Some questions on strange things in online courses

[Florian Geyer]

Hello there, I hope this message will find you all very well.

I have some experience with online courses, and I have found some "strange" things I want to ask about.
- First, why so many of them suggest time that is too short for the course? I will give an example here of a course I have studied in Coursera which is on vector calculus. the platform suggest that the time needed for the course is 29 hours, this is a link to the course:
https://www.coursera.org/learn/vector-calculus-engineers
and this is the link for the lecture notes https://www.math.hkust.edu.hk/~machas/vector-calculus-for-engineers.pdf .
first of all you may find 29 hours is enough, and this is entirely understandable, because I can suppose many of you have a PhD in physics or mathematics, but how about if the learner like me when I learned the course for the first time? it took me something between 250 and 300 hours, I needed this time for:
- Listening to lectures (of course).
- Reading the lecture notes and try to understand it, and doing all the derivations.
- Doing all the problems (and understanding everything in it).
- Doing some algorithms on doing the types of problems written in the lecture notes in their most general form (this of course a laborious work and takes a lot of effort and trying many things). this step is vital for my studying of mathematics.
- Trying many ways and (hitting the wall by my face as many prefer to say), and if I could not do a problem then I ask ChatGPT first (and trust me it gives me the needed insight most the time) and this of course demand that I type all the problem with all the needed steps I want to discuss and with my understanding of each step.
- If the previous step did not work, then I go to my professors and discuss the problem with them.
- Doing more work on topics which are not covered well (at least I cannot understand them) like some introduction to tensors like Levi-Cevita and Kronecker-Delta, and Einstein summation convention, and many other topics like the derivation of the gradient, divergence, curl and the Laplacian in each coordinate system (the last step regarding the del operator I just go over it like some others, because I am mortal after all).

These are the steps which I can remember right now, and I suppose there are some missing things I have done, but I thing the picture is clear now, which is there are so many things to be done and the suggested time for each course in mathematics and physics is much less than the actual needed time.. Bear in mind that I have not said anything about using even the smallest textbook on the subject, or even a chapter on a mathematical methods textbook.

so my question (especially for educators) is, why in online courses they prefer to use these very tight suggested time? please give me your insight.

 

[topsquark]

Hello there, I hope this message will find you all very well.

I have some experience with online courses, and I have found some "strange" things I want to ask about.
- First, why so many of them suggest time that is too short for the course? I will give an example here of a course I have studied in Coursera which is on vector calculus. the platform suggest that the time needed for the course is 29 hours, this is a link to the course:
https://www.coursera.org/learn/vector-calculus-engineers
and this is the link for the lecture notes https://www.math.hkust.edu.hk/~machas/vector-calculus-for-engineers.pdf .
first of all you may find 29 hours is enough, and this is entirely understandable, because I can suppose many of you have a PhD in physics or mathematics, but how about if the learner like me when I learned the course for the first time? it took me something between 250 and 300 hours, I needed this time for:
- Listening to lectures (of course).
- Reading the lecture notes and try to understand it, and doing all the derivations.
- Doing all the problems (and understanding everything in it).
- Doing some algorithms on doing the types of problems written in the lecture notes in their most general form (this of course a laborious work and takes a lot of effort and trying many things). this step is vital for my studying of mathematics.
- Trying many ways and (hitting the wall by my face as many prefer to say), and if I could not do a problem then I ask ChatGPT first (and trust me it gives me the needed insight most the time) and this of course demand that I type all the problem with all the needed steps I want to discuss and with my understanding of each step.
- If the previous step did not work, then I go to my professors and discuss the problem with them.
- Doing more work on topics which are not covered well (at least I cannot understand them) like some introduction to tensors like Levi-Cevita and Kronecker-Delta, and Einstein summation convention, and many other topics like the derivation of the gradient, divergence, curl and the Laplacian in each coordinate system (the last step regarding the del operator I just go over it like some others, because I am mortal after all).

These are the steps which I can remember right now, and I suppose there are some missing things I have done, but I thing the picture is clear now, which is there are so many things to be done and the suggested time for each course in mathematics and physics is much less than the actual needed time.. Bear in mind that I have not said anything about using even the smallest textbook on the subject, or even a chapter on a mathematical methods textbook.

so my question (especially for educators) is, why in online courses they prefer to use these very tight suggested time? please give me your insight.

