Questions related to the teaching and learning of mathematics.

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9
votes
3answers
320 views

Examples of useful, insightful, and interesting hand-waving [closed]

It seems to me that some hand-waving (by which I mean some arguments that aim at giving some form of intuition on the problem even at expenses of complete rigour [and not mnemonics for high-schoolers ...
2
votes
5answers
143 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
259 views

So bad at maths sometimes I feel depressed about it [closed]

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
40 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 ...
12
votes
6answers
262 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 ...
2
votes
1answer
181 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 ...
1
vote
0answers
24 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
61 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 ...
1
vote
1answer
126 views

Question about independent study in differential geometry for an undergraduate. [closed]

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 ...
9
votes
1answer
149 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 ...
0
votes
1answer
39 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.
6
votes
1answer
129 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 ...
17
votes
1answer
601 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
3answers
88 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
85 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
66 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 ...
0
votes
1answer
127 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
103 views

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

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 Erwin ...
5
votes
2answers
64 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
104 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
69 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
35 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, ...
74
votes
5answers
3k 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
733 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
64 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
178 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
126 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 ...
9
votes
3answers
198 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
37 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
56 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
26 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
33 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
179 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 ...
23
votes
6answers
571 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
44 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.
2
votes
2answers
263 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 ...
3
votes
2answers
173 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, ...
1
vote
2answers
31 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: $f(0) = 1,$ ...
0
votes
0answers
27 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
176 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
44 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.
0
votes
2answers
42 views

Arithmetic Progressions Formula

I'm studying progressions in math class in Portugal, and I don't know the words/translation in english for certain things so I'll try to explain. I have this arithmetic progression: 2, 8, 18, 32 ... ...
3
votes
1answer
101 views

How can I learn to recognize the obvious questions?

I have heard and seen several references to "obvious questions", "obvious axioms" and other "obvious" things (I am not referring to obvious results!). Now, in a seminar I am taking, at the end of each ...
0
votes
1answer
432 views

Taking Calculus II and Calculus III at the same time?

A little background: I'm a high school student enrolling at a local university next fall. I plan to pursue a mathematics degree, have studied this Calculus book. During the next semester, I plan to ...
1
vote
1answer
48 views

Teaching non-integer exponents

Say I'm teaching a younger student the concept of exponents. Now the basic example to begin with is say $2^3$ where it can be 'visualised' as having two blocks, then doubling the number of blocks, ...
1
vote
2answers
26 views

Large round brackets in equation

I cannot recall what the large () brackets mean - Google seems to be full of links on how to create them but not what they actually are or how to resolve them. $ ...
6
votes
2answers
72 views

Is there a way to simplify this equation

Is there a way to simplify this equation? $$ CE = 2 FD \sin \left( \arctan \left( \frac{AF}{FD} \right) - \arccos\left( \frac{AB}{\sqrt{AF^2+FD^2}}\right) \right) + \sqrt{AF^2+FD^2-AB^2} $$ Edit: ...
0
votes
2answers
44 views

Why do we need zeroes when writing some of those kinds of numbers?

I've looked up that zero is a placeholder in numbers that have this digit. I also figured out what would happen if there's no zero in 5,074 in a math journal. The number would be 5,74, which would ...
1
vote
2answers
117 views

How to find the order of a group generated by two elements?

What is the order of a group $G $ generated by two elements $x$ and $y$ subject only to the relations $x^3 = y^2 = (xy)^2 = 1$? List the subgroups of $G$. Since the above relation is the 'only' ...
2
votes
1answer
63 views

Order of a study

So i just recently had to drop two math courses, topology, math logic, because my math maturity wasn't up to the level needed to excel in them. I intend on taking them again, but not without first ...