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Questions tagged [education]

For math 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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Seeking advice on this method of calculating the square of an integer

#Hi all. I would like to ask for advice on this method of calculation Example 1. 19 multiply by 19 Multiply 9 by 9 to get 81, then carry over (8) so we have 1 Bring 19 plus 9 to get 28, then bring ...
kajami 001's user avatar
1 vote
0 answers
14 views

Historical Account on the Solution of the System of Quadratic Equations in the Doubling the Cube's Double Mean Proportion

What related articles and RRLs can you share for the validation of the Historical Account on the Solution of the System of Quadratic Equations in the Doubling the Cube's Double Mean Proportion? Below ...
Annauen Ravacio's user avatar
1 vote
2 answers
100 views

Prove maximum of $p\cdot(1-p)^{n-1}$ is at $p=\frac{1}{n}$ without differentiation

I would like to do a proof with my high school students that for $0\le p\le 1$, the maximum of $p\cdot(1-p)^{n-1}$ is reached for $p=\frac{1}{n}$. Proving this with differentiation is quite trivial, ...
Daniele's user avatar
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0 answers
87 views

Book recommendation for mathematical physics [closed]

Recently, I was going through some of the mathematical physics books (online) : three of them are Arfken , ML Boas and Riley I want to know what are the prerequisites required for the each of them ...
CP of Physics 's user avatar
3 votes
0 answers
68 views

Math programs in Russia and post-Soviet states - how do they compare to US?

I studied math in college and also took a few years of Russian. For a time, I was looking for a way of living in Russia post-graduation (well before the recent war) and I asked one of my professors, ...
David Anderson's user avatar
14 votes
2 answers
661 views

Can the definition $i=\sqrt{-1}$ be made sense of rigorously without using $\mathbb R^2$ or similar construction of complex numbers?

For me, the natural way to define complex numbers seems to be to take $\mathbb R^2$ and then define addition and multiplication on top of that an boom, you have complex numbers. You then pretty ...
user1747134's user avatar
0 votes
0 answers
51 views

Challenging yet accessible problems for middle school students

I'm currently working for a Math summer camp and am tasked with providing 7th grade students with math problems that are challenging yet accessible problems that could be solved by most students ...
Michael's user avatar
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1 answer
39 views

Expression for dividing by 100, based on the number of factors, minus one factor.

I'm trying to convey a way to calculate the aggregate device downtime in a proposal that I'm writing, and I'm struggling, since I don't have a formal higher-math background. My premise is that, if x ...
user501798's user avatar
0 votes
1 answer
22 views

Fraction word problem that a total includes uneven groups

There are red, blue and yellow pens in a box. The ratio of the number of red pens to blue pens is 2:3. The ratio of the number of yellow pens to the total number of red and blue pens is 5:6. What ...
Mark K's user avatar
  • 181
-3 votes
0 answers
47 views

Area of a quadrilateral with only sides [closed]

Well, this is very simple Question but I am not good with Maths. Can someone suggest me what is the area of an irregular quadrilateral with sides measurement as A, B, C and D. Here A < B < C <...
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1 answer
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How to express the originals system of equation in terms of its Groebner bases?

As a network engineer I need to explain some mathematical stuff to my fellow coleagues. Particularly, I need to explain the fact the the Groebner Basis will create an equivalent system. One particular ...
Tuong Nguyen Minh's user avatar
0 votes
1 answer
99 views

Are mathematical journals generally readable for graduated students? [closed]

I'm an undergraduate-level self-taught mathematics student. I'm estimating I might be around the second year of the degree on mathematics in terms of general knowledge. While I love the subject, i'm a ...
Simón Flavio Ibañez's user avatar
2 votes
1 answer
138 views

does dx equals to (x+h)-x? If it is, why isn't it explained like this?? [duplicate]

While I was looking at a question regarding derivatives, I suddenly got enlightened when I realized, $dx=\lim_{h\rightarrow 0} (x+h)-(x)$ I noticed this while considering on the equation $\frac{df(x)}{...
Emin Bedir's user avatar
1 vote
1 answer
109 views

Teaching material for a one hour refresher on probability theory (conditional probability)

