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Questions tagged [education]

For questions related to the teaching and learning of mathematics. Note that Mathematics Educators Stack Exchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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1answer
22 views

Combinatorics, number theory, and graph theory, in what order should they be learnt?

Combinatorics, number theory, and graph theory, in what order should they be learnt? I would like to learn discrete math; these are the three main branches that compose it. I was wondering if there's ...
-1
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0answers
33 views

If any alternative numbering systems exist that simplify thinking about arbitrary numbers [duplicate]

In modern Western culture we think of numbers typically in base 10. By "we" I mean the vast majority of the public. For some reason this is easy, and I'm not sure why or how to pinpoint it down to ...
3
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3answers
64 views

What are some applications of mathematics whose objectives are not computations?

In mathematics education, sometimes a teacher may stress that mathematics is not all about computations (and this is probably the main reason why so many people think that plane geometry shall not be ...
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0answers
14 views

Curvilinear abscissa = radius * angle - Circular motion

I would like to understand why: $$ s(t) = r \, \theta(t) $$ where $s$ is the curvilinear abscissa, $r$ the radius and $\theta$ the angle in circular motion. Thank you for your time.
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0answers
62 views

How do I solve $\int_0^1 \frac {\ln \frac {x^2 + \sqrt 3 x +1} {x^2 - \sqrt 3 x + 1}} x dx$? [duplicate]

I don’t know how to solve this integral. Can someone give me a step-by-step solution to this, explaining how to get to the exact result, please? PS: The answers given in the other question may not ...
6
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5answers
507 views

Famous businessman mathematical puzzle ${}{}$ [closed]

question: A Businessman advertised two job openings for peons in his firm. Two men applied and the businessman decided to engage both of them. He offered them salary of $2000$ rupees per year. $1000$...
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2answers
28 views

Symbol for “take the positive solution of this formula”

I got a formula: x=√(((−2*aks)/(r*(s-k)*v))) Notice it is all wrapped inside a square root. When taking the square root, there are to possible outcomes as we all know. How do I denote that one ...
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1answer
34 views

How would you grade me on Monotonicity/Extremas task? [closed]

My question is specifically addressed to the people who have experience in grading students, however everybody's opinion is very much welcomed! The more, the better. Thank you. I do understand that ...
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0answers
13 views

hypothesis testing and confidence interval for a population proportion

I'm trying to understand why a basic undergraduate intro to statistics still uses the normal approximation to do hypothesis tests for population proportions. It used to be that the computations were ...
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0answers
26 views

The bare basics of linear algebra for multidimensional analysis?

As part of the first quarter of a very fast-paced undergraduate analysis course at my university, we had to learn linear algebra by ourselves from Sergei Treil's Linear Algebra Done Wrong (we did ...
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0answers
22 views

Measure of Improvement in Math Skills from Remediation with ALEKS

I am analyzing some data on ALEKS for my home institution. Specifically, I am analyzing placement scores for ALEKS where the students are allowed to take the placement test multiple times and are ...
7
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1answer
130 views

How to move forward in Mathematics Studies with poor foundation

So I discovered halfway through my first year university math term that my foundation of mathematics is very poor. I would memorize stuff rather than understand it and still get 95+ in high school so ...
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0answers
29 views

From direction cosine matrix to Cardan angles - Two different Matlab codes, different results

I have two Matlab codes to get the Cardan angles (ZXY sequence) starting from a given direction cosine matrix (dcm), but the results are different. Why? The dcm is: ...
0
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1answer
15 views

prevent time collision in N Course initiation for M Student

Hypothesis: we have n courses and m students. we decide to initiate a sample course program named ...
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0answers
47 views

List of mathematical notations - International convention [duplicate]

I'm wondering if exist a list of mathematical notations accepted internationally (book, handbook, textbook etc.). I tried to search online, but without success.
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2answers
25 views

Proof related to vectors: collinear points, position vectors

I'm wondering if the following sentence is correct: "Given 3 collinear points (A,B,C) and the relative distances (m and n), the position vector OC of the central point is mOA+nOB." EDIT: mAB+nAB=AB -...
2
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3answers
255 views

A path to mathematical proficiency

I have been looking for a new hobby and I have chosen mathematics. I was wondering what the path would be to self-teach (books, online courses/videos...free preferred) oneself to go from basic ...
0
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2answers
79 views

How do you like to take / store math notes?

