Questions tagged [education]

For math 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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58 views

What is the probability that a rod broken into three pieces forms a right angled triangle? [closed]

Let the rod be cut at $x$ and $y$. So the three pieces are $x$, $y$ and $l-(x+y)$. What is the probability that the three pieces form a right angled triangle?
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Graphic understanding of derivative

I'm about to teach some basics of Math and Phyisics to someone who studied Law and now want to start a Medicine Major. I'm a Phyisics student and I already got some good approaches for every topic, ...
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1answer
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Prove that triangle $\triangle ABC \cong \triangle G H I$ . Explain each step.

My question: Prove that triangle $\triangle ABC \cong \triangle G H I$ . Explain each step. Here are my triangles I proved that $\triangle ABC \cong\triangle DEF$ because the first sign of ...
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1answer
22 views

How do I Find Preparatory Exposure?

I always prefer to be prepared ahead of time, but I am not sure of how to be for a career in mathematics. How do I immerse myself in a formal, mathematical environment without necessarily enrolling in ...
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Is it a bad idea to use visualizations in studying linear algebra? [closed]

many concepts in linear algebra are explained using visualizations. However, many practical applications of linear algebra use spaces whose dimension is larger than 3 which you cannot visualize. When ...
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1answer
50 views

Best way to spend three months before entering masters program: Review fundamentals, or pre-study topics in the program?

Recently I got an offer letter for a master program (with courses like algebraic topology, algebraic geometry (first chapter of Hartshorne), differential geometry, representation theory, etc... ). Now ...
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What would be good foundations in order to approach manifolds considering an engineering formation?

I am currently studying control engineering on a sort of graduate level (mostly on my own). However every book on the area mentions certain subjects or areas of mathematics (particularly manifolds and ...
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2answers
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Inconsistent notation for vectors and points in textbooks

Many books on calculus or advanced calculus distinguish between points and vectors. Usually points are denoted by italic letters like $P, Q$, and $R$, and vectors are denoted by bold letters such as $\...
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2answers
585 views

Is it bad to resort to numerical examples to understand the idea behind a proof?

When reading proofs, I often get confused and need to devise my own examples to understand what's going on. Is this practice ok or should I train myself to think in abstract terms? As an example, here'...
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What could be an example of a convex compact set in $\mathcal{R}^2$

I know what are the conditions for a set to be convex and compact but can't imagine any graphical representation of that, could give some example? I was thinking in an ellipse, since its bounded.
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Topology and algebraic topology have any application in biology? [closed]

If so, In what area? evolution, genetecs .... And how good do my computer skills need to be to work in these areas?
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What are Colleges Using for Math During COVID?

$\textbf{Question:}$ What are colleges using for technology in order to assess students during COVID? I currently use Canvas and I do not feel up to date at all with what I am using. I am wanting to ...
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understanding of the number relation for all n, n^3 mod 9 is 0,1, or 8

In the book, Elements of programming CASE ANALYSIS has been listed as one of the approaches to solve a problem. As an example, the book states that for all n , n^3 mod 9 would either be 0,1,8 and even ...
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Courses to take during pure math masters to keep data science and applied work as a possibility

I was wondering what courses you can take in a pure math masters to preserve the opportunity to go into data science, economics, policy research or other applied work while preserving the opportunity ...
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Axial vector of a skew symmetric tensor

What is the relationship between the magnitude of axial vector and the magnitude of its corresponding skew tensor? How can we derive it?
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I'm new to Trig and don't understand…

I do not understand how to solve this question. I have searched many websites and have not found any information on how to do it. Find the values for $\theta$ that make each statement true $$\sin(\...
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1answer
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What is the real need and concept of average in normal sense (not in form of calculus)? Please see below what I mean by asking this question.

