usaco explicitly nudges you towards C++ on the first page itself. problems are graded on running time, even with moderately large datasets, Python simply doesn’t make the cut. So most high schoolers end up using C++ for usaco, and Java for AP Comp Science.
...Begun November 4, 2024, published December 28, 2024.
...assisted by Claude 3.5 sonnet, trained on my previous books...
...puzzles co-created by the author and Claude
...GPT-4o and -o1 were useful in latex configurations...doing proof-reading.
...Gemini Experimental 1206 was an especially good proof-reader
...Exercises were generated with the help of Claude and may have errors.
...project was impossible without the creative labors of Claude
The obvious comparison is to the classic Strang https://math.mit.edu/~gs/everyone/ which took several *years* to conceptualize, write, peer review, revise and publish.
Ok maybe Strang isn't your cup of tea, :%s/Strang/Halmos/g , :%s/Strang/Lipschutz/g, :%s/Strang/Hefferon/g, :%s/Strang/Larson/g ...
Working through the exercises in this new LLMbook, I'm thinking...maybe this isn't going to stand the test of time. Maybe acceleration is not so hot after all.
"The story of linear algebra begins with systems of equations,
each line describing a constraint or boundary traced upon abstract space.
These simplest mathematical models of limitation — each equation binding variables in measured proportion — conjoin to shape the realm of
possible solutions. When several such constraints act in concert, their collaboration yields three possible fates: no solution survives their collective
force; exactly one point satisfies all bounds; or infinite possibilities trace
curves and planes through the space of satisfaction. This trichotomy — of
emptiness, uniqueness, and infinity — echoes through all of linear algebra, appearing in increasingly sophisticated forms as our understanding
deepens."
Maybe I'm not the target audience, but... that really doesn't make me interested in continuing to read.
That is such supremely bad writing that it can only come from AI being told to spice up the original opening paragraph, and short of the original author being barely literate (and possibly even then), the original text would have been better writing.
The overuse of the $15 synonyms is almost always a bad idea--you want to use them sparingly, where dropping them in for their subtly different meanings enhances the text. But what is extremely sloppy here is that the possibilities of "no solutions, one solution, infinite solutions" is now being described with a different metaphor for solution here. And by the end of the paragraph, I'm not actually sure what point I'm supposed to take away from this text. (As bad as this paragraph is, the next paragraph is actually far worse.)
Mathematics already has a problem for the general audience with a heavy focus on abstraction that can be difficult to intuit on more concrete objects. Adding florid metaphors to spice up your writing makes that problem worse.
its been a long time, but when i was taught this material, i was told there are only 3 cases -
x+y=1, x+y=2 clearly has no solution since two numbers can’t simultaneously add to both one and two.
x+y=1,2x+2y=2 clearly has infinitely many solutions. There’s only one equation here after canceling the 2, so you can plug in x’s and y’s all day long, no end to it.
x+y=1, 2x+y=1 clearly has exactly one solution (0,1) after elimination.
This example stuck with me so I use it even now. The author/Claude/Gemini/whatever could have just used this simple example instead of “trichotomy of curves through space conjoin through the realm of …” math, not Shakespeare.
Also, isn't this a great example of "when you have a hammer, everything looks like a nail" ?
To explain this I would first and foremost use a picture, where the 3 cases : parallel, identical, intersection can be intuitively seen (using our visual system, rather than our language system), with merely a glance.
^ This perfectly encapsulates the story I see every time someone digs into the details of any llm generated or assisted content that has any level of complexity.
Great on the surface but lacks any depth, cohesive, or substance
I started a book about CIAM (customer identity and access management) using Claude to help outline a chapter. I'd edit and refine the outline to make sure it covered everything.
Then I'd have Claude create text. I'd then edit/refine each chapter's text.
Wow, was it unpleasant. It was kinda cool to see all the words put together, but editing the output was a slog.
