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.

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calculate minimum of max value of set of numbers

Suppose to have a set of numbers: $$S:=\{ 1,2,3,9,10,56,58,60\}$$ How can i group this number like this: group 1:$\{1,2,3,9,10\}$ group 2:$\{56,58,60\}$ and then take "56" as minimum value of ...
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0answers
85 views

Help me out please with Algebra? [on hold]

OK. Listen, guys, maybe this question is unorthodox, and "it may be unclear to tell what I am asking" and "this is not a real question" and, obviously this question is "too broad". But please, let ...
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0answers
11 views

Why is Distribution Prioritized Over Combining?

In every algebra (or basic analysis) book that I've seen, three properties of real numbers are taken as axiomatic: commutativity, association, and distribution of multiplication over addition [a(b + ...
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3answers
888 views

Infinite Series: Fibonacci/ $2^n$

I presented the following problem to some of my students recently (from Senior Mathematical Challenge- edited by Gardiner) In the Fibonacci sequence $1, 1, 2, 3, 5, 8, 13, 21, 34, 55,\ldots$ each ...
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10answers
2k views

Are there 3 trig functions or are there 6 trig functions?

In my algebra class we are being taught that there are only the 3 basic trig functions (cosine, sine, and tangent). But my friend who is 2 math grade levels ahead of me is saying that there is 6 trig ...
5
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2answers
72 views

How to get the most out of attending a conference talk or a research presentation? [on hold]

I'll say up front that I imagine there's a resource for this somewhere, but I was unable to find it. I've been attending conference talks and research presentations for about a year at my university, ...
0
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0answers
22 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 ...
6
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1answer
229 views

Fundamental theorem Galois Theory

From time to time, I try to give my non-mathematician scientist friends descriptions of important theorems that I come across. One friend, watched a video on Galois and now I'm at a loss on how to ...
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0answers
250 views

Programmer understanding academic writings on maths

I would like to know in which order I should learn different areas of maths so I can have a robust overview of all the theory in case I need something for a computer programming problem. So I've ...
10
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1answer
637 views

Undergrad Student Trying to Figure Out What to Study

this is my first time on stack exchange and I am seeking advice for my future studies. Some background first; I am a undergraduate student pursuing a degree in mathematics and I hope to pursue ...
4
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1answer
435 views

Learning approach of simultaneously enhance creation and imagination skills instead of 'follow' approach

I am a math-major bachelor student. And I want to get some advice about the approach I'm trying now for learning maths, not for efficiency, but for depth and fully-mastered. Firstly, I want to know ...
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5answers
9k views

Which calculus text should I use for self-study?

I am 36 years old, and have forgotten a lot of math from high school, of which I only took up to Algebra 2. However I am teaching myself mathematics and am now, as an adult, completely fascinated ...
5
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1answer
169 views

How can I retain the mathematics that I've supposedly learnt?

So my question simply is "What is the best method to make sure you retain what you have learnt?" Okay so I've tried learning mathematics up to where I should be at in the past. Every time though I ...
0
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0answers
25 views

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

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
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2answers
122 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 ...
11
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2answers
311 views

Importance of Exercises in Mathematics for Self-Studying

I am a high school student wanting to major in Mathematics in the future. I started to like Mathematics recently, starting a year ago and I watched some interesting math videos on YouTube for fun (ex: ...
2
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2answers
52 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 ...
60
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1answer
3k views

About Euclid's Elements and modern video games

Update (6/19/2014) $\;$ Just wanted to say that this idea that I posted more than a year ago, has now become reality at: http://euclidthegame.com/ 12.292 users have played it in 96 different ...
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3answers
11k views

Self-study Real analysis Tao or Rudin?

The reference requests for analysis books have become so numerous as to blot out any usefulness they could conceivably have had. So here come another one. Recently I've began to learn real analysis ...
9
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9answers
402 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'} ...
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0answers
41 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)$$ P = \{(x_1, x_2, x_3 x_4|x_1+ x_2+ 0.5 x_ ≤ 1, x_1 x_2,x_3,x_4≥ 0\}. $$ ...
0
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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 ...
88
votes
23answers
7k views

Why is there no “remainder” in multiplication

With division, you can have a remainder (such as $5/2=2$ remainder $1$). Now my six year old son has asked me "Why is there no remainder with multiplication"? The obvious answer is "because it ...
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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. ...
37
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7answers
2k views

Why is there antagonism towards extended real numbers?

In my backstory, I was introduced to the geometric concept of infinity rather young, through reading about the inversive plane. In the course of learning calculus, I'm pretty sure I formed a concept ...
2
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1answer
112 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 ...
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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
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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 ...
311
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35answers
36k views

Do complex numbers really exist?

Complex numbers involve the square root of negative one, and most non-mathematicians find it hard to accept that such a number is meaningful. In contrast, they feel that real numbers have an obvious ...
0
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1answer
35 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 ...
6
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1answer
250 views

What is meant by “mathematical maturity”?

I have often heard people talk of "mathematical maturity", sometimes in the sense of the maturity required to understand an area of mathematics or in the approach to a problem or proof. However, it's ...
4
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1answer
70 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 ...
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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 ...
2
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3answers
54 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 ...
6
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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
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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 ...
4
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2answers
716 views

Prison problem: locking or unlocking every $n$th door for $ n=1,2,3,…$

I have a problem called "The Prison Problem" that I need to explain to my 9-year-old cousin. I would think that he has just started learning about divisors and perfect squares, and as such, I have a ...
1
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0answers
29 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 ...
18
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5answers
669 views

Big list of serious but fun “unusual” books

I would like to have some suggestions about serious (that is, with good mathematical content) but fun books that cover topics (or propose problems) in "recreational mathematics"; in any other field ...
12
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4answers
1k views

Motivation behind the definition of GCD and LCM

According to me, I can find the GCD of two integers (say $a$ and $b$) by finding all the common factors of them, and then finding the maximum of all these common factors. This also justifies the ...
3
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2answers
276 views

Functions that generate “easy” matrices of full rank

While explaining how to invert matrices I once used this ill-fated example $A=\begin{pmatrix} 1&2&3\\4&5&6 \\7&8&9 \end{pmatrix}$ which can not be inverted ($\det(A)=0$). That ...
8
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1answer
437 views

What is good chalk for lecturing?

This question might be odd, but after watching one of Gilbert Strang's lectures I find I am jealous of his great, smoothly flowing chalk that never seems to get dulled down. Anyone know what it is, or ...
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 $x=4$ . ...
2
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1answer
51 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 ...
6
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1answer
148 views

Help with diagram chasing

Given the diagram $\require{AMScd}$ \begin{CD} 0 @>>> A @>f>> B @>g>> C @>>> 0 \\ @. @V\alpha VV \#@V\beta V V\# @VV\gamma V @. \\ 0 @>>> {A'} ...
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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
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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)?
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8answers
995 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 ...