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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1answer
49 views

Can we find $ a + b $? [closed]

How can we find the value of $ a + b $ in the following question? a & b are integers. Question: If $ a^{2} \times b^{3} = 216 $, find $ a + b $.
2
votes
2answers
109 views

What (previously and currently unsolved) problems motivate the study/development of analysis?

As I had ever know there are at least two (previously unsolved) problems motivate the study/development of abstract algebra: (1) the ancient Greeks' three problems in compass-and-straightedge ...
2
votes
0answers
39 views

Flat Tax vs. National Income Tax Average

If the national income tax average under a progressive system is 30%, will tax revenue change if the progressive system is changed to a flat tax also at 30%? In other words, if the mean average ...
1
vote
0answers
29 views

in nested brackets which would be outermost bracket

i wanna know that in an algebric equation of 2 level nested brackets which format of nested bracket is correct {4[3+5(3+2)]} [4{3+5(3+2)}] is curly would be outermost or square
3
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0answers
61 views

What to do with java-based math demos? [closed]

A large volume of mathematical demos were written in Java. Then came security warnings of all sorts. Currently it does not seem viable to direct students to such demos. Do you think an organization ...
0
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2answers
36 views

problem proof of induction $2\cdot3^0+2\cdot3^1+2\cdot3^2+…+2\cdot3^{n-1}=3^n-1$

I need to prove that $2\cdot3^0+2\cdot3^1+2\cdot3^2+...+2\cdot3^{n-1}=3^n-1,\, n=1,2,3,4...$ I know when n = 1 the left side $=2\cdot3^{1-1}=2$. The right side is $2^n - 1=2^1 - 1 = 1$. Thus the ...
3
votes
1answer
53 views

Could someone make the proof into a hinted exercise?

Let $(c_n)$ be a sequence of positive numbers. Could someone make the proof of the inequality $\displaystyle\limsup_{n\to\infty}\sqrt[n]{c_n}\leq\limsup_{n\to\infty}\frac{c_{n+1}}{c_n}$ into a ...
1
vote
1answer
55 views

For an introductory analysis class, why is it that many people avoid teaching it using sequences?

I am currently taking an honors introduction to analysis course, and it seems to me that to me defining all of the concepts in terms of sequences allows for much cleaner proofs, and the concepts are ...
1
vote
1answer
63 views

Variation on the “Number of non-bald people in NYC” problem

I have two questions about the following problem, taken from Challenging Problems in Algebra by Posamentier and Salkind: (1) Why is the answer not 1 person? (2) The answer given, without solution, is ...
0
votes
1answer
44 views

Subtraction and borrowing for dummies

Regarding the subtraction and borrowing a digit from upper digits, I know how that works for more than one digit numbers. However, I can not figure out for one digit numbers! It is an obvious thing ...
3
votes
0answers
57 views

On teaching elementary co-ordinate geometry. [closed]

I am presently teaching eleventh grade (XI standard) students an introductory course in co-ordinate geometry with a focus on preparations for competitive exams. I have seen books like S.L.Loney's ...
0
votes
1answer
68 views

Looking for interesting problems to solve numerically

I am giving tomorrow an introduction to Python to undergraduates and have to present how it can be used to solve some mathematical problems. I have been looking for some nice or challenging problems ...
0
votes
1answer
14 views

building blocks

My little sister used her alphabet blocks to build a wall 8 blocks long, 8 blocks high, and 2 blocks wide. This took her 8 minutes. At this rate how long would it take her to build a wall 4 blocks ...
1
vote
1answer
67 views

Find a polynomial $p$ in $\Bbb P_2$ that spans the kernel of T, and describe the range of T.

Define $ T: \Bbb P_2 \to \Bbb R^2 $ by $ T(p) = \begin{bmatrix} p(0) \\ p(1) \end{bmatrix} $. For instance, if $ p(t) = 3 + 5t + 7t^2 $, then $ T(p) = \begin{bmatrix} 3 \\ 15 \end{bmatrix} $. Find a ...
0
votes
3answers
26 views

Cannot understand this property about column space

Here is a property given to me in my textbook. $ ColA=\Bbb R^m \text{ if and only if the equation } Ax=b \text{ has a solution for every } b \text{ in } \Bbb R^m $. What does it mean by every $b$?
1
vote
1answer
76 views

How does a $2$ horizontal row ABACUS work? Till what number can u Add & Subtract…can it be used for Multiplication & Division? SEE DETAILS

For design class (grade $10$), we have to make a Learning Product/Tool. I decided to make an abacus with 2 horizontal rows (it s easier) like the one in this picture: The abacus isn't for very ...
0
votes
1answer
145 views

how to find the distance between two points in the polar coordinate system?

Help me, please! how to find the distance between two points $ A( x_1,y_1 )$ $ B( x_2,y_2 )$ in the polar coordinate system?
4
votes
2answers
138 views

Good example showing why limits must exist in limit product rule

I'm looking for a way to show my calc 1 students not to use the limit laws without knowing that the individual limits exists. I could use $$\lim_{x\to 0} x^{2} \sin(1/x),$$ but by doing it wrong, one ...
3
votes
1answer
77 views

Being ready to tackle the math courses in my CS program

Here's my (long) story cut short. I was awful at math in high school. I did 4 years in the service and now I'm going to start college in just a few weeks. I am really nervous because I will have 5 ...
2
votes
0answers
53 views

Circular Logic and Continuity

So, I was doing a Calculus problem a few minutes ago and just recalled something that my real analysis professor said during a lecture years ago... To provide context, take the function $f$ defined ...
4
votes
5answers
403 views

What mistakes, if any, were made in Numberphile's proof that $1+2+3+\cdots=-1/12$?

