Questions related to the teaching and learning of mathematics.

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6
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0answers
55 views

Examples of useful, insightful and interesting hand-waving

I am really amused by the answers to this question on "Most harmful heuristic" posed on MathOverflow, from which I've benefited a lot. However, it seems to me that some hand-waving may be really ...
2
votes
5answers
105 views

Is there a proof that $\int \frac {dx}{x}=\ln |x|+c$?

Is there a proof that $$\int \frac {dx}{x}= \ln|x|+c$$ for $x\neq 0$ I would be interest for any replies or any comment.
7
votes
1answer
87 views

So bad at maths sometimes I feel depressed about it

I taught myself how to count before I even learnt how to talk or read. Playing with numbers was all I did when I was young. I didn't have anyone to foster that type of passion that I believe I still ...
2
votes
2answers
37 views

Printer toner coverage

I have a printer that I used for $2$ years. First year I printed $9630$ pages, with $17\%$ ink coverage per page. Ink coverage is the percent of the page that is not white. Second year I printed ...
1
vote
0answers
33 views

Sources for mathematics outside the mathematics world

In this question I would like to ask you about material showing the uses (or occurrences) of mathematics in the everyday world. The aim is to encourage with it a group of young undergraduate ...
1
vote
1answer
121 views

Why is the axiom of choice not taught from the start to mathematics undergraduates?

I've recently discovered that the following theorems require the axiom of choice to be proven: every surjective function has a right inverse. a real-valued function that is sequentially continuous ...
0
votes
0answers
32 views

Algebra Questions-Academic

ı must solve this ı only know question 2)s' b) option is Euler's prime-generating polynomial.But ı dont know to show that,too.please help :(
1
vote
0answers
19 views

Calculate year for a provided yield

\$146.25 will yeild \$46.25 at 7.5% per annum. How to get the number of years? Answer is 6 but how do you get it? What is the formula?
3
votes
2answers
47 views

Condition of the mean value theorem

The usual formulation of the mean value theorem in a real analysis course is something like this: Let $f\colon [a,b] \to \mathbb{R}$ be continous on $[a,b]$ and differentiable on $]a,b[$. Then there ...
0
votes
1answer
53 views

Question about independent study in differential geometry for an undergraduate.

I am a senior undergraduate math and physics student applying to graduate school in math for this upcoming fall. I have had classes in: Abstract Algebra (Rings, Fields, and Groups), Point-Set ...
7
votes
0answers
93 views

How to listen math lectures?

Many times, the lectures goes beyond the head and not easy to follow, (at least with me),mainly in the workshop/conferences, though the audience are eager to learn something from it. Also, most of ...
-1
votes
0answers
51 views

What to mathematics books to read? [closed]

What are the top 20 mathematics books you should read before you die? I am not necessarily looking for classicals like Principia Mathematica.
0
votes
1answer
32 views

How do I remove decimals from cent amounts?

How do I change "23.96" CENTS into something that makes sense? Can I just say \$ $0.2396$? It's important that I keep the value behind the decimal I just don't know how.
0
votes
2answers
70 views

What have been “taught” without being proved? [closed]

I would like to make a list investigating the following:- Can you recall (if any):- What topic(s)/formula(s) were being ‘taught’ and told to be true/memorized and subsequently applied without being ...
4
votes
1answer
92 views

How to get university level Mathematics education on my own?

As far as Mathematics go, I have a highschool level education. I wonder how I could learn more about Mathematics to be on the level of those who had Mathematics level education at a university. Is ...
15
votes
0answers
329 views

Which universities teach true infinitesimal calculus?

My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by ...
0
votes
2answers
72 views

Area+Pythagoras Theorem

In the figure below show that Area A + Area B = Area C. What is the answer to this question?
0
votes
3answers
64 views

Is there an elementary “proof” that the first degree equation has only one solution?

