Which to show rigor? Discrete vs Linear Algebra vs Calc 2? Science course?

Pre-College Issues High School Life
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Hi, my DD is a rising senior and wants to apply to highly selective academic schools. She plans to have a career in the performing arts. Her extracurriculars will demonstrate this, as will her essay. However, she is very academic, too, and definitely wants to take other classes that are not arts-related (Asian studies, psychology, etc). Her high school curriculum is VERY rigid. It will even say on the school profile that even the most ambitious students will have limited access to AP classes (and at her school, those AP classes that are available are in math and Spanish). That being said, she managed to self-study and place herself in AP Calc AB in her sophomore year (final grade is 99/100 and exam score was 5) and is thus taking AP Calc BC in junior year (will be similar to AB).

For senior year, ALL the students take a freshman course load at a university, which includes a concentration in their major (in her case, Theatre). Her high school is fairly new, only about 12 years old, and during that time, very few students in the past, if any, have managed to finish AP Calc BC, so it’s kind of new to them for my daughter (and one other classmate) to need to register for a math class beyond AP Calc AB. The original list of math selections were math classes that would be going backwards from Calc BC. This is a partnership between the high school and the university, so they had to get back to us with a different list, approved from both parties. The courses available for her to choose from the new list were: Stats, Applied Stats, Matrix & Linear Algebra, Discrete Structures , and Calc II.

My DD chose Discrete Structures (with Linear Algebra as the backup, in case Discrete doesn’t work with the schedule…the university puts the schedule together, so she won’t know what she gets until August).
We figured Calc II would be too similar to AP Calc BC. We heard Stats and Applied Stats is generally not considered as rigorous in the eyes of admissions.

As I mentioned above, she will be studying performing arts in college and is unlikely to need advanced math. She is only taking advanced math classes because she is very good at it and it was the only AP courses she was qualified to take in her school curriculum (she is not advanced in Spanish at all). And now, she has to choose a math class for senior year, but not sure which of those math classes will continue to show that she picked a “rigorous” schedule.

And on a different note, she also had to choose a science class, and from this list, she chose General Physics at the University: (she would have taken honors bio, honors chem, and honors physics in high school, but she felt the physics class in high school was very very slow for her and wondered if maybe the college course might be more challenging and interesting and maybe sort of equivalent to AP Physics): Principles of Bio, Chem I, General Physics, Intro to Meteorology, Intro to Astronomy, and Intro to Geology, all with labs. (The last three seem like they would be tricky to transfer credit).

Thoughts? There may still be time to ask for a change.

Thanks in advance!

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Any of the three math classes will show equal rigor. They cover quite different topics, and I would suggest your D to flip through the textbooks to see which topics she likes the best. I personally strongly dislike linear algebra and wouldn’t have taken the course voluntarily. :slight_smile:

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What does the college say as far as math placement for students with AP calculus AB and BC? (Check the AP credit listing on the college’s web site, or the web site of its math department.)

The typical math progression after single variable calculus (calculus 1 and 2 in college, or a high enough AP calculus BC score) would be any or all of the following:

  • Multivariable calculus (calculus 3)
  • Linear algebra
  • Differential equations
  • Discrete math (of most interest to computer science majors)

Linear algebra or discrete math should be considered rigorous follow-ons to calculus BC. Calculus 2 will be considered at least a partial repeat. For the statistics courses, it would depend on which kind. There are non-calculus-based statistics courses that high AP statistics approximates. There are also calculus-based courses that may be more worthwhile for a student who is good at calculus. Statistics could help her determine her interest in statistics or data science.

Physics courses in college typically come in multiple varieties. A course called “general physics” commonly is one of the following:

  • A non-calculus or light calculus course intended for biology majors and pre-meds. AP physics 1 and 2 or the old AP physics B emulates the non-calculus version.
  • A calculus-based course intended for physics and engineering majors (with expected progression in math in tandem – multivariable calculus is commonly a co-requisite to the second course in the sequence with E&M). AP physics C mechanics and E&M try to emulate this type of course, although E&M is limited in its use of math, since high school students do not normally get to multivariable calculus.

She should consider backup plans, because arts tend to be elite or bust (or barely scraping by) career paths (it helps if she has frugal spending habits and no debt from college or otherwise). At a previous workplace, I knew people who did performing arts as an “extracurricular” with community theater groups, but their day job was something else that paid the bills. If she likes math, then adding a major in applied math, statistics, or data science may give her backup career options in that area.

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I agree with this.

Is Physics C available?

If she’s that advanced in math and has self studied then she has an affinity in math. It’s likely that can/will be used in her future. The arts are low paying and hard to break into. She might want to combine the arts with a degree in math and physics. It’s fairly common for people who are mathematically to also be artistic/musical.