I don't know much about STEM classes, or teaching an online class, but the 29 hours probably simply refers to time spent for instruction. If you took the class in person, the usual figure for homework is (as I recall) is 3 - 5 hours/course hour... throw in expected self-study/review time, 2 hours/course hour, and figure that you don't have an instructor to ask questions of, throw in an extra 2 hours/course (as an estimate) for research and you get a total of 29 + 29*4 + 29*2 + 29*2 = 261-ish hours, which is right around what you are talking about. Obviously these figures will vary, but it sounds about right.

-Dan

 

[kuruman]

Why are you so concerned with the 29 hours that someone said is needed for the course? The bottom line is are you learning or not? If the answer is "yes", then learn at your own pace and be happy about it. For reference, at the U.S. university where I taught, the rule of thumb for STEM courses is that students should spend at least 3 hours per credit per week outside contact hours on the course material to have a chance of success. That's quite a mouthful so let me do a sample calculation to illustrate.

The material you posted would be appropriate for a 3-credit course taught over 14 weeks in the format of forty 50-min lectures. These lectures are the contact hours and amount to a total of 2000 minutes. In addition to this, students are expected to spend 9 (3 credits times 3 hours) hours per week for 14 weeks studying the material, doing homework, etc. This amounts to 9×14×60 = 7560 minutes. Adding the contact hour minutes gives a grand total time investment of 9560 min ≈ 160 hrs. Of course that is the minimum time one should spend so 250-300 hours is not excessive especially when you have to teach yourself without the benefit of live in-person lectures. Feeling better now?

On edit: After posting this I noticed that @topsquark has produced a realistic time estimate by another method that is in agreement with mine.

 

[Florian Geyer]

Thanks for taking time reading and answering my question, here I will clarify some points:

- First, of all it seems we have agreed in our estimation of the required time for each course, and this is a good thing to begin with.

- second, the reason why I have I have asked this question is to assess my achievements and see if I need to modify my methods. There are many things I have considered before like the whether my language level is sufficient of not, I believe I need a level like C2 or higher (of course the higher the level the better the understanding and learning), yes I know Mr. Gerard t'Hooft once said that we do not need a high level in English to learn physics, but I do not think he will disagree about what I have read here... anyway, I think let us not delve into this matter of language since improving the languge level cannot be done in the short run.

However, there are many other aspects I always want to consider and see if I need to improve them, and if there are some disagreements between my opinions or expectations, then I will benefit from hearing your opinions, and this is exactly why I ask questions like this, because I think they are invaluable to my learning journey and give me a lot of insight.

- I may add that I think when an expert do something, then he has a meaning and understanding this meaning can help me a lot, so when the professor of the course give an estimated time for the course, then he must have done that based on something I do not understand, and asking the expert teachers and professors like you is what I need.

- After all self-learning is hard, and require much more self-assessing.

Again, thank you all for considering my question.

 

[kuruman]

After all self-learning is hard, and require much more self-assessing.

I couldn't agree with you more here. You seem to have a good grasp of what you are about and ask the right questions. I wish that all my students were like you. Also, please keep in mind that were are here to help you with more specific questions on physics or math. I am pretty sure that our combined natural intelligence at PF beats hands down the artificial intelligence of ChatGPT. For example, when a student asks a homework question, ChatGPT will give a straight answer to the best of its ability. At PF we require the student to provide some attempt at a solution before receiving help. Why do we do this?

At the top level of reasons is the message "We don't hand out answers just because you asked. You have to show some willingness to help yourself." If the student doesn't quit at this level, he takes charge of his progress and shows his attempt which, most often, is off the mark. That is a valuable piece of information because it allows the PF helper to diagnose the shortcomings in the student's understanding that prevented him from finishing the problem. Thus, the helper not only guides the student step by step to the answer, but also removes the misconceptions and misunderstandings that lay hidden underneath the original question. ChatGPT (so far) is incapable of providing such a diagnosis. It will you what's right and what's wrong but not how to fix your understanding of things.

Bottom line: If you're stuck, come to us. We do it on a volunteer basis and strictly because we enjoy doing it.