I was asked from a student why the first degree equation has only one solution (if it has a solution) Let's consider the equation $2x+5-3x=-4x+14$ for example. How can I explain to a 13 year old ...
0
votes
1answer
77 views

How can I convince students a certain polynomial equation is symmetric?

How can I convince students that $p(x)=0$ is a symmetric equation if they ask me, where $p(x)$ is polynomial of degree $n$ with reals coefficients. For example : $A(x)=2x^4-9x^3+8x^2-9x+2=0 $ is ...
2
votes
1answer
49 views

Characteristic of a Ring not making sense.

The characteristic of a ring with unity is defined to be the least positive integer $n$ such that $1$ plus itself $n$ times $=0$. How does this make sense? $1$ plus itself $n$ times $=n1=n=0$, but ...
1
vote
1answer
84 views

What's the value of tau?

I've seen $\tau$ on a title of a YouTube video and I need help knowing what the value is. I'm serious. I've never heard of the value. So, what is it? Also, is it rational or irrational (this part ...
0
votes
0answers
71 views

Complexity of graph radius algorithm

I am a bit new so I hope I don`t break any rules. I have an algorithm: Given H = (V, E) a graph. If v ∈ V and r ∈ N, we will note with SH(v, r) the sphere of radius r with the center in v: SH(v, r) ...
0
votes
0answers
30 views

Where can I get detailed and comprehensive notes of a functional analysis course taught using the book by Erwine Kryszeg?

Where on the Internet can I find detailed and comprehensive lecture notes of an elementary functional analysis course taught using the book Introductory Functional Analysis with Applications by Erwine ...
5
votes
2answers
42 views

How to improve concentration when beginning to work on a math problem that seems boring?

I am a college student and my current situation is that I have an extremely hard time getting myself to start doing math. I feel like math is 'boring,' but ONLY until I start actually doing it. Once I ...
3
votes
1answer
76 views

Studying for analysis- advice

I find that studying for analysis is unlike other math classes that I've taken. I dedicate a lot of time to studying for it, but it seems like no matter how much time I put into it I am not getting ...
5
votes
1answer
55 views

Is a thorough study of algorithms useful for a mathematician?

In my university, there is a core course called "basics computer science for mathematicians". The topics covered range from algorithms, to the bases of programming, to theory of computability. The ...
1
vote
1answer
22 views

math classes to take for path

I have taken: Calc 1, 2, & 3, Introduction to Discrete Math, and Introduction to Statistics. The maths I learn I wish to be most applicable to programming (any kind of programming, game, physics, ...
0
votes
0answers
28 views

Dividing from right to left

Suppose a number is given 6401024, I want to divide it by 1024. But I want to do it from right to left. so in a computer memory storage, Here Let us assume its an array, we hold the remainder of the ...
54
votes
4answers
1k views

“Advice to young mathematicians”

I have been suggested to read the Advice to a Young Mathematician section of the Princeton Companion to Mathematics, the short paper Ten Lessons I wish I had been Taught by Gian-Carlo Rota, and the ...
2
votes
14answers
574 views

Interesting piece of math for high school students? [closed]

I'm giving an hour long lecture to high school math students with a fairly high aptitude in math. I want to present something a little advanced for them (undergrad level) that they have to struggle ...
2
votes
0answers
51 views

How to decide which theorems from textbook to prove

I've noticed that theorems in textbooks roughly come in two varieties: those that are worth trying to prove yourself, and those that aren't. I'm not going to try and give criteria for "worth trying" ...
3
votes
1answer
80 views

Advice for Math Majors -What to do if you come into college with a lot of college credit? [closed]

In high school I was a good maths student and took AP Calculus BC my freshman year and got a 5 and then took Multivariable Calculus, Linear Algebra, Differential Equations, Introduction to ...
4
votes
2answers
86 views

where to start if you lack basics? [closed]

I've joined this forum for few weeks now and it amazes me that so many people are good at math. For me, I'm more of a history person rather than math person, so I hated math since I was young, not ...
6
votes
3answers
67 views

Video Lessons in Complex Analysis

Does anybody have some link for good video lessons of a complete course in Complex Analysis? Grateful.
1
vote
1answer
29 views

Introduction to Newtons method

I'm supposed to come up with two ways to introduce Newtons method for the approximation of zeros for highschool students. (That is the method using tangents and with the formula $ x_{n+1} = x_{n} - ...
0
votes
0answers
32 views

Fun Lagrange multiplier problem?

