My son, who will be an entering freshman, wants to take discrete math his first semester. (Partly because he and his current sophomore sister want to take a class together but at present it looks like they will have to take same class, different sections if at all.) He plans to double major in math and computer science and is planning to make use of his advanced standing in both subjects.
Sister got the class no problem because she has honors standing and enough hours to take anything she wants, but it looks like all sections of discrete math are at capacity and even the wait lists are pretty close to full. He is coming in with enough AP and dual enrollment credits that he will be able to have his choice of classes from second semester on, but he wants to take discrete math first semester. Any experience?
His second choice class would be linear algebra – which sister is also taking – but the only remaining slots are in a class with a prof with mixed reviews – and who knows whether even those spots will remain by the time Bama Bound Honors II rolls around. (Sister has the vastly preferred prof for both discrete math and linear algebra).
Note to parents of new students – don’t worry if you are reading this that your kids are going to have scheduling problems their entire time at UA. This is strictly a problem that arises first semester only and then only for kids who have pretty much completed the core, placed out of the entry level classes in their major and want to take upper level classes in their major. My son is my third child at Alabama and the first semester is the only tough semester in terms of class schedules for the kids with advanced standing in lots of subjects. From second semester on, like my daughter, they tend to have the pick of the classes and sections they want.
Once the summer hits, and a few more people need to register for these classes (there will be just a few at your son’s advanced level, tho), UA will allow those few students to get an override, I’m sure.
Is Diff EQ an option? (or do you need prereq for that, or did your son already take it?)
My S had Evans for Linear Alg; Lee for Diff EQ; and Liem for Discrete. Had no issues with any of these professors.
Taking the classes w/ different teachers might actually help your 2 students - they will get a different ‘version’ of the material, and this could help them help each other.
Make sure you don’t run out of classes at UA by coming in with too much credit! He’s going to get into some wild and wonderful imaginary math to complete his major in it! 
Good luck!
Students switch schedules throughout the summer, so there’s no telling when a space might open up. Your son is benefiting from going to an earlier Bama Bound in this situation because he will have more time to find space in one of those courses. There’s also a possibility that the maximum number of students is lower than the capacity of the room and thus the math department can simply expand the size of the course or move it to a larger room. Looking at the number of people on the waitlists, there might be an additional section opened up.
Thanks @aeromom and @sea_tide – differential equations would be an option, but doesn’t fit the bill for sister – who is just now adding a double major in Applied Math – Optimization. She doesn’t need differential equations and will probably run out of time to take all the classes she needs if she were to add it “for fun.” (And she would have to drop one of the other classes because she is already signed up for a heavy 19 hours as it stands). Also, discrete and linear algebra are slightly preferable because they are also on the CS flow chart, allowing him to make progress on both degrees initially, while differential equations only applies to the math major. He is going for the pure math track and will need differential equations, so that is an alternative if the plan to take a class with his sister doesn’t work out and seats don’t open in either of the other classes.
He is really looking forward to the"wild and wonderful" imaginary math classes. Luckily he is coming in with enough credits all around – core complete except for fine arts – that he can comfortably complete the CS/Math double major, but won’t run out of classes in either subject.
Who are the profs teaching that?
Discrete: Corson (class and waitlist full); Alli (class full, 6 waitlist spots); Moore (class full; 1 waitlist spot); Viem (class full; 8 waitlist spots)
Linear algebra: Belbas (20 spots of 40 remain); Perry (class full; 4 waitlist spots); Moore (class full; waitlist full); Liu (class full; 4 waitlist spots); Sun (class full; 10 waitlist spots); Hoang (2 spots of 40 remain; 10 waitlist spots)
The good news is that at this point all continuing students are registered so now we are just contending with students who switch schedules around and Bama Bound Express 1 and Honors 1 before he registers – and then he can try to pick up seats all summer.
I know my ds could not get into theory of probability 1st semester. Sections were full but did have an open wait list. He checked all summer but no actual class seat ever came open. He got into it without any difficulty this semester, so it definitely was only a problem with full sections when trying as an entering freshman.