 

[Florian Geyer]

I couldn't agree with you more here. You seem to have a good grasp of what you are about and ask the right questions. I wish that all my students were like you. Also, please keep in mind that were are here to help you with more specific questions on physics or math. I am pretty sure that our combined natural intelligence at PF beats hands down the artificial intelligence of ChatGPT. For example, when a student asks a homework question, ChatGPT will give a straight answer to the best of its ability. At PF we require the student to provide some attempt at a solution before receiving help. Why do we do this?

At the top level of reasons is the message "We don't hand out answers just because you asked. You have to show some willingness to help yourself." If the student doesn't quit at this level, he takes charge of his progress and shows his attempt which, most often, is off the mark. That is a valuable piece of information because it allows the PF helper to diagnose the shortcomings in the student's understanding that prevented him from finishing the problem. Thus, the helper not only guides the student step by step to the answer, but also removes the misconceptions and misunderstandings that lay hidden underneath the original question. ChatGPT (so far) is incapable of providing such a diagnosis. It will you what's right and what's wrong but not how to fix your understanding of things.

Bottom line: If you're stuck, come to us. We do it on a volunteer basis and strictly because we enjoy doing it.

I am very grateful for your encouragement and kind words Mr. Kururman.

As for the help in math and physics, well it seems the environment here is more encouraging that the other websites I have tried before (most of the time my questions were considered "off topic) yes I know I have made some silly miscalculations and other dummy mistakes, but when I asked the question I really needed help in them. Since this forum is more acceptable (as I have seen) I will try to ask my question (regarding my studying in physics in this forum).

Regarding the use of ChatGPT, well first of all, what I will say here does not mean I will ignore your kind offer above, nor I think it (or he) is better than the esteemed members here, But I will try to give my opinion in it briefly, since I have not done that, nor I intend to do that in a different thread.
I agree with you totally that it gives you the solution without the needed feedback and explanation, but you can make it ore useful if you asked it (or him) the right questions, and if you started a full discussion on the topic with him it can give you a lot of insight.

an example of a good question there is:
tell me how can I prove ...... is equal to ...., I have tried to do the problem this way ....(write everything you have tried in LaTeX and maybe with your full explanation)... and I have reached to the following results ......, but it seems to me that my solution is wrong, because of ...... . please tell me what is the wrong in my solution, and what I have done incorrectly. Give me a detailed/ step-by-step solution, use LaTeX in your solution.

Also the Chat can do some amazing explanations of tough points many may just look over without understanding them. Here is an example I have faced:
The problem was in the explanation of the lecture: see 24:25 section momentum, I could not understand it first, and then I used ChatGPT as follows:

The text then added this step $$(\vec{\nabla^{\prime}}\cdot\vec{J}(x^{\prime}))\vec{\nabla^{\prime}}\left(\frac{1}{|\vec{x}-\vec{x^{\prime}}|}\right)=\vec{\nabla^{\prime}}\left(\frac{(\vec{\nabla^{\prime}}\cdot\vec{J}(x^{\prime}))}{|\vec{x}-\vec{x^{\prime}}|}\right)-(\frac{1}{|\vec{x}-\vec{x^{\prime}}|})\vec{\nabla^{\prime}}((\vec{\nabla^{\prime}}\cdot\vec{J}(x^{\prime}))$$ and said that "this last simplification is done by using the chain rule". Can you explain that in detail?

its reply:
Yes, I can explain the step in detail. Let's break down the chain rule application:
Consider the function $$g(\vec{x^{\prime}}) = \frac{(\vec{\nabla^{\prime}}\cdot\vec{J}(x^{\prime}))}{|\vec{x}-\vec{x^{\prime}}|}$$. We want to find the gradient of this function with respect to $\vec{x^{\prime}}$. The chain rule states that:
$$\vec{\nabla^{\prime}}g(\vec{x^{\prime}}) = \vec{\nabla^{\prime}}\left(\frac{(\vec{\nabla^{\prime}}\cdot\vec{J}(x^{\prime}))}{|\vec{x}-\vec{x^{\prime}}|}\right)$$
Now, notice that the function $g(\vec{x^{\prime}})$ is a product of two functions, namely $$h(\vec{x^{\prime}}) = \vec{\nabla^{\prime}}\cdot\vec{J}(x^{\prime})$$ and $$k(\vec{x^{\prime}}) = \frac{1}{|\vec{x}-\vec{x^{\prime}}|}$$
To find the gradient of the product of these two functions, we can apply the product rule for differentiation, which states:
$$\vec{\nabla^{\prime}}(h(\vec{x^{\prime}})k(\vec{x^{\prime}})) = k(\vec{x^{\prime}})\vec{\nabla^{\prime}}h(\vec{x^{\prime}}) + h(\vec{x^{\prime}})\vec{\nabla^{\prime}}k(\vec{x^{\prime}})$$
Substituting $h(\vec{x^{\prime}})$ and $k(\vec{x^{\prime}})$ back into the equation, we get:
$$\vec{\nabla^{\prime}}g(\vec{x^{\prime}}) = \frac{1}{|\vec{x}-\vec{x^{\prime}}|}\vec{\nabla^{\prime}}(\vec{\nabla^{\prime}}\cdot\vec{J}(x^{\prime})) + (\vec{\nabla^{\prime}}\cdot\vec{J}(x^{\prime}))\vec{\nabla^{\prime}}\left(\frac{1}{|\vec{x}-\vec{x^{\prime}}|}\right)$$
This is the result given in the textbook. The chain rule is used to differentiate the product of the two functions, and the product rule is applied to find the gradient of this product with respect to $\vec{x^{\prime}}$.