Do any of you have a fun or interesting Lagrange multiplier problem that would be suitable for undergraduate calculus students? I'm planning on working through a standard Lagrange multiplier problem ...
0
votes
1answer
19 views

Systems of Inequalities question

Amy is a landscaper and has been given an assignment to modify the plans for a park in a small neighbourhood. The land she is working on is covered in trees and shrubs. Amy needs to make the park ...
2
votes
0answers
23 views

Ratio Question (Primary School)

Now, there are 6 students who are sharing 4 desks at the library. While 4 of them are using the desks, the other 2 students have to wait and watch. If they have to use the desk for the same amount of ...
8
votes
1answer
119 views

How to draw greek letters on paper / blackboard?

For $\gamma$ (gamma), I've noticed people doing a sort of $\alpha$ (alpha) rotated by ninety degrees, which seems to be the standard on-paper-or-blackboard equivalent of $\gamma$. But for letters ...
17
votes
6answers
351 views

Open source lecture notes and textbooks

This question is inspired by the popular "Best Sets of Lecture Notes and Articles". Indeed, I would like to collect a "big-list" of open source (that is, with $\LaTeX$ code available) high-quality ...
0
votes
1answer
25 views

Formula to find the sum of digits

I want to know if there is a way to find the sum of the digits of a power $a^b$ For exemple $9^{14}$ = 22876792454961 , Sum is 2 + 2 + 8 + .... + 6 + 1 Thanks in advance.
1
vote
1answer
32 views

Why can we square both sides when LHS and RHS is square rooted?

When we have something in this form: $\sqrt{x + a} = \sqrt{y + b}$ A common technique to solve is to square both side so that: $(\sqrt{x + a})^2 = (\sqrt{y + b})^2 \implies x + a = y + b$ I'm an ...
2
votes
2answers
234 views

Real numbers as decimals

I'm looking for a book that develops the theory of real numbers in a rigorous way in terms of their decimal expansions. The exposition should be concrete and preferably aimed at mathematically ...
4
votes
2answers
104 views

Why learn abstract mathematics? What is the point? [closed]

I'm a mathematics college lecturer and have an mphil degree in the subject. But I often wonder why I'm learning this senior undergrad level mathematics---analysis, topology, functional analysis, ...
0
votes
0answers
29 views

Motivation for an undergraduate major in statement of purpose [migrated]

Is it okay to mention in my statement of purpose for admission to grad school in math, that my undergraduate major is engineering because my parents wanted me to do it? I was initially wrote my ...
1
vote
2answers
29 views

Countability - Constant Functions

I am learning about countability. I know about diagonalization and I am confused about constant functions and whether or not they are countable. A constant function in my case would be: $f(0) = 1,$ ...
-2
votes
1answer
60 views

Mathematical thinking

I was curious to know some books that would lead to more mature development of mathematical thinking? I know mathematics is not just the computation, but the science of developing patterns and ...
0
votes
0answers
15 views

Example of caculation the cummulative probability

I have a question about probability that I am confusing. I have k bit symbols. Now, I want to calculate the successful decoding probability for k bits. It can defined by this equation ...
3
votes
1answer
96 views

Prove that the exponential function is differentiable

Imagine that you are writing a book on the foundations of analysis. You have already proved that for each $a > 1$ there is a unique function $f_a(x) = a^x$ satisfying the following: $f_a$ is an ...
2
votes
1answer
36 views

A Very Elementary Article or Webpage about Secret Sharing

I'm looking for an article or webpage about secret sharing with Latin squares, accessible to middle school students. I searched but found none. Can you help me? Thanks.