I know how to calculate average, but never get the idea why we need to do that. For example see a question I did correctly just by following only some steps. I got the correct answer, but don't know ...
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1answer
58 views

Correct way to announce a theorem

Reading the following statement : Theorem : An operator $A$ has the property $P$ if $\underset{\lambda \rightarrow 0}{% \lim }\left( A-\lambda \right) ^{-1}$ exists. Does the reader understand that $...
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1answer
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How Can I Keep Advancing in Linear Algebra?

I recently graduated with a bachelor's in computer science and a minor in mathematics. Since I won't be enrolled in any more math classes, I want to continue learning and honing my skills by myself. ...
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4answers
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Intuitive, possibly graphical explanation of why rationals have zero Lebesgue measure

I know that rationals, being a countable set, have zero Lebesgue measure. I think one way to prove it is to find an open set containing rationals that has measure less than $\epsilon$ for every $\...
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Is there any standards that will differentiate reading $x+y^3$ to $(x+y)^3$?

Which of the following is read as "x plus y cube"? a. $x+y^3$ b. $(x+y)^3$ Is there any standard in reading expressions that will address this question?
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saddle point method with conjugate complex roots

Here I want to use the saddle point to calculate something. My equation is $$f(x,t)=\int_0^\infty\exp \left(\underbrace{a N^{\frac{1}{1-\alpha }}+b \ln (N)-\frac{x^2+A^2N^2-2ANx}{2 N \sigma ^2}-\frac{...
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Bibtex Sources for mathematics

I need a website where I can find the bibtex citation source for papers and books. What is the best website for this purpose?
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1answer
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Why is it possible to divide by 0 in wheel theory?

I have been looking into wheel theory and have been wondering how it is possible to divide by 0 in it. Also, what are some good books for learning about wheel theory?
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1answer
60 views

Is there a path to learn all mathematics? [closed]

What I mean is that if it's an order in learning all areas of math like first arithmetic, then algebra, etc.
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1answer
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What are the most interesting math riddles you know? [closed]

I am talking about riddles that do not involve play on words. The riddles should be logically and mathematically correct too.
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30 views

How to solve this equation , one parameter depend to its sum

Known $$ a , B=\begin{pmatrix}b_0\\b_1\\ \vdots \\b_i\end{pmatrix} , C=\begin{pmatrix}c_0\\c_1\\ \vdots \\c_i\end{pmatrix} $$ Equation $$ Y=\begin{pmatrix}y_0\\y_1\\\vdots\\y_i\end{pmatrix}, $$ $$ ...
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Prerquisites of starting real analysis by N.L Carothers

So I know the elements of analyis up to Riemann intergals nicely. I want to start Carothers' real analysis but some friends are discouraging. What are the prerequisites of starting real analysis by ...
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2answers
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In how many ways, Miyad can do the Trick? [closed]

The numbers 1 to 6 are written on six balls. Miyad took four balls from there such that if he multiplies the numbers of the balls and then say it to Mun, then Mun can’t say the number of the balls ...
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2answers
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What is something incredibly interesting/insightful about mathematics that requires only a basic understanding of mathematics? [closed]

As a fun project, I want to create an interesting, insightful, yet educational video about some fascinating topic/concept/idea in mathematics that only requires a basic understanding of mathematics so ...
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1answer
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Accessible examples of using ideas in mathematical logic to solve problems in “main-stream” mathematics

It is perhaps well-known that ideas from mathematical logic (esp. model theory) can help solve problems in "main-stream" mathematics, e.g. using ideas from model theory to solve problems in algebraic ...
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What is the best book for the following mentioned courses?Internet resources too please.

1.Motivation:Learning physics and computer science and of course the enchantment of maths itself. 2.Background:A little bit of algebra,Trigonometry utmost basics and basic geometry 3.Why it is ...
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2answers
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Structured math learning(how to learn maths step by step?) and resources for all the courses mainly books [closed]

1.My question:Could you please recommend the resources and structure of learning maths from algebra to higher level like calculus and beyond?Mainly books please. Something like books for Algebra I-...
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1answer
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Could you suggest basic mathematics textbooks (calculus, linear algebra) that are written in an intuitive manner?

