Questions tagged [teaching]

For questions related to teaching mathematics. For questions in Mathematics Education as a scientific discipline there is also the tag mathematics-education. Note you may also ask your question on http://matheducators.stackexchange.com/.

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Any suggestions for a course in Mathematical Logic?

I am teaching a topics course for Mathematics majors (at Temple), and am considering Logic as the topic. I was wondering if people (a) have suggestions for an appropriate text and (b) how much might ...
12 votes
17 answers
3k views

Short Course Suggestions For High School Students

I am planning to teach a course for talented high school students at a summer camp and I need suggestions for possible topics. The students usually have different backgrounds but most of them are ...
24 votes
8 answers
20k views

Interesting Applications of the Classical Stokes Theorem?

When students learn multivariable calculus they're typically barraged with a collection of examples of the type "given surface X with boundary curve Y, evaluate the line integral of a vector field Y ...
59 votes
5 answers
24k views

Are there any "related rates" calculus problems that don't feel contrived?

I just finished teaching a freshman calculus course (at an American state university), and one standard topic in the curriculum is related rates. I taught my students to answer questions such as the ...
14 votes
5 answers
2k views

How to make a lecture series useful

I have been to a number of advanced lecture courses (of between 3 and 10 lectures) over the years, given (in principle) by experts to graduate students and experts in neighbouring fields. Examples of ...
27 votes
17 answers
9k views

Using slides in math classroom

I am toying with the idea of using slides (Beamer package) in a third year math course I will teach next semester. As this would be my first attempt at this, I would like to gather ideas about the ...
28 votes
6 answers
2k views

Means of Promoting Mathematics in Young Countries!

We all know mathematics is life, this question is for Mankind. It's mathoverflow here when some parts of the world we have mathunderflow! I think we can do something through ideas. A similar ...
3 votes
3 answers
2k views

What to teach in a second graduate course in algebra? What textbook to use?

There is a standard syllabus for a first graduate course in algebra. One teaches groups, rings, fields, perhaps a little bit of Galois theory, perhaps a little bit of category theory, perhaps a ...
12 votes
11 answers
2k views

Giving a math talk with no blackboard or projector

I need to give a math talk to a group of undergraduates. I am asking for advice because this talk will take place at a department picnic and there will be no blackboard or projector. I would like to ...
7 votes
5 answers
2k views

Commutative algebra final project

I'm looking for a topic for a final project in commutative/homological algebra, for first year master's students (in a decent European university). During the course, they will cover the following ...
74 votes
51 answers
27k views

An example of a beautiful proof that would be accessible at the high school level?

The background of my question comes from an observation that what we teach in schools does not always reflect what we practice. Beauty is part of what drives mathematicians, but we rarely talk about ...
103 votes
13 answers
36k views

How misleading is it to regard $\frac{dy}{dx}$ as a fraction?

I am teaching Calc I, for the first time, and I haven't seriously revisited the subject in quite some time. An interesting pedagogy question came up: How misleading is it to regard $\frac{dy}{dx}$ as ...
25 votes
5 answers
5k views

The Matrix-Tree Theorem without the matrix

I'm teaching an introductory graph theory course in the Fall, which I'm excited about because it gives me the chance to improve my understanding of graphs (my work is in topology). A highlight for me ...
Daniel Moskovich's user avatar
7 votes
8 answers
4k views

Mathematical Advice for Interested Highschool Students

This may not be a research level math question, but I believe it is still relevant to Math Overflow. What general resources exist for students in highschool who are very interested in Mathematics?...
5 votes
3 answers
641 views

Looking for ideas concerning the teaching of lower-division differential equation courses...

I'm looking for problems/lessons plans that could be used in a lower-division differential equations course that involve discerning properties of solutions of an equation, IVP, or BVP, without looking ...
3 votes
0 answers
428 views

Concrete questions that turn into math problems [closed]

I'm writing an article about the way we teach math, trying to find out why so many people are discouraged from learning, and have no interest for math and logic. At some point, I want to show that ...
salezica's user avatar
  • 131
5 votes
9 answers
2k views

Suggestions for teaching advanced high school students

Hi all, I'm a grad student and just joined a mentoring program in which I will visit a group of advanced year ten high school students (around 16 years old) from a group of schools in the area. I don'...
18 votes
14 answers
3k views

Teaching a pedagogy course

At my institution incoming graduate students must take a semester long course on pedagogy taught by current grad students. I may soon be in the position of having to teach this course and I'm looking ...
158 votes
8 answers
6k views

Resources for mathematics advising.

