All Questions
Tagged with curriculum undergraduate-education
30 questions
8
votes
3
answers
1k
views
Dominance of connectives: Why do we teach this?
These were two actual exercises given to students I have been tutoring for a college algebra class:
I have been working very hard to convince my students of the importance and utility of learning ...
- 404
1
vote
0
answers
145
views
Math curricula\programs or any experience using "The Road to Reality" as the\a primary textbook
Primarily a reference request, collaborator search-tips requests, and question-improvement request (including improveent by deletion and re-posting to more appropriate stack, meta, wiki, etc). Rank ...
4
votes
2
answers
892
views
Why are "homogeneous differential equations" in the standard ODE curriculum?
Here I mean a differential equation of the form $y'=f(x,y)$ where for some $\alpha$, we have $f(tx,ty)=t^\alpha f(x,y)$ for every $t$. I have no idea why this topic seems to appear in every ODE ...
- 641
3
votes
1
answer
256
views
Teaching Quantifiers Before Logical Connectives
In this short question, I would like to ask whether it is possibly good to teach quantifier before logical connectives in a logic introduction lecture?
I know there is a relationship between them but ...
- 153
1
vote
1
answer
188
views
Math undergrad courses [closed]
Awhile back I was very weak with my trigonometry so I came to this site asking for help, and it turned out the few answers I got made a huge difference. I excelled at the trigonometry section in my ...
- 496
8
votes
2
answers
443
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"Personalized System of Instruction" (PSI) vs. "Individually Prescribed Instruction" (IPI)
This question may be a bit overly-broad for MESE, but I am hoping to find some responses that can help to fill in my understanding of two similar forms of instruction that had their heyday in the ...
- 17.4k
0
votes
2
answers
775
views
Is it possible to have taken intro to proofs, calculus 3 and differential equations and still lack the ability to do proofs?
Ideal Undergraduate Sequence
Main question:
I looked above and what I'm interpreting out of it is that one should be able to do proofs after studying some intro to proofs class, calculus ...
user8788
11
votes
3
answers
242
views
Pedagogical Purpose in Making Students Do Problems in A Less Efficient Way First
Let's assume that a group of students need to learn to solve a certain type of mathematical problem for which there is two general methods of solving it, $X$ and $Y$. We also assume that $Y$ is more ...
- 273
10
votes
8
answers
606
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What topics should be included in a course matching these specifications?
I posted this question on m.s.e., where I upvoted the two answers, both of which said rather little by comparison to what the question asks. Hence this present posting.
Say you have a calculus ...
- 1,933
23
votes
8
answers
3k
views
Should we teach trigonometric substitution?
This is the question that was not asked here. Also related is this question, but both presuppose that it will be taught and ask about how best to do it. My question here is, suppose we are designing ...
- 6,680
9
votes
1
answer
2k
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Which math classes should be included in an undergraduate computer science program?
As part of my job search, I've come into contact with universities that are beginning to offer new majors at their university such as applied mathematics or computer science. A frequent interview ...
- 11.7k
15
votes
1
answer
360
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Order of Topics in Introductory Proofs Class
Beginning next semester I am teaching a course in proofs and mathematical problem solving at my local university. For some background, the university is primarily a commuter university and the ...
- 153
6
votes
2
answers
494
views
Summer program for 'international' undergraduate students of mathematics
I see that most of the american universities have mathematical summer programs with lectures and mini-courses (note: I'm not talking about undergraduate research programs in this question) for ...
- 1,131
14
votes
4
answers
1k
views
Key theorems in undergraduate linear algebra
I've been asked by an high school student what are the $5$ major theorems in Lang's Linear Algebra (and therefore, by extension, in an undergraduate linear algebra course). Firstly, I bluntly said ...
- 1,131
9
votes
3
answers
408
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Lie Theory: significance and relevance to undergraduate education
I have been strongly recommended to read the book Naive Lie Theory. In the introduction one can read: "This naive approach to Lie theory is originally due to von Neumann, and it is now possible to ...
