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Results tagged with undergraduate-education
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user 117
For questions about teaching students at the undergraduate (university) level.
6
votes
Accepted
How do I become a Scarer?
I do not think you can change the opinions of professors who hold these views. All you can do is be a human: interact with undergrads, and let them know that you do not think inherent ability is nee …
- 22.1k
34
votes
Accepted
Epsilons and deltas in a first calculus course
For some reason there is a wide spread view that the $\epsilon-\delta$ definition of a limit is an obscure thing, relevant only to mathematicians, and that the only reason to care about them is to mak …
- 22.1k
8
votes
Should we teach functions as sets of ordered pairs?
I think as long as students know that:
A function $f:A \to B$ assigns one and only one element of the codomain $B$ to each element of the domain. We write $f(a) = b$ if $a \in A$ is assigned to $b …
- 22.1k
12
votes
Should we teach abstract affine spaces?
I am sure you know this, but the Euclidean plane is a prime example.
The Euclidean plane starts as just a collection of points together with a group of isometries. There is no natural origin. Howev …
- 22.1k
31
votes
Accepted
Why is the concept of injective functions difficult for my students?
I think you will find that almost everyone has this problem when they first starting to learn rigorous mathematics, and many students will never overcome this difficulty.
The following three statement …
- 22.1k
10
votes
How to teach if calculations and algebraic manipulations are off limits
I highly recommend looking at the Calculus exams from the University of Michigan.
https://dhsp.math.lsa.umich.edu/examshops.html
These problems tend to focus on extracting relevant information for sol …
- 22.1k
2
votes
Where can I find hard exercises for logic?
Here are all of the textbook chapters and assignments related to logic which I wrote for my Discrete Mathematics course last semester. We spent about half of the course time (8 weeks) on this content …
- 22.1k
2
votes
Motivating students to take homework seriously without grades
I think my system solves your problem
Assign homework due by date $X_1$ and time $t_1$. The submission is accepted electronically until that date and time.
The solutions to this homework are automa …
- 22.1k
7
votes
Alternatives to University Lectures: Non-lecture Mathematics Classes
Jim Fowler and I created a hybrid linear algebra/multivariable calculus/multilinear algebra course at
https://github.com/kisonecat/m2o2c2
The structure of the course was:
$\mathbb{R}^n$ as an inner p …
- 22.1k
9
votes
What's the most effective way to introduce/motivate the anti-derivative of $\sec x$?
In my opinion, a good story to tell about techniques of integration in general goes something like this:
We know that some functions (like $x^2$) have elementary antiderivatives, and some (like $e^{ …
- 22.1k
10
votes
Accepted
What's the most effective way to introduce/motivate the anti-derivative of $\sec x$?
To expand on Gerald Edgar's comments above:
Assume that you have already covered partial fractions.
Develop a general strategy for integrals of powers of trig functions: If a power is odd, you can …
- 22.1k
14
votes
Do you mention the continuity and the differentiability of the empty function
I think that this would be too much of a detour in a regular Calculus class.
You would need to first establish that the empty function is even a function. This requires a really pedantic reading of t …
- 22.1k
7
votes
Accepted
What are the essential mathematics skills that uni based STEM math educators want high schoo...
This is entirely opinion based, but I don't really care what content is "covered" at all. I care that students are engaged with thinking about problems which involve quantitative and spatial reasonin …
- 22.1k
4
votes
Unique steps leading to a non-unique answer
A "non-mathematical" answer: If you are in need of a doctor, then one unambiguous algorithm for finding one is to call everyone in the phone book, in order, and ask them if they are a doctor. Eventu …
- 22.1k
2
votes
Encouraging students to see value in things that can't be measured
Take this advice with a grain of salt, as I have not implemented anything like it yet.
I have been thinking a lot about the responsibility that we have, as mathematics educators, to not only give stud …
- 22.1k