really happening? [closed]

Many book I've read teach you symblobic manipulations instead of pointing out what's really happening. So my question would be: what mathematics textbooks don't do that? Books that rather than listing ...
11
votes
2answers
312 views

Importance of Exercises in Mathematics for Self-Studying

I am a high school student wanting to major in Mathematics in the future. I started to like Mathematics recently, starting a year ago and I watched some interesting math videos on YouTube for fun (ex: ...
2
votes
0answers
60 views

What are the current frontiers of mathematics? [closed]

In language suitable for an undergraduate student familiar with the basic objets of interest and classical techniques used in the major subfields of mathematics, what are the ''frontiers'' of modern ...
-1
votes
2answers
122 views

Mathematics problems clock

Long ago, I had an idea of creating (actually, labeling) a clock that will have, instead of the numbers 1,…,12, important mathematical problems whose solution turned out to be that number. Such a ...
3
votes
0answers
117 views

Examples of categories which appear naturally without objects

Regarding the morphisms-only-definition of a category (which is equivalent to the usual one dealing with objects and morphisms), I would like to ask: Which examples of categories in practice appear ...
0
votes
0answers
41 views

Variable weight more than another in probability

I'm about to create a ICU pediatric indicator about died and survived patients. I have the next table about the formula that I wish create. My question is... is there any subject inside the ...
2
votes
8answers
362 views

A pedagogical proof that 9's can be ignored when calculating digital roots

I was asked by an elementary school teacher for a proof that you can ignore all 9's when calculating the digital root of a number. For instance, when calculating the digital root of 7593329, you ...
0
votes
1answer
331 views

Does one necessarily need an MS in Math before taking a PhD in Math? [closed]

I finished bachelor's in mathematical finance and am nearly finished with master's in mathematical finance (I am already done with thesis), and I plan to pursue a PhD not in mathematical finance but ...
0
votes
1answer
50 views

Help needed for a step by step calculation

I hope I can get some help to understand step by step calculations for formulas below. If I have a weighted distance formula like below: $d(O, P) = \sqrt{\frac{\hat{x_1^2}}{\hat{s_{11}}} + ...
11
votes
1answer
159 views

Has the age at which we teach Mathematics changed over the last two centuries?

My experience of learning Advanced Trigonometry and Calculus is that it was done to 17 and 18 year olds (School Curriculum in Australia). I assumed that it was similar in the UK, US and Europe. In ...
2
votes
2answers
105 views

How should a DE course be re-written, if Gian-Carlo Rota is correct?

Admittedly a soft question but an important one, I think. The questions I've asked below are questions that can be answered, and not just discussed. I read this essay yesterday by Gian-Carlo Rota ...
1
vote
5answers
96 views

What does the solution of a PDE represent?

So I took a course in PDE's this semester and now the semester is over and I'm still having issue with what exactly we solved for. I mean it in this sense, in your usual first or second calculus ...
3
votes
1answer
157 views

Advice on mathematical cources and profession [on hold]

I am a class 9 student studying in India. I deeply love mathematics and I am aspiring to become a mathematician ( I am aiming for research and development). My hobbies include learning and trying to ...
0
votes
0answers
49 views

Finding extrema of a cubic equation

I'm brushing up on my calculus and working through Dennis Zill's Calculus w. Analytic Geometry. Problem #39 in section 4.7 describes two light sources and gives the illuminance function of a light ...
2
votes
3answers
99 views

Teaching cardinality

I would like to give a class of 60 minutes to my undergraduate students about cardinality. I would like to begin with the definition of cardinality and end with one or two good application of this ...
1
vote
2answers
64 views

If negative of negative (--) = positive then why not positive of positive(++)= negative

As per my understanding positive and negative are just indicative of direction of number axes with zero at the center. If that is the case we should apply same laws to both positive and negative ...
3
votes
8answers
197 views

Find Matrix $A^{50}$?

