For questions related to the teaching and learning of mathematics. Note that Mathematics Educators StackExchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

learn more… | top users | synonyms (3)

0
votes
0answers
19 views

Identity and equality [duplicate]

What is difference between identity and equality in math? when to use identity and when equality? Most of math identity also defined as equality how to distinguish between identity and equality. in ...
0
votes
0answers
25 views

Moving to UAE. I do plan to start my teaching career. [on hold]

I'm about to complete my master degree in the subject of Math. I've two options in my mind and I'm analysing which one to go with...! Option 1: I should go after completing my master degree, to UAE, ...
0
votes
2answers
119 views

How do mathematicians find the underlying idea?

While reading through the lecture notes here (http://www.math.ucla.edu/~tao/resource/general/131ah.1.03w/week2.pdf , page 22, last paragraph), I came across the following " Thus there must be some ...
2
votes
2answers
48 views

Variable in Math

What is formal definition of "variable" ? I cannot able to understand variable because some times it is varying or some time used for approaching. Arbitrary constant also confusing me. In Multi ...
2
votes
3answers
31 views

Intuitive explanation of second derivative test for functions of two variables.

I will be teaching multivariable calculus again this semester, and I am not so happy with the explanation I have for the second derivatives test for functions of two variables. QUESTION: What is a ...
-1
votes
0answers
37 views

Find the extreme points of the below polyhedral sets

Find the extreme points of the below polyhedral sets: (a)$$ P =\{(x_1,x_2,x_3)|x_1 +x_2 +x_3 ≤1,x_1,x_2,x_3 ≥0\}.$$ (b)$$ P = \{(x_1, x_2, x_3 x_4|x_1+ x_2+ 0.5 x_ ≤ 1, x_1 x_2,x_3,x_4≥ 0\}. $$ ...
9
votes
9answers
394 views

Motivation for the Definition of Compact Space

A compact topological space is defined as a space, $C$, such that for any set $\mathcal{A}$ of open sets such that $C \subseteq \bigcup_{U\in \mathcal{A}} U$, there is finite set $\mathcal{A'} ...
0
votes
2answers
16 views

Define temperature by clustering with math operators

I can´t figure out how to cluster the temperature for the weather in 3 optimal cases: hot, mild, cold My data contains: air temperature(the average daily value), max air temperature(highest daily ...
-1
votes
0answers
32 views

Suggest a topic for project in elementary math

I need to develop a project in elementary math of about 20 pages. There should be some new results in it. Please suggest me a topic which is relatively simple. It can be in either algebra or geometry. ...
2
votes
1answer
111 views

What are the (most) essential/interesting sections of The Princeton Companion to Mathematics a junior math student better have a read?

I am studying The Princeton Companion to Mathematics, but it is heavy, the sections have different difficulties, and time is limited for me. Assuming that I have only some knowledge of undergraduate ...
0
votes
0answers
17 views

Is there a big difference between runge kutta 4th for ODEs vs SDEs?

I was working on 2nd, 4th order runge kutta method for stochastic differential equations. I saw 2nd formula for ODEs and SDEs. There is some difference between their formulas . Unfortunately I can't ...
0
votes
1answer
29 views

Good math websites for elementary geometry and algebra?

I would appreciate it if someone could suggest good websites where we can find English written geometry and algebra exercises for beginners, say junior and senior high school students. I have ...
0
votes
1answer
33 views

Program languages recommended for complexity theory

I am an undergraduate studying mathematics and one of my interests include complexity and computability theory. I have no experience in programming. The computability theory books I looked into didn't ...
4
votes
1answer
69 views

“A real polynomial of degree $n$ cannot have more than $n-1$ local extrema”: a proof without derivatives?

I am looking for a proof that does not use derivatives of the elementary theorem given in the title: Theorem: A polynomial $p:\mathbb{R}\to\mathbb{R}$ of degree $n$ cannot have more than $n-1$ local ...
0
votes
0answers
10 views

Abbreviation of logarithmic sum of squared differences

I would like to find an abbreviation for the logarithmic sum of squared differences between two data sets. I am thinking of log(SSD) but it doesn't look so nice. Can anyone propose me something?
2
votes
4answers
50 views

For what values of $p$ does this series converge?

This is a question we asked on a second semester calculus test. For what values of $p$ does this series converge? $$\sum_{n=1}^{\infty}\frac{\sin(1/n)}{n^p}$$ I believe that it actually can be shown ...
6
votes
2answers
308 views

Why don't we start studying calculus via series instead of the calculus on finite expressions?