I always have difficulty with things like this but how do you like to take and store notes for later reference? Paper and pencil? Physical books? Online notes? Where do you like to write them / ...
2
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1answer
59 views

Self-Teaching from Big Rudin

first post here so sorry if this question is answered somewhere, but I couldn't find it. I'll start with some background before the question: I've recently completed an undergraduate math degree, ...
1
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1answer
45 views

Theory of drawing (multivariable) functions (I am new)

My question is a bit different. When is it possible to draw a function? E.g a 4-dimensional vector space is no more imaginable. If we a function from $\mathbb R^2$ to $\mathbb R$, we can draw it 3- ...
3
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1answer
47 views

How to think about decimal exponents

I don't know if this is the right place to ask a question about middle school-level math, but I'll give it a shot. I don't have the background to fully understand related questions (like How to ...
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0answers
16 views

Difference between coordinate system and reference frame

I'm wondering what is the difference between coordinate system and reference frame. Maybe a reference frame is something physical (e.g. a rigid body), instead a coordinate frame is something ...
2
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0answers
40 views

What courses should I take in my Masters for PhD in mathematics - artificial intelligence? [closed]

I am currently enrolled in a masters programme in mathematics and I am taking mostly courses in mathematical statistics, but also dynamical systems and analysis. And I'm wondering if I want to go ...
0
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1answer
33 views

What to teach in a 20 minutes class about affine functions to middle school students?

Tomorrow I have to teach about affine functions ($f(x)=ax+b$) during 20 minutes. I want to know if someone has a suggestion what things I should teach. I want to make this into something interesting, ...
3
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2answers
158 views

Should we use “pythonic” indexing when teaching about permutations

When teaching abstract algebra for undergrads, I taught them that there is a permutation group $S(A)$ of automorphisms on any set $A$, and then defined the group $S_n$ to be the group of permutations ...
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0answers
23 views

Do cocycles “break” symmetry? [migrated]

In an article by A. Borovik, “Is mathematics special?”, he talks about the fact that carrying is a cocycle. He then says [A student] discovered that carry is doing what cocycles frequently do: they ...
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0answers
30 views

Finite Horizon Dynamic programming optimization (consumption-savings problem)

I am trying to solve this finite horizon dynamic problem (consumption-savings) using backward induction. Maximize $\sum_{t=0}^{T}u(c_{t})$ subject to $w_{0}>0, c\in [0,w],w(t+1)=(w_{t}-c_{t})(1+...
0
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1answer
58 views

What is the best way to learn mathematics? [closed]

As the title, I concern about what is the best way to learn mathematics. I've asked some of the professors in my university. Some said that I should intuitively understand mathematical concepts and ...
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3answers
32 views

Interpreting an agreement function

Consider the following function: $$ P = \frac{1}{n(n - 1)} \sum_{j=1}^k n_{j} (n_{j} - 1) $$ where for $n = \sum_{j=1}^k n_{j}$. Intuitively, this function measure concentration of values the ...
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1answer
60 views

Why was it that past mathematicians researched in multiple fields?

Looking at biographies of past mathematicians, I notice that these biographies state that these mathematicians had contributions to things like mathematics (obviously), physics, chemistry, biology, ...
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1answer
31 views

Pin Point Theorem & Pin Point-Reverse Theorem Calculation

I was given this question to do over the weekend by my professor and I'm at a roadblock. We wont over the theorem during class but I cant seem to find much about it. Any help in solving this would be ...
1
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1answer
93 views

Lost the love for Mathematics and want to find it again. [closed]

today I want to ask a question, that might sound a little bit strange. It all began when I was quite young, around 6-8 years old. At that time I loved mathematics, it was one of the topics I really ...
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6answers
3k views

Adult learner returning to maths [closed]

I've got a problem with regards to grasping and conceptualising mathematics. I've been out of education for around 15 years and was OK with maths in school. However, I missed a lot of high school due ...
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0answers
31 views

Suggestion of a topic to give a seminar on [closed]

I've been attending a seminar series titled Geometric Structures on Manifolds these past few weeks as a part of my semester requirements, and therefore I'm expected to give a seminar as well. The ...
1
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1answer
33 views

How to make a kid understand geometry and help him solve problems?