my reply:

can you give me a latex code for a sketch of the previous problem?

Certainly! Here is a LaTeX code snippet that uses the TikZ package to create a simple sketch of the problem:

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, positioning, calc}

\begin{document}
\begin{tikzpicture}
% Axes
\draw[->, thick] (-0.5, 0) -- (4, 0) node

{$x$};
\draw[->, thick] (0, -0.5) -- (0, 4) node[above] {$y$};

% Charges
\node[circle, fill=blue!50, inner sep=0pt, minimum size=5mm] (q1) at (0, 2) {$q_1$};
\node[circle, fill=red!50, inner sep=0pt, minimum size=5mm] (q2) at (0, 0) {$q_2$};

% Velocity vectors
\draw[-{Stealth[length=5mm, width=2mm]}, blue, very thick] (q1) -- +(90:1.5) node[midway, left] {$\vec{v}_1$};
\draw[-{Stealth[length=5mm, width=2mm]}, red, very thick] (q2) -- +(0:1.5) node[midway, below] {$\vec{v}_2$};

% Distance d
\draw[<->, thick] (0, 0.2) -- (0, 1.8) node[midway, left] {$d$};

% Coordinate system for q1
\draw[->, dashed] (q1) -- +(0, 1) node

{$y^{\prime}$};
\draw[->, dashed] (q1) -- +(-1, 0) node[above] {$x^{\prime}$};
\end{tikzpicture}
\end{document}

This code creates a standalone document with a TikZ drawing that shows the $x$ and $y$ axes, the charges $q_1$ and $q_2$, their respective velocity vectors $\vec{v}_1$ and $\vec{v}_2$, the distance $d$ between them, and a coordinate system for $q_1$. You can copy and paste this code into your LaTeX document, making sure to include the TikZ package in your preamble if you haven't already.
Well, I have had some experience with ChatGPT, and I decided to share it here, again only to show that it can do a lot of amazing things, or maybe only as a defend of a close friend :).​

 

[Florian Geyer]

sorry I wanted to insert a code but I could not find LaTeX in options... I know this may seems messy, but hopefully I will learn a way to compile my LaTeX code in the next posts. regarding the video I have only add a link, but it seems to be added as a video here automatically.
Sorry for this.

 

[topsquark]

sorry I wanted to insert a code but I could not find LaTeX in options... I know this may seems messy, but hopefully I will learn a way to compile my LaTeX code in the next posts. regarding the video I have only add a link, but it seems to be added as a video here automatically.
Sorry for this.

Use ## instead of $.

-Dan

 

[berkeman]

sorry I wanted to insert a code but I could not find LaTeX in options... I know this may seems messy, but hopefully I will learn a way to compile my LaTeX code in the next posts.

I will send you some LaTeX tips via PM now...

 

[berkeman]

Thread closed for Moderation...

 

[berkeman]

Regarding the use of ChatGPT, well first of all, what I will say here does not mean I will ignore your kind offer above, nor I think it (or he) is better than the esteemed members here, But I will try to give my opinion in it briefly, since I have not done that, nor I intend to do that in a different thread.

AI chatbots are not valid references for the technical PF forums (see the rules under INFO at the top of the thread). This thread will remain closed now.