The Optimal APMA-CS Spreadsheet

June 20, 2025

Everyone at Brown has a spreadsheet. Spreadsheet? You ask. What kind of spreadsheet? A course spreadsheet. With the Open Curriculum, students here concoct weird and wacky courseloads for themselves, and we need a way to keep track of concentrationWhat we call a major requirements. The basic solution is the best, and so the simple spreadsheet solves all of our problems.

My spreadsheet consists of my semesterly plan, as well as a list of concentration requirements and which classes I currently have fulfilling those roles. Here is my current semesterly plan, including classes I have taken and classes I plan to take. I will only attach the course codes, so feel free to reference C@B for course titles and descriptions.

My Coursework

Sem 1	Sem 2	Sem 3	Sem 4	Sem 5	Sem 6	Sem 7*	Sem 8*
MATH 0350	APMA 0350	APMA 0360	APMA 1200	APMA 2110	APMA 1740	APMA 1710	APMA 2070
MATH 0540	MATH 1010	APMA 1650	CSCI 0300	APMA 1690	APMA 1360	APMA 1170	MATH 1530
CSCI 0150	CSCI 0200	CSCI 1010	CSCI 1420	CSCI 1570	APMA 1930W	CSCI 2951F	CSCI 2952N
LATN 1110S	CSCI 0220	ECON 0110	CSCI 2470	ECON 1090	CSCI 1520	DATA 1030	CSCI 2951O
MUSC 0610**	MUSC 0610**	CLPS 0300	LATN 1150	LING 1741	CLAS 0855	Thesis	Thesis
MUSC 0810**	MUSC 0810**

*Semesters not yet completed
**Half-credit courses

At some point, I plan to delve into some of what I have taken personally outside of my degree. For now, however, we focus directly on the MATH, APMA, and CSCI.

My (Tech) Coursework

Sem 1	Sem 2	Sem 3	Sem 4	Sem 5	Sem 6	Sem 7*	Sem 8*
MATH 0350	APMA 0350	APMA 0360	APMA 1200	APMA 2110	APMA 1740	APMA 1710	APMA 2070
MATH 0540	MATH 1010	APMA 1650	CSCI 0300	APMA 1690	APMA 1360	APMA 1170	MATH 1530
CSCI 0150	CSCI 0200	CSCI 1010	CSCI 1420	CSCI 1570	APMA 1930W	CSCI 2951F	CSCI 2952N
CSCI 0220		CSCI 2470		CSCI 1520	DATA 1030	CSCI 2951O

While I could hardly say that I regret taking any of these courses, there is certainly much to be desired in the order I took these courses, and there are certainly some course variants I wish I had taken over others. A quick list:

MATH 0350 as a course really just doesn’t… work. It tries to be rigorous, but so much of the rigor requires some real analysis that it ends up being something like “we can’t say that we can swap the order of integration for any given function, we need to show that Fubini’s Theorem holds. When does Fubini’s Theorem hold? Haha, that’s a great question, and it’s outside the scope of this class.” Just take 0180 or 0200, and then take Real Analysis later if you’re hung up on not knowing what Fubini’s Theorem is.
CSCI 0150 (cs15) is a great class, and I do not regret taking it as my introduction to computer science. However, I do wish that I had taken CSCI 0170 (cs17) intead. Given the type of person I am and the type of coding that I will be doing, I do feel that it would have been a slightly better introduction for me. Though, as Andy van Dam nears retirement, I do believe that cs15 will be dropped from the offerings in the near future.
CSCI 1420 requires a much stronger mathematical background than is assumed by the class, and to some degree this is understandable, as it is a CSCI course and not an APMA course, but it involves a great deal of probability and information theory that is not learned in APMA 1650.
Speaking of information theory, I should not have waited until senior year to take APMA 1710. Frankly, it should be taken right after APMA 1650. Having not taken it, information theory shows up in just so many different places that it really feels important to have an intuitive grasp of it, and while I have definitely learned content from information theory before and am confident that I can apply it, I don’t really have as good of an intuition around it as I would like.