I have been teaching a course on stochastic processes to master students in theoretical physics, and half of my students seem to have never taken a probability course and struggle with some basic ...
stochastic's user avatar
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1 vote
0 answers
92 views

Elegant way to write $g(f(x))$

I've a very ugly expression: $$ \frac{d^2 g(f(x))}{d (f(x))^2} \, \left( \frac{d f(x)}{dx} \right)^2 + \frac{d g(f(x))}{d f(x)} \, \frac{d \left( \frac{df(x)}{dx} \right)}{d f(x)} \, \frac{d f(x)}{dx} ...
Federica Guidotti's user avatar
3 votes
3 answers
642 views

Fraction word problem that dividing a whole into equal parts

Alice, Grace and Pauline shared the cost of a present for their father equally. Alice used $\frac{2}{3}$ of her money, Grace used $\frac{3}{4}$ of her money, Pauline used $\frac{2}{5}$ of her money. ...
Mark K's user avatar
  • 181
0 votes
1 answer
81 views

Show that GF(81) is an $x^{26}+x^{8}+x^{2}+1$ decomposition field

I tried decomposing the polynomial, but after taking out $(x^{2}+1)$ you have to break the remainder into polynomials of degree 4, which is manually hard. Perhaps this is solved by using Frobenius ...
mackenzie's user avatar
9 votes
3 answers
455 views

Circular definition of continuity

When evaluating limits, it's tempting to just plug in the approach value into the function to get the answer. For example, if $f(x) = x^2$ and we need to solve $\lim_{x \to 2}(f(x))$ then we want to ...
Lauren S's user avatar
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0 votes
0 answers
18 views

How does the name group/ring reflect the nature of group/ring as an algebraic structure? [duplicate]

The names group / ring were chosen before we carefully study them. So now in a retrospective way, can we say that these namings capture the good nature of the corresponding algebraic structures? What ...
corindo's user avatar
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1 vote
0 answers
62 views

Why number 6 is the most frequent gap when subtracting all consecutive primes(the smaller from the larger)?

Using JavaScript, i felt like collecting all the distances between primes and see what pattern they may have. here is what i got: i generated all primes up to a 1000000, and made an object that counts ...
ZAK's user avatar
  • 11
2 votes
1 answer
342 views

Can a connected planar graph have 10 vertices and edges? is this possible?

Can a connected planar graph have 10 vertices and edges? is this possible? Using Euler’s formula, $V − E + F = 2$. $10 − 10 + F = 2$, Therefore $F = 2$. Do I also need to use this formula: $2E$ $\geq$ ...
Glo's user avatar
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1 vote
1 answer
110 views

*easy* examples of fact in one area of maths proven by a different area of maths

Example (something I raised my hand to ask when I was in secondary school): How do you know that $\dfrac{a!}{b!(a-b)!}$ is necessarily an integer whenever $a$ and $b$ are natural numbers such that $a&...
Chris Sanders's user avatar
0 votes
1 answer
53 views

Find the difference of $4b^3 + 6b - 7$ and $-12b^2 + 11b + 5$. [closed]

Trying to make some sense of this seemingly easy problem: Find the difference of $4b^3 + 6b - 7$ and $-12b^2 + 11b + 5$. Trying to prepare for my Algebra 1 final, which is a week from Thursday, and ...
YourLordJoyBoy's user avatar
3 votes
1 answer
88 views

Historically, when have the the real numbers been constructed via the "positive" (non-negative) reals first, and then usual real numbers second?