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In the first post, the OP mentions that the only AP courses are in math and Spanish. So any calculus-based physics would have to come through taking courses at the college, but the OP did not mention whether “general physics” is the calculus-based one for physics and engineering majors.

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@tarator @ucbalumnus @Htas
Thank you for your input!
The General Physics class in the option is listed as:
GENERAL PHYSICS I (4 Credits)
Mechanics, wave motion, and sound. An algebra-trigonometry based sequence designed to give the student a general understanding of the laws and principles of physics.

There were other physics classes listed at the college, including Physics I, and the description for that said it was calculus-based. But that wasn’t one of the options for her from her list to choose a science class. I wonder if she should talk to the guidance counselor. It could be that they just haven’t had many students in this position before. The reason she found the h.s. physics incredibly tedious was because the math seemed simple and it “felt like” the teacher was taking a whole period (one hour and twenty-three minutes) to explain one problem, when it only took her 5 minutes to do it. I’m sure she is exaggerating just a little bit, but she did say that she would get bored and sometimes doze off.
According to the AP credit policy of the university, AP Physics 1 score of 4 would substitute for General Physics I, AP Physics 2 would substitute for General Physics II, and AP Physics C: Mechanics would substitute for Physics I.

I appreciate the concern about a performing arts major. Actually, she has already worked professionally (has worked on national Broadway tours, a commercial, and some short films), so I know she will work. She said she will supplement as a substitute teacher (she’s a really good tutor, too), if she needs in-between income.

I should add that, for years, she has always said that she hates math but she knows she’s really good at it. Most recently, she started saying that she doesn’t hate math anymore and that maybe she only felt that way because she wasn’t at the right level for her before (before she self-studied into AP Calc AB). She still doesn’t love math. But she wants to use her strengths to her advantage. She picked Discrete Math because it involves logic, and she feels that’s something she would be interested in.

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For someone interested in a Performing Arts field of study and career I would advocate for Stats or applied Stats, particularly if those courses include an intro to probability. These are very useful courses for the understanding of risk and decision making for everyone. Good luck!

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Could it be because the high school physics course had to explain concepts with less advanced math, even though it would have been easier and faster to explain the concepts if students all knew more advanced math?

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@teleia Thanks! I agree that Stats or Applied Stats would be more useful for non-stem careers. She felt that wouldn’t show enough “rigor”, given her course load in high school already limited her ability to take AP classes, she wanted to show she kept trying.

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Yeah, I’m pretty sure it was because 3/4 of the class started pre-calc at the same time as her current Physics class, and so it just had to go at a pace slower than D desired. The thing about her school is that it’s performing arts academy on a campus with four other academies (which have STEM majors and courses), and only when necessary or to consolidate resources, the performing arts students take courses in the other academies (like spanish, and in her case the AP math classes). After the first two weeks of school, she already complained about the pace of the physics class, and I suggested that she ask the guidance counselor if there was something she could do to maybe place in AP Physics that is taught at one of the other academies. She was afraid to ask, afraid to be embarrassed about asking for something that’s never been done at her school before. A friend from one of the other academies mentioned to her recently that students in that friend’s academy couldn’t take AP Physics until they took calculus (or maybe it was pre-calc), and my D at the point wondered if she should have said something at the beginning of the school year, because she was definitely qualified, if it was just because of the math level. And I think her own school probably never made that an option because, as I mentioned, it was rare that any of the performing arts students, given their rigid curriculum, could take an AP Calc class. It would have been possible in their senior year (but they do dual enrollment at the university senior year, so no AP classes to take senior year). I think my D and her one classmate are the first two from her performing arts academy to take the AP Calc BC course. So, I guess there was no precedent for this. But it might be something that I’ll bring up to the principal for future students.

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My D18 just graduated with a BFA in ballet and was also a strong academic student. She ended up double majoring in environmental studies but thought about math at the start (she had done Calc BC in HS then took Hons Calc 3 her first semester of college). I do think math can be an “easy” double major if you are good at it, because then it takes less time than almost any other subject (and in particular has no labs to conflict with studio time, unlike other sciences). The choice of either linear algebra or discrete math would be the most challenging courses amongst those listed. Personally (as a math major myself) I’d consider discrete math more fun but linear algebra somewhat more fundamental for more advanced math courses.

It looks to me that if the General Physics I course is equivalent to AP Physics 1 then it will be a very basic course for someone with Calc BC. I’d look at Chem 1 or if you have to do Physics than either ask for Physics I or stick with Honors Physics at HS (though if most people haven’t done Calc BC I doubt that will be calculus based either).

