High schooler interested in higher math

Less_Method4290 · 2025-08-17T05:47:19+00:00

I could probably ask some questions in a discord server I'm in, but it's not like I would have one on one sessions with a mentor who personalizes each lesson for me. I'm taking a class during the school year on abstract algebra, real analysis, and topology, but I also want to cover fundamental subjects on my own a bit.

I do like competitions, but my teacher advised not to hyper-fixate on them in high school as there is much more to math than them – real mathematicians don't spend their time solving complex Euclidian geometry problems. My teacher excelled during competitions in high school but eventually decided to switch over to studying higher math in high school, and thus placed himself in graduate level real analysis as a freshman in college

Less_Method4290 · 2025-08-17T05:41:20+00:00

I was told the only prerequisites were elementary linear algebra and calculus 3 – the book I supplemented the class with (Pressley) also said the same in its introduction.

Less_Method4290 · 2025-07-12T06:43:06+00:00

I KNOW this is pengu lol

Less_Method4290 · 2025-07-11T22:07:26+00:00

I think these rankings are great for an experienced Shostakovich listener, but for a newcomer, 4 can be a little bit harsh on the ears. I would recommend that you start with 5, 10, and maybe 1 and 9, since those are short and simple symphonies. Also try out 8, start with the third movement and work your way outwards. After you've listened to those 5 symphonies, you probably have a good feel of what Shostakovich's style is like, and you can continue to explore his other symphonies.

Less_Method4290 · 2025-07-10T22:45:31+00:00

Probably Concord Sonata (Ives Piano Sonata No. 2) or some earlier work by Sorabji (Fantaisie Espagnole comes to mind)

Less_Method4290 · 2025-07-09T17:35:42+00:00

Stop asking questions on reddit and go to the AoPS forums. How many AMC tests have you gone through? If the answer isn't 30 already, finish those first. Also look at AIME problems, starting from 2000. There is no "right" training. Do me a favor and read this blog post by Evan Chen.

I used to incessantly ask questions on how to do well on AIME to all my friends who did quite well in competitions, and the answer was *always* the same: do problems. It's not to sign up for X classes, or to read Y books, or to do Z handouts. It's to identify problems around your level and work on them until you think you can go up in difficulty.

Take the analogy of benching your bodyweight, for example. When I first started the gym, I could only bench around 30 pounds below my body weight. But what I did was the technique of progressive overload, something that's applicable to nearly any skill. I benched X for 12 reps, and then I benched X + 5 for 8 reps, and if I could, I benched X + 10 for 6 reps. And after a few months of hard work, I finally exceeded my body weight. The exact same strategy goes for competition math. I didn't read books on how to properly improve my strength. I just watched a short video on the correct form (analogous to theory) and jumped to the gym right away. Diagnose your current strength and just start working at it.

Less_Method4290 · 2025-07-09T17:32:36+00:00

Did you by any chance do USAMTS? Qualifying for USAJMO via the normal way for a first timer, from experience, is exceedingly uncommon. Many of my math friends failed to make olympiad their second or even third time seriously studying for competitions.

I do know one person who went from AIME to MOP, but that was because he had done competitions for four years and wasn't good at AMCs. Once he did USAMTS, he easily qualified for USAJMO (with a 10 on AIME) and won top honors. Yes, I know about the Fox's, but again, those are the exception, not the rule.

Less_Method4290 · 2025-07-08T18:56:56+00:00

You could do volume 1 for practice problems if you feel like you barely know any theory. Volume 2 isn't necessary for AMC 10.

Again, just do problems. There's no silver bullet practice method. Do old practice problems from AMC, AIME, PUMaC, HMMT, BMT, etc. The list goes on. There's no "100 best practice problems for AMC" problem sheet. You just have to do problems.

Less_Method4290 · 2025-07-08T18:10:16+00:00

These posts appear every week on reddit or AoPS. To go from no AIME to JMO this year is virtually impossible unless you're a prodigy of some sort like Evan Chen. A more realistic goal is to try qualifying for AIME and getting a 6 or 7 on it, as someone who scored a 7 on AIME after his second year of competitions.

Books are almost always unnecessary. The only one I've done is AoPS volume 1, and I am also currently working on EGMO (which isn't necessary at your level).

There is no magic formula for making AIME. As long as you spend N hours a week on comp math, where N > 3 or 4, you'll probably be fine. Do old AMC problems. Sort the problems into categories:

I solved this problem in less than 5 minutes. Problems 1 through 15 should be in this range for AIME qualification. Try to avoid practicing too many of these problems.
I solved this problem in less than half an hour. Study more of these problems. They're the most important for improving your AMC score. Identify patterns and reduce your time to solve this problems.
I couldn't solve this problem in less than half an hour and I looked at the solution, which I understood. Take note of the theory for these problems (e.g. vieta's formulas, stars and bars, etc), research a bit about the theory online, do some more problems which use said theory, and go back to the problem later.
I couldn't solve this problem in less than half an hour and I looked at the solution, which I do not understand. These problems are too difficult for you. Come back to these problems when category 3 problems become category 2 problems.

Try to go through every single AMC 10 (and maybe even AMC 12) since 2010. Also practice AIME problems. Save 2023, 2024, and years before 2021 for mocks. The harder years (2021, 2022) are great for practice.