I'm tutoring a 13 year-old boy, a middle school student. He has almost no problem with elementary algebra: he just applies the rules and everything falls into place. However he does struggle with ...
1
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1answer
42 views

Nets of Dice - how to know if it is a Nets of Dice

I am school student and learning Visualizing Solid Shapes. In this chapter we have a concept that if piece of paper is cut in a net shape we need to prove that the same can be formed into a dice (...
5
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1answer
114 views

Who said (a variation of) this? “Mathematics didn't teach me how to reason correctly, but […] how easy it is to make an error when reasoning.”

I remember I once read a quote of a mathematician at the beginning of a book, or article, which said a (possibly) small variation of: Mathematics didn't teach me how to reason correctly, but at ...
0
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1answer
78 views

Will Math Ever Stop Using Paper? [closed]

This is an odd question, yet I must still inquire: will math ever stop using paper? In the writing industry, paper is dead; we do all our writing on computers. Yet with all of mathematics' complex ...
2
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1answer
131 views

Is pursuing a maths degree right for me? [closed]

I'm currently going torough the most humiliating moment of my life and I would really apreciate a honest advice from someone who works in the field of mathematical research. This year was my first ...
3
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1answer
47 views

Is understanding math deeply important at my level? How do I balance time spent understanding vs learning new mathematics? [closed]

My goal is to become a mathematician. I am just starting to learn math on khan academy. I solve the problems but I do not understand how or why what I am doing works and I have a lot of questions. The ...
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0answers
22 views

Rare Entropy sources and Hidden Markov

when selecting rare entropy sources for trng and one can see similarities trough an applied hidden markov model, will it be still good entropy? (structure is the same, even though type of source input ...
3
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4answers
221 views

Proof without words of the Quadratic Formula?

As suggested by @Moti and @YvesDaoust in this post, a simple way to identify the roots (red dots) of a parabola (given focus and directrix, blue) by means of straightedge and compass is to draw the ...
8
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3answers
541 views

Dealing with frustations at tests

I'd like to talk about some things that are quite often for me when dealing with math tests... I don't know if this is the right place to talk about it, so if it's not, please comment and I'll delete ...
0
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1answer
32 views

atan2 and Cardan angles - Problem with sign

I'd like to get the three Cardan angles starting from the below matrix and by using the function atan2. The problem is that I get two conflicting results. where $- \pi/2 \le \beta \le \pi/2$. If I ...
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2answers
102 views

Short mathematical proofs for teaching

I am looking for short proofs in order to illustrate undergraduate notions. Most of the time students struggle with technical exercises without having the time, before going on with the following ...
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2answers
835 views

Making modular arithmetic interesting for school kids

This is a pattern even school kids could discover (when gently pointed to). I never did conciously, and cannot remember to have been pointed to explicitly, neither at school nor later: $$\color{red}{\...
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0answers
56 views

Ways to learn mathematical analysis. [closed]

I'm studying mathematical analysis, more specifically differential calculus in $\mathbb{R}^n$, my main problems is that I didn't realize what is the best way to abbord some exercises, like what ...
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1answer
62 views

how to show that two stets of vectors have the same linear? [closed]

Let $v_1=\begin{bmatrix}1\\-2\\1\end{bmatrix}$, $v_2=\begin{bmatrix}2\\-1\\1\end{bmatrix}$, $v_3=\begin{bmatrix}-2\\-2\\0\end{bmatrix}$, $v_4=\begin{bmatrix}1\\-2\\-2\end{bmatrix}$ $S=\{v_1,v_2,...
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0answers
16 views

I need to know the formal-logical statement?

I thought it might be Q→(P∧ ¬R), but I also really do not understand. p = there is water in the cylinders q = the head gasket is blown r = the car will start Based on the above information, construct ...
5
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1answer
67 views

The role of constant of integration

Let us consider the following integral $$\int \frac{\sin x}{\cos^3 x}dx\, .$$ If we note that $\tan x= \frac{\sin x}{\cos x}$, we have $$\int \frac{\tan x}{\cos^2 x}dx = \frac{\tan^2 x}{2}+C \quad (1)$...