I’m going to be a senior in high school, and I’m in need of another class for my spring semester. Since I’d have all the core classes barring math, I was thinking of ending the year with another self-study math course. Any suggestions?
Discrete math, college level Probability, college-Level Statistics would be 3 good ones. (College Level implying calculus-based)
@ProfessorPlum168 Actually, statistics might be an interesting route since I’ll have the foundation of AP Stats. What is Discrete Math like?
Kinda hard to describe - it’s math that is binary/countable as opposed to continuum calculations like in calculus. Routinely needed for any type of Computer Science curriculum. So things like logic, combinatorics and set theory are prominent in discrete math.
@ProfessorPlum168 might be surprised, but I actually agree 
- Discrete Math or Calc-based statistics.
https://www.eecs70.org/ is the home page of a discrete math (with some probability theory) course, including lecture notes that this course uses instead of a textbook.
If you are still a prospective biology major pre-med, here is the syllabus of a one year math course covering topics that are considered useful in that context:
https://math.berkeley.edu/~stankova/10AF18/Student%20Handout%2010AF18.pdf
https://math.berkeley.edu/~stankova/10BS19/Student%20Handout%2010BS19.pdf
Note that medical research papers commonly use statistical analysis, so a strong knowledge of statistics should be helpful.
However, given your interest in math, you may want to consider a major in math or statistics, which can be done alongside pre-med courses. Math or statistics majors tend to have more backup career options than biology majors if they do not get into medical school (only about 40% of pre-med who apply get into any medical school, and that does not count the many pre-meds who decide not to apply for various reasons, like college GPA or MCAT scores too low for a realistic chance of admission) or decide not to pursue medical school.
I often see calculus-based statistics as a answer when questions like this come up. I’ve tried a couple times looking for an online college class in calculus-based stats, but I couldn’t find one. Any suggestions?
https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/ is a calculus-based introductory probability and statistics course.
A break ?
Introduction to analysis, Abstract Algebra, or partial differential equations… but honestly TAKE a break
@ucbalumnus Thank you for all these course suggestions! Question, though: would I be able to receive tangible credit from these courses, like a grade on my high school or college transcript? Or are these more “for fun?” Also, are they free?
@NASA2014 Thanks for the concern, but I’m only taking 7 courses next year. These courses bring enthusiasm rather than stress. Plus, not to sound arrogant, but they’re easy A’s for me, so it’s a win-win.
@ucbalumnus Also, I honestly am starting to consider doing a math-related major. I really like chemistry and biology too, but I feel that I’ve been passionate about math longer and that I have more of an innate “math sense” than in the other two subjects. The only thing is that it will probably be harder to find medical research/projects.
Few top colleges, if any, will give you credit for these courses. Some schools may allow you to be placed out of some required courses/prerequisites if you pass their placement exams. If you major in math or applied math, you’re more likely required to take these courses again. You’ll probably be better off focusing on depth rather than breadth in math. Taking part and doing well in math competitions will demonstrate your ability in math better than getting an A in some college-level math course. And it may help with your college application.
@brobdingnagian17 the links to courses that @ucbalumnus provided are course syllabus descriptions/outlines complete with slides and materials. But it’s strictly for information, there’s no way to connect it to an actual class to get a grade unless you are actually registered and taking the class physically.
@ProfessorPlum168 In that case, I’ll find equivalent courses at my local community college and do a self-study of one of them.
@INJParent I already partake in the AMC series and have been invited by my local community college to do AMATYC and other math competitions after being inducted into their Mu Alpha Theta society. Plus, I co-founded and preside over the math club at my school. Finally, if anything, it would make a math major easier while also doing pre-med prereqs.
OP, you can certainly take these courses for your own enjoyment, but they won’t be of much use beyond serving as an intro to these subjects. As a premed, your time may be better spent on sciences. Statistics will surely be useful, but you’re likely required to take it again in college. Similarly, if you decide later to major in math or math-related subject, these courses won’t be adequate. How well did you do in AMC? Were you qualified for AIME? And USAMO?
Qualified for AIME but didn’t go on from there.
@INJParent An issue is that if I drop the math, my schedule would only be 4 APs and 2 PLTW Biomed courses, which looks a bit underwhelming in comparison to my sophomore and junior year schedules (8 and 7 courses, respectively). Plus, I’d want to do a course like Orgo I, but that requires transportation to the college for labs which is not accessible.
I didn’t go into these courses thinking that I’d get credit for everything. But I do feel that the challenge of completing these courses without instruction and yet still being held to the same standard as the students in-class has been quite rewarding. It’s boosted my discipline and made me more adaptive, making me more confident that I’ll do well in other areas like chem and bio. Not to mention that it shows colleges that I can think independently and that I’ll do better on the placement tests. Given that and the GPA boosts it has been giving me, I feel like I am only gaining.