29 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

I think a more correct view is that proof is the LAST of several stages involved in researching something in math. What follows is a quickly sketched out scenario of what is often the case. Before ...
Dave L Renfro's user avatar
21 votes

What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?

I am really at a loss as to why this is happening and what should be the correct remedy, as it seems that it is not easy to address this late into their study. Also there seems to be no improvement ...
Justin Skycak's user avatar
18 votes
Accepted

How to improve atmosphere in male-dominated courses

I'm a female who was often 'the only one' and later became a teacher in classes with 'only one' or very few females. When I was a student in a normal (say 100th-ranked university), I just worked ...
lifelib's user avatar
  • 196
18 votes
Accepted

What famous graduate math textbooks use color?

One of the comments above mentions "the huge increase in cost" for using color in a book. The large cost increase for using color in a book was true twenty years ago. However, now the cost ...
Sheldon Axler's user avatar
18 votes
Accepted

If I take Modern Analysis next year, will I be prepared to teach multivariable/vector calculus?

It is impossible to say whether you will be ready to teach multivariable calculus after taking this course. Certainly many of the topics you list will employ some multivariable calculus, but using ...
Steven Gubkin's user avatar
16 votes

Are students majoring in pure mathematics expected to know classical results in mathematics very well by their graduation?

For the project, you would need to define what are "classical results in mathematics". I suspect that different people would disagree on the classicalness of various results. Furthermore, it is ...
Tommi's user avatar
  • 7,015
16 votes

How do I learn advanced mathematics without forgetting?

For context, I have a lot of experience self-learning mathematics. I spent a summer learning additional algebra, point-set topology, linear algebra, and analysis (to extend my undergraduate degree) ...
Opal E's user avatar
  • 3,986
16 votes

If I take Modern Analysis next year, will I be prepared to teach multivariable/vector calculus?

Assuming you already have a good understanding of the material in a standard course in multivariable calculus and vector calculus, I would recommend that you take a class in electricity and magnetism ...
Timothy Chow's user avatar
14 votes

Are students majoring in pure mathematics expected to know classical results in mathematics very well by their graduation?

This is an interesting question, but, understandably, confounds at least two different things. E.g., is it really the case that to "know" a true mathematical fact is to be able to produce its proof on ...
paul garrett's user avatar
  • 14.6k
14 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

I have taught Discrete & Computational Geometry to US undergraduates project-based, as opposed to assignment- and test-based. Some of the projects do involve proofs, but others are more ...
Joseph O'Rourke's user avatar
14 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

With the technological advances of the past couple decades, computational mathematics is now somewhat accessible to undergraduates. The wikipedia entry for computational mathematics lists out the ...
Aeryk's user avatar
  • 8,013
14 votes

What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?

I'd like to offer a bit of a frame challenge here. Whenever I made these sorts of mistakes during my mathematics education it was normally because I didn't understand what the symbols in the more ...
andypea's user avatar
  • 257
12 votes
Accepted

A4 paper of notes in an exam

I believe allowing students to prepare notes for use on an exam is a valuable way to help them focus their exam studying. I do not see the creation of the sheet as a waste of time. To make the notes, ...
Chris Cunningham's user avatar
11 votes

What is gratifying in being a mathematics teacher?

Since one point was not made very forcefully in the other answers: I like teaching mathematics because, even on the worst days, I get to talk/think/engage about mathematics... which I somehow find ...
paul garrett's user avatar
  • 14.6k
11 votes

What does one full year of calculus mean?

Asking random math educators about the policies of a specific graduate school makes absolutely no sense at all. The page you were looking at has this contact information at the bottom. Use it! ...
Chris Cunningham's user avatar
11 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

In other words, "knowing" math meant pretty much diddily-squat unless I could formally and rigorously write out proofs for everything I thought I knew. You appear to believe that somebody ...
kaya3's user avatar
  • 530
11 votes

What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?

I deal with a dash of this phenomenon in the context of teaching an "advanced programing techniques" course (i.e., 2nd semester programming) in a community-college CS program. There's ...
Daniel R. Collins's user avatar
10 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

When I describe undergraduate research to students majoring in mathematics, I ask them to browse the abstracts of the most recent MAA undergraduate poster session. Here is a link: Abstracts for the ...
user52817's user avatar
  • 10.8k
10 votes
Accepted

Resources for designing math degree programs

For undergrad, the MAA put out "Guidelines for Programs and Departments in Undergraduate Mathematical Sciences" about 20 years ago. We used this when preparing for program review about a ...
Aeryk's user avatar
  • 8,013
9 votes

What is gratifying in being a mathematics teacher?

With respect to Benjamin's answer, the top reason in his graphic "to make a difference." I received the note above at the end of the last school year. The first few reasons listed are slight ...
JTP - Apologise to Monica's user avatar
9 votes

L'Hopital's Rule: Why do we need it?

This is an answer to the title. Defining APOS & RME framework would make answering the question easier. As Massimo Ortolano mentioned in a comment, l'Hôpital's rule is one tool in a box. Maybe ...
Tommi's user avatar
  • 7,015
9 votes
Accepted

Where can I find new types of problems regarding graduate level mathematics?

As per my information , standard books from renowned authors and publications are the only sources of problems but still I want to know some sources where I can get difficult problems which can be ...
Justin Skycak's user avatar
9 votes

Where can I find new types of problems regarding graduate level mathematics?

Nowadays, you will be able to find many research mathematicians' websites with lecture notes for advanced courses, many with exercises/examples, many with solutions/discussions. I myself certainly put ...
paul garrett's user avatar
  • 14.6k
8 votes
Accepted

How much prior math should I review in teaching a graduate-level course?

Even for math grad students, I'd forcefully review much more than many traditions seem to indicate. That is, I would not presume perfect recall of the standard curriculum, especially either in detail ...
paul garrett's user avatar
  • 14.6k
8 votes
Accepted

What does one full year of calculus mean?

In the US, the stereotypical "one year of calculus", means "calculus one" and "calculus two" (semester system). It would rather approximate what is in AP Calculus BC, except perhaps without graphing ...
guest's user avatar
  • 96
8 votes
Accepted

Is the Wronskian still assumed for graduate education?

I would say the assumption is that people heading to mathematics graduate school know about the Wronskian, but this assumption isn't universally true. Certainly, anyone who has studied a semester of ...
Alexander Woo's user avatar
8 votes

What are some research-level opportunities in mathematics that do not focus on proofs?

Not quite an answer to your question, but if you have students who are interested in mathematics but not interested in (generating their own) proofs, encourage them to go into mathematics ...
TomKern's user avatar
  • 4,327
8 votes

Are the standard of questions provided in reputed institutions like MIT, Stanford, Oxford, etc., as good as the problems of IMO?

Will the institution give problems related to the theory but the difficulty standard of the problems equivalent to that of an imo or Putnam problem? Probably not. The whole point of a class (or ...
Justin Skycak's user avatar
7 votes

L'Hopital's Rule: Why do we need it?

When teaching calculus I like to include L'Hospital's Rule because it exemplifies how the subject is an impressive arsenal of calculational methods, and because it is easy to explain why this rule is ...
user52817's user avatar
  • 10.8k

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