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“Hi, my DD is a rising senior and wants to apply to highly selective academic schools”

Since this is the aim, along with her math background, ask to see if Physics 1 will be allowed.

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I’d suggest taking linear algebra. As @Twoin18 has said, linear algebra is more fundamental for more advanced math courses. I’d add that linear algebra is much more fundamental and useful to many other subjects, including nearly all sciences, economics, statistics, etc., in case she becomes interested in one of those areas later.

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Agree with above posts. I’d also say that kids who fly through math have to be sure that their curriculum doesn’t skip bits and pieces. There are some things which I believe a strong math student can teach themselves fully ( trig is one). But with my own kids, I tried to make sure that if they skipped grades in math that they covered it elsewhere so nothing came up as a hole. Nothing worse than an easy problem where you are missing a simple piece you’ve never been exposed to.
My kids have skipped, repeated classes they tested out of, and did courses which they didn’t have an exposure to the fundamentals. It’s hard to get it right in terms of level, esp if kids are a few years ahead of their peers in math/science. English is easy if ahead, so is history. I’d just keep that in mind when choosing.

I’d opt for linear/discrete over stats. . Stats is very easy for math people. Like trig. And she might be bored out of her mind. Kids who are far advanced are often bored and even if they skip grades/classes can bored because the match is hard to find. Stats is highly useful (in almost any field) but easy to learn. She can pick this up in college, if needed.

Sounds like your daughter is on her way in the arts. So great. Also great to have an aptitude in anything. Math and science is a good one as there are many open fields.

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If your daughter was not challenged and didn’t enjoy math when the kids were not also as advanced as her in math, I would definitely have her choose Linear Algebra over Discrete Math. My son took both Linear Algebra and Discrete Math this past year in college. He loved Linear Algebra but was frustrated by the Discrete Math class. Although he found that class fairly easy and interesting, the class was filled with many non-math computer science kids which slowed down the pace off the class and included several group projects with kids not on the same level of understanding of the material as my son, leaving him to do most of the work.

My son was ready to quit on math & science in high school until I had him skip ahead to Physics C to go with Calculus BC his junior year. Now in college and with his courses finally more challenging, he is trying to take as many math and physics courses as he can and loves learning.

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I would suggest taking the easiest class that will allow for the most time for prescreens, auditions and other activities over the next year. She will be missing class to travel to auditions if she is interested in a BFA in theater and there is only one program who cares at all about this level of academic rigor (Northwestern which is not audition based). If her goal is audition based programs she will be overwhelmed by the process over the next year and you should balance that time constriction that will last through February with any rigorous academic plans.

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It depends what you are looking for from a college. Merit hunters can benefit greatly from high scores and a challenging academic courseload as it stands out far more in performing arts. D18 had much better offers than her twin brother (with very similar stats) who was applying for more conventional academic majors (she had 4.0UW/35 ACT/9 APs with 8 5s). She got Regents at multiple UCs, an OOS tuition waiver at UT Austin and a full ride (which is what she took).

Yes the application process is painful and time consuming. But so is doing 25 hours a week of performing arts all the way through high school. A parent can definitely do a lot to help with coordinating the audition schedule.

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Agreed, but if OPs child is looking to taking a very demanding college course and planning college auditions this may be challenging. The number of schools that kids have to apply to and audition for is now around 20, and this can lead to a very stressful season if there are compounded rigorous academic schedule and senior year performances. My understanding is that the merit scholarships are generally on GPA and standardized scores, not rigor.

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Actually, she won’t be able to take anything at her high school next year. All the seniors take a full course load at the university, so it has to be from this of college courses that the high school and university negotiated. Physics I wasn’t on the list, but I’m wondering if I should reach out to the counselor and ask if she will have the opportunity to do a drop/add if she feels the General Physics class is too slow a pace again. Or maybe just leave it be and hope the colleges see it as the course progression from honors high school physics (which she takes now as a junior).

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D18 had 14 applications and 11 auditions, while doing 4 APs and competitive dance, so it was definitely very hectic (and we had twins applying at the same time). But it was also very busy in college trying to do a double major and honors thesis (155 semester credits in 4 years), so it was good practice having to be that organized. I agree OP has to know what she’s getting into and basically become her D’s scheduler/personal assistant from October to February.

Some scholarships (eg Oklahoma, Fordham for her) were auto-merit but the ones listed above were much more than that: UC Regents is holistic, the Austin tuition waiver was apparently the only one given for the whole college of fine arts and her full ride involved a separate application and competitive interview. USC would be another one where getting more than NMF auto-merit is holistic. So in all those cases course rigor is very important.

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