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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41 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; ...
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2answers
279 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 ...
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0answers
22 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 $m=-1$, $b=2$
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1answer
37 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.
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0answers
23 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 $\quad$ $(a + b)^n = \sum_{m=0}^n C_n^m a^{n - m} b^{m}$,...
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18 views
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18 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 $b$ ...
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40 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 ...
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1answer
65 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 ...
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2answers
54 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 ($r_{n_{k}}$...
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2answers
57 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!
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2answers
49 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 ...
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0answers
50 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 ...
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1answer
85 views

How is it possible to teach probability theory without sigma fields?

In introductory undergraduate probability courses, even those with a focus on set theory, I've often seen the definition of a sigma field entirely skipped over. Indeed, I've often seen the definition ...
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0answers
27 views

Explain random variables in analog derterministic terms

I struggle to explain discrete and continuous random variable, what it mean to integrate in terms of Ito, covariance as a measure for how much two variables jointly vary, and the like. It would be ...
2
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2answers
84 views

An algorithm to check if two polygons have the same area

With Euclid's propositions I.45 (constructing a rectangle equal to a given polygon) and II.14 (constructing a square equal to a given rectangle) one can reduce the comparison of areas of polygons (...
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2answers
128 views

How can I develop “mathematical thinking” as a student? [closed]

In my humble opinion as a math student and considering that my main area of interest is computer science, I see that one of the most important skills required to solve problems is the mathematic ...
4
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1answer
98 views

Teaching a differential equations course to computer science majors

I am currently teaching an undergraduate course on elementary differential equations in a mixed class of natural science (physics, chemistry, biology, etc) and computer science majors. Since none of ...
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2answers
105 views

Find a solution of $t\frac{dy}{dt}=t^2−t$ and determine a function $y(t)$ that passes through the given coordinates $(t, y)$ [closed]

Find a solution of $t\frac{dy}{dt}=t^2−t$ that passes through the points: i) $(0, 1)$ ii) $(0, 0)$ iii) $(1/2, 1/2)$ iv) $(2, 1/4)$ SOS: I don't know where to start and my professor is no help.
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1answer
148 views

Why are AM-GM inequality related exercises so popular

Everyday I visit this site I come across plenty AM-GM inequality related exercises. Where I went to high school (Switzerland) we were never taught this inequality. I thus fail to see the need to talk ...
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0answers
25 views

I want to write an algorithm for two circles intersection and touching cases . How can I do it with a quadtratic equation? [duplicate]

Given that two circles with coordinates (x1, y1) and (x2, y2) and radius r1 and r2 respectively . I need to find an equation , which can be used in code to to find the coordinates and the presence of ...
2
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2answers
518 views

Is undergraduate “complex analysis” actually kind of “complex calculus”? Please provide references. [closed]

As far as I know: After Calculus I, II and III, math majors have basic real analysis that covers topics including uniform continuity, Riemann-Stieltjes, Bolzano-Weierstrass and is mainly proving ...
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2answers
62 views

Interesting example of linear congruence

I am about to give a talk on linear congruence to high school students. Can you suggest an example of linear congruence that will immediately make students fall in love with linear congruence?
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1answer
56 views

Find X in the Equation

I'm not a mathematician and I have forgotten about some basics in mathematics. I have this equation: $$x^y \pmod z = w$$ Given $y, z,$ and $w,$ how will I find $x$? How will I get the equation for $...
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1answer
32 views

The definition of “term” and its use in teaching algebra especially distribution

Context: While teaching algebra I taught the distributive property of numbers. For any number A, B, and C, the following holds. $$A(B+C)=AB+AC$$ (Recall juxtaposition symbolizes multiplication.) ...
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1answer
93 views

Surds (or square roots) and Irrationality

Sorry if this has been asked before, but can't find what I'm looking for on here. I'm currently preparing an early lesson for my new A-Level class about surds. I'd like to be quite formal and ...
3
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0answers
58 views

Math Major Having Trouble [closed]

I am a freshman at Alfred University. I've been out of school for 6 years and am returning as a non-traditional student. I'm having some trouble that I hope someone may have insight for me. I love ...
1
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0answers
116 views

What subjects to study to improve “mathematical maturity/fluency” to learn more efficiently?

tl;dr: What advanced math subjects should I study to be able to learn new material more efficiently? I recently finished undergrad as a computer science major, but in my current work there's a ton of ...
0
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3answers
111 views

How do I solve $z+z^{-1}=2\bar z$ using $z=x+iy$ and $\bar z =x-iy$ substitution? [closed]

How do I solve $z+z^{-1}=2\bar z$ using $z=x+iy$ and $\bar z =x-iy$ substitution? zconjugate is also $\bar z$ in some countries.
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1answer
55 views

O is the orthocentre of △ABC if and only if AP⊥BC, BR⊥AC and CQ⊥AB. Prove that angle OPQ= angle OPR

enter link description here O is the orthocentre of △ABC if and only if AP⊥BC, BR⊥AC and CQ⊥AB. Prove that angle OPQ= angle OPR
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2answers
35 views

Let $f$ be an entire function such that image of $f$ lies in $L=\{2+iy:y\in R\}$ if $f(2+i)=2+i$ then show that $f(z)=2+i$ for all $z \in C$

Let $~f~$ be an entire function such that image of $~f~$ lies in $L=\{2+iy:y\in R\}$ if $f(2+i)=2+i$ then show that $f(z)=2+i$ for all $z \in C$
5
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1answer
159 views

Differential Geometry or Functional Analysis? [closed]

I am starting my Master's degree, and I have to chose between these two courses that I have not taken during my Bachelor's (I can only chose one!). I am interested in group theory and in particular ...
0
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1answer
39 views

does every algebraic concept theoretically have an equivalent geometric concept?

