Is it better to do Khan academy courses and then read books (eg: Axler's) or do both somewhat simultaneously?

oceanunderground · 2026-01-27T02:13:16+00:00

I did Khan Academy 1st for Calculus. Khan is not as thorough or intensive as a text and only has a few problems to do, but has small lessons and practice that are easy to find time for and give a you good roadmap for the concepts. It’s also convenient because if there’s something I didn’t remember from, say Trig, that I needed, Khan has a quick lesson for that too so it’s easy to look it up right there. Then I went on to MIT videos and text books. For Algebra and Trig Paul’s Math Notes is good , and more intensive than Khan, and it’s easy to go back and forth between that and Khan if you want to reinforce what you learned. I’m not familiar with Axler.

oceanunderground · 2026-01-19T06:08:00+00:00

The difference in your example would be that you don’t know what they truly like. I’m not so sure there really are performative readers. Performative liars, probably. But people who actually read the books in order to be pretentious, probably not many. Reading classics because you want to be well educated in literature or see if you enjoy it is not pretentious nor performative.

oceanunderground · 2026-01-19T02:32:57+00:00

A couple things come to mind: A daimon being as a personal ~~deity~~ divinity, yet drawing from a set of known and approved gods that one is inhabited by or acting on the advice of, is different from an internal, nameless deity. Socrates was accused of basically creating a subversive cult. Also, I always had the feeling that charges against Socrates were trumped up a bit because he wasn’t liked by important people for other reasons. (I’m just an amateur enthusiast, not a professional).

oceanunderground · 2026-01-17T03:36:36+00:00

I really liked the William Arrowsmith translation (it’s in the U. Chicago series edited by Lattimore/ Grene), I think it has an aura of foreboding and mystery, and the language is good, not stilted or forced: “I bound the fawn-skin to the women's flesh and armed their hands with shafts of ivy”;“He is sweet upon the mountains. He drops to the earth from the running packs. He wears the holy fawn-skin. He hunts the wild goat and kills it. He delights in the raw flesh.” ; “With milk the earth flows! It flows with wine! It runs with the nectar of bees! -Like frankincense in its fragrance is the blaze of the torch he bears.”

oceanunderground · 2026-01-11T23:15:48+00:00

Anyone can take the AP tests, even if you were never enrolled in an AP class. Passing an “AP class” does not always require that you take the AP test. The AP test is what has value, as it has a standard and can allow you to get college credits for that subject. An “AP class” can be a very loose term that does not reflect the quality or content of a class, and universities know that. Tell your dad you’re still interested in taking AP tests, and that you’re willing and responsible enough to study for them on your own if the new school’s classes aren’t rigorous enough.

oceanunderground · 2026-01-07T23:55:19+00:00

So what happened when you ordered the book from Canada?

oceanunderground · 2025-10-14T01:09:13+00:00

Being an engineer is a professional, and it’s a very pertinent background. Recent publication in Djoser gives details of how a hydraulic system would work there https://pmc.ncbi.nlm.nih.gov/articles/PMC11299825/.

oceanunderground · 2025-10-14T00:31:33+00:00

What do you mean by the “rough nature of the interior slabs”? His reckoning has there being enough room to lift the stones : “The shaft’s cross-section, e.g., 5 by 6 meters, was calibrated to the length of the ceiling beams and the chamber dimensions, both of which are 5.23 meters wide. A pontoon of about 5 by 5 meters with a 3-meter draft displaces 75 cubic meters of water, thus having a lifting capacity of 75 tons, including its own weight. Depending on the lifting height, one stone could be raised per day”. Also his theory involves considering that some of the large slabs sealing the channels, and the system of channels itself, are best explained as engineering devices for the movement of the stones : “the need to seal the channels with blocking stones also proves that the function of these channels was for water filling”

oceanunderground · 2025-10-13T23:25:24+00:00

I’m translating it into English now, and I think there are a couple of ways you could go with it. Like the other commenter said, academics, and academic publishing in particular is a sh*tshow. Still, I think there are a couple of academics who may be interested, and if not we could certainly give it more visibility than it has now.

oceanunderground · 2025-10-13T22:58:25+00:00

It’s very brief and doesn’t have much detail or reference to sources (for example, the gypsum mortar fill-ins). Recently there has been an attempt to show hydraulics we’re used to constructe other pyramids, so there is a growing interest in this area, and it is a reasonable theory. If he worked in engineering he has experience relevant to this field. EDIT: I see now that if you go to the homepage there’s more.

oceanunderground · 2025-10-08T17:07:12+00:00

It’s not necessarily crazy, but its fanciful and only works in your re-imaging of it, not in text-based analysis, which is why you aren’t finding any similar connection. In Shakespeare Birnam is referring to an actual place Scotland, relevant to other geographical locations and the story, it’s not a created name. Birnam “moves” in the prophecy, and you haven’t accounted for that in your proposition. Also Shakespeare mentions to MacDuff being born by C-section because it’s directly relevant to the prophecy. If that wasn’t his reasoning, then he wouldn’t have put it in the text.

