Questions related to the teaching and learning of mathematics.

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Other conditions than necessary and sufficient conditions, $\Rightarrow$, $\Leftrightarrow$?

I know that $$A\Rightarrow B$$ means that $A$ is a necessary condition for $B$ and $B$ is a sufficient condition for $A$. Also, $$A\Leftrightarrow B$$ means that $A$ is necessary and sufficient ...
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0answers
21 views

Tools (electronic notebook and ontology viewer) of mathematical formulas (definitions and facts)

I am reading math books and articles (for applications in other disciplines, mostly about logics for computer science and AI) and the hardest part is to memorize formulas, to look up some ...
2
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0answers
103 views

Interacting with high school teachers (US) [migrated]

I am a parent of a HS freshman who is taking precalc/trig now. His teacher is pretty much useless; my son has to come to me or my wife (let's just say that each of us has about 100+ college and ...
10
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9answers
816 views

A Poster About Prime Numbers [on hold]

We're going to design a poster about prime numbers, which will appear in a mathematics magazine for middle school students. The poster should be both visually attractive and mathematically rich. Do ...
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5answers
87 views

How to teach newbie multiply of complex number

I want to teach a newbie the arithmetic law of complex numbers. the law of add is acceptable psychological. but multiply is not. for example, assume $$z = a+bi, w = c+di$$ He (She) may ask me: why ...
3
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1answer
21 views

Finding Multivariable Limits

Is there any good way to find a multivariable limit other than switching to polar coordinates? For example, students each year are inundated with problems like $$\lim_{(x,y)\to ...
33
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16answers
5k views

If there are obvious things, why should we prove them?

Obviously, there are obvious things in mathematics. Why we should prove them? Prove that $\lim\limits_{n\to\infty}\dfrac{1}{n}=0$? Prove that $f(x)=x$ is continuous on $\mathbb{R}$? $\dotsc$ Just ...
3
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1answer
60 views

Mathematics or physics at university

I have a strong interest in maths, and I feel that advanced physics is cool too (although I've only studied classical mechanics at high school, which is kind of boring). So I'm not sure about which ...
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2answers
45 views

school exersise/ Differentiation

If $f$ is differentiable in ${\bf R}$ and for every $x \in {\bf R}$, $$ f(x+\cos x)-f(1-x) \leq x\cos x , $$ then prove that $f'(1)=1/2$. How is a school kid supposed to solve this exercise ? ...
2
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0answers
29 views

Revise high school material

Can you suggest me a comprehensive book to revise high school mathematics (up to besic calculus)? It should be extremely clear and complete and "scientific" (not like most high school books). Thank ...
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0answers
24 views

POISSON DISTRIBUTION between two values help [closed]

LET x= NUMBER OF FLAWS OF THE SURFACE OF A RANDOMLY SELECTED BOILER OF CERTAIN TYPE. WITH MEAN = USE POISSON DISTRIBUTION to find p(5 please help me with this
3
votes
3answers
87 views

Things to do before starting math (or physics) at university

What is better to do before starting a math degree? I was thinking that maybe I should do something like: learning latex learning how to use matlab Any other suggestions?
8
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5answers
283 views

Why does $n^0 = 1$?

Why is it that $n^0 = 1$? I understand how $n^2 = n*n$ and how $n^1 = n$ but I can't understand why $n^0 = 1$.
2
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1answer
35 views

Math literature for teaching kids

If you were going to teach you kids programming and asked me what book to use as a guide, I would recommend you either Java programming for kids or Python for kids. But what if I want to teach kids ...
10
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2answers
254 views
+100

Create a Huge Problem

I am wondering if any problems have been designed that test a wide range of mathematical skills. For example, I remember doing the integral $$\int \sqrt{\tan x}\;\mathrm{d}x$$ and being impressed at ...
0
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1answer
29 views

Why all games are not Potential?

A definition given in wikipedia of an exact potential game as follow: A game $G=(N,A=A_{1}\times\ldots\times A_{N}, u: A \rightarrow \mathbb{R}^N)$ is: an exact potential game if there is a ...
1
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1answer
33 views

Why optimization problems cannot be solved by simple derivative?

