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How to find similarity ratio?

Helllo, I am not very good in math and I have simple question My question is: say I have 2 groups (A and B), where A has 17 pens (for example) and B has 13 pens. If 12 pens were the same from A and ...
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2answers
47 views

Geometric False Result Based on SSA Congruence Criterion for Triangles

I'm writing an article to warn students not to use SSA (Side-Side-Angle) criterion to prove congruence between two triangles. I'd like to add to the article an example of a geometric fallacy based on ...
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2answers
50 views

Should one always perform logical reasoning intuitively and contentually?

I have been studying mathematics for more than a year now. In general, it's relatively easy for me to solve the exercises and to find proofs for certain propositions myself. In this sense, I would say ...
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1answer
27 views

Conversion of Excel formula back to written Formula…if possible!

I turn to you as a last resort, in the hope that you will forgive my Maths ignorance and help me with what may be a simple problem. Essentially, this involves converting an excel formula to written ...
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38 views

what are the number of ways to select a 4 digit number with a 3 digit number always included? [closed]

Number of ways to select 4 digit number( X X X X ) should have three digit number ( say 1 2 3 ) It should be in same order.
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1answer
80 views

Does anyone know a no-nonsense intro to “logic for mathematics” that I can give to a Year 11 student?

I'm looking for material on propositional and first-order logic to give to a Year 11 student that explains how they're used "in practice." For example, I want to be able to write the null-factor law ...
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1answer
16 views

Plotting triangles based on a single point with distance and angle.

I'm tasked with creating an arrowhead within a pdf program. I have a single point with at $x=5.6$, $y=4$ this would be point A of my triangle I want to make the sides equal at $90$ degrees angles ...
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0answers
27 views

How can I make separate sentences or paragraphs? [migrated]

Hello I am new to Stackexchange and I'm trying to learn how to make separate sentences, paragraphs and to write proper math script. So, everytime I try to make a paragraph or separate 2 sentences ...
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1answer
44 views

Long Division and why we need it? [closed]

Why do we still teach Children Long Division when we'll never use it in life? Whats the point of all that stress vs a few strokes of a calculator?
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0answers
47 views

Applied mathematics job [closed]

I am on course applied math and I don't understand where can i find job by my education. Our teachers got their long time ago and others just working as teacher. My question: "Is there are opportunity'...
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1answer
37 views

Geometry and trigonometry Courses [closed]

I have recently finished my higher maths in Scotland which is equivalent to A-Level maths in the uk or APs in the USA (I think). I want to concentrate fully on geometry and trigonometry so I don't ...
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1answer
47 views

Integer solution to the equation below

I wanted to know integer solutions to the equation (1/k1) + (10/k2) + (100/k3) + ..... + (10^18/k19) = 1 (where k1,k2,k3.... are integers) which I believe is ...
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1answer
29 views

Proving the concurrency of angle bisectors in a triangle analytically

I'm taking a course at teaching and we have some geometry questions. Among the questions there was one I couldn't solve. I'm trying to prove that angle bisectors in a triangle intersect at a single ...
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0answers
18 views

Change the intersection's points of a paraola

I have the parabola $$y=-10\cdot x^2+10$$ I want to obtain a parabola which passes in $(-10^{-6},0);(10^{-6},0);(0,10)$. Is it possible to write the equation modifying the above equation? Thank ...
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26 views

how can i now position my character set in Pi?

i have characters (10 numerals) how can i count position number of beginning my collection in PI like ...
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0answers
22 views

Quick question regarding the work of a dynamical system

I'm sitting in on a course in dynamics and I've noticed something very strange that I can't get my mind around. So when they do problems that involve springs, they are saying that the work is $$U_s=-...
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1answer
47 views

Trying to prove that geometric and algebraic interpretations of the dot product are equal.

