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.

2
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44 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
39 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
169 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 ...
1
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0answers
73 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
87 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 ...
1
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3answers
36 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 ...
1
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1answer
63 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, ...
-1
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1answer
39 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
101 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 ...
28
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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 ...
1
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0answers
33 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
36 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
251 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
139 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
93 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 ...
3
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1answer
156 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
56 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
24 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 ...
4
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4answers
255 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
552 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
40 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
112 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 ...
12
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2answers
846 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}{\...
2
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0answers
67 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 ...
-3
votes
1answer
70 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
68 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)$...
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0answers
140 views

Graphical multiplication tables for $\mathbb{Z}/p\mathbb{Z}$ and $\mathbb{Z}$

Inspired by Burkard Polster's beautiful video on Times Tables, Mandelbrot and the Heart of Mathematics I wondered how this graphical approach to visualize the multiplicative structure of finite rings ...
0
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0answers
28 views

Prove by strong mathematical induction: Every natural number can be written as a sum of a power of 2. [duplicate]

For any positive integer n, n has a unique representation in the form: $$n = c_r 2^r + c_{r-1}2^{r-1} +\cdots+ c_2 2^2 + c_1 2 + c_0$$ where $r$ is non-negative integer, $c_r = 1$, and $c_j = 1$ or $...
1
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2answers
48 views

Solving $\sin x = \sin y$ by using the prosthaphaeresis formulas

I'd like to solve the equation $\sin x = \sin y$ by using the prosthaphaeresis formulas: $$ \sin(x)-\sin(y)=0 $$ $$ 2 \cos \left( \frac{x+y}{2} \right) \, \sin \left( \frac{x-y}{2} \right) = 0 $$ ...
0
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1answer
31 views

If $\sin(\beta+\gamma)= \sin\epsilon$ and $\cos\beta\cos\gamma<\sin\beta\sin\gamma$, then $\beta+\gamma=\pi-\epsilon$

I have the following system: $$\begin{align} \sin\beta \,\cos\gamma + \cos\beta\,\sin\gamma &= \sin\epsilon \\ \cos\beta\,\cos\gamma &< \sin\beta\,\sin\gamma \end{align}$$ In other terms: ...
0
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0answers
139 views

Cardan (or Tait-Bryan) angles z-x-y and rotation matrix - Proof

I'm trying to get the following rotation matrix (cardan angle sequence z-x-y): To do that, I multiplied the three elementary rotation matrices $R_zR_xR_y$, but the result is different: Can you tell ...
2
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1answer
75 views

Being less sloppy while doing exercises

I'm working through a pre-calculus course and I'm getting bad results while reviewing my exercises with the answers. It's not that I don't grasp the concepts, I make notes of the concepts, with ...
2
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0answers
53 views

Great Math Youtuber [closed]

Who's a youtuber that demonstrates math concepts really well with great visuals. The only other youtuber I watch on math is 3blue1brown and I'm looking for another one.
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2answers
45 views

Dot product between two vectors and its independence from reference frame

I found in the equation (2) here the dot product between two vectors and the author said that it is independent from the reference frame. What does it mean in this particular case? The notation is: $...
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0answers
23 views

Rotation with respect to the fixed/moving frame - Proof

I consulted many books to understand the proof of the formula corcerning the rotation with respect to the fixed/moving frame. Each author uses different notation and I am confusing. For example (slide ...
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0answers
140 views

Utility Function - Calculating consumer surplus

Consider the utility function $U(X_1, X_2) = X_1X_2$. Assume that the consumer has budget $M=18$, that the prices are $p1 = p2 = 1$ to start, and that the price of good $1$ rises to $p1 = 2.25$. Find ...
1
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0answers
114 views

Changing nature of mathematics from Bachelors to PhD [closed]

There is an obvious and explicit change in the nature of Mathematics education from Bachelors to Masters. In Bachelors, somehow, there are lots of books available to read and people enjoy working on ...
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0answers
32 views

Elementary geometry using vectors

Generally vectors are taught to students much after they have studied the Euclidean geometry. Is there a book that teaches classical elementary geometry using vectors, making for example finding ...
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0answers
56 views

What is the more primitive notion in the 'serious' study of math - exponentiation or multiplication?

As you get serious with math the first order of business is to learn some set theory and get $\mathbb N$ going with addition and multiplication. Then you will usually learn Euclidean division. Next ...
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0answers
116 views

Examples of functions that are not Borel measurable that will be accessible to 1st year undergraduates

While teaching statistics, I've grown sick of using terms such as "under (very) weak regulatory conditions..." and would like to be able to provide some solid examples of when these conditions are not ...
3
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3answers
240 views

Proving Sums or Products by Induction

I am currently teaching Extension 1 Mathematics and seem to be coming unstuck on a few induction questions. $$\sum_{k=1}^n\frac{1}{(2k-1)(2k+1)}=\frac{n}{2n+1}$$ First step is to prove the equation ...
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0answers
28 views

Digesting math heavy academic reading material

As anybody going through STEM-education, you'll be faced with reading material, possibly littered with mathematic formulas that you will not simply understand by merely reading it. What is your ...
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0answers
29 views

Difference between mathematical interpolation and numerical interpolation?

I have a data set of points. This data is not of full points. Instead, I have to generate a python code using tck = interpolate.bisplrep(xx, yy, zz, s=0) to ...
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5answers
169 views

How do I prove that $\sqrt 5 + \sqrt 7$ irrational?

I got stuck at : $a^2/b^2 = 12+2 \sqrt 35$ I understand that $12$ is rational and now I need to prove that $\sqrt{35}$ is irrational. so I defined $∀c,d∈R$ while $d$ isn't $0$ that: $c^2/d^2 = \...
4
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2answers
58 views

Reformulating the definition of compactness

Consider the following alternative definition of a topological space. Definition: A topological space is an ordered pair $(X, \lessdot)$ consisting of a set $X$ and a binary relation $\lessdot$ ...
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0answers
34 views

Problem for elementary school -find letter a number such that - $SEND+MORE=MONEY$ [duplicate]

Problem: Find the number for every letter(different letter is a different number) such that this equality holds. $$SEND+MORE=MONEY$$ My solution: Because idea of this problem isn't to solve it's to ...
1
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1answer
25 views

How to incorporate meaningful and purposeful technology into math lessons. [closed]

A big part of today's learning is centered around technology. As a math teacher, I sometimes find it difficult to incorporate meaningful and purposeful technology into my lessons. Are there any things ...
1
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2answers
61 views

Iteration to guess formula and simplify and use mathematical induction to prove right

I have this homework question, but my teacher didn't explain how to do these kind of problems too well. So basically the question is, Use iteration to guess an explicit formula for the sequence, then ...
0
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2answers
22 views

By M.I prove that? [closed]

$(2n)! < 2^{2n} (n!)^2$; How to prove this by mathematical induction ?