Name: Problems from the book
ISBN: 9780979926907

What Hacker News says

generationPJul 2020

Concrete Mathematics by Knuth and Patashnik (already mentioned for u/pmiller2) if the kid likes numbers. That's perhaps the guiding thread of the book -- it's about the beautiful (yet usually very elementary and natural) things you can do with numbers.

Geometry Revisited by Coxeter and Greitzer and/or Episodes in Nineteenth and Twentieth Century Euclidean Geometry by Honsberger if the kid is into plane geometry. It's an idyllic subject, great for independent exploration, and the books shouldn't take long to read. Not very deep, though (at least Honsberger).

Anything by Tom Körner, just because of the writing. Seriously, he can make the axiomatic construction of the real number system read like a novel; open https://web.archive.org/web/20190813160507/https://www.dpmms... on any page and you will see.

Proofs from the BOOK by Aigner and Ziegler is a cross-section of some of the nicest proofs in reasonably elementary (read: undergrad-comprehensible) maths. Might be a bit too advanced, though (the writing is terse and a lot of ground is covered).

Problems from the BOOK by Andreescu and Dospinescu (a play on the previous title, which itself is a play on an Erdös quote) is an olympiad problem book; it might be one of the best in its genre.

Oystein Ore has some nice introductory books on number theory (Number Theory and its History) and on graphs (Graphs and their uses); they should be cheap now due to their age, but haven't gotten any less readable.

Kvant Selecta by Serge Tabachnikov is a 3(?)-volume series of articles from the Kvant journal translated into English. These are short expositions of elementary mathematical topics written for talented (and experienced) high-schoolers.

I wouldn't do Princeton Companion; it's a panorama shot from high orbit, not a book you can really read and learn from.

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kidintechDec 2019

My compiled list for 2020, as suggested by friends I respect and HN:

General

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- Master & Margarita (w reader's guide)

- Why we sleep

- The righteous mind: why good people are divided by politics and religion

- The wisdom of insecurity

- The denial of death

- The three body problem (friend's advice: slow burn, stick with it)

- The dubliners

- The devils (Dostoyevski)

- The name of the rose

- Enten-Oller (Kierkegaard)

- Zero to one (Peter Thiel, recommended reading as palantir new joiner - not fantastic but has some thought provoking ideas; i.e. which very important truth would very few people agree with you on?)

Economy/finance

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- Basic economics (Thomas Sowell)

- How an economy grows and why it crashes

- Know the city

Math

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- Coffee time in Memphis

- Real analysis (mathematics textbook)

- Problems from the book (Halfway through this one, and I found it really enjoyable, even with only a CS bachelors)

If anyone has read any and has feedback/notes, I'm looking forward to hearing them!

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nestesMar 2024

Not the original poster, but I learn best reading textbooks cover-to-cover. A couple things that help me:

1) I buy physical textbooks and absolutely destroy them with notes in the margins, highlighting, etc. It helps me to interact with the material instead of letting it wash over me, which means I'm both thinking about it more in-depth and as side effect I'm less bored. Otherwise I'll fall asleep and won't learn anything. 2) I accept that I'm not going to remember the entire book. A lot of books are most useful as references anyway. But if you ever find yourself going, "Oh that's really handy to know," then you can make a special note of it or even put it into flashcards. I've been using Anki. The trick is to recognize what is actually worth doing this for. 3) If something is especially worth knowing, (see point 2), see if you can either do problems from the book or try out the concept in some way if there are no problems available.

If you're reading something just because you feel like you should, you won't get anything out of it (or a least I don't).

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nohaydeproblemeMar 2023

A major limitation exists for spaced repetition software (e.g. Anki, SuperMemo, or other flashcard-style systems), in my experience using them for several years for long-term memory: it's neither necessary nor sufficient to use this software to learn certain topics.

Several excellent physics and math students I worked with have never used spaced repetition software, but were excellent at their studies because they consistently solved textbook problems. For them, they got the "repetitions" (aka exposure to facts and problems) via solving more new problems from the book nearly every day. Later problems in the textbooks would provide review of previous problems. This method can be far more effective than spending too much studying with spaced repetition software (which I have done in the past), as the time spent creating new cards and reviewing cards that are due comes at the expense of time spent solving new problems.

Ideally, you can perhaps find time for both activities. But in my personal experience, I learned mathematics more effectively by focusing primarily on textbook problems (reviewing older material through new problems) and spending a very limited amount of time with spaced repetition, versus even a fifty-fifty split between a textbook and spaced repetition that I've experimented with in the past.

In the past, I also spent too much time in the past remembering phrases and vocabulary when learning new languages, and not enough time practicing listening, writing, and especially conversation. Certain skills can only be efficiently developed by directly practicing them. While spaced repetition software remains an essential part to my language studies, it is very far from sufficient (even just a couple hours of conversation practice per week over three months, got me much further than primarily focusing on Anki/spaced repetition for six months).

Spaced repetition systems like Anki (though I moved to SuperMemo about a year back) are vital to my daily studies, but I've learned far more effectively by treating these systems as a supplement to more traditional and tested study methods that rely on active problem-solving. For technical fields, these are textbook problems from books by well-regarded authors, and for languages, these are conversation practice and writing articles that I request feedback on (in particular, teachers in small group classes have given me great, useful feedback on my writing).

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michaericalriboJan 2023

In my experience, the best way to get better at math is to do a lot of it. Find some book that's "good enough" for some topic you're interested, and work many many problems from the book. You'll learn about the topic, but more importantly you'll learn problem solving skills. I recommend working the problem until you're sure the answer is right -- in grad school problem sets didn't have answers you could check, and full understanding was necessary to get the problem sets correct.

For me, a watershed book was Introduction to Analysis by Rosenlicht [1]. Proof-based, very "mathy", small and compact (so to speak) but with a massive scope. A great introduction to a really important topic, and it'll put your brain through its paces.

Again, I recommend working nearly every problem.

[1] https://www.amazon.com/Introduction-Analysis-Dover-Books-Mat...

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bcbrownJan 2023

In early high school in the 90s, I got my parents to buy me an (expensive) copy of Chaos and Fractals: New Frontiers of Science by Peitgen, Jurgens, Saupe. The end of each chapter was a Basic program for calculating and displaying various fractal/chaos theory images, and that's what got me started programming.

It also included a bunch of mathematics involving "neighborhoods", meaning the set of all points within a distance of an arbitrarily small epsilon from some point X. Although I never did any of the math problems from the book, that early exposure to epsilon made calculus vastly easier to understand, and for that, it's close to my heart.

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