Questions related to the teaching and learning of mathematics.

learn more… | top users | synonyms (1)

17
votes
6answers
4k views

How to go from beginner to expert in mathematics?

I'm particularly interested in knowing the order of subjects one should study to become good in mathematics. In my not so great knowledge of the subject I would say that the best place to start could ...
12
votes
1answer
973 views

What is the expected mathematical repertoire of a Ph.D. program applicant?

I am an undergraduate (currently a sophomore) studying to prepare for applying to a Ph.D. program in mathematics. I have thus far structured my course selection upon the advice of a friend I met ...
5
votes
0answers
146 views

Bayes analysis as used in a Presidential Election - with calculations shown

Can you show all the steps needed for a Bayesian probability progression as new information is received. As an example, initial estimate for Obama to win (popular vote) is 55%. In state-A, Democrats ...
15
votes
5answers
1k views

Is high school contest math useful after high school?

I've been prepping for a lot of high school math competitions this year, and I was just wondering if all the math I learn would actually mean something in college. There is a chance that all of it ...
5
votes
2answers
273 views

How does one best balance learning from a “problem based book” with supplementary material?

We all know that when learning math, one has to do more than just simply read - one must try to solve problems and work actively with the material. Many books try to force the reader to participate ...
1
vote
2answers
91 views

Can anyone explain the method used for finding the answer to this question?

I was practising questions on principles on mathematics. I stumbled onto this question and I don't know where to start. Can anyone please help?? If $P_1\,P_2\,\ldots\,P_n$ is a regular polygon in ...
4
votes
2answers
797 views

Is set theory taught in middle school in the US?

I recently learned that one of my cousins who is a 7th grader in the United States is learning naive set theory (sets, maps, 1-1, onto maps, relations). Is this part of middle school math curricula ...
6
votes
3answers
980 views

Good way to learn Ramsey Theory

What are some good books on Ramsey theory? I have Van Lints book on Combinatorics: is this enough preparation to start reading about Ramsey theory? I want a book that includes important results and ...
9
votes
5answers
2k views

Mathematics, Philosophy and writing.

Do you know of any famous mathematicians who were also philosophers? I have heard of Descartes, Plato and Leibniz. Are there other good examples, especially more modern examples? Also welcome are ...
5
votes
3answers
228 views

Studying at home and finding good resources in Algebra

I'm a graduate student studying at home. I find that ressources in Mathematics on the web are easier and easier to find, and I am happy for that, because I like to have different points of view about ...
5
votes
1answer
1k views

Mathematical competitions for adults.

I live in Mexico city. However, I am not so interested in whether these exist in my vicinity but want to learn if they exist, if they do then It might be easier to make them more popular in other ...
1
vote
3answers
155 views

My brothers share from income.

My brother is driving a limo with his partner who told him that they will go 50-50 on income and also 50-50 on gas. So if my brother earns \$1000 by spending \$200 on gas, what will be my brothers ...
3
votes
0answers
139 views

Is there a way to determine how many solution does “ The hundred Fowls problems” have looking at the coefficients?

I was looking at the different versions of the hundred fowls problems. I came across the problem posed by Chinese mathematicians posed in 5th century,and then Indians in 9th, 10th centuries. Alcuin of ...
1
vote
1answer
119 views

Riemmans hypothesis and its implications.

Ok so I have heard in all sorts of places that Riemmans hypothesis has very important uses in cryptography. I have heard in many places that if someone solved it he would be able to hack various ...
-2
votes
4answers
112 views

Complete instead of Complex, Irregular instead of Imaginary

Will the terms complex and imaginary ever be replaced? At least within beginning classes? I imagine it is more of a kind of hazing into the "mathemitician's club" to allow the terms to confuse ...
83
votes
3answers
8k views

Topology: The Board Game

Edit: I've drawn up some different rules, a map and some cards for playing an actual version of the game. They're available at my personal website with a Creative Commons Attribution 4.0 license. ...
6
votes
1answer
354 views