This is not a duplicate question because I am looking for an explanation directed to a general audience as to the mistakes (if any) in Numberphile's proof (reproduced below). (Numberphile is a YouTube ...
0
votes
1answer
25 views

Finding arithmetic mean, with hidden ratios, HOW?

I have twelve items each with with their own percentage of 100%. I'll label them.. English(A):67 -MATH(B):60.5 -Biology(B):67.5 -Chemistry(C):80 -Physics(E):67 ARABIC(F):63 -Economics(G):78.5 ...
4
votes
3answers
98 views

What is the equivalent of musical ear training with regards to studying mathematics

When one aspires to be a professional musician, it is made clear that ear training is a very valuable skill that must be cultivated on a daily basis. The student is advised to put in the time and ...
1
vote
2answers
68 views

What is the linear transformation $ x \mapsto Ax $?

I am told by my textbook that, $ \text{Nul }A = {0} \text{ if and only if the linear transformation } x \mapsto Ax \text{ is one-to-one.} $ $ \text{Col }A = \Bbb R^m \text{ if and only if the linear ...
0
votes
0answers
23 views

3 variables 'linked' to one outcome (for lack of better words)

Paper route salary formula (reverse engineer...again for lack of a better word;) Ok suppose I have these variables: Pieces of mail : 302 Number of stops: 177 TotalWeight* : 272 Hours allocated: ...
24
votes
12answers
4k views

How do I make a student understand contradiction?

We were trying to prove that if $3p^2=q^2$ for nonnegative integers $p$ and $q$, then $3$ divides both $p$ and $q$. I finished writing the solution (using Euclid's lemma) when a student asked me ...
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votes
1answer
238 views

Solve $|z|+z=1+i$ [closed]

Solve the equation $|Z|+ Z=1+i$ please help me describe me how to solve it.
4
votes
2answers
98 views

I need a good reading list of the Masterworks of mathematics. [closed]

I'm interested in a solid list of the greatest textbooks in the major* fields as written by the "Masters". The problem I have is that after many years of a high-level, rigorous education in ...
0
votes
0answers
36 views

Are some Types of Proportional Relationships more useful than others?

Responses from a previous math stack exchange question (see link below) have lead me to this related question. Link to previous question Based on these responses, it seems that in just about any ...
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votes
1answer
46 views

a local government is planning to build new roads that will divide a forest into several fragments [closed]

a local government is planning to build new roads that will divide a forest into several fragments the roads can follow several different designs each of which design will minimize the edge effect on ...
2
votes
0answers
54 views

Is the precise definition of a limit worth covering in Calc 1?

I'm teaching calc 1 this semester and am trying to decide if I should cover the precise definition of a limit. My first impression was that I should. It helped me to gain a deeper understanding of ...
4
votes
4answers
134 views

Is the anti-derivative another way of saying the derivative?

This question is being posted so that I can understand a definition and concept. The definition - F(x) is an anti-derivative of f(x) if F'(x) = f(x) Therefore, $$F(x) = x^2$$ is an ...
0
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0answers
26 views

One Million Proficiency Efficiency Calculations

I have been playing the "Million" game on my apple device after discovering it through the trending applications in the search function. After beating the game I began to wonder to myself if there was ...
12
votes
9answers
810 views

Proof that doctors could relate to [closed]

I am supposed to present a mathematical proof to a lecture hall full of doctors in order to show them how mathematicians think. I'm having trouble picking a proof that will be easily followed by ...
1
vote
3answers
118 views

How to explain Clairaut-Schwartz's Theorem, $f_{xy}=f_{yx}$?

I am looking for a non-technical explanation of Clairaut's theorem which states that the mixed derivative of smooth functions are equal. A geometrical, graphical, or demo that explains the theorem and ...
2
votes
1answer
50 views

A different method for solving 2nd order ODEs

For constants $a,b$ there are many ways to find the solutions to $$y^{\prime\prime} + (a+b)y^\prime + aby = \phi(x). $$ Perhaps the most popular is to first solve the homogeneous case when $\phi(x) ...
0
votes
2answers
118 views

How complex can a Differential Equation be? [closed]

When I was first being introduced to differential equations, my teacher began by asking the other student and me to write down the most complex differential equation we could think of and gave us 10 ...
0
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0answers
15 views

Convention as to differentiability defined in terms of local extension?

Let $X \subset \mathbb{R}^{n}$. In differential topology or allied areas, people may define that a function $f: X \to \mathbb{R}^{m}$ is of class $C^{r}$ if and only if $f$ can be locally extended to ...
0
votes
1answer
157 views

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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votes
1answer
134 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 + ...
0
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0answers
23 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
2answers
134 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
65 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
81 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 ...
11
votes
9answers
626 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
32 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 ...
2
votes
1answer
267 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
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0answers
47 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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0answers
73 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
42 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 ...