It seems that historically, there were two trends on the idea of integration: Newton's work which depended on infinite series. Leibniz work which depended on the dream of integration of elementary ...
2
votes
3answers
53 views

Are there any significant differences between studying functional analysis from a normed space perspective versus a metric space perspective?

Does it matter if functional analysis was introduced from a normed space versus a metric space formulation? Are all major theorems from functional analysis (such as Banach contraction mapping, Hahn ...
2
votes
1answer
48 views

How To Prove Irrational Square Roots and Inequalities In Courant's Calculus Book? [closed]

Here's the proofs questions in a screenshot The first questions ask about proving the irrationality of non perfect squares. Numbers 3,5, and 6 ask for inequality proofs. I find it daunting that the ...
1
vote
0answers
26 views

Who knows Krotov's Method in Optimal Control Theory

I'm finishing my PhD thesis about applications of optimal control theory in the field of energy harvesting. In the course of my PhD I dealt with different ways to compute optimal controls, and I found ...
4
votes
7answers
135 views

How do i convince students in high school for which this equation: $2^x=4x$ have only one solution in integers that is $x=4$?

I would like to convince my student in high school level using a simple mathematical way to solve this equation: $$2^x=4x$$ in $\mathbb{z}$ which have only one integer solution that is $x=4$ . ...
0
votes
0answers
17 views

Hoeffding's inequality, number of samples required

I was deriving the number of samples required to qualify certain confidence bounds, at the end I am getting slightly different results from what is stated in my lecture notes. can anyone explain why ...
0
votes
1answer
38 views

Projecting functions onto planes

I understand the concept of projecting vectors onto the span of a vector but I'm having trouble projecting functions i.e How would I project the function cos(x) onto the vector that spans (1,1)?
2
votes
1answer
48 views

Alternative proof that base angles of an isosceles triangle are equal

The "classic textbook proof" of equality of base angles of an isosceles triangles which I studied in my school days is as follows: Let $\Delta ABC$ be a triangle with $AB = AC$ and let $D$ be the mid ...
5
votes
8answers
990 views

Is it too much rigor to turn a set into a vector space?

I was reading some online notes on vector spaces and one authors insisted on turning a set $\mathbb{X}$ into a vector space. I thought it was quite insane but maybe I am not seeing the point. The ...
1
vote
1answer
97 views

New idea to solve $\int x^n e^x dx$

I have this problem $$\int x^n e^x dx= x^ne^x -nx^{n-1}e^x +n(n-1)x^{n-2}e^x- \cdots+(-1)^nn!e^x $$ my try was to use integration by part . $$I_{n}=\int x^n e^x \, dx=e^x x^n -\int (nx^{n-1})e^x \, ...
1
vote
1answer
84 views

Books on complex analysis (Ahlfors, Conway and Lang)

To make my question slightly different from others, I would like to know how would you rate on the complex analysis books by Ahlfors, Conway and Lang? I had a basic course on complex analysis during ...
0
votes
6answers
262 views

Alternate ways to prove that $4$ divides $5^n-1$

I was working for various method to solve this: For all $n\in \mathbb N$: $4\;\mid\;(5^{n}-1)$. My try was: 1st: $$n=1 \to 4|5^1-1\\n \geq 2 \to 5^n=25,125,625,3125,...\\ n\geq 2 \to ...
2
votes
1answer
90 views

Difficult to read about different subjects simultaneously, should I leave one for now? [closed]

I learn math by reading books. Usually I read 3 books (about 3 different subjects) simultaneously and switch focus every couple of days. The books i'm studying right now are Rudin's functional ...
3
votes
1answer
63 views

Factoring bivariate quadratics with real coefficients (for high school students).

I was tutoring a Year 10 student last night (he's learning about quadratics). Unfortunately, we ran into a class of problems that I couldn't explain how to solve (beyond simply guessing and checking), ...
7
votes
5answers
409 views

New idea to solve this equation

I was teaching $\left \lfloor x \right \rfloor$ function properties and equation . I solved this equation in my class . My works are show below. Some students ask me for new Idea...,and now I am ...
0
votes
0answers
18 views

Proper name and access of the constituents of an equation.

