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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17answers
2k views

What are some math books written in dialogue or story form, e.g., a teacher explaining to a student?

Good examples would be The Square Root of 2 by David Flannery or Math Girls by Hiroshi Yuki.
1
vote
1answer
27 views

Finding the probability of X_Bar with sample variance included?

The question I am asked is $P(\bar{X} > 3 + 0.4984S)$, where I am additionally provided $n = 25, \mu = 3.0, \sigma^2_\text{pop} = 3.0$. $\bar{X}$ is the sample mean and $S$ is the sample variance. ...
0
votes
1answer
119 views

Questions wrong or theorems useless because hypothesis impossible [closed]

Consider the following question: The area of a right triangle with integral sides is 5. What is twice its area? The answer is 10. But on closer inspection, there is no such right triangle. What can ...
-1
votes
1answer
29 views

defining the (cw/ccw) in radians (pos/neg) [closed]

are there any negative radians? **deg° 0.0 32.9 /-32.9 **rad* 0.0 0.5742133 / -0.5742133 enter image description here
5
votes
1answer
360 views

Dividing numbers with dots?!

OK. This intrigues me. I recently came across this video. Which presumably tells you how to divide 133,342 with 121 only using hand drawn dots! Fair enough but I don't think this works for every ...
0
votes
0answers
32 views

Equation for circle tangent to differentiable functions.

This question addresses a problem from this question. Sketching a possible approach to attack it. If we have the differentiable function $t(x)$ which we want to create a sequence of circles as ...
1
vote
0answers
36 views

Is it possible to visit all points on a differentiable function by “rolling”?

I recall from a discussion thread some week ago we talked about different ways to pedagogically explain differentiability. So I came up with this idea that if there for each point there exists a ...
3
votes
3answers
122 views

What to teach first: Riemann sums or anti-derivative? [closed]

In some text books, I see that they teach Riemann sums first. In other texts, I see they teach anti-derivatives first. Is there any pedagogical preference? It seems to me that we should teach ...
1
vote
0answers
23 views

Trying to learn about kernel PCA but cannot understand some math.

I'm trying to learn about kernel PCA by reading through the paper of it's creators (I assume) "Nonlinear Component Analysis as a Kernel Eigenvalue Problem", Bernhard Schölkopf, Alexander Smola, ...
0
votes
1answer
45 views

Suppose that $R_1$ and $R_2$ are reflexive relations?

I need some help with this problem, Suppose that $R_1$ and $R_2$ are reflexive relations on a set $A$. Show that $R_1 ⊕ R_2$ is irreflexive?
0
votes
2answers
64 views

Are Standalone Introductory Linear Algebra Classes Bad? [closed]

The author of the textbook I will be using for my combination linear algebra/differential equations course next semester, Introduction to Differential Equations by Michael E. Taylor ...
4
votes
1answer
56 views

ELI5: What are pointwise and uniform convergence and what is the difference?

I have been fiddling around with some series of functions and analyzing whether they converge pointwise or uniformly. Furthermore I know that continuity and convergence of integrals does not always ...
0
votes
1answer
28 views

How to calculate the controls of this Bézier curve?

How to calculate the controls of this curve if I know three points: start, one on the curve and the end? Here is the curve with the coordinates I know: The curve with the points I've never done this ...
40
votes
11answers
4k views

Does “Doing a thing to both sides of an equation” have a name?

A two part question. 1 True or False: when working with an equation or inequality, everything that you do is either: a substitution, or an operation performed on each side Note that algebraic or ...
10
votes
7answers
431 views

Teaching integration to kids

I have been selected by my college to teach integration to kids in the age group of 8-12. I am an engineering major who has finished Calculus 1 and 2 but I have no idea how to teach integration from ...
0
votes
0answers
17 views

Is there more RBF's kernel?