- 1,131
11
votes
4
answers
2k
views
Topics that should be in an undergraduate math programme
According to your experience as students and professors, what are (and why) the courses that should be part of a math undergraduate degree, but that are missing in most institutions?
- 1,131
5
votes
2
answers
8k
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Naming of calculus courses
Many people on this site refer to undergraduate courses called "Calculus I" or "Calculus II".
In my country (Australia) there is no standard naming convention for university maths courses, and ...
- 9,123
3
votes
0
answers
239
views
Most important nonstandard math courses [closed]
Most students with aspirations of a pursuing a PhD in pure mathematics at a top grad school takes the "standard" curriculum as an undergrad which includes 2x algebra, 2x analysis, 1x complex analysis, ...
- 31
9
votes
7
answers
2k
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Galois Theory: necessary?
I noticed the discussion of whether the teaching of Galois Theory is necessary on MathOverflow. Here at LSE, everything we teach in mathematics should have some application to the social side of life.
...
Robert Simon
11
votes
2
answers
2k
views
Advanced Calculus vs. Analysis for a first proof-based course
Question: Why was advanced calculus removed as the first proof-based course in favor of real analysis in most curriculums?
I regularly see in advanced calculus books either that:
its purpose is, ...
- 3,060
15
votes
2
answers
1k
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Introducing the Lebesgue integral before Riemann's
Has anyone attempted to introduce, or has data on such endeavor, Lebesgue integration before Riemann? I've seen many discussions about how the Riemann integral is obsolete and that it is presented ...
- 3,060
15
votes
6
answers
15k
views
Ideal Undergraduate Sequence
What is the perfectly (maybe unrealistically) ideal undergraduate sequence for a undergraduate majoring in pure mathematics who takes 2-3 mathematics courses per semester assuming a strong AP Calculus ...
- 151
31
votes
7
answers
2k
views
Mathematical education by country
Depending on the university, there are always slight differences in the syllabus and the structure of the standard material undergraduate students learn.
But I also noticed that undergraduate ...
- 419
47
votes
12
answers
31k
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What should be included in a freshman 'Mathematics for computer programmers' course?
Many universities are changing up the way that they teach math service courses. 1-3 semesters of calculus and maybe a course in linear algebra are often included in majors (such as computer science) ...
- 11.7k
24
votes
3
answers
1k
views
What can be said about Lie groups in a first abstract algebra course?
Lie groups are among the most important examples of groups in mathematics and physics, but they are rarely discussed in introductory undergraduate abstract algebra courses, which tend to focus on ...
- 8,339
7
votes
1
answer
837
views
What universities in the United States have Spanish-language mathematics classes?
This is a simple question, which I haven't found the answer to online.
Due to the increasing number of Spanish-speaking students in American universities, I've been interested in teaching Spanish-...
- 11.7k
22
votes
3
answers
2k
views
How to advise students who want to do a "Bourbaki"-style study?
There are some good students who understand a lot and are very critical. Such students tend to think that they will only understand abstract algebra if they have followed a course about logic; or they ...
- 9,468
27
votes
4
answers
2k
views
How should LaTeX be taught to university students?
There are several groups of people that would benefit from learning LaTeX in college. Future teachers can use it to write exams, scientists and mathematicians can write papers, and everyone can write ...
- 11.7k
24
votes
2
answers
1k
views
Should geometric algebra be presented early on in undergraduate education?
The Cambridge University GA Research Group’s website along with the “Geometric Calculus R & D Home Page” should serve as a good introductions to geometric algebra, along with the Wikipedia ...
user89
13
votes
2
answers
469
views
What prerequisites would college students need for a course based primarily on Euclid's elements?
I love Euclid's elements, and would like to base a course around them. Before I can pitch it to my supervisors, I need to know where it would fit in the curriculum. While it begins from elementary ...
- 11.7k