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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Are there any online math games similar to CheckIO or CodeCombat?

There are several nice online programming games where you need to solve problems in one place to unlock other places on the map. Are you aware of similar games focussing on math problems? Or (even ...
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0answers
173 views

Freshman calculus - Stokes's theorem proof

Many calculus text books and courses do not introduce full proof of Stokes's theorem because of differential forms and topological concepts. There are only restrict proofs (for example, simple ...
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0answers
17 views

Input a matrix with integral element in matlab

I am working on stochastic fractional differential equation , like below $$ D^2y+D^{\frac{3}{2}}y+y=1+t ,\space y(0)=0 ,y(1)=2$$I use RBF's (radial basis function) to solve it .so $y \sim \lambda_1 \...
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1answer
104 views

Scratch paper alternatives? [closed]

How do you practice complicated calculation when the problem is displayed on your computer screen? Do you always have pieces of paper on the side, or do you have a Wacom tablet connected to your ...
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0answers
41 views

New method to solve this fractional differential equation

this is my problem \begin{align} & D{{\text{ }}^{2}}\text{ }y\left( x \right)\text{ }+\text{ }D{{\text{ }}^{\frac{3}{2}}}\text{ }y\left( x \right)\text{ }+\text{ }y\left( x \right)\text{ }=\...
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2answers
135 views

why don't standard analysis texts relax the injectivity requirement of the multivariable change of variables theorem? [duplicate]

In standard multivariable analysis texts, the change of variables for multivariable integration in Euclidean space is almost always stated for a $C^1$ diffeomorphism $\phi$, giving the familiar ...
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1answer
53 views

Is there a place that lists graduate institutions and their specialties? [closed]

I'm currently a sophomore at a Canadian university, and due to some recent head butts in a few maths classes, I'm realizing I don't know what I want to do in grad school (or if I even want to go for ...
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1answer
113 views

New Elementary Function?

In the February 2000 issue of FOCUS magazine, a short article suggests that the Lambert W function could be introduced into curriculum as a new elementary function saying: "... a case can be made for ...
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4answers
252 views

How to explain “why study prime numbers” to 5th Graders?

I tend to teach 5th graders math ever so often just so they can be "friendly" with math in a playful manner, instead of being afraid. However, one question that I constantly struggle with is this: ...
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3answers
77 views

What is the Pedagogical Justification for Substitution?

My mom is re-learning calculus for the third time (She tutors High School students). And she asked me a question invovling limits: $$\lim_{x\rightarrow \infty} \frac{\ln 2x}{\ln 3x}$$ I led her ...
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7answers
3k views

Why does topology rarely come up outside of topology?

I am currently taking topology and it seems like a completely different branch of math than anything else I have encountered previously. I find it a little strange that things are not defined more ...
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17answers
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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.
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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. ...
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1answer
126 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 ...
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1answer
34 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
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1answer
561 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 ...
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0answers
38 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 ...
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0answers
37 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
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3answers
128 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 ...
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0answers
25 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, Klaus-...
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1answer
60 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?
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2answers
69 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 (http://www.ams....
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1answer
62 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 ...
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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 ...
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12answers
5k 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 ...
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7answers
561 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 ...
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0answers
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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 $$\phi=\frac{1}{\sqrt{2\pi}}e^{-\frac{(x-x_0)^2}{2}}\\\phi=\...
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3answers
55 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
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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 \beta}{\...
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3answers
160 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 ...
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3answers
58 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 + \frac{\...
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0answers
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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 ...
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0answers
46 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 dependence,...
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0answers
63 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 ...
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0answers
87 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 ...
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2answers
54 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 ...
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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 ...
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3answers
56 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 ...
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2answers
236 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 ...
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1answer
28 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 ...
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3answers
526 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 - ...
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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 ...
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1answer
59 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 ...
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5answers
368 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 ...
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0answers
55 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 ...
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1answer
88 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 ...
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4answers
149 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 ...
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1answer
47 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 ...
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0answers
69 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. , Z(...
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1answer
57 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 ...