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 ...
- 5,768
28
votes
What am I supposed to be learning with long proofs of the main theorems in class?
Hmm apparently I will be the dissenter here. I think that long proofs taught in lectures are very much a good thing. This is particularly true for hard proofs. I will try and split the reasons why I ...
- 1,018
23
votes
Accepted
What am I supposed to be learning with long proofs of the main theorems in class?
I agree with the sentiment in this question. I too often feel that lecturers go through a detailed proof because they think that everything must be proven pedantically to be able to use it. Sometimes ...
- 3,720
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 ...
- 6,191
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 ...
- 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 ...
- 296
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 ...
- 24.3k
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 ...
- 6,741
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) ...
- 3,996
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 ...
- 493
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 ...
- 14.2k
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 ...
- 29.5k
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 ...
- 7,500
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 ...
- 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, ...
- 21.2k
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 ...
- 14.2k
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!
...
- 21.2k
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 ...
- 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 ...
- 24.3k
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
...
- 10.3k
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 ...
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 ...
- 6,741
8
votes
What am I supposed to be learning with long proofs of the main theorems in class?
I view
avid19's frustration as an argument for presenting proofs within some historical
context.
Few major theorems have been achieved without a struggle, often involving
several mathematicians over ...
- 29.5k
8
votes
What am I supposed to be learning with long proofs of the main theorems in class?
This is a great question. Here are some thoughts on it.
A theorem statement is a sign of an idea that tends to be useful in the pattern of mathematical inquiry in a given subdomain. A good theorem ...
- 6,045
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 ...
- 14.2k
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 ...
- 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 ...
- 2,484
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 ...
- 3,927
8
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 ...
- 6,191
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