I was always team MATLAB/Maple rather than Mathematica — I found Mathematica much less intuitive than that combo. Engineering tends to prefer MATLAB usually although I’m also seeing a lot of Python now.
As far as students having trouble with understanding functions, the biggest problem I see is that they don’t understand the concept of scope for variables (the idea that each function has its own separate memory, and variable names inside the function don’t have to match the place they are called from, nor will those variables be visible from the “outside”).
I used Matlab for a bunch of stuff when I was a postdoc, and it was definitely friendlier in having less complicated syntax. One of the biggest stumbling blocks with Mathematica is all the weird capitalization and different brackets and so on. Matlab felt more ordinary. We've got a site license for Mathematica, though, so that's the thing I use now..
I'm always amazed at how compact Mathematica notation can be, and doubly amazed at how it always takes me about four times as long to come up with the right combination of /@ and # & and all that than it would to write out the same thing in a more conventional programming language.
I know when I first learned about computers, I was almost immediately learning about programming, and learned a number of ways of writing subroutines and functions with arguments and so forth. But I wonder if your students, even if they're science- and math-minded, don't really do any computer programming unless they have to for a class, because learning about computers these days is about browsing the web?
Twenty years ago (!) there was a book, Visual Quantum Mechanics, which made heavy use of Mathematica. The website is still up, but I suspect that all the included software can only run on outdated platforms. https://vqm.uni-graz.at
I think that's probably it-- for all the talk about how today's students have grown up with computers, they don't grow up with programming in the same way that Nerds Of A Certain Age did, and that leads to some conceptual blocks. Which are really persistent-- there are students seeing Mathematica exercises for the third or fourth time who still don't get what's going on.
I've never taught that course -- I'm at a community college and am able to do the "Modern Physics" one, but that's as far as it goes. I remember when I took Quantum 1 we used the set of notes from Mike Morrison that became his textbook (https://www.amazon.com/Understanding-Quantum-Physics-Users-Manual/dp/0137479085), and I loved it. It's crazy wordy as well as thoroughly taking its mathematical time plowing through wavefunctions, but it always felt like an enthusiastic guide helping me through the tough parts. I've also heard that some peeps are using McIntyre because of the spin-first approach, and I like its organization, though I haven't been through that one in detail yet. Anyway, thanks for the thoughts! I like hearing about how other profs think about and put together curricula.
I remember some engineers of my acquaintance speaking very highly of Morrison, but I've never looked at it that closely. McIntyre has come up in several discussions; I'll have to look for that one, because the only undergrad state-vector version I've seen is Townsend's.
I was always team MATLAB/Maple rather than Mathematica — I found Mathematica much less intuitive than that combo. Engineering tends to prefer MATLAB usually although I’m also seeing a lot of Python now.
As far as students having trouble with understanding functions, the biggest problem I see is that they don’t understand the concept of scope for variables (the idea that each function has its own separate memory, and variable names inside the function don’t have to match the place they are called from, nor will those variables be visible from the “outside”).
I used Matlab for a bunch of stuff when I was a postdoc, and it was definitely friendlier in having less complicated syntax. One of the biggest stumbling blocks with Mathematica is all the weird capitalization and different brackets and so on. Matlab felt more ordinary. We've got a site license for Mathematica, though, so that's the thing I use now..
I'm always amazed at how compact Mathematica notation can be, and doubly amazed at how it always takes me about four times as long to come up with the right combination of /@ and # & and all that than it would to write out the same thing in a more conventional programming language.
I know when I first learned about computers, I was almost immediately learning about programming, and learned a number of ways of writing subroutines and functions with arguments and so forth. But I wonder if your students, even if they're science- and math-minded, don't really do any computer programming unless they have to for a class, because learning about computers these days is about browsing the web?
Twenty years ago (!) there was a book, Visual Quantum Mechanics, which made heavy use of Mathematica. The website is still up, but I suspect that all the included software can only run on outdated platforms. https://vqm.uni-graz.at
I think that's probably it-- for all the talk about how today's students have grown up with computers, they don't grow up with programming in the same way that Nerds Of A Certain Age did, and that leads to some conceptual blocks. Which are really persistent-- there are students seeing Mathematica exercises for the third or fourth time who still don't get what's going on.
I've never taught that course -- I'm at a community college and am able to do the "Modern Physics" one, but that's as far as it goes. I remember when I took Quantum 1 we used the set of notes from Mike Morrison that became his textbook (https://www.amazon.com/Understanding-Quantum-Physics-Users-Manual/dp/0137479085), and I loved it. It's crazy wordy as well as thoroughly taking its mathematical time plowing through wavefunctions, but it always felt like an enthusiastic guide helping me through the tough parts. I've also heard that some peeps are using McIntyre because of the spin-first approach, and I like its organization, though I haven't been through that one in detail yet. Anyway, thanks for the thoughts! I like hearing about how other profs think about and put together curricula.
I remember some engineers of my acquaintance speaking very highly of Morrison, but I've never looked at it that closely. McIntyre has come up in several discussions; I'll have to look for that one, because the only undergrad state-vector version I've seen is Townsend's.