This question is possibly ill-advised. (If it is not right for this site I will delete it.) I, suddenly, have students. It is very clear to me that there is nothing in my education that has ...
32 votes
23 answers
29k views

Textbook recommendations for undergraduate proof-writing class

I am teaching the proof-writing class (for the 3rd time) in the Fall and plan to buck the party line and use a different text than the default Bond and Keane. My parameters are as follows: Logic, ...
9 votes
4 answers
1k views

Characterization of the Poisson law

This semester, I teach an introduction to probability course tailored for students with no science background and so with very very little prerequisites. We started with the basics of analytic ...
Olivier's user avatar
  • 10.2k
13 votes
1 answer
2k views

conditional equality symbol

Is there a standard notation (perhaps $A \stackrel{\leftarrow}{=} B$) meaning "in all situations where $B$ is defined, $A$ is defined and equals $B$"? The kind of situation in which such a notation ...
James Propp's user avatar
  • 19.4k
5 votes
5 answers
2k views

Topics for a matrix analysis course

I recently taught a new (to my department) course titled "Matrix Analysis". For various reasons that I won't go into here, I was dissatisfied with the textbook I (loosely) followed, and with every ...
9 votes
7 answers
1k views

Mathematics seminar for "non-mathematicians"

Next term I am leading a seminar for students, who will become teachers for elementary school i.e. for kids of age 6-10. The students in the seminar will have no mathematical background beyond the "...
11 votes
1 answer
2k views

Good chalk in the UK

Sometime ago it was asked in Mathoverflow about good chalk in the US Where to buy premium white chalk in the U.S., like they have at RIMS?. I will be grateful for any recommendations on good chalk in ...
97 votes
19 answers
36k views

Collecting proofs that finite multiplicative subgroups of fields are cyclic

I teach elementary number theory and discrete mathematics to students who come with no abstract algebra. I have found proving the key theorem that finite multiplicative subgroups of fields are cyclic ...
10 votes
4 answers
1k views

Reference for working with the implicit function theorem

I just had a student come to my office hours and ask me a ton of questions, the answer to all of which was "that's a slight variant to the implicit function theorem, which is proved by formal ...
David E Speyer's user avatar
21 votes
4 answers
5k views

What is the best way explain to undergraduates that all 1-dimensional manifolds are orientable?

Let's suppose that $M$ is a connected $1$-dimensional smooth manifold (Haussdorf and paracompact). We know that there are exactly two types, up to diffeomorphism (even up to homeomorphism), namely $\...
Spiro Karigiannis's user avatar
7 votes
1 answer
4k views

Who is this guy : Z.A. Melzak (wrote Companion to Concrete Mathematics) ? [closed]

Author : Z.A. Melzak Book Title : Companion to Concrete Mathematics. Publication : Dover renewed 2004 2 volumes in one. Copyright 1972/1976. I found this book extremely nice. To whet your appetite ...
Jérôme JEAN-CHARLES's user avatar
108 votes
27 answers
40k views

Why should one still teach Riemann integration?

In the introduction to chapter VIII of Dieudonné's Foundations of Modern Analysis (Volume 1 of his 13-volume Treatise on Analysis), he makes the following argument: Finally, the reader will ...
52 votes
22 answers
19k views

Interesting Calculus Questions/Exercises

I am in the process of redesigning the calculus course that I have taught five or six times. What I would like to know is if anyone has some really good examples or exercises that I could either do ...
3 votes
3 answers
1k views

Pedagogical question concerning $\Gamma(z)$

Pedagogically speaking, I see two problems with defining $\Gamma(z)$ (at least for real $z$) by the limit $$\Gamma(z)=\lim_{m\to\infty}\frac{m! m^z}{\prod_{i=0}^m (z+i)}$$ as compared with the formula ...
David Feldman's user avatar
2 votes
0 answers
3k views

What is the geometric meaning of the third derivative of a function at a point? [closed]

What is the geometric meaning of the third derivative of a function at a point? This question is now asked on the sister site: https://math.stackexchange.com/questions/14841/what-is-the-meaning-of-...
AJAY's user avatar
  • 61
4 votes
2 answers
849 views

