Tagged Questions

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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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 ...
22 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, ...
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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?
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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 ...
47 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 ...
26 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 ...
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 ...
381 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 ...
15 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 ...
51 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 ...
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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 ...
41 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 ...
50 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 ...
77 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 ...
44 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 ...
55 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 ...
54 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 ...
178 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 ...
24 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 ...
481 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 - ...
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 ...
21 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 ...
319 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 ...
50 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 ...
84 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 ...
142 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 ...
42 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 ...
65 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. , ...
47 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 ...
23 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 ...
314 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, ...
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 ...
20 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 ...
15 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 ...
26 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 ...
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 ...
41 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 ...
366 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 ...
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 ...
86 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 ...
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Can sombody give me an ntuitive explanation about regression estimates as weighted averages?

I am trying to study weighted least square and found one article that sounds like it is explaining what I am trying to study. But I want to get some intuitive explanation about each calculation and ...
15 views

Percentage Calculation - Cells per micro litre

I came across this simple percentage calculation and I couldn't solve it (I couldn't prove otherwise). Here's the problem. Find percentage for 11/0.1 ul (11 cells per 0.1 micro litre). Any pointers ...
28 views

Note-taking Software Reference Request

I'm currently doing AS-level in pure mathematics and I'm looking for a good app that will help me keep and organize all my notes and equations that I should memorize. I tried using Microsoft OneNote ...
32 views

Prove that $|x − y| < \epsilon$ , $|y − z| < \epsilon$ implies $|x-z|<2\epsilon$

I need the math.triangle inequality formula, but I still didn't get it fully. be die|x|+|y| <= |x+y| |x|+|y| <= |x+y| I put in the values |x-y| < ε <= |x|-|y| < ε |y-z| < ε ...
29 views

How can I explain a Zero Knowledge Proof with minimal mathematics

I asked this earlier on how to explain a Zero Knowledge Proof to a layman. but I'm looking for a mathematical analogy that might "enhance" the superpower explanation. In that linked superpower, that ...