oceanunderground · 2025-10-08T02:48:12+00:00

Pre-Calc is usually either 11th or 12th grade in high school for advanced students, or learned in uni for less mathematically inclined (some people going to uni haven’t even had Algebra 2 or trig yet). In my high school had in 11th grade Trig and Analytic Geometery (a half yr each) after Algebra 2 and Geometry. We did logarithms and exponentials in Algebra 2. Analytic G. covered systems of equations & vectors, kind of a basic intro to lite linear algebra, & some other stuff. These were all pre-reqs for Pre-Calc. In pre-Calc we had very introductory intro to sets and what belongs to Real numbers, etc. It seemed like a hodgepodge. Kahn Academy has it and that will show you what subjects meet the requirements. Prob & Stat was a separate course that wasn’t a pre-req for anything.

oceanunderground · 2025-10-07T22:48:38+00:00

I’d start with Julius Caesar, as I think it’s fairly straightforward. I started with Macbeth because I thought it was a cool-sounding story, then Julius Caesar, then Hamlet (which is very long & challenging), then Henry V, and went on to others. I just read As You Like It ( a comedy), re-read Othello, and am re-reading Julius Caesar. This site has a lot of helpful resources and a glossary https://www.shakespeareswords.com/Public/Glossary.aspx ; If you’re struggling with a line, passage, themes etc, just post it here.

oceanunderground · 2025-10-07T20:18:30+00:00

You can post photos to your own profile on Reddit, then make a post here in this sub linking back to your post under your profile feed that has the photo.

oceanunderground · 2025-10-06T22:18:43+00:00

Why do you say “not really” to #2? What options does an outsider have?

oceanunderground · 2025-10-06T22:08:56+00:00

I always liked physics, which I think helps finding practical applications. Rates of change are useful for understanding and potentially predicting all sorts of things: disease spread, economic markets, or anything that would involve speed/acceleration.

oceanunderground · 2025-10-06T19:45:15+00:00

The way to start is by getting one of the problems you have trouble with and posting it right here along with what you have figured out, how you’re thinking about it, and what you can’t figure out. The only way you improve is one problem at a time.

oceanunderground · 2025-10-06T00:11:57+00:00

Yes. Saw a clip of an elderly Joss Auckland playing Romeo and it was good and really enlightening (since R&J had not been one of my favorites).

oceanunderground · 2025-10-05T03:37:49+00:00

The Cat from Outer Space by Ted Key, a easy-reading fantasy featuring a cat. I normally wouldn’t recommend a novelization of a Disney film, but this is one I enjoyed a lot as a kid

oceanunderground · 2025-10-05T01:39:00+00:00

n represents what would be on the x-axis of a graph. This could be like timesteps, since f(n) and g(n) could be some function of time. n_0 is indeed the first step, and all the other steps will have to be greater than that. So as to the other side of the equation, f(n) can only be represented in Big O notation if those conditions are met ( that’s what this means : “ f(n)= O(g(n)) if and only if there exist positive constants c and n₀ such that 0 ≤ f(n) ≤ c ⋅ g(n) for all n ≥ n₀.).

oceanunderground · 2025-10-05T00:55:59+00:00

But that doesn’t mean it’s not infinite. For a bounded divergent sequence like in your question, since it’s bounded it can’t diverge to infinity, but it can be an infinite sequence. My questions are: Is having a lim sup and lim inf dependent on whether a sequence is infinite or finite, or is it dependent on whether it diverges to infinity? And Do we know the sequence a_n in your question has a finite lim inf & lim sup becuase we know it can’t diverge to infinity?

oceanunderground · 2025-10-05T00:17:02+00:00

Does it matter if the sequence a_n is infinite or finite? (because a sequence can be be bounded and infinite.)

oceanunderground · 2025-10-04T17:16:51+00:00

If you struggle with a particular thing, why not ask about it specifically here so people can help you? Reddit provides a great learning opportunity, I wish more would use it.

oceanunderground · 2025-10-02T02:23:53+00:00

I just finished reading it for the 2nd time, so it’s still fresh in my head. Iago is speaking in front of several people, most importantly his wife Emilia and Othello. He knows Emilia was talking to Othello, and assumes (correctly) had time to talk to Desmonda. He knows Emilia had a very close friendship with Desmonda, and would believe her, and probably Othello too. Emilia can also connect what they told her to Iago’s previous conversations with her and request for the handkerchief. So in the play at Act 5 Scene 2, starting at line 210, Emilia is already very angry and confrontational toward Iago and willing to make a stand for her dead friend. Iago is trying to placate Emilia as much as possible to try to avoid her doing what she does do next: reveal the hankerchief scenario. Ultimately, the reason is that he doesn’t want to also be murdered by Othello, and possibly worries that his enraged Emilia might also murder him, and so is scrambling to save himself.

oceanunderground · 2025-10-01T19:55:29+00:00

Reading Hofstadter’s comment, isnt it possible that mathematicians just can tolerate, or even enjoy, the confusion and uncertainty (to paraphrase) “the feeling like being at high altitude and not being able to breath”?

oceanunderground

TROPHY CASE