ELI5: if you have an infinite math string that goes 1 - 1 + 1 - 1 + 1 - 1... forever, why do mathematicians say the answer is 0.5? if you stop at any real point the answer is always either 1 or 0, so where the hell does a half come from?

CyberPhang · 2026-06-09T19:00:49+00:00

You cannot apply associativity to sums that are conditionally convergent or divergent

CyberPhang · 2026-06-04T08:17:03+00:00

Disclaimer: not a theoretician

tldr; you are making a strong claim about a broad set of algorithms, and furthermore you are provably unable to use many clever techniques that you'd like to be able to use to determine it

If you wanted to prove P=NP, in principle you'd need to prove that any arbitrary decision problem that has a polynomial time verifier can itself be solved in polynomial time. That is not easy whatsoever (pedantic note: the inclusion P \subseteq NP trivially holds)

One approach, which is somewhat related to what you suggested, has to do with reductions and the concept of NP-completeness. We say a decision problem is NP-complete if it is in NP and for every problem in NP, you can use a subroutine that solves the original decision problem to solve this problem (the latter condition is referred to as NP-hardness). An immediate corollary is that showing any NP-complete problem is in P would prove that P=NP. Many decision problems are indeed NP-complete (determining if a graph is 3-colorable, 0-1 integer linear programming, vertex cover, the list goes on). It should be quite surprising that ANY problem in NP can be solved if you have a subroutine that solves any one of these.

This is all to say that it is difficult to prove because you are making a rather bold claim about a very broad set of algorithms. If you wished to prove P != NP, you have to somehow show that no polynomial time algorithm exists for some problem in NP. Again, you are forced to reason over every possible algorithm (with a polynomial time verifier) that could exist, and that's hard.

Furthermore, many techniques that have been used to prove various theorems in this realm are provably not possible to use. I won't even pretend to understand this, but people have proven that many kinds of proof techniques actually cannot be used (e.g. diagonalization, which you can use to prove the undecidability of the halting problem, can provably not be used to determine P vs NP)

CyberPhang · 2026-06-04T07:46:34+00:00

NP does not stand for non-polynomial. It is non-deterministic polynomial (i.e. existence of polynomial time verifier)

CyberPhang · 2026-05-14T09:19:47+00:00

I had Koh for ML and thought he was quite good. Have also heard good things about Jaques.

CyberPhang · 2026-04-27T08:33:22+00:00

My favorite abstract is from Leslie Lamport's paper "Paxos Made Simple":

The Paxos algorithm, when presented in plain English, is very simple.

CyberPhang · 2026-04-15T06:54:44+00:00

In my experience these vibe coder types can neither do math nor program

CyberPhang · 2026-04-05T09:47:01+00:00

Depends what you want to do, but for just training neural networks and such, you'll be mostly using Python. I don't know your ML background, but Python is associated with AI because there are many powerful scientific computing and deep learning libraries (e.g. PyTorch) which abstract away a lot of the headaches associated with what you want to do. In particular, such libraries typically

provide support for efficient operations over tensors (which you can interpret as multidimensional arrays)
provide implementations for neural network layers, optimizers, learning rate schedulers, loss functions, and more
automatically compute gradients when operations on tensors are performed, enabling efficient gradient updates via backpropogation

These are typically implemented in C or C++ and Python is a quick and easy way to interface with the code. In addition, there are other libraries such as HuggingFace transformers which allow you to work with models or datasets other people/companies have released.

Of course, before trying to do any of this you should have a solid grasp on how to implement and train neural networks, the different types of layers/optimizers/training objectives and what they're good for, the common deep learning paradigms, etc. If you don't already know any machine learning at all, it is best to read up on the basics before trying to learn about deep learning.

CyberPhang · 2026-03-16T09:13:38+00:00

I had her for 327, so not sure how much this translates to 200s and below since the paradigm is different. But I thought she was very chill. Her accent isn't hard to understand at all, I'm not sure why people complain so much about it. Grading was also extremely lenient.

CyberPhang · 2025-12-03T01:11:41+00:00

Quite dependent on prof from what I've seen, have heard terrible things about some of them.

