Questions related to the teaching and learning of mathematics.

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4
votes
0answers
55 views

Algorithm for finding “fact families”

My friend's 3rd grader encountered the following question regarding "fact families" on her math homework: I was in 3rd grade sometime in the 1980s, so I don't believe I ever encountered this term ...
4
votes
3answers
293 views

What things should one know in order to enjoy their undergraduate degree? [closed]

From looking at undergraduate mathematics programmes it's quite apparent that mathematics degrees are demanding, one could even say the work load is grueling. However I'm certain that there are ...
3
votes
5answers
207 views

Does taking courses in mathematics give any help for mathematical logic?

I'm undergraduate student of philosophy department and I think I'll major in mathematical logic. For studying mathematical logic, I thought studying math lectures would give help to logic. So I ...
3
votes
1answer
78 views

Math or Physics

I'm a Master Math Student And I'm very interested in Some fields in Physics Like Cosmology. I even Considered Changing my field and Apply for physics(Cosmology) but wasn't really possible (my ...
2
votes
3answers
125 views

Why do some accept zero as a natural number but others don't? [duplicate]

I have had many teachers who have told me that zero is a natural number but then there is those teachers who say its not. why is that ?
-1
votes
0answers
28 views

question on Stieltjes-Lebesgue Measure [closed]

I began learning Real Analysis last year and always couldn't find someone to answer my questions till I found this site recently. Hope can find some answer here :) And...BTW, how to display LaTeX ...
0
votes
1answer
57 views

Which topics in maths should I know before I dive into programming for image processing?

I am a student who wants to start out with programming for Image processing but as I do not have a good mathematical background(I haven't studied A-level Maths) I would like to know what are the ...
2
votes
3answers
89 views

Prove “the length of the arc is proportional to the central angle subtended”

Depending on individuals’ experiences, the following might not (and hope not) happen to you. However, it did happen to some (including me). When I first studied the topic on “central angle + arc ...
1
vote
0answers
33 views

Understanding mathematical syntax in SO(3) - Part II

In a paper I found in internet there is a relation about mapping a matrix into a vector and viceversa. One question has been already kindly answered here, but since I'm new to this kind of syntax I ...
1
vote
1answer
36 views

Help for understanding a vectorial equation found in a paper.

Trying to implement a code for the algorithm described in this paper I found something not very clear to me that leads me to misunderstand the whole concept. To calculate the vector $\vec{b_{3d}}$ ...
0
votes
1answer
85 views

Which topology textbook has the greatest amount of ancillary support available on the Internet?

I'm considering to begin upon the study of topology and am wondering which book would the best option. I've even started reading Munkres and G. F. Simmons, but the problem is neither book has any ...
0
votes
1answer
49 views

Understanding mathematical syntax in SO(3)

In this paper, pp. 2, I found the following differential equation system and a statement: There are two things not clear to me: the hat map symbol seems to make mathematical symbolics shorter and ...
90
votes
17answers
7k views

What parts of a pure mathematics undergraduate curriculum have been discovered since 1964?

What parts of an undergraduate curriculum in pure mathematics have been discovered since, say, 1964? (I'm choosing this because it's 50 years ago). Pure mathematics textbooks from before 1964 seem to ...
19
votes
2answers
474 views

Collections of undergraduate research projects

I would like to compile a "big list" of undergraduate research projects in the following areas of mathematics: calculus; analysis; abstract algebra; linear algebra; number theory; geometry; ...
1
vote
2answers
89 views

Let $\{a_n\}_{n=1}^\infty$ be an infinite sequence. Does there exist an infinite series whose partial sums is $\{a_n\}_{n=1}^\infty$?

Definition: By an Infinite Sequence of real numbers, we shall mean any real valued function whose domain is the set of all positive integers. Definition: By an Infinite Series of real numbers, we ...
2
votes
1answer
133 views

Natural progression in a curriculum for self-study of analysis

Would you list what is a natural and effective progression to self-study topics in analysis in order to gain a broad knowledge of the enormous corpus of knowledge that modern analysis involves. As a ...
2
votes
2answers
205 views

I want to learn math from zero

I finished high school 2 years ago and now I'm stuck in a university in Turkey. I am interested in learning precalculus, discrete mathematics, physics and chemistry. Question: I need to learn math ...
4
votes
2answers
175 views

Solving min-max optimization problems in original ways (that is, avoiding the frenzy of differentiation)

As I see from the students I'm tutoring, once faced with a min-max problem, the average student is taken by the frenzy of differentiation. I would like to show that sometimes it is better to use ...
0
votes
2answers
26 views

Is it correct to define variables and functions that are more than one character?

Most of the time (at least at my high school student level), we are using variables such as a, b or $\theta$, and functions such as f, g etc... But would it be possible to use multiple characters ? ...
1
vote
2answers
38 views

components of a vector

If I have the angle between two vectors and , I have the components (x,y,z) of the first vector ( xi + yj + zk) how can I know the components (x,y,z) of of the second vector ?
2
votes
3answers
157 views

Education problem - what to do ? Very intriguing problem [closed]

I really love maths, I see some people complaining of being afraid of maths, or finding it difficult to have motivation to do maths and I can't understand them. Since I'm blinded by my love of maths; ...
17
votes
4answers
2k views

Why do we need to learn Set Theory?

I was planning to write some article for the Mathematics magazine of our college and it occurred to me that it will be a good idea to write about the impact and importance of Set Theory. I plan ...
9
votes
3answers
300 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
139 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
177 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
249 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
168 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
55 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
105 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 ...
8
votes
1answer
140 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
36 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
124 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
517 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
83 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
84 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
63 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
120 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
80 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
89 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
57 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
99 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
68 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
28 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, ...
73
votes
5answers
2k 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
685 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
56 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
140 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
115 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 ...