Questions related to the teaching and learning of mathematics.

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2answers
44 views

How to score a second try on a multiple choice test

Suppose a multiple choice question has $n$ answers. You allow a student $m$ tries. The student gets the correct answer on the $k$-th try. What is a "fair" score?
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1answer
31 views

Understanding and teaching the concept of derivative

I need to prepare an introductory lecture about derivatives and the concept of differentiation to a class of people with a general mathematical background (who have also studied calculus a few years ...
1
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0answers
18 views

Is there a standard notation for $(p_i-k)(p_{i-1}-k)(p_{i-2}-k)\cdots$ where $k$ is a small positive integer

For $k=0$, there is: $p_i\# = (p_i)(p_{i-1})(p_{i-2})\cdots(5)(3)(2)$ For $k=1$, there is: $\varphi(p_i\#) = (p_i-1)(p_{i-1}-1)(p_{i-2}-1)\cdots(5-1)(3-1)(2-1)$ Is there any other notation that ...
0
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0answers
30 views

Prob. 2.7-10 in Kreyszig's Functional Analysis Book: Is my solution good enough for anciliary purposes?

With valuable help from the SE community, I've managed to come up with the following solution to Prob. 10 after Sec. 2.7 in Introductory Functional Analysis With Applications by Erwine Kreyszig. I ...
1
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0answers
37 views

Ideas for math problem solving class for undergraduate students in university

In our university there is a huge gap between two group of students. a group of them came from Math Olympiad competitions and have a very strong background from high school but others, they have just ...
5
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4answers
667 views

Albert, Bernard and Cheryl popular question (Please comment on my theory)

Here is the problem, I think that there is one point that makes the question ambiguous, I think they should explicitly say the reason why Albert knows that Bernard does not know the date. Case 1: ...
4
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3answers
155 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
18 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? ...
1
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1answer
51 views

How I can solve this exercice? [closed]

We want to divide \$34800 over a group of people with equality. If there are 5 absent persons, The amount of each person of this group will increase to \$1160. How many of those persons are ...
3
votes
1answer
97 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 ...
8
votes
1answer
70 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
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0answers
50 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 ...
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2answers
89 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
32 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
240 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
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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
81 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
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5answers
61 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
131 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
35 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
50 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
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8answers
171 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
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1answer
45 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
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0answers
19 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
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1answer
54 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
122 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
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2answers
96 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
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1answer
22 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
30 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
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1answer
17 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
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1answer
54 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
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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 ...
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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 ...
1
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0answers
59 views

Undergraduate research in logic and/or algebra

I am currently an undergraduate in my junior year and am planning to do a yearlong project next year (essentially a yearlong undergraduate thesis). I am interested generally in algebra and logic, and ...
5
votes
2answers
88 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
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2answers
60 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
40 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
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1answer
10 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
18 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 ...
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0answers
38 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
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1answer
235 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
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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 ...
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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
52 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
78 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., ...
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0answers
15 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
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0answers
72 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
152 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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7answers
843 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 $4$ ...
1
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1answer
192 views

Late summer 2015 opportunities for undergraduate [closed]

I am an undergraduate who was just accepted into an REU (yay!), but it only runs through July meaning I will have all of August free. As such, I am looking for some opportunities appropriate for 3rd ...