Mathmari, what is the target audience for this presentation? I don't think I've seen you mention this. It matters a lot when it comes to structuring your talk.
HallsofIvy, I would just like to point out that tetrahedrons are also pyramids, but not every pyramid is a tetrahedron. A pyramid is a polyhedron of which one face can be any polygon (called its base) and all other faces (called lateral) are triangles meeting at a common vertex. A pyramid can be...
Perhaps this less-than-artistic picture will help.
When we consider angles between lines (and vectors) we always assume the angle that is less than or equal to $\pi$. The picture illustrates the scenario you are considering. In this case what we call the angle between the vectors is the...
Because in the interval $[0,\pi]$ the sine function $\sin(\theta)$ is nonnegative. He could have chosen $| {\mathbf a} \times {\mathbf b}| = {\color{red} (-1) } |{\mathbf a}| |{\mathbf b}| \sin(\theta)$, but then he would have reversed the orientation of the cross product.
Thank you for your response, Ackbach. I wanted to read that book since I've seen it in your signature, but I didn't buy it. Glad to know it is online. :)
Let me discuss Dijkstra's arguments. Indeed, programming is no longer a radical novelty, although I agree that some people still believe in...
This is an article I just found out about. It deals with computer science on about half of it, but the most interesting discussions concern educational values. Here is the article:
https://www.cs.utexas.edu/users/EWD/transcriptions/EWD10xx/EWD1036.html
I would like to know others' thoughts on...
Sorry for not answering earlier, I didn't see you answered the thread until two days ago. The answer to your question is no. I don't think the wedge makes much of a difference, notation-wise. You know it is there and what you must pay attention is to operate with it according to the wedge rules...
The whole set is expensive, so perhaps if you stick to your decision of acquiring it you should buy only volume one at first.
As for the proofs, his proofs and methods are not all short and slick. In fact, he is rarely short and slick. He prepares the chain rule for three sections before...
While not a book on differential forms, I recommend J. J. Duistermaat and J. A. C. Kolk's two-volume set Multidimensional Real Analysis. It aims to teach you analysis in $\mathbb{R}^n$ but it is just as much a beginning differential geometry book. Differential forms will be touched upon in the...