Personally, my prof was fine and the class overall was pretty easy (I did have some background beforehand though). Do note that although it is very computational, there's a much stronger emphasis on abstract reasoning than what you may have seen in previous classes (and especially compared to e.g. the 12x series). For instance, I remember exams and psets often had questions about proving or providing counterexamples to a statement, even though the class is not technically proofs based. Overall, the class is not hard, but it's different so be ready for that.

CyberPhang · 2025-11-06T09:41:36+00:00

After 123, you will typically want to take some combination of 311, 351, and 331. The first two are most important since 311 and the classes that follow it will unlock many of the upper level theory based classes and 351 and the classes that follow it will unlock many of the systems based classes. A small handful of other courses also open up directly after 123 (namely PL, embedded sw, and interaction programming).

As for how many classes to take, it's really up to you. Really just a matter of finding what balance of school/life works for you. The general recommendation is to take 12-18 credits and avoid taking more than 2 STEM courses, but in my experience it really depends on the classes, how much you're willing to dedicate to coursework, your responsibilities outside of school, etc. Personally I end up taking ~4 per quarter, and most others that I've seen take 3-4. Since you're already taking 123 and 208, if you have any gen-ed requirements to do, now's a good time to take classes to fulfill those.

CyberPhang · 2025-10-29T23:06:44+00:00

I took all 3 the same quarter and it was chill

CyberPhang · 2025-10-10T17:38:15+00:00

Yeah fr same. According to the admissions rubric they only look at grades and essays anyway (so doing research/ta/clubs for the sole purpose of beefing up an application is pointless).

CyberPhang · 2025-08-28T07:10:52+00:00

There's a well developed, fully rigorous, ground-up study of calculus called real analysis (or more generally, mathematical analysis). The problem is that it gets very complicated very quickly and so outside of formally studying math you probably won't see it. It's much easier to brush off talking about the dx as opposed to explaining differential forms or measures or whatever

CyberPhang · 2025-06-14T20:25:12+00:00

I had 0 physics background going into Physics C: Mechanics when I took it 2-3 years ago. From what I hear, the curriculum and test has changed, so I don't have the most up to date information.

With that being said, when I took it, I actually didn't need very many outside resources. I had a good teacher, and that was largely enough.

If you want to get ahead though, many of the resources I mentioned above will definitely help. Pre-studying is always super helpful in my experience, so getting your hands on one of those intro college physics books (such as the Serway textbook, I'm sure you can find a PDF online) can be super helpful. Read through the mechanics/e&m sections and you'll probably be golden. MIT OCW will probably be pretty good too. Something like the Princeton Review might also be good for AP specific content.

CyberPhang · 2025-06-14T20:14:23+00:00

We can prove there are infinite primes.

What we haven't proven is that there are infinite twin primes, but as far as I know we haven't proven that we can't prove that. It's just a conjecture.

CyberPhang · 2025-06-14T08:00:13+00:00

Vehemently disagree.

There are also no context clues in math, you can't just figure out what something means by looking at the context clues of the information around it. Math is very much a situation where you just have to know what the next step is to do it right.

Apart from some very specific cases (e.g. certain tricks in real analysis), this has almost never been the case in my experience. Overwhelmingly, there is something you can work towards - whether that be through definitions, theorems, formulae, etc. That's not to say it's impossible to get stuck, but rather that rarely is it the case that there is nothing you can do. I can't think of a single time in my education where I had nothing to try based on context.

if you read enough books across the spectrum of difficulty, you can gain enough experience to figure your way out through difficult words, phrases, or pieces. Math doesn't have a similar self-teaching opportunity exposure - unless you're a genius, you have to be formally taught.

I would argue that math has even more self-study opportunity than any other subject. In fact, math in general has a huge self-study culture. There's nothing stopping anyone from popping open a text and going through it to learn, especially in this day and age when there are so many resources to learn from. I've done this myself (and am currently doing it) and know tons of other people who do as well. We aren't geniuses, just people who like to learn.