In any math problems for example: ... B = (1 + B) A = (A + B) ... How can I definitely define a variable that points to the ...
3
votes
0answers
83 views

Opportunities to learn algebraic geometry outside of PhD education [closed]

After a lot of deliberation, I decided to go to professional school instead of pursue academic mathematics. I don't have research aspirations, but I do have an obsession with "getting" esoteric ...
-1
votes
1answer
28 views

Any idea how to approach this problem

A rectangular meadow will have a fence around it. The long side is $130$ m longer than the short side. The sides lengths can be written $x$ and $x+ 130$. Write a simplified expression for 1) ...
1
vote
1answer
31 views

Probability of 2 students being chosen the both have under 100 books at home

Suppose we select two students at random from the class of fifteen. What is the probability that both students chosen have less then 100 books at home? Data provided is the amount of books each ...
15
votes
5answers
2k views

When I was teaching absolute function properties, I suddenly made this question …

I was teaching absolute function properties in a K-12 class. I made this question in my mind. Suppose $f(x)$ is a one-to-one function, and its definition is $f(x)=max\left \{ x,3x\right ...
0
votes
0answers
37 views

Demonstrative geometry around the world and its significance.

This is not exactly a mathematical question. I am from Pakistan; and over here students are taught a subject 'demonstrative geometry' (as a part of mathematics) from secondary level education. ...
3
votes
3answers
218 views

How to overcome the temptation to read many books covering the same topics [closed]

S.E advisers, I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the computational complexity theory. I have been reading some math books on different topics, ...
8
votes
4answers
379 views

How To Develop A Higher Mathematical Aptitude? [closed]

First off I must say I'm pretty blown away by the vast majority of the people in this forum. I do aspire to reach the knowledge of mathematics as shown on the site, but honestly it's a little daunting ...
1
vote
1answer
33 views

How to calculate percentile?

I am reading a document issued by UK Gov about minimum salary for work visa, it is using word percentile, which I don't understand, Could anyone explain what would be the 50th or 75th percentile IF, ...
5
votes
3answers
686 views

Which background is more suitable to study “Cryptography”

I am a student of Pure Mathematics and also interested in programming .I have learnt C++,SAGE . Recently I have started learning "Cryptography" .But there are many definitions involved here like ...
6
votes
1answer
164 views

Reading mathematics at the graduate level - does every single proof matter?

I would be interested in hearing from PhD students (and upwards) specializing in pure maths (in particular, the more algebraic aspects). My question is this: When reading to learn mathematics at ...
1
vote
0answers
43 views

A harder long division puzzle than the first; what should “Algebra I” solution look like?

Here's another problem, significantly harder than the first, but still accessible to target audience. The statement of the problem (i.e., northwest corner only) comes from a PennyDell puzzle magazine: ...
6
votes
3answers
108 views

“Long-division puzzles” can help middle-grade-level students become actual problem solvers, but what should solution look like?

This is my first post. I hope it's acceptable. EDIT Since there are people to whom such notation is foreign, I will point out that the problem represents KRRAEE / KMS, where PEI is the quotient and ...
0
votes
1answer
72 views

Is this Applied Mathematics?

I wanted to learn Applied mathematics, mostly due to it being similar to or having relation to Object Orientated Programming (OOP), and thought it would help alot. I searched all over the internet. ...
7
votes
8answers
897 views

Most natural intro to Complex Numbers [closed]

This is a soft question but I'm willing to ask. There are few ways to introduce the field of complex numbers, but if You had the opportunity to write an elementary textbook, what would be the most ...
3
votes
0answers
36 views

Looking for Math books recommendations to study Electronics

My background is the very basics, and I mean, literally, I can add, sub,mul,div and a little of algebra (near, nothing) and that's it. As you can see I need the best Total Beginner Book(s) that can ...
0
votes
1answer
58 views

Cartesian Product how can this be used in real life situations [closed]

I am learning about the cartesian product as defined by The New Oxford American Dictionary as: the product of two sets: the product of set X and set Y is the set that contains all ordered pairs ...
12
votes
5answers
272 views

Is $1 : 7 = 1 / 8$ or is it $1/7$?

In a certain (non-mathematical) Stack Exchange, when I wrote $n : m = n / m$ where $n$ and $m$ are positive integers, one of the moderators said "No! $n : m$ is usually the notation for "$n$ parts in ...
0
votes
3answers
50 views

Factoring Trick - Adding Up Coefficients

My professor told me this for factoring polynomials: Add up the coefficients and if they equal 0 then the polynomial has root of 1. Add up, but switch the signs of the coefficients with odd ...