Questions related to the teaching and learning of mathematics.

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6
votes
4answers
286 views

The meaning of various equality symbols

I'm interested in knowing what is the meaning of the various equality symbols: $=,\sim, \cong,\approx,\equiv$. For example, the speed of a car $V$ in m/s: what would be the meaning of each of these ...
-2
votes
0answers
27 views

Couldn't find answer using the Fourier Transform and Fourier series

I am fond of Fourier series &transform. In Fourier domain we can come to know what frequency components are present and the contribution of each component in forming the given signal.But I ...
2
votes
1answer
46 views

What are the primary disadvantages of Dummit and Foote's abstract algebra text (3rd ed.)?

I have done a fair amount of research concerning which abstract algebra book to "settle down into"; that is, I wanted to pick an algebra text and really commit to it as my "primary text," more or ...
-2
votes
0answers
35 views

Solve the diophantine equation $n!=m^2-1$ where $n,\,m \in \mathbb{Z}_+$ [on hold]

Brocard's problem is a problem in mathematics that asks to find integer values of $n$ for which \begin{equation*} n!+1 = m^2, \end{equation*} where $n!$ is the factorial. It was posed by Henri ...
4
votes
1answer
104 views

What are the limitations of the Fourier Transform and Fourier series?

I am fond of Fourier series & Fourier transform. In Fourier domain, we can come to know what frequency components are present and the contribution of each component in forming the given signal. ...
2
votes
2answers
55 views

Explaining intersections to a 6th grader

$A=\{1,2,3,4,5\}$ $B=\emptyset$ How to explain to a learner from 6th grade the result for $A \cap B$ ? For a 6th grade student, it could be difficult to understand why the result is $\emptyset$. ...
1
vote
2answers
29 views

Help Finding the Equation of a Line with a Given a Point and a Slope

I have been receiving a lot of help today and I really appreciate it, I am nearing the end of my class and need help studying for my final. In my review I came across a problem that i am having ...
1
vote
2answers
23 views

Simplify the Complex Fraction

I am having trouble with the following complex fraction. I have simplified everything for the most part, but I am stuck on the last part and need to know what I have to do next. ...
0
votes
5answers
74 views

Help understanding how to factor completely $x^3-x^2-x+1$

I need someone to help explain the steps to completely factor the problem $x^3-x^2-x+1$. Here is what I have done so far: $x^3-x^2-x+1$ to $x^3-x^2+-1(x+1)$ Since there is a ...
6
votes
0answers
82 views
+100

How to fill my mathematical gaps?

To do the story short, I became interested in mathematics in a serious way like two years ago, I'm currently in graduate school, but the problem is that my mathematical background is not as good as ...
2
votes
0answers
35 views

A question on the remainders of integer division

This is a question on the remainders of integer division from my student. Notations. Let $p$ be a positive odd prime integer. We write $r_{i,j}$ for the remainder of $i \times j \div p$. Now for an ...
0
votes
1answer
57 views

What are the minimal mathematical prerequisites for starting to study Artificial Intelligence? [on hold]

This question is really broad as there are many aspects to the AI research. However, I just need a bare minimum of prerequisites that will allow me to approach any sub-field of the AI (coupled with ...
0
votes
4answers
34 views

Trignometry, Unable to solve this .. [on hold]

Prove that .. $$2\sec\theta=\frac{\tan(90-\theta)}{\csc\theta+1}+\frac{\csc\theta+1}{\cot \theta}$$
1
vote
0answers
22 views

Preparation for research in statistical inference for stochastic processes [on hold]

I am interested in building capacity to do research (and ultimately building a career) in statistical inference for continuous time stochastic processes. I am seeking advice on how best to go about ...
5
votes
1answer
58 views

How to get the most out of attending a conference talk or a research presentation?

I'll say up front that I imagine there's a resource for this somewhere, but I was unable to find it. I've been attending conference talks and research presentations for about a year at my university, ...
4
votes
1answer
25 views

Best program for creating educational math animations?

I'm looking for recommendations on what program to use for creating mathematical animations. These animations will be used in creating educational videos for high school math -- Trigonometry first, ...
0
votes
2answers
27 views

Get an alternate form of an equation

I am trying to prove the following limit value: $$\lim_{n\to \infty} \frac{n^3 + 1}{n^2 +1} = \infty$$ But how does $$\frac{n^3 + 1}{n^2 +1}$$ become this $n + \frac{1 - n}{n^2 +1}$?
0
votes
0answers
35 views

How many counts the square number?