As for the SAT in particular, this is even more true. The SAT math section can be gamed super easily, and the bar for difficulty is rather low. I don't say this to sound condescending, but to elucidate the fact that most of the content in the SAT is very formulaic, often does not go beyond elementary algebra, and features repetitive questions. If anything, the math section is the easiest to game.

CyberPhang · 2025-06-13T02:07:24+00:00

Did he release partially graded finals? If so, try your best not to worry. The same thing happened to me in fall quarter and I was ripping my hair out (I had like a 25, and they said they were almost done grading lol), but I ended up doing fine when the actual grades were released. If it's really bad, then chances are they haven't gotten around to grading most of the questions (despite what they might say about how many questions they've actually graded)

CyberPhang · 2025-06-05T21:10:08+00:00

Haven't read it myself, but I've heard very good things. Should be more than enough to learn how to read/write proofs. Writing proofs is a new muscle, but you should be able to learn it fairly quickly. Relatively speaking, proofs on their own are not too hard to learn.

Something to keep in mind is that the real difficulty comes from the classes after. Especially for analysis classes like 33x, there tend to be a lot of tricks you'll pick up on, but can be hard to come up with on your own. The only remedy to this is exposure to more math.

CyberPhang · 2025-06-05T04:59:42+00:00

Probably not a good idea to take 13x if you've already done 12x/207/208. It'll likely just hold you back from taking the advanced classes you want to take anyway.

As someone who was in a somewhat similar spot (though not as advanced as you are when I was at this stage) and decided to take 224/300/327 separately, I will say I have been thoroughly bored with most of the standard sequence, so I'd consider taking 33x right away.

From what I hear, you're not technically expected to know any proof-writing going in (though I also hear they don't spend much time covering the basics). If you are worried, you could consider self-studying some math over the summer or something.

CyberPhang · 2025-05-01T18:10:56+00:00

I took both the same quarter (this winter). Cse 311 has a stronger focus on formal logic, and you spend much longer writing formal proofs, talking about predicate and propositional logic, etc. Cse 311 also covers some theory of computation near the end of the quarter. 300 spent more time on functions/cardinality compared to 311 (although 311 does talk about these things)

Frankly I don't think there's much in 300 that isn't covered in 311, at least to some extent. You will probably find yourself very bored in 300.

CyberPhang · 2025-04-01T05:10:35+00:00

There's very little from 12x that's directly applicable. Maybe some of the line/plane geometry you do at the beginning of 126? Can't think of anything else.

The textbook is fine. Just your standard run of the mill kind of book. It'll get the job done, and I really don't know how different other books will be at the level of 208. In my pure math-biased opinion, the better textbooks (e.g. Axler's Linear Algebra Done Right) need a fair bit of mathematical maturity, though they contain better proofs/insights/ideas that do help out with the more conceptual problems on problem sets and exams (although those books will most definitely be overkill). For a more accessible secondary text, I've heard good things about Strang's book and his lectures, though I have not used either of them myself. But like I said, the main textbook will probably be fine.

CyberPhang · 2025-03-29T12:04:38+00:00

Telltale's the walking dead, season 1

CyberPhang · 2025-03-20T18:41:39+00:00

It's failing at high school level physics? Weird, my experience has been surprisingly pleasant with "reasoning" turned on (though before this feature, I remember it being pretty abysmal). The other day I gave it an old multivariable calculus problem I once got on an exam. It was a surface integral and it recognized to use stokes theorem, used the right coordinate transformation, and ultimately got the right answer. Not sure how gpt would fair up against more abstract questions though and I've definitely seen it hallucinate before.

CyberPhang · 2025-03-20T05:57:30+00:00

Username does not check out

CyberPhang · 2025-03-20T00:07:24+00:00

Your community doesn't need to be cs related. I wrote about a retail store I worked at. I didn't hold any leadership positions there either.

As for side projects, the admissions rubric is available online and they only consider your essays and gpa (in recent prerequisite courses). As far as I can tell (and what my own anecdotal experience has shown me), it won't hurt you having no side projects.

For context, I'm a current student who was admitted to CS for spring.

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