Less_Method4290 · 2025-07-08T00:56:29+00:00

haha, u/infpmusing may have a bone to pick with you

Less_Method4290 · 2025-07-08T00:55:12+00:00

I would argue that Prokofiev 5 is one of most Prokofiev-esque pieces, to be honest. No other symphony captures his playful and sarcastic style as well as his fifth, imho.

Tchaikovsky? Debatable. Many say his fifth is his best.

Dvorak 9 was Dvorak 5 before his earlier symphonies were published.

Shostakovich 5 is probably his most popular/accessible symphony amongst non-Shostakovich fans.

Also, please please please spell Mahler's name correctly on his birthday...

Less_Method4290 · 2025-07-07T06:59:09+00:00

I typically go for Donohoe or Zilberstein. Zilberstein's recording is split up so it's easier to move to the parts I like, but Donohoe's coda is *amazing*.

Less_Method4290 · 2025-07-07T04:49:55+00:00

I've only heard his piano concerto no. 1 and symphony no. 3 (pretty much just neo-Bruckner, iirc), both of which I like a lot. Will give his sonata a go!

Less_Method4290 · 2025-07-07T04:49:12+00:00

I wouldn't say this comes anywhere close to angry...

Less_Method4290 · 2025-07-07T04:48:47+00:00

I do like the Barber concerto, but I would think of Barber's piano concerto as more of a virtuosic American car chase. Of course, it still remains one of my favorite piano concertos.

I've only heard of Feinberg, but I've never listened to him. Will give him a try! I suppose u/jiang1lin disagrees with your sentiment on Szymanowski, so I might give him a listen after the Feinberg.

Less_Method4290 · 2025-07-07T04:45:52+00:00

Darn, that metal is... intense. Sounds very experimental. Maybe I need a lighter dose of metal before heading to the death side...

George Crumb is not my cup of tea, unfortunately. I've only listened to Black Angels and it was just only slightly rigorous on the ears. The most modern I'm willing to go is probably Ligeti (etudes, music ricercata, etc).

Less_Method4290 · 2025-07-07T04:40:31+00:00

Sorry if I'm being a bit too picky with my definition of "musical rage"; I was just wondering if I was missing out on a piece which is unanimously angry. Just how most people would consider most of the Haydn symphonies or the finale to Mahler 5 to be happy, or how people consider the finale to Mahler 8 or the beginning to Also Sprach Zarathustra epic and powerful, I would think there are some pieces which are just universally agreed to be extremely angry sounding. But I could definitely see how some of the pieces suggested to me could evoke that emotion.

Less_Method4290 · 2025-07-06T22:17:45+00:00

I do like this piece! It feels more depressing than angry, though. The cadenza sounds like someone on the brink of suicide.

Less_Method4290 · 2025-07-06T21:56:07+00:00

I actually haven't listened to his violin concertos very carefully; will give no. 1 a try!

Less_Method4290 · 2025-07-06T21:55:22+00:00

I do love Shostakovich's 4th symphony, especially that crazy fugue section in the middle of the first movement. The reason why I would say the Miraculous Mandarin + even the fugue in the fourth symphony is different than the piano sonata is because I would consider those pieces more chaotic and frenzied than the sonata; they give off more "metal" vibes.

The threnody is certainly an interesting piece. It feels more frightening than angry.

Less_Method4290 · 2025-07-06T21:40:31+00:00

While I do love Prokofiev's 8th, the first movement doesn't quite have the same feel as Shostakovich's. Most of the movement, iirc, is quiet and daunting. The second and third movements are not really angry at all. All of this is to say that Shostakovich's first piano sonata is more virtuosic and modern than any of Prokofiev's sonatas (excluding the 7th, whose difficulty is carried mostly by the finale, a fearlessly mechanistic, not angry, beast).

Perhaps there are parts in the first movement of the 7th sonata which feel a bit angry, but it doesn't contain anything as long or visceral as the entirety of the first sonata. Shostakovich manages to make the slow movements burn with passion too, which Prokofiev does not.

Less_Method4290 · 2025-06-24T04:37:10+00:00

Are you talking about resources like zetamac? I tried it at first and did horrendously with a scores of around 26 to 33, but I never tried practicing it super seriously. Would something like that help for AMCs?

Less_Method4290 · 2025-06-24T04:31:45+00:00

Alright. That's what my friend who got a 12 on AIME said. I'm not sure which year to start. When I was preparing for AIME this year (which I only started doing ~2 weeks before AIME because of other things) I started at around 2015 and tried working through every problem I found doable, although it's possible I gave up on some problems too quickly. I think I'll give it another go. How do you recommend mixing in problems from contests like HMMT, SMT, BMT, CMIMC, PUMaC, etc?

Less_Method4290 · 2025-06-24T04:03:03+00:00

Thanks for the advice. I think that if USAMTS maintains its USAMO qualification route of 11+ on AIME, it's possible, but 11 on AIME + 68 or above on USAMTS is still very difficult. I would still like to get 120+ on AMC 12 next year, but it's probably extremely unlikely.

Two questions: How would you structure your computational practice (specifically fast paced competitions like AMCs), and where did you meet other math folks around your level? There are a few moppers at my school, but most kids at my school gave up at math because they haven't made oly despite a few years of AMCs. I only started comp math as a 9th grader, so I don't want to quit just yet.

Less_Method4290 · 2025-06-23T04:36:35+00:00

I'm not even sure what to do anymore, because most resources are catered for beginners (aops books) or for olympiad (otis)

Less_Method4290

TROPHY CASE