I am a Classics major trying to teach myself physics. I am on summer vacation at the moment, and I am going through a book called Classical Mechanics by J. Taylor. I am on the first chapter, and I ...
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4answers
453 views

How to stay motivated when solving diffucult problems? [closed]

From your experience, what is the most effective way to solve competition math problems without getting discouraged/frustrated because you cannot find the solution? For example, I was trying to solve ...
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0answers
54 views

How can I understand the step by step calculations for the formula from the blog below?

I am studying clustering and found a useful article on the blog post here Finding the K in K-Means. But I am having difficulty in understanding the formulas below and how I can do step by step ...
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1answer
40 views

Grading a question about the continuity of $f(x,y)$

If $\displaystyle \ \ f(x,y) = \begin{cases} \frac{3x^2y}{x^2+y^2}, &(x,y) \neq (0,0) \\ a, &(x,y)=(0,0) \end{cases}$ find the value of $a$ such that $f$ is continuous at the origin. I ...
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0answers
27 views

What topics would be included a restudy of mathematics? [closed]

Assume that up until this point my entire mathematics experience has been gone about in a terrible way. What topics would I start with in order to rebuild to a level in which I could approach ...
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0answers
25 views

Can somebody help me understand the formulas in the image below?

I got the image from this web site. The site talks about how to determine optimum number of clusters. I understand the first two but having a hard time to understand the last two. And what does "a ...
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1answer
22 views

Adding and Subtracting Powers of 10

I am entirely new to this subject and am already lost. The problem is Five x Ten to the power of Negative Two, + Four x Ten to the power of Negative Three. I was told that I have to make the exponents ...
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0answers
58 views

Online Video Lectures for Graduate Level Mathematics?

I am wondering if there is a nice compilation of good video lectures in graduate level mathematics? I mean a website, or a forum, or maybe something like course-era (which is mostly undergraduate ...
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4answers
855 views

Is advanced college math (eg analysis, abstract/linear algebra, topology) supposed to be as intuitive as elementary math? [closed]

So I don't know if I'm not smart enough for math, but lately, it seems to me as if some advanced topics are just too unintuitive in my opinion. For example, I have no idea what eigenvalues, ...
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4answers
625 views

Is it necessary to prove everything and solve every problem in the books? [closed]

I am an undergraduate really passionate about the mathematics and microbiology. I have few big problems in learning which I would like to seek your advice. Whenever I study mathematical books (...
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5answers
389 views

Simple Proof of the Euler Identity $\exp{i\theta}=\cos{\theta}+i\sin{\theta}$

My question is too simple. We know all that if we define the exponential function on $\mathbb{C}$ then we define the real part and imaginary part of $\exp{it}$ as $\cos{t}$ and $\sin{t}$. So if we ...
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0answers
85 views

Is group theory and in general pure maths useful in applied mathematics?

I've just finished the first year of Mathematics at University. I've already encountered groups, in a soft mini-course that took around half semester. My idea would be to study applied mathematics, ...
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22 views

What is the best way to teach trigonometry and higher level mathematics to young students?

I am teaching some kids (ages 13-15) some basics of functions and trigonometry in a summer camp. I have noticed that 90% of the class is above average and quickly resolve most of the problems. Soon ...
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5answers
488 views

Visualization of surface area of a sphere

I help mentor some really young, bright kids in mathematics. We were looking at geometric properties of various shapes, and one of the kids noted that the surface area of a sphere $S = 4\pi r^2$ ...
3
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1answer
126 views

Are there any modern mathematicians whose research interest is in “Probability Theory”? [closed]

I have seen professors in universities list "stochastic calculus", "stochastic analysis", "stochastic processes", "stochastic geometry" and "applied probability" as research interests, but are there ...
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1answer
33 views

How to solve task? With simultaneous movement

Sorry for my bad English. I was preparing for entry into physical and mathematical School high school in my city. But I am stuck while trying to solve this task: On a river, at the same time from ...
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15 views

problem on the concept equation

in this equation why we want to tend the epsilon to zero? What the application of this work? Do we want to calculate of limit value? enter image description here
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0answers
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Simple Composite of Relations