With all this, I propose a do-over, with a few particular caveats. I am assuming…

… that someone has the same exact prob/stat/ML interests that I do, except in upcoming semesters, vith various upcoming requirements.
… someone has as many alternate interests as I do and wishes to take at least one every semester, but usually takes 2-3, sometimes 4 courses in MATH/APMA/CSCI.
… that this someone is willing to take five courses in a semester, and difficult ones at that.

With that out of the way, I present The Optimal Prob/Stat/ML APMA-CS Spreadsheet:

Sem 1	Sem 2	Sem 3	Sem 4	Sem 5	Sem 6	Sem 7	Sem 8
MATH 0180	MATH 1010	APMA 1710	APMA 1200	APMA 1690	APMA 1740	APMA 2110	APMA 1930W
MATH 0540	APMA 1655	APMA 0365	APMA 1660	CSCI 1010	CSCI 1520	APMA 2630	APMA 2640
CSCI 0170	APMA 0355	CSCI 0410	CSCI 1420	DATA 1030
	CSCI 0200	CSCI 0300	CSCI 1470

Let me discuss the rationale behind some of these choices.

As previously discussed, replace MATH 0350 with MATH 0180 and CSCI 0150 with CSCI 0170.
I am abivalent between APMA 1650 and APMA 1655 when I had the opportunity to choose, as my section of 1650 covered slightly more content, such as MLE. However, APMA 1655 is the new requirement.
Likewise, APMA 0355 and APMA 0365 are new prerequisites, as is CSCI 0410.
APMA 1710 early will provide quite a bit of motivation for categorical cross-entropy, which made no sense to me as a term when it showed up in CSCI 1420 and CSCI 1470.
The pathway of APMA 1200 -> APMA 1690 -> APMA 1740 makes a lot of sense to me. APMA 1200 builds up Markov chains, 1690 provides some necessary review and a major application of Markov chains, while introducing Gibbs sampling, which then gets expanded on in 1740, along with a number of other statistical methods.
I did not take APMA 1660, and I have no plans to do so, as I think there were more interesting courses to take, and most of 1660’s content can be learned independently. This is still probably true, but because I am not considering other courses offered in a given semester, I have included it on this list.
As much as I would love APMA 1740 to precede CSCI 1420, it simply does not make sense to hold off on 1420 for so long. But a significant portion of the math required can be intuited in 1420 with an understanding of APMA 1710.
APMA 2110 is a corequisite of APMA 2630. While the graduate probability courses have somewhat standardized curricula nationwide, if a given person has the opportunity to take it, they should. The alteratives include various graduate-level CSCI courses, which is what I plan to do instead. But from an APMA-perspective, I would contend that this is a better option.
CSCI 1010 should precede CSCI 1520, as knowing about time complexity and NP-hard problems becomes helpful when learning how some algorithms in practice can achieve better results. Additionally taking two topics at the same time in 1520 and APMA 1740 also makes sense to me.
DATA 1030 after CSCI 1420 makes sense, as after you learn the machine learning methods and mathematics, you learn how to use them in a practical setting.
Some people consider APMA 1690 to be a continuation of APMA 1660. In that case, it is worthwhile to be taking 1690 immediately after 1660.
MATH 1010 is good to have before attempting APMA 2110. While the amount of time passing in between is not desirable, it is good to have some basic real analysis before attempting some higher level courses, and will ultimately be kept fresh by the time senior year arrives.
Certainly, many of the remaining slots can be filled with MATH, APMA, or CSCI courses as well as courses outside of these departments. I omitted APMA 1360, CSCI 1570, and MATH 1530 intentionally, as even though I believe that they are important to have, they are not necessary for this pipeline. And of course, all remaining classes can be filled with courses outside the mathematical sphere! Utilize the Open Curriculum to its fullest extent!

If I could go back to 2022 and take these courses again, I think I would design a schedule as close to this as I could get. But my road was fogged by the now-cancelled Concurrent Masters program requirements, as well my then-lack of knowledge on what was useful to have until after taking it. But this is just what I would do, you should feel free to take what you want from this and modify it as will! Don’t let me tell you what to do. The Open Curriculum is your oyster!