For example I have a number is $55$. Can I check this for how many counts number's square create this number. For example I have $55$ So, I know this number total from 5 number, which are $$55 = ...
0
votes
1answer
18 views

Why is it important to recognize CRT establishes an isomorphism between $Z/p\#Z$ and $Z/qZ$

As I understand it, it is well known that CRT can be used to show that $Z/p\#Z$ as a ring is isomorphic to the product of the finite fields $Z/qZ$ where $q$ ranges over the primes up to $p$. For ...
1
vote
1answer
53 views

Is self study of proof-based mathematics difficult?

I heard from a renowned Mathematician that self study of proof based Mathematics is extremely difficult as there is not only right and wrong but also degree's of correctness. So without a teacher ...
3
votes
2answers
77 views

Why do we need to rationalize fractions? [duplicate]

Teachers often take off points from students who write 1/sqrt(2) instead of sqrt(2)/2. Why do we need to write it as sqrt(2) / 2 ? Where did that convention come from? Do we need to even do it? Why do ...
0
votes
1answer
46 views

High School Geometry problem with a triangle and trapezoid in a larger triangle.

In school, I have an assignment to write a problem for geometry students. I have written the following problem. Draw triangle ABC. Let the height have magnitude h. Draw a line segment, DE, which is ...
2
votes
0answers
88 views

Are “Transition Books” (Spivak/Apostol/Courant) really necessary?

Why do so many people recommend Spivak, Apostol, and Courant calculus textbooks, especially as a preparation toward the advanced courses like analysis and abstract algebra? Are they really necessary? ...
0
votes
3answers
61 views

I can't understand how to factor a quadratic

I can't figure out why some actions are possible in factoring $\frac{r–3}{r^2+11r–42}$. Factor the quadratic out of the denominator $\frac{r-3}{(r-3)(r+14)}$. This does not make sense how can $+11$ be ...
0
votes
1answer
30 views

Textbook error or my own error, Law of sines question.

A triangle with side 8 inches and corresponding angle 13 degrees, side x inches and corresponding angle 120 degrees. To answer this I set up a proportion: $sin(13)/8=sin(120)/x$ ...
6
votes
3answers
163 views

What are the differences in mental skills required to master abstract algebra and analysis?? [closed]

I had took undergraduate-level abstract algebra and analysis courses before. And I find I can do proofs in analysis faster than in abstract algebra. However some other students is opposite to me. I ...
-1
votes
0answers
49 views

Why do some mathematics professors teach more/less courses than others? [migrated]

Not sure if this belongs on the Academia site, but since I'm a math major and the question is based solely on my observation of mathematics professors, I figured this site would be best. At my ...
0
votes
2answers
35 views

Are the geometric sequences a subspace of all infinite sequences of real numbers

I'm a little confused about how to prove that the given infinite sequence is a subset of "the space of all infinite sequences." so V = subspace of all infinite sequence of real numbers so $$(x_0, ...
10
votes
0answers
113 views

Is it a good approach to heavily depend on visualization to learn math?

I am a third year undergraduate and I am a beginner on these "real mathematics" (no pun intended). Before contacting the "real math", my math level should be considered to be "good", although I was ...
1
vote
1answer
37 views

Applied Linear Algebra | Linear Dependent Matrix

Question: My response: Am I solving the above question correctly? Or am I on the wrong path? Thank you for your help.
0
votes
2answers
26 views

Applied Linear Algebra |

Question: Determine whether or not any column in the matrix is a linear combination of other columns. Provide a general method for answering the same question for any n x n matrix A. My response: ...
0
votes
3answers
56 views

Struggling with integration/differentiation

quick question as I'm sure this is simple but it has me stumped. I have to integrate and differentiate this equation. Not sure on the exponential, had a couple of goes but it doesn't look right. ...
1
vote
2answers
48 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?
1
vote
1answer
54 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
vote
0answers
19 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
votes
0answers
40 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
vote
0answers
42 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
votes
4answers
874 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
votes
3answers
163 views

Monotonous function or monotonic function

I am from a non-English speaking country. Should we say monotonous function or monotonic function?
0
votes
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? ...
3
votes
1answer
110 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
89 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
51 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
93 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
votes
0answers
37 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
votes
1answer
256 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
83 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
69 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
139 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 ...