Let $f(\cdot)$ be a linear function. $f:\mathbb{R}^n\rightarrow\mathbb{R}$ $\;\quad\;\mathbf{x}\;\rightarrow f(\mathbf{x})$. Let $\mathbf{A}$ be a matrix in $\mathbb{R}^{m\times ...
0
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1answer
41 views

Establishing fairness in test grading

Consider a group of 75 students who sit an exam consisting of 20 open questions, and are then randomly divided into 3 groups of 25 students {A, B, C} for grading by 3 different persons. Let us ...
1
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3answers
31 views

Which discrete mathematics book to read for a software engineer?

I'm a computer science student, but I lack a good mathematics background. So I decided to start working on that. I was searching in the topic and I found that for computer science a good knowledge of ...
1
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0answers
29 views

What courses require multivariable analysis?

For which undergraduate and introductory graduate mathematics courses is a rigorous course in multivariable analysis an essential prerequisite?
3
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3answers
77 views

Why do we use $cm^2$?

I can't seem to wrap my head around why we should use $cm^2$ for area. According to my textbook we use it for converting units of area but I don't understand how $1cm$ is any different from $1cm^2$. ...
22
votes
8answers
6k views

Are there contradictions in math?

Someone told me that math has a lot of contradictions. He said that a lot of things are not well defined. He told me two things that I do not know. $1+2+3+4+...=-1/12$ what is infinity $\infty$? ...
4
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0answers
62 views

distance Pure Math graduate programs?

I would like to go to a graduate school for pure mathematics, but I do not live where such programs exits. Furthermore, I can not move. Question: Do any Universities have graduate program in pure ...
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2answers
60 views

Maths brain teaser. Fifty minutes ago it was four times as many minutes past three o'clock

Fifty minutes ago it was four times as many minutes past three o'clock. How many minutes is it to six o'clock..? I have got the solution online but have doubts in it : ...
1
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1answer
59 views

How to study analytic number theory?

Should i study many books at the same time? Or should i go one by one? I started with Apostol's book... But for example if i don't understand a proof, i check another book for a different proof of the ...
0
votes
1answer
19 views

What test could I use to test $\mu_1$ and $\mu_2$ instead of $\bar{x}$ and $\mu$?

A single sample $t$ test is only against a sample and a population correct? Can it test against a population and itself or two populations? ie $\mu_1$ vs. $\mu_2$....if not what tests would you use ...
0
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0answers
7 views

What are the most useful math classes to take for applications to machine learning/NLP?

I am a computer science/applied math major, and due to not starting off with the CS major, I have a long way to go before I get into any serious classes that deal with my focus areas (intelligence and ...
0
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2answers
23 views

Can someone very intuitively explain why the cross-product works, with respect to proportions?

Note: unrelated to matrices. I have to teach this concept, and I want to know what is the best way to show that the cross product is always equal if the two fractions are equal. Thank you so much.
5
votes
2answers
85 views

Looking for a specific female maths writer

This is going to be an annoying question, but I have to ask it as it is annoying me. I once read a book on infinity that was written by an American female maths writer. She was very easy to read and a ...
0
votes
2answers
24 views

Standard Deviation of Population from Sample.

I guess I am a little confused. I am doing t test statistics in my class. I think I know but I would love some insight. I am trying to get the estimated standard deviation for the population. These ...
1
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0answers
33 views

Matrices of the form $A^p=(a_{ij}^p)$

I am wondering if there is a name for these kind of matrices and if they are interesting or not? Do they even exist? Let $A$ be a $n\times n$ matrix with elements $a_{ij}$. $A= (a_{ij})_{i,j\in\{1, ...
5
votes
1answer
65 views

What's the trick to re-focusing on your math studies?

If you check my history on MSE, you'll see that I was very active about 1/2 a year ago. Right now I'm working and socializing a lot, which is important, but I also have spare time to devote to my ...
0
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0answers
11 views

Classroom enhancement resources for linear algebra

My university offers small grants (in the \$100 - \$300 range) for classroom enhancement resources. In the past, I've applied for and received a grant to purchase a Zometools kit used for ...
1
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2answers
49 views

What does $e^b$ means?

