Questions related to the teaching and learning of mathematics.

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0
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2answers
14 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
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5answers
61 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 ...
3
votes
0answers
33 views

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
33 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
53 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 ...
1
vote
3answers
44 views

What the terms Basis function and Orthogonal denote in case of signals?

I am a beginer. I have read that any given signal whether it is simple or complex one,can be represented as summation of orthogonal basis functions. Also,there are many ways through which basis ...
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
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0answers
14 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
55 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
20 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
26 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
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0answers
33 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
50 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
72 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
86 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
162 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
111 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
39 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
861 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
162 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? ...
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
82 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
36 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
253 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
138 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
votes
0answers
36 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
vote
2answers
53 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
179 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
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
votes
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
vote
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 ...