Roland
  • Member for 7 years, 10 months
  • Last seen more than 3 years ago
Encouraging class participation
15 votes

When presenting some example, I like to let them cast votes on the correct answer (e.g. for choosing methods of integration, or for the question how many solutions a given linear system has, after ...

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Is there any difference between teaching calculus for math and engineering students?
12 votes

Tentatively, yes. In the universities I've taught, there are substantial differences between those courses: For engineering students, the courses in calculus (and linear algebra) provide some ...

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What goes wrong when students interchange "there exists" and "for all" randomly? How to fix this?
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11 votes

One way to increase awareness of this issue is to explore what happens if the quantors are changed from exists to for all, and vice versa. On math.SE, there was a question which dealt precisely with ...

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How to choose/test future tutors?
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11 votes

The university I worked as a tutor at, involved an interview with a brief teaching situation. This was done for all students who applied to a job as a tutor at the math department, regardless of the ...

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What is a good motivation/showcase for a student for the study of eigenvalues?
10 votes

For a real showcase, I recommend a scenario where resonance frequencies play a role. Suspension bridges are real-world objects which are delicate enough that soldiers are usually not allowed to march ...

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When asked to by a religious university, how can an instructor make a mathematics course spiritually uplifting?
10 votes

Mentioning other mathematician's motivations (as Ken W. Smith did in his answer) might be indeed a good starting point. I'd like to highlight one particular case where beliefs and mathematics come ...

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An application-heavy functional analysis textbook?
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9 votes

There is Methods of Modern Mathematical Physics by Reed and Simon, which is a 4-volume book which teaches functional analysis, with a focus on operators in Hilbert spaces. Its main aim is to provide ...

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Good motivation for the introduction of Lebesgue integral?
9 votes

When learning a new concept, it might help to point out what's wrong with the old one. In this particular case, a function which cannot be integrated in the Riemann sense on any interval, but where ...

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Should the cross-product in $\mathbb{R}^3$ be discussed in Linear Algebra?
8 votes

One of the main reasons why the cross product is seldomly (to my experience) taught in linear algebra is not only the fact that this particular vector product only works well in $\mathbb{R}^3$ (a ...

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What topics could be covered in a course on fractals?
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7 votes

Some years ago, I attended a course where Julia and Mandelbrot sets were part of. It was called "Chaotic Dynamical Systems", and was held once a week for 90 minutes for a total of 14 lectures. It was ...

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Teaching by powerpoint presentation
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7 votes

There are different kinds of 'learning types'. Some people learn best by listening and talking, some people learn best by understanding the material with the help of pictures, and some learn best by ...

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Elementary physics course for pure math student
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6 votes

While I did not attend any elementary physics courses by mathematicians for mathematicians, I did attend a curriculum of courses called "Mathematical Physics" held by mathematicians for mathematicians ...

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How to design a fair oral exam for >10 students?
6 votes

Usually, the course material is more than you could talk about in 20 - 30 minutes. This means that you have a large array of questions at hand, and you usually won't be able to ask every student the ...

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What do you say to students who want to apply Banach-Tarski theorem in practice?
6 votes

It depends on the context of the course where Banach-Tarski is being presented. My answer relies on knowing a bit of measure theory. Let's call our intial set which we're going to split into some ...

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What are some good examples to motivate the implicit function theorem?
5 votes

I can't offer you a good and interesting example, but a nice geometric interpretation. My math professor (Rainer Wüst from TU Berlin) had presented the theorem in way which was easier to digest: He ...

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Ockham's Razor & Mathematical Proofs
5 votes

I'd choose the proof which helps to understand the theorem the most. If the long one is too technical, the message might get lost. If the short one is too mysterious, the time saved with the more ...

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Lecture Notes: Slides with extra detail or longer PDF?
4 votes

I can only offer my personal opinion on the matter, having witnessed both formats as a student. I think that the material you use should be designed for the specific use you want them for. Slides are ...

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Should one visualize properties of a matrix or/and state its properties?
4 votes

The pitfall of this notation is: In mathematics, if something has the same (variable) name, it is the same thing. Because of that, this notation needs to be read in a relaxed way, which probably only ...

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Is there a tag/competence classification for mathematics education?
Accepted answer
4 votes

Since this question is still in the unanswered category, I'll repost my comment as an answer: Similar to the tag graph of MathSE, there is the Mathematics Subject Classification of Math Reviews and ...

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Item Analysis in Mathematics Exams
3 votes

The comment of Mon Kee Poo raises an important point: The actual distributions of the points per item might offer some more insight than just the median and the standard deviation. For example, if ...

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It is good to have old exams (with solutions) published?
2 votes

Exam questions usually are similar to homework questions, but they are not quite the same. Especially for first-year courses, I think it's a very good thing to give an idea how the exam might look ...

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What is a good teaching example of machine learning?
1 votes

Coursera's Machine Learning Course by Andrew Ng used two examples to motivate the training of neural networks: Programming of Logic gates, such as AND, OR, XNOR and so on - the latter requires two ...

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What activities can enhance student comprehension of concepts involved in logarithmic and exponential integrals?
-1 votes

Since the integral of a postive function is the area under the function, a possible real-life application is the following situation: Suppose you want to paint the wall of your room in a fancy ...

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