Find the matrix $A^{50}$ given $$A = \begin{bmatrix} 2 & -1 \\ 0 & 1 \end{bmatrix}$$ as well as for $$A=\begin{bmatrix} 2 & 0 \\ 2 & 1\end{bmatrix}$$ I was practicing some questions ...
5
votes
1answer
79 views

Any elementary proof for Euler's product formula for sine

Is there a proof for the following fomula of Euler which does not use complex analysis or fourier analysis? $${\sin (\pi x)} = \pi x\prod_{n=1}^\infty\left(1 - \frac{x^2}{n^2}\right).$$ Suppose that ...
0
votes
0answers
21 views

rectangular prisms

The question I'm currently trying to solve calls for 6 different ways to stack rectangular prisms evenly. So, each outcome must differentiate from one another, in terms of surface area. L = 19.7cm / ...
1
vote
1answer
56 views

Why does Herstein define Normalizer and Centralizer to be the same?

Topics In Algebra 2nd edition, Section 2.5 exercise 13, "If $a \in G$, define $N(a)=\{x \in G \mid xa=ax \} \dots N(a)$ is usually called the normalizer or centralizer of $a$ in $G$." Usually the ...
3
votes
4answers
145 views

Good way to convince a young kid that $0*0 = 0$?

My little brother (6 years old) asked me a question ("What is $0*0$?") and gave an answer to his own question which I found ridiculous so I refuted it but he still thinks he is right. He says that ...
4
votes
1answer
174 views

Quality of Videos Lectures and Lectures vs Textbooks

I am a student trying to learn different subjects by watching video lectures and reading on my own time. I was wondering if the lectures from ICTP and nptelhrd are a great use of my time. I tried ICTP ...
0
votes
1answer
41 views

Find functions with ''smart'' tangents.

This is a didactic question. Given a differentiable function $y=f(x) \;, x,y \in \mathbb{R}$, I want to construct an exercise in which we have to find a straight line that passes through a point ...
3
votes
1answer
90 views

Two categories sharing the same objects and morphisms

Is there a natural example of two categories $\mathcal{C}$, $\mathcal{C}'$ which have the same class of objects and the same class of morphisms, including source and target maps, but different ...
0
votes
1answer
35 views

How to get real value after discount.

Suppose my item real value is 100. and i have given discount 10 % to my customer. Now the changed value of item id 90. If i set value 110 and give 10% discount then i got result 99. but i need result ...
0
votes
0answers
40 views

Potential Careers in Math For Someone with Testing Disability

I've been studying math for several years (Bachelor's in pure mathematics) at university, and so far, I've been receiving excellent scores on the homework exercises (over 95% average) in all subjects ...
0
votes
1answer
70 views

Finding the equations of two lines that meet in a point.

"Give the equations of two lines that meet at the point (2, -3, 5) and which meet at right angles, but do not use that point in either of the equations." I am having a bad time with this one. I ...
0
votes
1answer
94 views

Question about graduate textbook and class.

I am a senior in mathematics, and I have had Advanced Cal I, but currently go to a no name school (there were only three people in the class). I have also taken Advanced Cal II as an independent ...
1
vote
1answer
20 views

how many fewer grames of caffeine is she consuming each week?

how many fewer grames of caffeine is she consuming each week? I try with the following 2*97*7 + 5 * 6 *7 = 1358 +210 = 1568 mg convert to gram = 1.568 but not correct , please help how calculate ...
1
vote
0answers
15 views

Where can I find colleges around Tallahassee, Florida that offer math courses that qualifies someone to teach college level math classes?

Are there any colleges around Tallahassee, Florida where I can take 1 or 2 math classes to teach math on the college level? I applied to teach full-time at the community college in Tallahassee but ...
5
votes
2answers
96 views

How to prove whether the equation set has a unique solution?

\begin{eqnarray} \begin{cases} \sin A \sin C-(\sin B)^2=0 \cr AC-B^2=0 \cr A+B+C-\pi=0 \cr A>0,B>0,C>0 \end{cases} \end{eqnarray} How to prove whether the equation set has a unique solution ...
3
votes
2answers
82 views

Which optimization problem to use when I want to explain the concept of optimization to a layman?

