Questions related to the teaching and learning of mathematics.

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2
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0answers
52 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
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2answers
108 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 ...
0
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0answers
39 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 ...
0
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1answer
288 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}}} + ...
2
votes
2answers
89 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
85 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
144 views

Advice on mathematical cources and profession

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
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0answers
42 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 ...
1
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2answers
59 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
192 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
65 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
55 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
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4answers
139 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
133 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
27 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
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0answers
33 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
43 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
76 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
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0answers
14 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
93 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
74 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
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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
15 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
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0answers
22 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
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0answers
47 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 ...
10
votes
1answer
285 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} + ...
0
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0answers
56 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
84 views

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

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 ...
3
votes
0answers
81 views

Advancing in math [closed]

If this question have already been answered or doesn't belong in this forum I am sorry. I am currently in my second year in high school and i am planning on studying economics and finance in college ...
4
votes
1answer
201 views

Books Preparatory for Putnam Exam

I am extremely interested in the Putnam competition. Given that I am currently in 11th grade (so I have 12th grade and half my freshman year to study (plus summers and vacations, etc..)), what ...
17
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8answers
1k views

Undergraduate Research Thesis

1. General background information ★ At my university [whose name I will omit] the following practices are customary: ● During their third year of study, students have approximately $4$ ...
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4answers
38 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
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1answer
31 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
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1answer
74 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
333 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
102 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
38 views

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

Consider the group $\mathbb{Z}^{\ast}_p$ where $p = 8631907183416457710036142986950248939902071925468562052182263723074665 2812723253836453003270766004614328295206393288529828311628415785652726 ...
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0answers
110 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 ...
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0answers
45 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
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1answer
65 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
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0answers
21 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
100 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
91 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 ...