For questions related to the teaching and learning of mathematics. Note that Mathematics Educators StackExchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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Which Mathematical Analysis I Book or Textbook Is The Best?

I'm in search of a mathematical analysis text that covers at least the same material as Walter Rudin's Principles of ... but does so in much more detail, without relegating the important results to ...
5
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1answer
295 views

What should I be doing in a grad level math course?

I have an undergrad degree in an engineering field and switched to applied math for a PhD. In engineering, I have had my share of good and bad professors but I knew what I had to be doing during a ...
4
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0answers
77 views

Teaching Student's distribution

While it is fairly straightforward to show the basics of the normal distribution in a first year undergraduate course, how does a teacher provide good intuition when the Student distribution comes in? ...
1
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1answer
460 views

Determining Height of Tree

A surveyor needs to determine the height of a tree. She places a mirror on the ground and paces backwards until she sees the top of the tree reflected in the mirror. She marks where she is standing ...
3
votes
1answer
104 views

From (algebraic) topology to geometry

I am thinking about a "correct" didactic way of linking topology (algebraic topology) to geometry. Usually, we are taught introducing geometry first, then topology, almost as an abstraction of ...
1
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1answer
207 views

Question about the greatest lower bound of sets.

Let $A$ and $B$ be sets of real numbers. Define a set $A+B$ by $A+B =\{a+b|a \in A, b \in B\}$. Show that if $A$ and $B$ are bounded sets, then $g.l.b.(A+B) = (g.l.b. A)+(g.l.b.B)$. (The g.l.b. ...
2
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1answer
145 views

Is it possible to do math knowing just naive set theory?

As an undergraduate, I noticed none of my courses in analysis, topology, or algebra require the need to know any set theory beyond naive set theory. My question is is this true for even higher ...
4
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2answers
3k views

Math resources for electrical engineering?

I am considering electrical engineering as my field of study. However, my math knowledge might not be as good as it should be. What math books/resources would you recommend me to read?
8
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1answer
1k views

Is “A and B imply C” equivalent to “For all A such that B, C”?

So I mostly study PDE, harmonic analysis, image processing, and so on, but for whatever reason I decided to be a TA for an undergraduate "introduction to proofs" course this semester. I suppose I ...
16
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1answer
675 views

Alternative construction of the tensor product (or: pass this secret)

The paper Tensor products and bimorphisms by B. Banachewski and E. Nelson studies tensor products (defined by classifying bimorphisms) in concrete categories. It is quite interesting that their main ...
0
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1answer
115 views

Determining length of an “arc” drawn just below an another arc with known length by intuition

There is an arc a to b. The length is say 1 unit. There is an another arc c to d, drawn just below a to b, such that it sticks with it (ie. No vertical y space). Let us say i have my world ...
8
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5answers
3k views

How do you rebuild your Math skills after college? [closed]

I minored in Math in college (B.S. Software Engineering), and went through advanced Calc, Differential Equations, etc. But about 6 months after I graduated I had lost all my formulas. Now, about 5 ...
5
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2answers
238 views

Flexible distance learning Mathematics programme

I am looking for a flexible Mathematics degree programme from a reputable institution. By flexible here I mean: Able to take the programme at one's own pace The option to complete the programme at ...
3
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2answers
2k views

What are some effective ways in teaching fractions to 5th graders who are behind (special needs)

I am teaching a group of 8 kids on fractions and I did not realize how difficult this can be. These kids were selected by their teachers for needing additional outside help. I really need some advice, ...
0
votes
1answer
95 views

Why use notations like $f(x)$ while explaining mathematical proofs or equations etc

If there is a variable "$x$" , and another is "$y$", and let's say I know the relation between them as $$x= y+1$$ Now, I want to use them in the explanation of some mathematical ...
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3answers
130 views

Help on French Math Education Paper

I am looking for very basic (probably I should say very elementary) papers in french designed for elementary school teachers and elementary school educators. I would appreciate if someone can provide ...
19
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2answers
5k views

Path to Basics in Algebraic Geometry from HS Algebra and Calculus?

In this question, Why study Algebraic Geometry?, Javier Álvarez, develops a succint but encompassing description of algebraic geometry and its spread across different areas of mathematics. Indeed, it ...
6
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1answer
4k views

How should I approach the study of Linear Algebra?

I'm a second-year college student having just previously finished calculus (derivatives and integrals, we never really got too far into multivariable calculus though we briefly went over some Taylor ...
13
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1answer
450 views

Developing research experience in mathematics

I am not sure whether this is the right forum for this question, so it might be migrated somewhere else; but, it is, I think, certainly germane to the wider idea of pursuing interesting questions and ...
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3answers
235 views

Theory of Equations and Undergraduate Mathematics

I was browsing through a book entitled: Field Theory and Its Classical Problems by Charles Hadlock, one of the Carus Mathematical Monographs titles. In his preface he says the following: In ...
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6answers
5k 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 ...
13
votes
1answer
1k 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
164 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 ...
16
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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
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2answers
284 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 ...
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2answers
92 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 ...
3
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1answer
213 views

How should someone release their proof to the world? [closed]

Lets say someone (a reputable or non reputable mathematician) has come up with a remarkable one page proof to a famous maths problem. Lets say the proof is likely correct but hasn't been released to ...
4
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2answers
997 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
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3answers
1k 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
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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
242 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
2k 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 ...
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3answers
156 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 ...
4
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1answer
1k views

Teaching probability by using a deck of cards

I plan to teach two sessions of probability to 11th grade students using a deck of cards. My classes will be next week. I have already taught them the basic notions of writing sample spaces, computing ...
3
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0answers
157 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 ...
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1answer
120 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 ...
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4answers
116 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 ...
2
votes
4answers
98 views

Motivating complex structure on $\mathbb{R}^2$

I'm giving a talk to a group of bright but not all that mathematically sophisticated students on the subject of complex numbers. I'd like to introduce complex numbers via geometric considerations ...
87
votes
3answers
9k 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
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1answer
402 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
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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 ...
17
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4answers
2k views

Common student mistakes/misconceptions in a first year calculus course

What are the common mistakes and misconceptions students make in a first year calculus course? More importantly: What can I do to prevent/rectify them? Context: Soon I will be doing ...
3
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0answers
94 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
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0answers
985 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 ...
6
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2answers
1k views

Useless math that become useful

I'm writing an article on Lychrel numbers and some people pointed out that this is completely useless. My idea is to amend my article with some theories that seemed useless when they are created but ...
5
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2answers
205 views

What to give as final lecture in a differential geometry class?

During the fall semester, I had to give an exercise class to second year math students, as support for a theoretical class loosely based on the book `Differential geometry of curves and surfaces' by ...
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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
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2answers
640 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 ...
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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
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2answers
99 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 ...