Are there any online Abstract Algebra and real/complex analysis courses that are good? My child can also attend in person in the summer. It seems Harvard 55 has these, but 20 hours/homework may not be possible during school year.
I dont know of anywhere, but my son is taking real analysis this year as a sophomore at an LAC and he spends at least 20 hours a week on it. I would think that would be the minimum to be successful, especially for an online course.
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From my 25+ years ago Math major background in top 5 engineering school, these are very serious and upper level (3rd or 4th year in college) classes. Complex analysis is also often taken by engineers and not that bad. Anyway taking these during summer or online is not a good idea in my opinion. Why this should be done not during college years? Taking them online would not impress anybody. Credits will not be transferable. Is your child miserable without these classes? Is he/she in college or in HS?
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Agree – they are proof and theory focused courses, which may feel different from typical college frosh/soph level math courses like calculus and multi variable calculus.
What college math courses has the student completed, and are there local colleges where the student can take advanced math in person?
But why to take them in HS at all? It makes no sense to me. What is the purpose? Is it acceleration to 3rd year of college? Is student trying to skip BS? It is irrational to me. If the student loves math, there are numerous math competitions. Does kid have nothing to do but take math courses?
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OP, the world is not running out of math.
Slow down. Taking these courses will either be a joy for your kid– in person, with a real professor and other students– or torture (too many hours a week of homework to keep up, online with no human connection). Keep the joy. Let your kid find another activity to occupy the hours it would require to keep up.
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I agree with all the responses above. Slow down. This is unnecessary in HS.
And as a point of correction, Harvard’s Math 55 is neither offered online nor during the summer.
Other prior undergraduate-level courses have been taken, and this is of interest.
Terrific. But at some point- with only 24 hours in the day- one has to help one’s kid develop appropriate boundaries. Neglecting HS English or Foreign Language in order to take a heavy load of an online course seems short-sighted. And the best online course is still a shadow of the experience of taking the real thing- with real students and professors- all brainstorming together.
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I think we could keep everything aside and assume that all subjects have been taken care of.
The idea is to learn writing proofs, and no better courses than these. Not looking for all of Harvard 55 courses, just Abstract Algebra and real/complex analysis courses. This is stemming from individual interest and not to showcase.
Kind of like having a beginner swimmer jump into the deep end.
Many math departments now recommend or require an introduction to proof writing course, or a sophomore level course including proof writing (e.g. discrete math or a theory focused version of other typical courses) before taking abstract algebra or real analysis.
Since you referenced Harvard Math 55, note that Harvard says that it is for students who already have experience with proof writing. Students who want to learn proof writing are advised to take Math 23 or 25, not 55.
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Here is the UCB math department recommendations for choosing one’s first upper level math courses:
Note the recommendation to have taken Math 55 (discrete math, including introducing to proof writing) before, and choosing Math 110 (proof focused linear algebra) before other upper level math like Math 104 (real analysis).
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UCB and I appear to be in agreement that the world is not running out of math between now and when your kid gets to college.
OP- I get that your kid is passionate and advanced in math. But throwing the kid into the deep end of the pool isn’t a great pedagogical technique.
Discrete math and linear algebra is already done. There are many high school students these days who take undergrad level courses in high school. This is nothing new especially considering math interest. I was simply looking for some suggestions for good courses.
Did these courses include introduction to proof techniques and practice with such? Discrete math often does, but the level of such can vary. College sophomore level linear algebra is often more computationally focused, unless it is an honors or more theory focused version.
As noted above, the UCB math department recommends a college junior level linear algebra course (with more focus on theory and proofs than college sophomore level courses) as the first upper level math course, rather than jumping into real analysis first.
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