I am working on a sfde(stochastic fractional differential equation),I use some of Radial basis function to find solution.like this list ...
1
vote
3answers
53 views

How to summarize the sigma signs

I really don't know how to summarize the sigma signs in the best way, I know how to calculate with them, but to summarize them to just one sigma sign is quite new for me and I don't quite understand ...
2
votes
2answers
42 views

Proving of this trigonometric identity

$$\frac{\cot \beta}{\csc \beta - 1} + \frac{\cot \beta}{\csc \beta + 1} = 2 \sec \beta$$ What I've done: $$\frac{\frac{\cos \beta}{\sin \beta}} {\frac{1}{\sin \beta} +1} + \frac{\frac{\cos ...
3
votes
3answers
132 views

Effective Methods of Studying in different areas of Math

I apologize if this question isn't appropriate for this site, but I am looking for advice that I think other math students might be better able to give me. I am an undergraduate math major entering ...
1
vote
3answers
52 views

Proof of trignometric identity

Could you help me prove this? I've gotten stuck, need some help.. $$\sin^2\Theta + \tan^2\Theta = \sec^2\Theta - \cos^2\Theta$$ Here's what I've done so far: Left Side: $$\sin^2\Theta + ...
1
vote
0answers
91 views

Explaining Method of Pessimistic Estimators to Students

I need an alternative example for the Method of Pessimistic Estimators I need to give a lecture about the method of pessimistic estimators to computer science students. My lecture must be based on ...
1
vote
0answers
43 views

Recommendations on visualizing basic linear algebra

I am teaching linear algebra this semester, and I would really like to recommend my students some cool youtube videos visualizing some simple stuff like the span of a set of vectors, linear ...
0
votes
0answers
57 views

Learning multivariable/vector calculus through guided discovery

I am asking this question as a question similar to what has been asked previously for other topics as well as math in general. But I'd like to ask for text references specifically in the domain of ...
5
votes
0answers
86 views

Referral of a Textbook or Book that teaches Intuition, focusing on Calculus.

I was wondering if there is a book out there that doesn't teach you how to do calculus, but teaches you how to apply it in the physical or social sciences. I know calculus, integration and ...
0
votes
2answers
50 views

Examples of 3d visual proofs

I am looking for examples of three dimensional constructible proofs. By this I mean activities such as steps in proving $1^2+2^2+\cdots+n^2=n(n+1)(2n+1)/6$. In this construction the identity is proven ...
0
votes
2answers
56 views

Solve complex equation $|z|^5=z^5$ for $z$

I have a problem, this equation should be solved for $z$, with $z$ being complex. There should be $5$ solutions bc of the exponent. I already got the solutions from WolframAlpha, but dont know how to ...
1
vote
3answers
55 views

$x-12\%=100$, find $x$

I need to pay someone after deducting $12\%$ commission. I want to pay him round amount of $10,000$ What is the formula to establish the $112\%$ figure so that once I have deducted my comm I will be ...
2
votes
2answers
207 views

Theoretical and applied math help - what and why? [closed]

(Edit: If you wish to skip the prologue, you may go straight to the questions in the last few paragraphs.) I'm not very far ahead at the moment (going to begin my undergraduate years after next ...
1
vote
1answer
25 views

Determine the general solution of the inhomogenous system (Difference&Differential Equations)

Determine the general solution of the system $y(n+1)=\begin{bmatrix} 5 & 1\\ -1 & 3 \\ \end{bmatrix} y(n) + 4^n \begin{bmatrix} 1 \\ -1 \\ \end{bmatrix},\quad n \in \mathbf{N}$ The ...
7
votes
3answers
504 views

How does aptitude at solving Olympiad problems relate to success at further mathematical studies? [duplicate]

I spent last 6 years mostly practising my problem solving skills so I do well in my national Math Olympiad. Out of curiosity I did some reading on basics of what undergraduate students are taught - ...
12
votes
5answers
1k views

Mathematicians who overcame academic failure to achieve success [closed]

Does anyone have any story of mathematicians who overcame "academic failure" or setbacks to achieve success later as a result of their perseverance? This is a soft question, that hopefully can inspire ...
1
vote
1answer
32 views

What is( are) the advantage(s) of caputo's to Riemann-Liouville derivation?

I am new in fractional calculus. I see most of articles uses Caputo's derivation instead of Riemann-Liouville derivation. Is there some advantage? Can someone make some basic (simple) example for ...
10
votes
5answers
343 views

What are some of the best book in mathematics for general reader? [closed]

I am preparing a list for my department library, consisting books of mathematics for general readers. I've included The men of mathematics by Bell, Fermat's last theorem by S.Singh , The man who knew ...
2
votes
0answers
53 views

What makes a good mathematical poster? [closed]

During my second year of university I have done some assignments and some papers, but this is my first time I have to make a mathematical poster. What could make my poster stand up. So up to now I ...
0
votes
1answer
85 views

Is there a Hilbert's list for $21$st century?

