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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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Hey I need help in determining the truth value of a proposition, im not too sure where to start. :( [on hold]

$\forall x \in R, x^2 \gt x$ this is the proposition but I just dont know where to start determining how to prove it
2
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1answer
34 views

Is there a symbol to mean “$x$ fits completely $v$ times in $y$”?

Is there a simpler way to write "$x$ fits completely $v$ times in $y$," i.e. is there a mathematical symbol or way to write for example: "32 fits 0 times completely in 4" or for example "32 fits 1 ...
2
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2answers
37 views

Soft question: solution strategies, how to attack the problem when using pen and paper?

Whenever I solve a problem (textbook or exams), I always copy key parts of the question to my paper where I'm doing my calculations, even though I have the problem in text-format right next to me on ...
0
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0answers
10 views

Modeling the relationship between dilations and area?

On a rather basic high school level I want my students to understand the relationship between the scale factor of a dilation and the area of the pre-image and image. For instance if a rectangle has a ...
3
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4answers
68 views

Methodology for Verifying Trigonometric Identities

Lets say I have an equation like: $$\frac{\sin^2x+\cos^2x}{\cos^2x\sec^2x}=1$$ Our teacher said you have to verify the equality by simplifying the left hand side or the right hand side without moving(...
1
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1answer
74 views

If a ray r emanating from an exterior point of triangle ABC intersects side AB at any point between A and B, then r also intersects side AC or side BC [duplicate]

Prove Proposition 3.9: If a ray r emanating from an exterior point of triangle $ABC$ intersects side $AB$ at any point between $A$ and $B$, then $r$ also intersects side $AC$ or side $BC$. Can ...
2
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1answer
25 views

What is a good motivation or analogy for the maximum likelihood estimation problem?

I am trying to think of a good motivation for maximum likelihood estimation. Given a set of random variables $X_1, \ldots, X_n \sim f_X(x_1, \ldots, x_n |\theta)$, the maxmum likelhood estimation ...
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0answers
25 views

Division first?

I was arguing with my friend about the order to solve mathematical equations. I introduced it the way I learned: Parentheses; Exponents; Multiplications and Divisions; (from left to right) Sums and ...
0
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1answer
19 views

Polydivisble numbers using base b

Picked the definition from wikipedia: A polydivisible number is a number with digits abcde... that has the following properties : Its first digit a is not 0. The ...
2
votes
2answers
51 views

Is It necessary to get a course in Algebraic Number Theory before grad studies?

I am in a predicament when deciding on classes for my graduating year of my undergrad next year. In first year I thought I wanted to be in physics so I didn't take proofs in second year, so it ...
0
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2answers
26 views

IQR , standard deviation

there is a a sample such that the standard deviation is significantly smaller than IQR? I think that no but how to prove this?
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1answer
33 views

Simpler terminology for determinant and other matrix terms [closed]

Wondering what words you could use to describe the following Matrix properties. Determinant Eigenvalues and Eigenvectors Identity Trace Adjugate Cofactor Conjugate transpose The prefix eigen- is ...
0
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0answers
46 views

What are the prerequisites for studying modern algebraic geometry? [duplicate]

I have studied differential geometry , thought of starting to study algebraic geometry , but it seems completely different from differential geometry . It uses lots of abstract algebraic tools . I ...
4
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1answer
112 views

Why are monoids not treated in most algebra courses?

I’ve taken a look at a number of introductory books on abstract algebra. They all treat groups, rings, and fields, and many of them treat galois theory, linear algebra, algebras over fields. But none ...
1
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1answer
50 views

If X, Y independent then X/Y and Y are independent?

if two random Variables $X, Y$ are independent Does that mean that $\left(\frac{\ X }{Y}\right)$ and $Y$ are independent? for example is it true that E[$\left(\frac{\ X }{Y}\right)$|$Y$]= E[$\...
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1answer
73 views

About IMC (Invitational international mathematics competition)

Last year I was invited to the international mathematics competition, however, I wasn't well prepared. Can you guys please recommend some books for me to read, in order to get better, at solving IMC ...
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2answers
48 views

Is this true formula :$\lim_{x\to -\infty } \exp (x)=\exp(-\infty)=0$ for student in high school level?