I had a student ask what the relationship of algebra and geometry is. does every algebraic concept theoretically have an equivalent geometric concept, even if it's impossible to draw/picture/...
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2answers
1k views

Do Math Professors still do textbook problems to learn subjects foreign to them? [closed]

This question is very subjective and is of no technical detail, however since MSE is a place for working mathematicians, I thought I'd ask here to get the best answers! As a prospective graduate ...
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1answer
35 views

An algorithm to convert a number to a decimal

Does anyone know a simply conversion algorithm to turn a number range of 1 to 10 into a decimal range of .5 to 1? Even more complicated (to me), another algorithm to covert a range of -1 to -10 into ...
3
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1answer
48 views

What can I teach to non-maths major undergraduates in a $10$ minutes session?

I will be giving a $10$ minutes teaching session and my audience consists of five to six possibly non-maths major first year undergraduates in Asia. I am free to choose any topic for the session as ...
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0answers
31 views

Creation of inequality problems

How are inequality problems created? I refer to both the problems from olympiads and problems encountered in a real analysis course. Could anyone give me examples of problems you created involving ...
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1answer
40 views

What's the name/theory of the equation 7.11 in An Introduction to Probability Theory and Its Applications, 3rd Edition? [closed]

I'd like to find the same equation 7.11, inside the book An Introduction to Probability Theory and Its Applications, 3rd Edition, that is the equation: $ q_n \sim \frac{1-px}{(r+1-rx)q} \cdot \frac{1}...
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5answers
82 views

Name of a matrix with one column and row removed

I am looking for the exact name of a matrix where the i-th column and rows have been removed. I cannot remember how it is named in linear algebra, does anyone got an idea? Thanks!
0
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1answer
71 views

how to calculate volume in(liters) for a specific height in horizontal cylinder

I have horizontal cylinder with diameter = 193.04 inches and length = 548.64 inches I want to find the volume of an oil at specific height with the help of some formula. I came across below formula ...
0
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1answer
29 views

Is the speed at which someone does math inborn, or can it be increased through practice?

Is there scientific evidence (or at least personal experience) that shows that daily practice of math problems increases the speed at which those problems are solved? Mind you I am not talking about ...
5
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1answer
52 views

The convenient approach to a calculus problem in two variables

A student came to me with the following problem. Construct a function $g \colon {\Bbb R}\to {\Bbb R}$ such that the function $f \colon {\Bbb R}^2 \to {\Bbb R}$ defined by $$ f(x,y)= \begin{cases} \...
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0answers
75 views

How to create educational linear algebra animations?

I'm looking to create animations for a linear algebra course. I need things like writing and changing equations, including matrices, plotting of 2- and 3-dimensional axes with points, vectors, lines ...
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6answers
3k views

Is there a sufficiently reachable plausibility argument that $\pi$ is irrational?

I was teaching someone earlier today (precisely, a twelve-year-old) and we came upon a problem on circles. Little did I know in what direction it would lead. I was able to give a quick plausibility ...
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5answers
4k views

Is there much benefit in memorising proofs outside of an exam setting? [closed]

This is a question I have been thinking about for a while, which seems especially important as I hope to transition from undergraduate to graduate study in the next year, where studying for an exam ...
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2answers
148 views

Learning math while visually impaired

My eyes are destroyed. I have been unable to learn math beyond decimal division in school due to laziness and unhelpful teachers. I am now trying to mitigate this mistake by learning math from the ...
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3answers
92 views

Fermat's Last Theorem Resources

Are there any resources which describe FLT in a very tangible way which will motivate students to be interested in this subject?
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2answers
50 views

How would you explain commutativity of multiplication of naturals to kids?

I would do it like this, and you? Put in a rectangular basket apples in such a way that you have three rows and in every row 4 apples, then you have 3x4 apples in the basket. Stay where you are and ...
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1answer
468 views

How does this nursery rhyme pertain to power series: “There was a little girl Who had a little curl Right in the middle of her forehead…"

This is from The Way of Analysis by Strichartz, chapter $7$, section $7.4$, page $276$. He writes "In discussing power series it is good to recall a nursery rhyme:" "There was a little girl ...
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0answers
97 views

Writing for the purpose of showing that one knows something

Several styles of writing about mathematics are appropriate in different contexts. A mathematician writes something to be read by other mathematicians. A mathematician writes something to be read by ...