David Hilbert gave his famous list of $23$ unsolved problems presented in Paris in $1900$. Most of the problems are fully/partially resolved, some are still open (RH etc) and some are impossible to ...
7
votes
4answers
145 views

A new approach to find value of $x^2+\frac{1}{x^2}$

When I was teaching in college class ,I write this question on board . if we now $x+\frac{1}{x}=4$ show the value of $x^2+\frac{1}{x^2}=14$ Some student ask me for multi idea to show or prove that ...
1
vote
1answer
46 views

Applications of Random Walks for undergraduate students

Students are asking for applications of discrete random walks in "real life" problems. By real life they mean financial applications and industry. We have two more weeks on this subjects and I'm ...
0
votes
0answers
66 views

Hat check experiment and random variables.

E is the hat check experiment with n = 4 hats.Let X count the number who do not get their own hat and let Z be the indicator of the event A={ neither peron 1 nor person 3 gets their own hat}(i.e. , ...
0
votes
1answer
53 views

Artificial intelligence methods in mathematics

Are there aritficial intelligence methods in mathematics, automatic theorem discovery and proving? Google gives results in the opposite direction - mathematical methods of AI. Are there applications ...
2
votes
0answers
25 views

What is a point to give the Abel's Test for product series convergence a place in introductory textbooks?

One of the hypotheses of the Abel's test for product series convergence is stronger than the corresponding Dirichlet's test; that is, the former imposes the convergence of one of the series and the ...
9
votes
3answers
363 views

Developing Mathematic Intuition

I'm an engineering student, currently working my way through the fundamental mathematics courses. I've done reasonably well so far—mostly A's and a couple of B's in Algebra, Statistics, ...
39
votes
0answers
4k views

Explaining to a kid why a negative × negative = positive? [duplicate]

My son's just turning 8 this year and has just started to learn some of the basics of multiplications, including multiplication signs. However, he's started asking me why a negative multiplied by ...
0
votes
1answer
22 views

Question about a g-force simulator in question 6, part b, regarding the moments in a balanced system at rest.

The following is regarding question $6$, part $b$, in the following link: https://thol.sunway.edu.my/examdbase/alv/math/p3/math_p3_j96.pdf Using the principle of moments and considering the case ...
1
vote
0answers
19 views

Notation for points in 2d or 3d coordinate systems P(a|b|c)? Origin and reasons?

In every german high school book about vector geometry, points in 2d or 3d cartesian coordinate systems are denoted like $P(2|-1|5)$. Very rarely one also reads something like $P = P(2|-1|5)$. But I ...
0
votes
1answer
36 views

How do I find a percentage with only the mean and standard deviation?

'If we have a set of scores that are normally distributed and have a mean of 20 and a standard deviation of 5, what percentage of scores are greater than 20?' Now I know the answer is 50%, because ...
0
votes
2answers
29 views

Query on previous post regarding the distance formula for perpendicular lines and negative slopes made 2 years ago.

In the post made 2 yrs ago 'Explain why perpendicular lines have negative slopes', Explain why perpendicular lines have negative reciprocal slopes How does the distance formula get applied to obtain ...
2
votes
3answers
43 views

Suggestions on Progressing in (Meta)Mathematical Development [closed]

[Straight to the Point] I would really appreciate any suggestions on self-study materials that relate to math, logic, and/or the philosophy of both. Also, any thoughts or suggestions that you may ...
8
votes
4answers
408 views

Map closed under addition but not multiplication

I have been helping undergrads in an introduction to linear algebra course. When solving some exercise consisting in showing that a map is linear some get lazy after proving that it is closed under ...
1
vote
0answers
36 views

Can I get some help to make my answer more rigorous for this problem in the book Concrete Mathematics [duplicate]

I'm a freshman in college this semester without any previous experience in rigorous proofs or such, however I am interested in the learning more about mathematics and for that reason I picked up the ...
2
votes
2answers
89 views

What topics should be included in a course matching these specifications?

Say you have a calculus classroom full of liberal-arts majors who are not particularly mathematically inclined. Your goal is NOT to teach them everything on a list of topics that will be needed in ...