Problem Regarding Time Management

I don’t know whether it’s the right place to ask for such a request. I would like to express my apologies in advance if it anyhow goes against the dignity of the forum. I’m taking preparation for a ...
4
votes
8answers
2k views

Studying Math, All Over Again

I am 16 and never really paid attention to math. For me it was just one more obstacle in passing the exams. Now that I study computers, mostly on my own, I find that there is indeed a need for me to ...
3
votes
0answers
83 views

Niche topics in math useful for physics

I have a somewhat unorthodox question. What are some good niche topics that aren't typically covered in courses in math to self-study? Ideally, I'm looking for something that could ultimately be ...
3
votes
0answers
860 views

What should an undergraduate thesis be about? [closed]

I'm very excited to start my undergraduate thesis and I've heard some recommendations for topic but I have a questions and I'd like to hear your opinions. Should I look for the most advanced topic I ...
14
votes
5answers
1k views

Is the skill to learn new math by reading textbook alone (no lectures) required when one becomes a PhD student?

I've taken a few math classes in college. I'm wondering as one graduates college and applies to become a PhD student in math, is he/she going to be required to learn math related materials alone ...
8
votes
2answers
576 views

Strengthening My Foundation in Mathematics

"For every equation you introduce, you cut your audience in half." This expression, which I believe came from Stephen Hawking, summarizes why I believe that I have a weak foundation in ...
9
votes
6answers
3k views

What is the best base to use?

When I typed this question in google I found this link: http://octomatics.org/ Just from the graphic point of view: this system seems to be easier (when he explains that you can overlap the line). He ...
3
votes
2answers
87 views

Good Technology Resources for a Pre-Algebra Class?

I am looking for some recommendations for good and interesting technology resources for a pre-algebra class. My main goal is to allow the students to be able to self-pace the instruction, out of ...
2
votes
1answer
375 views

How to improve Maths skills after a physics degree.

A few years ago finished a physics degree and one of the biggest lessons I learned is that I need to spend some extra time on pure Maths. In fact I almost wish I done a maths degree first as that ...
8
votes
4answers
3k views

What are the prerequisites for taking introductory abstract algebra?

I am a maths student in my second year of university. I have taken and done quite well in Calculus I, II, III as well as a linear algebra (application focused) class. I have not worked much with ...
9
votes
3answers
326 views

Links to Online Videos of Good-Quality Lectures by Mathematicians

I am not trying to do anything new here, but I would like to start an activity that has been going on at Math Overflow. Hopefully, people here at the Math StackExchange can also enjoy the good stuff. ...
4
votes
0answers
208 views

Mind Maps for teaching Mathematics

Has anyone used Mind Maps to teach advanced mathematical topics? If so, how did it work, was it useful or a waste of time? Thanks for any insights. Regards -A
0
votes
1answer
136 views

How can I calculate log?

$$ -0.4 \cdot \log(0.4) - 0.3 \cdot \log(0.3) - 0.3 \cdot \log(0.3) = 1.571 $$ The answer is given. How can I calculate the equation for obtaining $1.571$? Please help me understand.
0
votes
1answer
249 views

how can i solve sigmoid function?

$$\frac{1}{ 1-e^ {-(-3.0)}} = -0.052$$ $-0.052$ is the answer. This equation is sigmoid function. How could I get the answer like that? Please understand me T.T
4
votes
3answers
349 views

participation in 1st year introductory pure maths classes

I have just started teaching a very elementary class for 1st year students on introductory pure mathematics. ( classes at my institution are groups up to 20 students and supplement the lectures. The ...
8
votes
2answers
263 views

How are more difficult proofs discovered?

Are there any resources that show how are the various proofs of important theorems in mathematics are invented? I don't understand how can anyone come up with this method for proof for example. I want ...
50
votes
15answers
5k views

How can I introduce complex numbers to precalculus students?