There has been something that has been bugging me for the longest time, at least since grad school. In the teaching of mathematics, during the construction of the "usual" real numbers, why ...
Rex Butler's user avatar
  • 1,642
0 votes
1 answer
94 views

How to make polynomials with so many exponents and variables within said terms easier to solve [closed]

Look guys, I want to level with you. I am reaching the end of my 4th-5th algebra 1 or MAT 101 class in college, and this is one of the classes I need to graduate altogether so it, in of itself, is ...
YourLordJoyBoy's user avatar
2 votes
2 answers
182 views

Just a simple algebra question

So I have this question: Solve: x = 3y, (a) x + y + z = 56, (b) x - 2y - 3z = -25 So you can substitute 3y for x to then eliminate the z by multiplying (a) by -3z then solve accordingly and you get z =...
Hogarth's user avatar
  • 21
0 votes
0 answers
24 views

question regarding the solution of a differential equation

I want to solve the question : $\frac{dy}{dx}= \frac{ln x}{xy}$, $y(1)=2$. Using simple calculus, we have $\int y dy = \int \frac{lnx}{x} dx$ $\frac{y^2}{2} = \int ln|x| d(ln|x|)$ and we reached the ...
G.t.g.h's user avatar
  • 161
0 votes
1 answer
34 views

Appropriate model to represent negative numbers

Negative numbers can be introduced by means of temperature, but it does not make sense to multiply two negative temperatures. Moreover, it is even objectionable to say 20°C is twice as hot as 10°C. A ...
apprenant's user avatar
  • 756
1 vote
0 answers
31 views

Inequalities. The method of rationalization.

Can someone explain me how to how to solve this task? $\frac{log_x(2x^-1)log_x(2x^2)}{log_2x(x)log 2x^-2(x)}\ < 40$ Screen of an inequalitie Well, I found the range of acceptable values. $x > 0$...
Matvey Belonogov's user avatar
-2 votes
1 answer
129 views

Prove that the statement $(1+2+3+ \cdots + n) \mid (1^m+2^m+3^m+ \cdots +n^m)$ is true for all odd numbers $m$ [closed]

My first idea to this problem is proved by induction (obviously by induction). So I tried to solve it by Induction, but after 30-45 minutes it just didn't give me enough information to prove it. Also ...
Lim Zhao Sen's user avatar
0 votes
1 answer
72 views

Great Picard theorem for $e^{\frac 1 z}$

In accordance with the Great Picard theorem, the function $f(z) = e^{\frac 1 z}$ assumes every complex value except $0$ in every neighborhood of the origin. I would like to know an elementary ...
AlpinistKitten's user avatar
3 votes
1 answer
140 views

The positive Laplacian is indeed the negative Laplacian

I know this question sounds like a joke. And it probably is:). I found it kind of annoying, but also interesting, to call $-\Delta=-\sum_{j=1}^n\partial^2_{jj}$ "the positive Laplacian" as ...
Liding Yao's user avatar
  • 2,269
0 votes
0 answers
59 views

Mathematical Logic Textbooks [duplicate]

Undergraduate (not graduate, the linked post is a bit too advanced) here looking for a logic textbook reference. Here’s a bit about me: Experience with basic proof-based linear algebra (Linear ...
RD Healthcare's user avatar
-4 votes
4 answers
110 views

why is the co-prime part not mentioned in the definition of the rational number?

Proving $\sqrt{2}$ an irrational number is a quite popular exercise, in precalculus courses, but if we look clearly the definition that is introduced, in the beginning of the course, it never ...
Yanjan. Kaf.'s user avatar
0 votes
1 answer
32 views

Extracting the vector field from equations

Given the following equation: $$ \dot{\Theta} = \operatorname{sgn}(z) \sqrt{| z |} $$ $$ z = \dot{\Theta}^2 \operatorname{sgn}(\dot{\Theta}) $$ $$ \dot{z} = 2 \sqrt{| z |} \ddot{\Theta} $$ how can I ...
Federica Guidotti's user avatar
0 votes
2 answers
46 views

From $z = \dot{\Theta}^2 \operatorname{sgn}(\dot{\Theta})$ to $\dot{\Theta} = \operatorname{sgn}(z) \sqrt{\left| z \right|}$

I read on a scientific paper (*) the following equations: $$ z = \dot{\Theta}^2 \operatorname{sgn}(\dot{\Theta}) $$ and then: $$ \dot{\Theta} = \operatorname{sgn}(z) \sqrt{| z |} $$ Could you tell me ...
Federica Guidotti's user avatar
0 votes
0 answers
18 views

How to calculate reversible speed value while accelerating

I am working on a special video editing task and I have faced some math problem I have video that I want to speed up for example to 200%, and to reverse (or 'cancel') it I need to do 100/200 * 100 = ...
Eugene's user avatar
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1 vote
0 answers
43 views