My lecturer has given this simple composite of relations question; R = {(1,2), (3,4), (2,1)} S = {(2, 1), (5, 3)} R o S = {(1, 1)} is the answer i acquire. he acquires the answer R o S = {(2,2), (5, ...
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1answer
24 views

Finite differential?

on my electronics book I found some equations in which there are $\Delta x$ and these are handled with the same rules of differential. For example, if $a$ is a constant: $$\Delta \left(ax\right)=a\...
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3answers
569 views

How do I accept that math is hard? [closed]

Ever since I began studying mathematics, there were times where I really enjoyed doing so, and then there were times where I didn't enjoy it at all and simply wanted to quit. I guess everyone knows ...
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2answers
520 views

Re-write a quadratic equation in another form?

$x^2 + \sqrt{2}x = \frac{1}{2}$ I need to find the real solutions for this equation and write it in this form: $$\frac{-\sqrt{A} \pm B}{C}$$ So when I work the problem out with the quadratic ...
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2answers
316 views

Do people with average intelligence stand a chance making a tenure track math professorship at a research university? [closed]

I am interested in math and have been thinking about going for grad school and becoming a research professor since graduating from college. However, a few things that happened recently really make me ...
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6answers
177 views

How to explain to a school kid that on a sphere the shortest path between 2 points is given by a great circle?

I will be teaching some "topology" to high school students. I was wondering how to explain to such a school student that on a sphere the shortest path between 2 points is given by a great circle? ...
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4answers
893 views

Roman Numbers - Conversion to decimal number

I have read that if a smaller number is to the left of a larger number means that the smaller number has to be subtracted from the larger number. Ok I can understand quickly for below Roman Numbers : ...
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1answer
48 views

How to create a counter example of a matrix with non orthogonal eigenvector?

I am trying to understand this orthogonal eigenvectors $$T = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{pmatrix}$$ let $$u ...
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1answer
14 views

How to find equation of a sphere

i'm having difficulty to find equation of a sphere in Mathematica. I already found the radius and center. ...
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3answers
126 views

The case for L'Hôpital's rule?

While this may seem very subjective — and, admittedly, my own dislike of L'Hôpital's rule is not entirely devoid of subjectivity — I am looking here for argumented, factual answers. From what I ...
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2answers
80 views

Studying mathematics as an Undergraduate [closed]

This is not a question related to a certain topic in mathematics, but more a question about studying mathematics generally. (please forgive me if my vocabulary isn't appropiate, I'm not a native ...
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2answers
62 views

Text for honors college algebra and trigonometry

I am looking for suggestions on algebra and trigonometry for students who are interested in majoring in mathematics. So typical texts written for average freshman who is forced to take math as a core ...
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3answers
283 views

How exactly does Mathematics help me becoming more intelligent (at least, in high school)? [closed]

[Please reditect me to a different site/sub-site/pretty-much-any-relevent-place if I've posted the question in the wrong forum, please do not downvote before attempting to redirect me to the adequate ...
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0answers
18 views

Technical Language Usage: Verb for an Equivalence Relationship “Forgetting” an Attribute that is “Modded Away”

This question is one of English usage, but I'm sure only mathematicians can answer it for me. I want to say in a technical report that an attribute is "ignored" or "forgotten" by an equivalence ...
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0answers
21 views

subtraction method

I have studied long ago different method for subtracting two numbers, for instance the borrow method or the Austrian method (I hope I am using the right names; I am not an english native speaker and ...
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1answer
76 views

How do I get good at calculus in specific, Mathematics in general? [closed]

I understand that this question might look like a duplicate to some others asked before, but I assure you, read on, you'll find my case different (hopefully). I am a 12 grade student from the ISC ...
2
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3answers
64 views

Switch from $a\cdot \sin(t) + b \cdot \cos(t)$ to $c \cdot \cos(t+f)$ [closed]

How could I switch from $a\cdot \sin(t) + b \cdot \cos(t)$ to $c \cdot \cos(t+f)$? Thank you for your time.