Terminology question on covering spaces

I'm teaching an elementary class about fundamental groups and covering spaces. It was very useful to use "fool's covering spaces" of a space $X$, defined as functors $\Pi_1(X)\to Sets$, where $\Pi_1(X)...
Pavol S.'s user avatar
  • 407
3 votes
1 answer
507 views

What are some interesting grading/curving systems you have seen for a course? [closed]

It seems like every math course has something unique in how things are graded. 1) What are some interesting grading systems you have seen/used? (include curving types, etc.) 2) What are some pros ...
11 votes
2 answers
1k views

Social Reading Platform for Math or LaTeX texts

Social reading is considered to be one of the big trends that could be catalysing learning by reading. Features could include: Highlighting or annotating paragraphs or single steps in a proof for ...
43 votes
9 answers
28k views

Applications of knot theory

An answer of André Henriques' inspired the following closely related CW question. Parts of the following is extracted from his answer and my comments. I regularly teach a knot theory class. ...
71 votes
11 answers
8k views

How to introduce notions of flat, projective and free modules?

In the coming spring semester I will be teaching for the first time an introductory (graduate) course in Commutative Algebra. As many people know, I have been plugging away for a while at this ...
Pete L. Clark's user avatar
15 votes
4 answers
3k views

How does one motivates the method of separation of variables when teaching PDE's?

I'm not sure if this question is appropriate for MO. Add comments if it is not. Thanks. How to explain/motivate the method of separation of variables for PDEs to undergraduates? What's the real math ...
Yuhao Huang's user avatar
  • 4,982
4 votes
0 answers
778 views

Almost linear ODE: how node becomes a spiral

Most introductory ODE books contain a discussion of almost linear systems, and there are two cases when the behavior of an almost linear system near an equilbrium point can differ from the behaviour ...
Igor Belegradek's user avatar
19 votes
1 answer
2k views

Resources for teaching arithmetic to calculus students

Every time we teach calculus we discover that a significant portion of our students never understood arithmetic. I don't mean that they can't multiply numbers, but rather that they don't know ...
Alexander Woo's user avatar
25 votes
5 answers
5k views

Varieties as an introduction to algebraic geometry / How do professional algebraic geometers think about varieties

This really is two questions, but they are kind of related so I would like to ask them at the same time. Question 1: In a question asked by Amitesh Datta, BCnrd commented that it is important to ...
2 votes
4 answers
3k views

Best way to introduce the Chinese Remainder Theorem (to a high school student)

What do you think to be the most effective way to teach the Chinese remainder theorem to a smart high school student, which is supposed to only have a soft idea about how modular arithmetic works, and ...
Maurizio Monge's user avatar
14 votes
2 answers
7k views

What is the dual concept to "annihilator" called, and do any linear algebra textbooks discuss this concept first?

When introducing dual spaces for the first time, most linear algebra textbooks proceed in what seems to me a rather backwards fashion: the annihilator $\{f\in V^*: f(u)=0\quad \forall u\in U\}$ of a ...
61 votes
10 answers
10k views

Teaching proofs in the era of Google

Dear members, Way back in the stone age when I was an undergraduate (the mid 90's), the internet was a germinal thing and that consisted of not much more than e-mail, ftp and the unix "talk" command ...
10 votes
7 answers
2k views

Proof that bases etc. exist in early linear algebra course?

I'm currently struggling to teach a 2nd course on linear algebra (in the UK, not at an Oxbridge quality university: the students have done a 1st course which concentrated upon algorithms you can apply ...
14 votes
7 answers
5k views

Freshman's definition of sin(x)?

I would like to know how you would rigorously introduce the trigonometric functions ($\sin(x)$ and relatives) to first year calculus students. Suppose they have a reasonable definition of $\mathbb{R}$ ...
Qfwfq's user avatar
  • 22.7k
110 votes
34 answers
84k views

Why do we teach calculus students the derivative as a limit?

I'm not teaching calculus right now, but I talk to someone who does, and the question that came up is why emphasize the $h \to 0$ definition of a derivative to calculus students? Something a teacher ...
6 votes
3 answers
1k views

Publishing with Undergraduates

Is doing research with a student considered to be good for a dossier? Is it okay to have few research publications but a lot of student projects? I am finishing up a grad program and am looking at ...
Tom P's user avatar
  • 61
3 votes
6 answers
2k views

Teach a course in 1 month

I need to teach an intro course on number theory in 1 month. I was just notified. Since I have never studied it, what are good books to learn it quickly?