For instance, I really loved reading the book " Div, Grad, Curl, and All That" by H.M.Schey. I would like texts closely written in that particular style.
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Dividing an integer by a number with a fraction

There is a way regular people use to multiply a number with a number with a fraction. For example, multiply 6*2.5. They multiply 6*2=12 then 6*.5=3 then they add 12+3 to get the final result 15. I am ...
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0answers
69 views

Which areas do students struggle with while learning real analysis? [closed]

I am planning to self study Real Analysis over the summer by following Abbott's Understanding Analysis and another set of lecture notes on an undergraduate single-semester Real Analysis course. Before ...
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0answers
42 views

Soft Question: Retaking Undergrad Courses vs Masters [closed]

Hopefully the title explains my question. I want to apply to PhD programs next fall (2021). My grades in algebra and number theory were rather poor (C+ and B- respectively). Analysis was descent (B). ...
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2answers
72 views

Why does multiplication always have the associative and commutative property?

We all know that Commutative property and Associative property of multiplication is always saved for the real and complex numbers. I know that if I recalculate it a million times, the result will be ...
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5answers
264 views

What should I do when I get stuck?

I come from the software engineering background. My main problem with math materials online is how dense and unforgiving those usually are. I often read a math article and get what the author is ...
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1answer
43 views

Intuition behind Heine definition of the limit of a function

I am teaching some high school students on the definition of the limit of a function and having a hard time explaining this to them. In our country's textbook, it is defined by using Heine's ...
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1answer
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A question about study methods

How to study advanced math books and papers? Advanced math books don't have exercises to practice. What study methods do you use? Could you explain me in detail what you do while trying to learn new ...
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2answers
163 views

Encounters with Zorn's lemma early in study of mathematics

Many mathematics students encounter the axiom of choice relatively early in their studies. For example, they see the claim that if we have a surjection $g\colon B\to A$, then there is one sided ...
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88 views

Are there any services where I can pay someone to help with advanced measure and integration theory? [closed]

Are there any services where you can pay someone to help with questions on advanced measure theory, and integration theory. Take for example, this, this and this question? Just establishing what I ...
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1answer
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Should the approximation sign be carried forward in derivations involving multiple rearrangements?

Suppose I have some function $F$ that can be written as an expression $A$, and that $A$ can be approximated as $B$, and that $B$ can be rearranged to give $C$. While demonstrating the derivation for $...
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3answers
47 views

Find a and b given $(3x + 2)$ and $(x - 2)$ are factors of $6x^3 + ax^2 - 4ax + b$. [closed]

$(3x + 2)$ and $(x - 2)$ are factors of $6x^3 + ax^2 - 4ax + b$. Find a and b.
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Why does Mathematics have no generally accepted definition?

I searched for the definition of Mathematics I found one definition on Wikipedia: Mathematics includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and ...
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Synthetic proof of the equation of hyperbola [duplicate]

Is there synthetic proof of the equation of hyperbola using this definition: A hyperbola is the set of all points in a plane such that the difference of the distances from two fixed points (foci) is ...
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1answer
24 views

Sets, subsets and Cartesian product.

I am studying computer science and I have Maths exam soon. While solving past exam papers, I encountered with a sets question and couldn't solve. It consists of two parts (a) and (b) and couldn't ...
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27 views

Intuition of product rule using graphs and slopes

I have seen formal proof of the product rule ($(f(x)g(x))' = f'(x)g(x) + f(x)g'(x)$) and one with rectangles and areas - explanation seems reasonable. But, is there direct and intuitive proof using ...
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15 views

A bounded sequence with a diverting subsequence?

Is there a bounded sequence with a divergent subsequence? My thinking is that if we take a bounded sequence then Bolzano-Weierstraß tells us there exists a subsequence that converges in the set of ...

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