Inspectors of mathematics recomonded teachers that this formula $\exp(-\infty)$ as a second step for computation of $\lim_{x\to -\infty } \exp (x)$ as $x \to -\infty$ is not true in mathematics and ...
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2answers
57 views

Are there non-standard roads to research available for gifted students?

This is my first post here so I hope this is the right place to ask about this. I am a 22 year old math fanatic in Sweden and have been put in the awkward position of having self-studied quite ...
2
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2answers
73 views

Slick and fast linear algebra treatment for finite field extensions?

I am looking for a quick introduction to linear algebra that is slick (i.e., proofs are easy to follow and don't require handwaving); general and comprehensive enough to serve as foundation ...
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0answers
16 views

Software allowing one to play with various permutation groups?

An example of a game that is a permutation group is rubix cube. It is illustrative to see an example of a permutation group. It would be nice if there is a game/piece of software that includes ...
0
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3answers
33 views

Easy derivation for area of obtuse triangle

I am looking for an easy derivation for the area of an obtuse triangle. As everybody knows the formula for any triangle is the same: half the product of the base and its height. The derivation for an ...
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3answers
32 views

Combination question on forming a committee [closed]

A committee of 3 experts is to be selected out of a panel of 7 persons. 3 of them are engineers, 3 are managers, and 1 is both an engineer and manager. In how many ways can the committee be selected ...
2
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1answer
62 views

What do I need to learn, to understand Galois' solution of the quintic?

I studied maths to degree level many years ago, but never got a "gut feel" for any of the "pure maths" side, because the way it was taught didn't fit at all with how I learn. I focused on numerical ...
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0answers
10 views

How to use one set of concrete axioms to build another (smaller) set of abstract axioms.

Say you have a system where your only axioms are: All foo are 10. All bar are 20. All baz are 30. Then from these axioms you can see a pattern, so you say that the underlying axiom is this: All $x$ ...
0
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1answer
36 views

Is this Power Rule correct? [closed]

$\left(\frac{\ 1 }{(1+x)^{1+b}}\right)$ = ${(1+x)^{-(1+b)}}$ where x and b are any real numbers
4
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0answers
31 views

Math Lessons with Two Parts and a Combination

This is fairly open ended, so I understand if people consider this to be off-topic. I'm interested in creating math lessons where two groups each learn how to use a different simple math skill, and ...
2
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2answers
83 views

Where to go after Dummit and Foote?

I am taking general abstract algebra soon and am covering most of Dummit and Foote’s book up to Galois Theory. If one wanted to continue their study of abstract algebra after this, would they read ...
1
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1answer
46 views

How to test if data diverge significant from exponential distribution using the Chi-squared test

How can I test, if the following data diverge from the exponential distribution with $\tau = 2.197$? The data has the form: $0 \leq x \leq 0.5 :$ 194 $ 0.5 \leq x \leq 1 :$ 117 $1 \leq x\leq 1.5 :$...
0
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3answers
33 views

Periodic function such that integral of $|x(t)|$ is finite

I'm wondering if there is a periodic function such that the integral of $|x(t)|$ is finite. I tried with various functions, but the result is always infinite. Thank you in advance.
0
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1answer
34 views

Integral $\lvert x(t) \rvert^2$ implies integral $\lvert x(t) \rvert$ and vice versa - Proof

I'm wondering if the following implications are true. If yes, how can I prove them? $$ 1. \,\,\,\,\, \displaystyle{\int \limits_{- \infty }^{+ \infty }} \lvert x(t) \rvert^2 \, dt \implies \...
0
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2answers
25 views

Absolute value squared - Meaning

I'm wondering if it's correct to say that the absolute value squared means that the values above $1$ are magnified, whereas the values below $1$ are damped (I'm considering only positive values ...
3
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4answers
141 views

How do I apply algebra/calculus to everyday problems in my life? [closed]

I am still a senior in high school and want to major in computer science when I go to college this fall. I still struggle to see how algebra and calculus is really used to solve problems in the world. ...
0
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0answers
15 views

Time derivative of a matrix by using “cross product” (skew-symmetric matrix)

I found a strange way to do the time derivative of a matrix (see eq. 3.159 please). Can you help me to understand why $\dot{I} = \omega \times I - I \times \omega $? I think that $\omega$ is written ...
0
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2answers
58 views

Probability - Too simple but confusing - Why two different approaches for similar problems?