I am looking some problem, which would be: Easy to understand Hard to solve intuitively Touch our everyday lives I am doing research in optimization using evolutionary computation. When people ...
0
votes
2answers
44 views

Consider the following expression about natural number: \forall n\exists m: m^{2}=n .

$$ \forall n\exists m: m^{2}=n $$ How do I interpret this? This is part of my assignment question but I cant carry on without understanding this.
1
vote
1answer
21 views

Finding the number of years in a compound interest formula

My question is: Suppose that I have $\$2,500$ in an investment account. I want this to grow to $\$5,000$. Approximately how long it would take to do this if my account earns $3.5\%$ compounded ...
1
vote
2answers
78 views

Abstract/formal interest of rings

I am about to introduce first year undergrads to the concept of rings, after spending some time looking at groups; and I would like to give them more than a practical motivation (the most usual rings ...
1
vote
0answers
23 views

Adjacency vs Laplacian matrix

There are different ways to represent a graph but adjacency and laplacian matrices are the two most powerful ones having various properties. Recently, a student asked me when exactly we should use ...
1
vote
0answers
49 views

Which book was used for Math 112 at Harvard back in 2001--2002?

I've downloaded problem sets for the course Math 112 of 2001--2002 at the Harvard Mathematics Department. In some of the problems, there're references to a certain book, but since there is no syllabus ...
12
votes
1answer
362 views

How to Self-Study Mathematical Methods?

Edit: Ok, user Chinny84 made comment that truly helps narrow the focus of my question. Basically, I'm asking for a self-study course of Mathematical Methods. Thanks to his recommendation I ...
16
votes
8answers
2k views

How to explain brackets to young students

It's amazing how simple questions from young students can often uncover unexpected gaps in (at least my) knowledge, or at least the ability to explain. Today, a student asked me why she can "forget ...
13
votes
13answers
4k views

How to explain the formula for the sum of a geometric series without calculus?

How to explain to a middle-school student the notion of a geometric series without any calculus (i.e. limits)? For example I want to convince my student that $$1 + \frac{1}{4} + \frac{1}{4^2} + ...
4
votes
2answers
104 views

Is there a way to prove that the order of an element in a Group divides the order of the Group, WITHOUT USING LAGRANGE'S

This is a very easy fact we use in Group Theory, But somehow, I wondered that whether there may be another way (other than Lagrange's Theorem) to prove that the order of an element divides the order ...
2
votes
2answers
62 views

Necessity of algebraic symbolism

We solve different problems algebraically .For example,if we add $20$ with a number and the sum is $42$.What is the value of the number.To solve we denote the number as $x$ and write like this ...
0
votes
0answers
58 views

How do I prove that a boolean function constructed using $\vee$ and $\wedge$ (without using $\thicksim$ ) must attain the value 1 at least once?

I made an attempt and got this solution. To prove this, lets construct a boolean expression using $\wedge$ and $\vee$ . In the boolean expression $(p\wedge q)\vee(p\vee q)$ , by entering the ...
3
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0answers
87 views

Undergraduate research program (REU) with focus on nonlinear analysis (accessible to European students) [closed]

Is there an undergraduate summer research program (REU) -- to which also European students can apply -- which usually has projects (i.e., specialized faculty) on nonlinear analysis (i.e., ...
0
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0answers
19 views

Difference of radian and degree measure.

I had noticed that in studying trigonometric functions some fields of Math favors the radian measure such as calculus and analytic trigonometry, while others favor degree measure for instance in ...
0
votes
1answer
128 views

How to explain this question to a 6 year old

My daughter who is in 1st grade is learning to grasp he meaning of multiplication and has not yet been introduced to division. she is appearing for Kangaroo Math Competition. Following question has ...
5
votes
4answers
125 views

Explaining that $1 \cdot 3 \cdot 5 \dotsm (2n+1) = 1 \cdot 3 \cdot 5 \dotsm (2n-1)(2n+1)$

I have a few students that are having trouble understanding that $$1 \cdot 3 \cdot 5 \dotsm (2n+1) = 1 \cdot 3 \cdot 5 \dotsm (2n-1)(2n+1),$$ specifically that $$\frac{1 \cdot 3 \cdot 5 \dotsm ...