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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.

3
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2answers
55 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
votes
0answers
20 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 ...
4
votes
2answers
86 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 ...
11
votes
2answers
771 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
votes
0answers
51 views

Ways to learn mathematical analysis. [on hold]

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
48 views

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

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,...
0
votes
0answers
14 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
votes
1answer
56 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)$...
0
votes
0answers
18 views

Calculating error from angle measurement to distance [closed]

I have the following question. I have an instrument which shows an error of 0.125 seconds @ 150 minutes. what is my error in mm? I am searching for the formula? I am getting an error of 0.2 mm @300 m, ...
6
votes
0answers
93 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
votes
1answer
33 views

How to define a relation? [closed]

I have to define this relation but am not sure on how to do so. Could someone help me with this and walk me through the steps? Define a relation R on the set of all people such that aRb if and only ...
0
votes
0answers
53 views

What math should I learn to advance my career in Computational Geometry/Graphics? [closed]

I took (and excelled at) standard math in U.S. high school. Algebra, Trigonometry, Pre-Calculus, Calculus. In college, I continued with Calculus 1 and 2 (and didn't do nearly as well), intro-level ...
-2
votes
0answers
74 views

How can I define my equation mathematically? [closed]

My equation is : $$ H = (X-Y)/(X+Y)$$ Where $X$ is a probability (posterior probability) and $Y$ is a scalar value (its a unitless value ). $ X$ and $Y$ are the characteristics of data $Z = [z1,z2,...
0
votes
0answers
25 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
vote
2answers
42 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
votes
1answer
27 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
votes
0answers
16 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
votes
1answer
47 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
votes
0answers
41 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.
0
votes
2answers
36 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: $...
0
votes
0answers
15 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 ...
1
vote
0answers
17 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
vote
0answers
78 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 ...
0
votes
0answers
26 views

Ethics of using “By Observation” in Writing Math Textbooks

I was wondering, from a perspective of a professional mathematician trying to publish a textbook, how would one view the ethical issue of deliberately using terms like "By Observation" to cut short ...
0
votes
0answers
20 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 ...
0
votes
0answers
53 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 ...
3
votes
0answers
76 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
votes
3answers
234 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 ...
0
votes
0answers
25 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 ...
1
vote
0answers
21 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 ...
0
votes
5answers
84 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 = \...
3
votes
2answers
52 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 $\lessdot$ ...
1
vote
0answers
32 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 ...
-2
votes
0answers
11 views

How many periods of artificial payments would you make…

How many periods of artificial payments would you make if you are to buy a commodity for quarterly payments of Php (Philippine peso) 8,000.00 for 8 years starting two years from now? The answer for ...
1
vote
1answer
23 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
vote
2answers
27 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
votes
2answers
18 views

By M.I prove that? [closed]

$(2n)! < 2^{2n} (n!)^2$; How to prove this by mathematical induction ?
0
votes
1answer
38 views

By mathematical induction prove that? [duplicate]

$\frac{1}{n + 1} + \frac{1}{n + 2} + \frac{1}{n + 3} + ..... +\frac{1}{3(n) + 1} > 1 $; Here in this sequence after checking the basis for n = 1 , i.e $\frac{1}{4} > 1$, Which cannot be true; ...
0
votes
2answers
24 views

What does a vertical line through the top and middle portion of an equals sign mean?

I came across a new symbol in the paper Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach by Stefan P. Domino. What does this symbol mean? It looks like it's being ...
0
votes
0answers
19 views

Find an equation in standard form of the line having slope m and y intercept b

What form is this? It's not $ax + by = c$ The given slope, $m$, and intercept, $B$, is $m=-1$, $b=2$
0
votes
1answer
19 views

Operations with oriented angles

If I have the figure below, how can I get the angle $a_2$ (the angle is >0 in counterclockwise direction)? $$a_2 = \frac{\pi}{2} + a_1$$ or $$a_2 = \frac{\pi}{2} - a_1$$ ? Thank you for your help.
0
votes
0answers
20 views

How to solve this problem by induction method, and derive neumann formula?

Some explaination would be helpful if$\quad$ $a^n = a(a - h)....[a - (n - 1)h ]$ $\quad$ and $\quad$ $a^0=1$ $\quad$ then $\qquad$ prove $\quad$ $(a + b)^n = \sum_{m=0}^n C_n^m a^{n - m} b^{m}$,...
0
votes
0answers
15 views

How to write a Optimization-Problem with independent variable und constraints correctly?

I want to write a simple Optimization-Problem in mathematics way. for example: a function $f(x) = ax + b$ has independent variable $x$ and unknow parameter $a$ and $b$. The Parameter $a$ and $b$ ...
0
votes
0answers
39 views

Using $E[S]=E[Y]E[X_1]$ where $S=\sum_{i=1}^Y X_i$ where Y is also a random variable.

I had some trouble working on some problems and I would appreciate some help. 1), Let $\sum_{i=1}^{N}X_i=S$ where each X are iid and N is a random variable independent from all Xs. My goal is to ...
1
vote
1answer
24 views

Find a vector that will make the set linearly independent

I have a set of vectors in $\mathbb{R}^{3}$: $\Biggl{\{}$$\begin{bmatrix}1\\2\\3\end{bmatrix}$,$\begin{bmatrix}-2\\2\\-3\end{bmatrix}$,$\mathbf{\vec{v}}$$\Biggl{\}}$ I want to be able to find the ...
2
votes
2answers
46 views

Showing a sub-sequence ($r_{n_{k}}$) converges to $x$

There exists a bijection that $f : N → Q, x \in R$ *$r_{n}$:=$f(n)$ I am asked to show that there exists a sub-sequence ($r_{n_{k}}$) of ($r_{n}$) so that the limit of the sequence ($r_{n_{k}}$...
1
vote
2answers
54 views

Convert $\sum_{k=1}^n k^2(k+1)!$ to closed form

Convert the following to closed form. $$\sum_{k=1}^n k^2(k+1)!$$ I've been trying to solve this .. no luck. You don't have to solve the whole thing, just point me in the right direction. Thank you!
2
votes
2answers
35 views

How do i show n + k is a integral multiple of 11

(the digits of a positive two digit integer N are interchanged to form a integer)I don't know what this question means so I'm clueless and what do i do to solve? please in steps so i can understand it ...
0
votes
0answers
36 views

How to create math ( Geometry , Analytic Geometry ) worksheets

I apologize if this is not the site for such questions. But I need a software that can create math worksheets in geometry and also adding axes with viewing important points in the plane, basically I ...