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 ...
- 22.9k
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) ...
- 3,887
14
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 ...
- 291
12
votes
Enlighten younger students about the concept of "procedural justice" in mathematics?
On the contrary, many seem surprisingly impatient when being asked to prove 1+1=4/2, whose proof (with properly delimited deepness) involves nothing beyond and possibly well below most people's ...
- 11.4k
8
votes
Accepted
When should an advisor assess a student's knowledge independently of their course grades?
I post this upon request, but I immediately must excuse myself as it doesn't give a practical resolution to what the OP asks. Having said this, this does respond to an underlying component of the ...
- 215
7
votes
Grad school after doing an online bachelor's degree without support for undergraduate research
It seems like some of the other answers are aiming at PhD programs. I would suggest (as your question on academia.sx suggests) that you may wish to look at a Master's program (at a non-PhD-granting ...
- 5,856
7
votes
When should an advisor assess a student's knowledge independently of their course grades?
The other answers made good points... and suggest continuations and qualifications. For example, some students seemingly benefit from being informed that courses and grades are merely a stylized ...
- 13.8k
6
votes
Will the low-achieving children always be there?
I think the question is one of perspective, and that really the answer should be about changing perspective and not about trying to answer the question from the perspective suggested by the question.
...
- 2,534
5
votes
When should an advisor assess a student's knowledge independently of their course grades?
It helps to place such assessments in light of the goal that inspired the question. I think this goal is most often "How do I manage my time to learn topics from area X?", although it could also be ...
- 2,534
4
votes
Accepted
How can I (failing Cambridge's BA Math) improve my grade to a 1st from a 3rd-class honours?
Ok so I suppose if your College was at all typical then after your exams they suggested to you that you might want to transfer to a different university/subject. And as you are still doing maths at ...
- 156
4
votes
Summer opportunities for math undergrads as an alternative to REU
Some local (or not) businesses may have fairly mathematical internships. For instance, a biotech company may have nontrivial graph theory or other discrete computational problems to solve that will ...
- 5,856
4
votes
How do I learn advanced mathematics without forgetting?
For most people, including myself, there is pretty much no chance that you’ll remember most of the things you’ll see and do in math-land the first time ‘round. It’s just an inevitable relic of the ...
4
votes
If I take Modern Analysis next year, will I be prepared to teach multivariable/vector calculus?
I'm going to throw in a frame challenge: you stated your goal is to be prepared to teach at a collegiate level.
All the other answers talk about whether you have the correct material, whether various ...
- 157
3
votes
How do I learn advanced mathematics without forgetting?
You don't describe engaging in conceptual chunking.
You mention the Sylow theorems as an example and I will also use them as an example. It is easy enough to memorize the theorem statements. If you ...
- 641
3
votes
Subject advice in Number Theory
I think it would be a good Bachelor topic to explain, at a high-level,
the MRDP theorem
(Matiyasevich–Robinson–Davis–Putnam),
which settled Hilbert's 10th problem:
A set of integers is Diophantine
...
- 28.7k
3
votes
When should an advisor assess a student's knowledge independently of their course grades?
The problem with course grades is that they measure the student's knowledge of the "book," or lecture notes, not the material or subject.
If the student knows things about the subject over and above ...
- 1,508
3
votes
How can I (failing Cambridge's BA Math) improve my grade to a 1st from a 3rd-class honours?
It's possible that you are at low end of the ability spectrum but given the thought in your post, I suspect that you can do better than 3rd.
I love probability and statistics (and plausable reasoning, ...
- 468
3
votes
If I take Modern Analysis next year, will I be prepared to teach multivariable/vector calculus?
I echo Steven's comments. Honestly, independently was writing the same and then dropped it when I saw his response...then came back like a dog.
It's pretty tenuous the connection. You could be a ...
- 41
2
votes
When should an advisor assess a student's knowledge independently of their course grades?
Chris, interesting questions and some good responses and your approximation is thoughtful. Just a few other soft thoughts to consider.
I wouldn't do a test on the kid. I just think that gets too ...
- 468
2
votes
Accepted
Subject advice in Number Theory
As mentioned in the comments, I used the topic of Continued Fractions when I had a similar paper to write. The applications include: rational approximations to irrational numbers, Diophantine ...
- 1,982
2
votes
Grad school after doing an online bachelor's degree without support for undergraduate research
Are you in the US?
It is probably true that you will not get into grad school in math at Princeton or MIT with no undergrad research. But many other US universities will gladly admit you with: good ...
- 6,986
2
votes
Enlighten younger students about the concept of "procedural justice" in mathematics?
"Since my home country's culture possibly overly stresses that sort of engineering mathematics all through the math classes prior to college education, I especially would like to show him a sense of ...
- 119
2
votes
How do I learn advanced mathematics without forgetting?
I think it is important to do some drill EVEN (maybe especially) with advanced concepts. This is because the concepts may be more strange and abstract. So you need to do some basic work to get ...
- 29
2
votes
Importance of asking questions in a mathematics class
From our experience we have seen that most of the times they do not understand what to ask. And this is basically because students usually feel disconnected with the subject. To change that, we think ...
- 151
2
votes
Accepted
Start drawing a graph
There is quite a bit of literature on this topic in the "Graph Drawing" community.
Although the goal is algorithms for automatically drawing graphs,
several papers offer criteria which could ...
- 28.7k
2
votes
How do I learn advanced mathematics without forgetting?
One way to remember the mathematics that you learn is to create a narrative that explains how the concepts are threaded together. This narrative need not have any historical relevance (and it usually ...
- 159
2
votes
Accepted
Importance of asking questions in a mathematics class
Should the students in a math class be encouraged to ask useful questions?
Yes.
Is it worth the effort in persuading and forcing the students to ask genuine questions?
No, that's the wrong approach....
- 204
1
vote
How do I learn advanced mathematics without forgetting?
I believe you should follow these steps:
Understand what the theorem says, with some applications of it (which also means to do the exercises, also show your work to TAs)
Try to prove it yourself and ...
- 131
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