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 ...
- 26k
17
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) ...
- 4,109
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
13
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 ...
- 11.6k
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 ...
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5
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 ...
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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
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 ...
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 ...
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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 ...
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3
votes
Summer or Semester Programs which bridge to Graduate Mathematics
I see how it looks like they stopped in 2018, but you might at least contact PSU Math. Call the department secretary and ask for a point of contact. Perhaps they are still running it, after all there'...
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
...
- 30.2k
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, ...
- 466
3
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 ...
- 129
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 ...
- 7,676
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 ...
- 2,129
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 ...
- 466
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....
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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 ...
- 30.2k
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 ...
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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
Advice and Remedial Algebra Resources for Students Committed to Calculus
I know this doesn't directly answer your question which is about helping one student. But I would be wanting to see my institution implement sections of calculus with support. This blog addresses that ...
- 21.5k
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 ...
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1
vote
Grad school after doing an online bachelor's degree without support for undergraduate research
The sad fact is that your mathematics preparation may very well be inadequate for graduate school. My department admits with some frequency people from small regional public universities or unknown ...
- 2,482
1
vote
Grad school after doing an online bachelor's degree without support for undergraduate research
How are your test scores? General as well as subject. The good thing about those is they identify smart people from less fancy schools.
Oh...and just apply. Mention your work background. I got ...
- 19
1
vote
Accepted
Complex Variables for Engineers versus Ordinary Differential Equations with Linear Algebra difficulty
The difficulty of the courses depends on the content and execution of the courses in question, and as such, the question does not have an answer.
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1
vote
How can I (failing Cambridge's BA Math) improve my grade to a 1st from a 3rd-class honours?
I can hardly improve on the detailed answers here but just wanted to add a few things.
I have seen fellow students lock themselves way for the requisite eight hours of study and fail straight out of ...
- 11
Only top scored, non community-wiki answers of a minimum length are eligible