What does it mean $a^b$ where $a$ and $b$ are real numbers not integers, not rationnals (I do not know the name of this set). Real numbers means $\mathbb{R}$ but $1\in \mathbb{R}$ So, what does it ...
3
votes
1answer
73 views

Where to begin my Math journey

I apologize if this is not the correct forum for this, but I felt it appropriate. I want to start getting into more mathematics and learning all I can to step up my programming career. I know plenty ...
2
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5answers
302 views

What area of Abstract Algebra do you find most interesting? [closed]

For my Abstract Algebra class, we will be doing small presentations (2 class periods) covering some topic in Abstract Algebra. Thus far, I have studied groups, rings, fields, modules, tensor ...
7
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1answer
95 views

why is that most of the books in mathematics don't include answers?

I am currently going through the " Topics in Algebra" By I. N. Herstein. The problems are pretty good. But there are no answers on the back. Same is the case with "Mathematical Analysis" by Rudin. I ...
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2answers
28 views

Power calculation for simplification?

I have this simple question I saw here: ±(2 - 2^(-23)) × 2^128 = ±6.8 × 10^38 How did they get to ...
0
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0answers
18 views

Help with GCF of algebraic equation [closed]

While doing my math home work I came across this question: "Find the GCF of $3(h+y)^3$ and $15(h-2y)^5$ and $9(3h-y)^6$". The first step I took was expanding the brackets which made it: $3h^3+y^3$ and ...
0
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1answer
42 views

Parabola problem. How far from the vertex is the focus?

A spotlight has a parabolic cross section that is 8 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? I'm getting 8/5 ft. Is this correct? Appreciated!
5
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2answers
124 views

Why the $\log$ is so special?

When I first learn about the logarithm function $\log$ or $\ln$. My professor said that $\log x$ is a function that when we derive we get the inverse function $1/x$. This $\log$ becomes very popular ...
2
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0answers
57 views

Is an undergraduate in engineering sufficient preparation for a masters in mathematics?

I'm a high school student who is considering doing an undergraduate in engineering. However my the long term plan is to pursue math at a higher level. I want to do engineering at undergrad because I ...
1
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1answer
28 views

Max value - Mantissa calculation clarification?

I've been reading this article about floating point representation floating point representation is : Where mantissa is : All understood. But they also say : How did they get to ...
74
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19answers
12k views

Visually deceptive “proofs” which are mathematically wrong

Related: Visually stunning math concepts which are easy to explain Beside the wonderful examples above, there should also be counterexamples, where visually intuitive demonstrations are actually ...
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1answer
27 views

Null Hypothesis and Confidence Intervals

I was told that If I reject the null hypothesis than my CI will not include the population mean. However the problem that I just did has a population mean of 2.72 and a lower CI of 2.5 and an upper CI ...
0
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1answer
28 views

Upper and Lower Bounds for Confidence Intervals on a one tail hypothesis test.

CI(99) = xbar ± Zcv( σ / √ n -1 ) My question is if the test is a one tail hypothesis test, do I still do two separate equations + and -. Here is the formula filled in (if it is the correct ...
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1answer
13 views

Why am I getting 84.25 instead of 97.68 for my Confidence Interval?

Why am I getting 84.25. I am doing 97.96*(6/sqrt[50-1]) = 97.96*(6/7) I am obviously not doing this correctly please help. It has been sometime since I have done any math.
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6answers
839 views

Should I do all the exercises in a textbook?

The problem sets that you usually get in a university course is a small fraction of the exercises in your textbook. Which raises a question: do you need to solve all the exercises from your textbook? ...
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0answers
19 views

Calendar problem

I have a problem to find the day at 15 Aug 1947 ? So I found number of century leap year Integer(1746/400)=4 Then 4*400=1600 is the century year . As we know ...
0
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0answers
16 views

Move Hill equation curve horizontally without changing its shape?

I have a normal Hill function of: $y = \dfrac{x^\lambda}{h^\lambda + x^\lambda}$; where $\lambda$ is Hill coefficient, and $h$ indicates the infection point. I am concerning if we could add another ...