There are two questions and the approach seems to be different. a) Probability of choosing 3 queens from a deck of cards? Ans: 4/52 * 3/51 * 2/50 However, if the question is how many diamonds ...
0
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0answers
40 views

I cant solve this calculus gravitational problem.

Question: Given a ball of radius R of uniform density δ, and a point mass m of distance a from the center of the ball, assuming the gravitational constant is G, find the gravitational force of the ...
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0answers
17 views

Programming Equivalent PBL (Project Based Learning) in Math

I have been doing programming for about 4 years now and I have learned alot by working on projects such as: 2D Games, Websites, Web Templates etc... and I worked on these projects with my own will, ...
1
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1answer
24 views

Collecting cross product inside a matrix

If I have a matrix represented by three column vectors like the one below, can I collect the cross product as I did below? $$ [ \overrightarrow{a} \wedge \overrightarrow{b} \quad \overrightarrow{a} \...
0
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1answer
41 views

Joint Probability Density Functions example [closed]

Consider the jpdf $$f(x,y)= \frac{3}{13}(xy-x^2)$$ For $x\in[0, 2]$ and $y\in[3, 4]$. Calculate the probability $y$ is less than $x+2$
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4answers
47 views

Is this $p \to (q \to p)$ a tautology?

Is $P \to (Q \to P)$ a tautology? I undertand this: $P \to (Q \to P)$ $(V \to F = F)$ $(F \to V = V)$ $(F \to F = V)$ $(V \to V = V)$ Why this expression is a tautology, if, $V \to F$ is not ...
3
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2answers
41 views

A is x% more than B

I am taking the AMC10 test, and I don’t want to lose points on silly misunderstandings. When a question says “A is x% greater/less than B”, or things like that sometimes with money, which respect ...
0
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3answers
48 views

What is the name of this notation for sum?

In my kid's school (age 6) they are using a variation of cuisenaire rods to learn mathematics. When they are doing the operations on paper the notation used is this one:, it's designed to ressemble ...
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1answer
18 views

Symbolic statement that represents the circuit

im over here a tad bit confused. Ive been asked to write a symbolic statement that represents the circuit in this picture. Circut Image Problem is I don't understand how. I've searched this on ...
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3answers
25 views

Difference between the equation inequalities and absolute value inequalities

Using symbol lab I put this in $|x+4|\le |2x+10|$ and the answer I get is $x \le -6$ or $x\ge -14/3$, but when I manually worked out it was $\;x \ge -6\;$ or $\;x\ge -14/3$. My working out is in the ...
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0answers
45 views

STA 3033 - Tchebysheff’s theorem

I'm learning how to apply the theorem and I saw the example below and I'm not sure if that person got it wrong or it's just like that: The time that takes to complete a certain type of construction ...
3
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3answers
48 views

Building a function out of a given domain and range

How does one build a function while given domain and range ? For example, the domain $(0,5]$ and range $[0, \infty)$
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1answer
16 views

Help finding a math tutoring webinar

So, in addition to teaching I do some college math tutoring on the side, and my employer wants me to find and watch an online seminar of roughly one hour in length as part of my "professional ...
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1answer
50 views

What is the difference between AP Calculus and Calculus ? Calculus is a mat. analysis?

I study myself and study math in English. Khan Academy is my main resource in the development of mathematics, but there courses are made on the American system. I do not know how the AP Calculus of ...
2
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2answers
56 views

Percentage Probability of Products when Multiplying 2d10

This is my first post to any Stack Exchange, so I only think I know what I'm doing. In short, my objective is to design a math game for my elementary students to practice multiplication facts (math ...
4
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0answers
71 views

Arc length of a Polar curve as a Riemann sum

Suppose we have a curve in polar plane satisfying the equation $r=f(\theta)$ with $\theta\in[a,b].$ To find the area enclosed by this curve in this range of $\theta$ using Riemann integrals, we ...
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0answers
15 views

Symmetry of a planar system and product of inertia

I read the following sentence here: "The products of inertia occupy the off-diagonal positions and measure the asymmetry of the mass distribution with respect to the planes of the inertia frame of ...