I teach a precalculus course almost every semester, and over these semesters I've found various things that work quite well. For example, when talking about polynomials and rational functions, in ...
5
votes
3answers
589 views

Example for a simple game of chance where the average value converges fast to the expected value

I want to introduce the concept of expected value (for a discrete random variable, finite case) in a high school class. My first idea was to start with a simple game of chance and let the students ...
2
votes
1answer
320 views

Getting Practice on Finding Charts for a Manifold

I just want to ask for a suggestion on the study of differential geometry. When I study it I understand the theorems, their proofs, I understand perfeclty the concepts and so forth, but I'm having ...
1
vote
1answer
429 views

Circular motion “calculate the angle”

I have a equation i need to find out how they hang together. angel = (velocity * time) - (acceleration * time * time / 2) I know circumference of a circle: ...
0
votes
1answer
682 views

In which branch of mathematics does “logarithm” belong? Arithmetic or algebra?

I'm currently working on an iOS & Android application for GCE O Level students. I have to classify everything neatly such that Maths never appears to be a messy subject to study and so should I ...
9
votes
1answer
257 views

Publishing mathematics

How or where does one express work they've done to others? What does it mean formally to 'publish' mathematical work you've done? How do you know if your work is any good? Or if someone has already ...
0
votes
2answers
102 views

Mathematics or statistics?

Can you please tell me what is ((stochastic modelling and statistical analysis of spatio-temporal data)) related to? I mean Mathematics or statistics? Is it good subject for student who interested in ...
14
votes
7answers
2k views

Films about math: a question about math education and motivation for learning math [closed]

I'm interested in movies about or related with mathematics or physics, I mean not documentaries which I also consider movies, but artistic or mainstream films about math. Now I have the following in ...
5
votes
2answers
291 views

Problem understanding math

sorry for my english but I am a foreigner. I'm writing to ask you for help with a problem I have with mathematics. I'm going to go to university physics but I have serious problems as regards ...
1
vote
1answer
218 views

Average Amount Of Math or Math-oriented Courses Taken Each Semester [closed]

I was wondering, from all of you, what the average amount of math and\or physics courses you were/are able to tolerate in one semester.
24
votes
6answers
1k views

Why do new rules cause students to forget and misapply older rules?

I teach at a community college. I have taught everything from arithmetic to linear algebra. I have also taught at 4-year schools, but at present, I'm devoting my energies to the problem of helping ...
10
votes
0answers
358 views

How to be a bird

Freeman Dyson has famously characterized two styles of mathematics, that of the bird and that of the frog. I was asked recently the following question, which I don't know how to answer: If, in ...
2
votes
1answer
90 views

What does brace below the equation mean?

An example of what I am trying to understand is found on this page, at Eq. 3. There are two braces under the equation... What is the definition of the brace(s) and how does it relate to Sp(t) and ...
11
votes
4answers
833 views

Best way of introducing determinants in a linear algebra course

What is the best way of introducing determinants in a linear algebra course? I want to give real life examples of where the determinant is applied. It should have a real impact.
11
votes
11answers
2k views

Good examples for mathemathical problems/statements that are easely solvable/provable in one theory and hard to solve/prove in another

Let $P$ be a mathematical statement or a mathematical problem. I am looking for a couple of nice examples for $P$ that satisfy the following criteria: Given two (or more) mathematical points of view ...
5
votes
2answers
271 views

Next Step in Mathematics Education

I'm not sure that this is the appropriate forum for this question but the snooping around that I've don of the site makes me feel as if I'll get solid advice. I'm currently finishing an introductory ...
5
votes
4answers
4k views

Where to begin in approaching Stochastic Calculus?

I have experience in Abstract algebra (up to Galois theory), Real Analysis(baby Rudin except for the measure integral) and probability theory up to Brownian motion(non-rigorous treatment). Is there a ...
4
votes
1answer
101 views

Proof of existence of the number of solutions

I'm not sure how to tag this question, as I don't know what area of math covers these problems. For example, I know two or three ways of proving that $$ S=\sum_{k=0}^{\infty}p^{k}=\frac{1}{1-p} $$ ...