Ways to learn mathematics [closed]

I will be graduating with my bachelor's degree in mechanical engineering, in a few months, but I want to pursue master's in mathematics after 2-3 years. To prepare, I am currently doing "Advanced ...
Rohan Garg's user avatar
1 vote
1 answer
54 views

Easy to understand proof of Self-similar IFS fractal dimension

I'm preparing for a seminar talk on fractals, the topic is Self-similar IFS fractal dimension, proving the main theorem used: Given $IFS=\left\{ \mathbb{R}^{n};w_{1},...,w_{N}\right\} $ with ...
Nadav's user avatar
  • 479
1 vote
0 answers
69 views

Book recommendations and study aid; in need of a little help

Please excuse the placeholder header; I currently don't know what to put up there, yet I might change it in the near future! Today, I wanted to make a slightly different post and instead of asking a ...
b00nn1e's user avatar
  • 101
0 votes
2 answers
44 views

Query regarding approach to solve a given differential equation.

There's a equation $$N(t) = N(t)\frac{P(t,z)}{B}-C\frac{d(P(t,z))}{dz}$$ $$N(t) = A\frac{dP(t,z)}{dt}$$ Constants: B, C=3.9878*10⁻⁷, $A=0.11941$, Variables: N(t) is a function of t and is defined at a ...
Qwerty's user avatar
  • 101
1 vote
1 answer
99 views

why learning math in elementary school was harder for me rather than upper grades? [closed]

When I was an elementary student, I'd suffered from understanding basic things like multiplication table and other simple things and I had to memorized them. Last hours I was searching for genesis of ...
User14373's user avatar
-2 votes
1 answer
80 views

Is there anything currently that generates rejection from the mathematical community? [closed]

Is there anything currently that generates rejection from the mathematical community, as happened with the complex roots of algebraic equations?
FRED ANTHONY VIGORIA HUALLA's user avatar
0 votes
0 answers
57 views

Fundamental Branches of Mathematics

I'm trying to drill down to the core branches of mathematics and it seems to me that Algebra, Analysis and Geometry are the fundamental branches of mathematics––every other 'branch' (topology, number ...
polarise's user avatar
  • 123
1 vote
0 answers
70 views

Looking for an example for Fubini's theorem

I am preparing a lecture about Fubini's theorem. For me, in "real life" the most common application of Fubini's theorem is to "change the order of almost-everywhere quantifiers". I....
the_lar's user avatar
  • 781
2 votes
2 answers
111 views

How to train myself to not think visually for simple math problems?

I have a problem where it is often very difficult for me to solve simple math problems without thinking about them visually, but at the same time, I have poor spatial reasoning and so I'm unable to ...
asdfasdf's user avatar
0 votes
0 answers
62 views

Resources for designing math degree programs

I'd like to know where I can find resources which are helpful when one has to design or improve grad and undergrad degree programs in pure and applied mathematics. In particular, I'm searching for up-...
Uagi's user avatar
  • 151
1 vote
1 answer
115 views

Do the mathematicians/physicists that come up with these useful formulas picture the equations in their head? [closed]

For example in this three blue one brown video he shows the visualization of the derivative of x^2 it's relatively easy to see how it works and intuitively I could see how I could come up with this ...
Stef's user avatar
  • 93
15 votes
2 answers
1k views

When studying a book (like Rudin ) where the problems are not intended to be fully solvable by a student, what criteria show you're ready to advance?

When self studying a text where it is not expected to be able to solve all (or most) of the problems, what are the appropriate criteria to use for advancement? A word about the problems. There are a ...
SRobertJames's user avatar
  • 4,450
1 vote
0 answers
171 views

Doubt in proof of limit of $\frac{\sin(x)}{x}$ [duplicate]

Was reading Thomas Calculus and came across the limit of $\frac{\sin(x)}{x}$ at $x \rightarrow 0$. The method they used was comparing areas of sector and $2$ triangles to prove the inequality $\sin(x) ...
Macron's user avatar
  • 117

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