It's bad enough editing your own writing, but for some reason this was even worse.
just to clarify - I have nothing to do with this book. I was just forwarded a copy and I thought its relevant to the topic at hand.
from the wild swings in karma, looks like people are annoyed with the message and shooting down the messenger.
aside: As the Professor points out, the ratio of pi to its evil twin is ~1.198, the arithmetic-geometric mean of sqrt(2) and 1. The geometric part involves a square root, and square roots are expensive. So I was like, well, if the AM converges to GM, then due to AM-GM-HM inequality, it must converge to the harmonic mean as well. And the HM does not need an expensive square root!
Its quite wild that the AM GM convergence is almost immediate - in just 2 steps, whereas to get a decent convergence for the Gauss's constant via HM, you need like 15 steps.You can dispense with expensive operators like square root but you end up paying for it with numerous iterations.
The c value you compute depends on computing the b value, though. It's not a recursion carried out in a way which avoids square roots. It's just carrying out the same AM-GM sequence computation, and then taking a certain weighted harmonic mean over that sequence, which converges just because that original sequence converges anyway.
Author has computed BBMI (baby baby money index) but mistakenly calls it BMI. If he divides the BBMI by the TFR, one B goes away and you get the true BMI which is a different ranking altogether. For bonus points you can compute which country has the same ranking whether BBMI or BMI.
what an amazing turn of phrase - “reset and synchronization once the talking points get assembled”
Literally describes 99 of the 100 post-jira action items coming out of the clueless PM’s mouthhole.
Amazing story. I enjoyed reading this so much. The sad fact that this was written in 1966 - like the gentleman advocated for gutting the public school system 6 decades ago, and only now we are getting around to the business of defunding the dept of education. The story has foretold everything - the culture wars, the sacred cow/buffalo, utterly divergent visions of the left and right when it comes to what education means…Rafferty seems to be a futuristic mind reader. Amazing.
You are deliberately missing the point and confusing X with ‘something that looks like X’.
For eg., using QBasic, you can pick some random spot on the monitor and have a white dot show up at that spot. What you end up doing is directly writing to the vga buffer address of that spot. That’s the X. You can directly talk to LPT1 and directly get the dot matrix printer to print an ascii character. That’s the X.
All these things were possible because the synergy between the hardware and the software was extreme. QBasic was just a shim. You were directly talking to the hardware in as few steps as you possibly could. The assembler code for your BAS file could be inspected and you could even muck with that.
All of that has gone out the door. What you have with javascript is something that looks like X. So I can use a html canvas element and get its drawing context and do an arc with the right parameters and fill and hide the scrollbar with some css and pretend that what you now see is like the X. But its not! To actually get rid of the browser window and only have the white dot, you would need a full blown electron install or worse. And it still wouldn’t get you to the X. We already had X. Now we have something that barely approaches X after a great deal of effort.This is supposed to be progress ?!!
From 2022 stats:
Roughly 4 million students in each grade in the US.
8th,9th,10th,11th & 12th graders = 20 million.
So 20 million students are eligible for AMC10/AMC12
Of them, only 300K took the AMC10/AMC12
Of them, only 10K were invited to take the AIME
Of them, only 500 were invited to take the USAMO
Of them, only 50 went to the MOPs
Of them, only 6 went to the IMO & won.
The article is about 4th & 8th graders, of which we have 8 million.
Now, suppose those 4th graders get to 8th grade, then the 8th graders would be in 12. That makes both cohorts eligible for AMC10/12. At that point, they become 8 million out of the 20 million. So 120K of them take the AMCs, 4K take the AIME, 200 get into USAMO, 20 get invited into the MOPs, and best case 2 kids make it into the IMO.
So from this grand experiment, 2 kids will emerge the victor, and we are supposed to back-extrapolate that 8 million kids do ok. Aaalright then.../s
Aside - a long time ago, I worked on a high school math problem which involved summing the thousand fractions 0/1, 1/2, 2/3,...upto 999/1000, so I did the obvious iteration.
(display (foldl + 0 (map (lambda (x) (/ x (+ x 1))) (range 0 1000))))
The solution matched and I was happy. Then I thought wouldn't it be neat to do this in a dozen languages and benchmark...but got nowhere with that idea. None of the languages supported fraction addition without jumping through whole bunch of hoops. I wonder if its still the same situation. If someone wants to give this a shot, the answer if you do this for the first ten is 17819/2520.
