[dragontamer]

> I don't think Knuth's books are impossible to read, but a primer to some of the material can help (and understanding mathematical proof is a prerequisite).

Its like no one has read "The Art of Computer Programming".

Page 10 is an introduction to mathematical proofs !! Knuth covers this very early, because its so fundamental to the rest of the book. The book assumes the reader doesn't know rigorous math or proofs, and has an extremely solid section full of exercises for mathematical induction and proofs.

The following sections are on the absolute barebones of math. Page 21 starts the section on numbers (really starting at the basics here). It covers integers, rationals, reals, complex numbers, logarithms and exponents. Honestly, this is like sophomore high-school level stuff, maybe even middle school to an advanced student ("Talented and Gifted" middle-school should cover this stuff actually ). I kid you not, I think an advanced 13 year old can handle this section.

Page 27 explains sums and products ("sigma" notation). This should have been covered in high-school level pre-calculus, but we're finally approaching later high-school level math. There are discussions about how sigma is similar to calculus, but it doesn't seem necessary to understand the section.

Page 39 is floor, ceiling, modulus arithmetic. While fundamental to discrete mathematics (arguably college level), its so elementary I'm not sure if it really counts as college level yet.

Page 45 remains in high-school level: Permutations, Combinations, and Factorials, but also includes the Gamma function (which I'd argue is college-level). But given how Gamma is so similar to Factorial, I'd argue that the high-school level reader would still have an easy time with the concept.

Page 53 are binomial coefficients / combinations, including pascal's triangle, and a huge number of identities. I'd say this is the first, college-level section. But by this point, the reader should be very much used to the idea of rigorous math.

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Seriously, if you've never given it a read... its pretty simple. Start at page 1, and work forward. Eventually you'll come across some exercises. At this point, test your knowledge to see if you truly understood the previous section.

Do a few "level 10" or "level 20" problems (2 minute problems to 30 minute problems). Maybe think about level 30 or level 40 problems (1 day to 1 month problems), but don't feel like you actually have to solve them. Just read them over and "see why they're difficult" and make sure you understand the concepts.

Then, start the next section.

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Spend days or weeks per section, or even on a single page if you get stuck. Skip over * sections ("advanced"), unless you're confident in your abilities to read some of the most difficult comp. sci concepts.

If you think you're bad at math, skip over "M" or "HM" exercises and sections (Math and High Math respectively).

[dc-programmer]

When you say he discusses how sums are similar to calculus, does that mean he relates sums to integrals (e.g Riemann sums)? Asking because I'm wondering if there's other connections I haven't been exposed to.

For Christmas, I (an adult) asked my mom to get me a few volumes instead of clothes this year. I'm looking forward to giving them a go like you described.

[dragontamer]

Oh, its just a throw-away sentence about infinite sequences / sums, and the usage of lim x->infinity to solve that kind of problem.

The bulk of that section is about distributive property of summations, sum_A(foo) + sum_B(foo) == sum_AorB(foo) + sum_AandB(foo), and other such properties.

Its a primer on the mathematics of programming, which is almost entirely discrete mathematics. There's no integral or derivative in that section!

[gh0std3v]

I know that Knuth has some introduction in the beginning, but he goes over it pretty quickly, which is why I was saying that some primer material is helpful just to get a headstart and not feel confused (plus Knuth himself says that you should just skim over the beginning material if you want to get to the "exciting" stuff).

> Spend days or weeks per section, or even on a single page if you get stuck.

This is asking a lot for people who don't have much time to spare. That being said, it's also why many people struggle to start Knuth's books. Most people have forgotten high school math at this point, and it's hard to learn and re-learn when you get older. I think some introductory coursework like the book posted by OP might be more fast-paced for people looking to start learning about algorithms.

[dragontamer]

Of the 672 pages of Book 1, at least 200 of the pages are about introductory Math subjects (if we include the dozens of pages of exercises in the back of the book associated with the math sections, and probably a good chunk of the Index/Bibliography too).

And as I stated earlier: this is elementary stuff. Like "What is a number", and "Summations". Yes, its difficult to _truly understand_ summations, and you may have to spend days or weeks relearning the material.

But that's just what math is. If you want to understand all the ins-and-outs of how numbers add together, you just gotta study it for longer than a day or two.

But Knuth provides something like 80+ exercises (and all of them worked out completely in the back of the book) to get you started on this subject.

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Summations are really useful for understanding for-loops and inductive reasoning anyway. A deep study into summations / loops / in general probably benefits the typical programmer, despite being a theoretical math subject.

> This is asking a lot for people who don't have much time to spare.

It takes far less time to read through a Knuth section than technical documentation for CPUs or GPUs, or spec-sheets on protocols, or any of the other stuff our field has to regularly deal with.

Reading and learning takes time. You have to be patient with yourself. You aren't going to be an expert on HTML, CSS, OpenCL, CUDA, x86 processors, ARM processors, or anything unless you spend days, weeks, or months reading, studying, and exercising (aka: writing simple programs or even advanced programs) on the subject.

That's the nature of our field. In the case of Knuth's approach on Algorithms, its Math heavy because you must understand the inductive reasoning that underlies it all.

Its one thing to say "Quicksort is fast". But what Knuth says is "This implementation of Quicksort executes in 3n * log(n) + X time" (or something like that, I forget exactly. But Knuth calculates it out exactly).

And furthermore, Knuth offers a mathematical proof, showing the student how to evaluate unknown algorithms.

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Knuth's book isn't about "Quicksort", even though it discusses it. Its about how to use Math to calculate how fast some algorithms are vs others. That's a lot of math to learn, go over, and become an expert in. Permutations, Random variables, summations (over the loop), induction and proofs.

This is all stuff a high-school student can learn, but whether you're 15 or 55, it will take weeks to learn and go through.

[gh0std3v]

Yeah, math (or any subject really) takes a lot of time to learn, and Knuth’s books do a good job of providing plenty of exercises and explanations. I was just saying that it can initially be overwhelming for some, which is why they might want to try attacking something smaller and more broad (though this has more to do with someone’s mentality than the book itself).