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A Programmer's Introduction to Mathematics

jeremykun.com

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Re: A Programmer's Introduction to Mathematics

#121

Post by username90 »

ptd wrote: post #53
chii wrote: post #51

Earlier quoted context omitted.

being told a solution can sometimes lead to "rote" learning - where you learn a particular way of solving the problem, rather than applying creative thinking. Also, if you can't prove a solution correct, then you haven't solved it!

Is this a feature or a bug? If it takes you two weeks to apply creative solutions and it take me one week to apply a “rote” solution, what is the benefit?

The main reason to study mathematics is to build and fix your intuition, hence studying rote solutions is a waste of time. It might help you pass the class but it wont help you much at all in other parts of life.

For example, at work nobody will care if you have rote memorized a solution or not since they will have already done the math, you will just apply formulas others have came up with. In order to do anything important with the math (not just solving school problems) you need to have intuition for it.

Re: A Programmer's Introduction to Mathematics

#123

Post by esalman »

amelius wrote: post #91
threwythrw wrote: post #30

Do the exercises have solutions? The most annoying things about math books is the lack of solutions. A beginner absolutely needs to know whether or not their solutions are correct. The “the reader should know if they are correct” logic doesn’t apply here. A beginner could easily have faulty logic and fool themselves into thinking their solutions are correct. I usually don’t buy math books without solutions if I’m sel…

> The most annoying things about math books is the lack of solutions. To me the most annoying thing about math books is hand-waving, lack of rigor, and unexplained notation. At least in programming, everything is formal and I can figure out the entire problem by looking at the source.

Advanced math topics are based on layers upon layers of abstraction (theorems, corollary etc.), like an enterprise software. I also dislike the hand-waviness, but I do understand that I have to read up on the basics in order to grasp the advanced concepts.

Re: A Programmer's Introduction to Mathematics

#124

Post by smadge »

threwythrw wrote: post #30

Do the exercises have solutions? The most annoying things about math books is the lack of solutions. A beginner absolutely needs to know whether or not their solutions are correct. The “the reader should know if they are correct” logic doesn’t apply here. A beginner could easily have faulty logic and fool themselves into thinking their solutions are correct. I usually don’t buy math books without solutions if I’m sel…

A good math book has examples and proofs of theorems in the text that demonstrate what a solution should look like. In a sense, these ARE worked solutions to some problems. If you ever get stuck on an exercise, it helps to go back and look at those. Nothing beats having an expert to look at your solutions and provide feedback, though.

Re: A Programmer's Introduction to Mathematics

#125

Post by username90 »

amelius wrote: post #91
threwythrw wrote: post #30

Do the exercises have solutions? The most annoying things about math books is the lack of solutions. A beginner absolutely needs to know whether or not their solutions are correct. The “the reader should know if they are correct” logic doesn’t apply here. A beginner could easily have faulty logic and fool themselves into thinking their solutions are correct. I usually don’t buy math books without solutions if I’m sel…

> The most annoying things about math books is the lack of solutions. To me the most annoying thing about math books is hand-waving, lack of rigor, and unexplained notation. At least in programming, everything is formal and I can figure out the entire problem by looking at the source.

How do programming books prove correctness of the algorithms taught? Hand waving. It is very frustrating to read for me, mathematical texts are a lot better at proving things.

Re: A Programmer's Introduction to Mathematics

#126

Post by username90 »

billfruit wrote: post #118
kccqzy wrote: post #100

Earlier quoted context omitted.

I think you aren't buying very good math books then. I find the exact opposite: the thing about math books I have read is that they overemphasize rigor at the expense of intuition. Everything is painstakingly illustrated in such great detail that I sometimes see the trees and lose sight of the forest. I feel as if reading proofs and doing problem sets in math books is just manipulating symbols in well-known ways with…

But at least all imperative procedural steps are clearly understandable from source code given in many programming books. Where as maths books routinely leave out many steps in proofs and calculations, on top of many ambiguously used notations and terminology that can leave a self-student confused.

A program proves nothing at all so I am not sure what you can understand from it? Typically in programming you are presented with a piece of code, a statement that this piece of code solves a specific problem and then a proof of that it actually works. Those proofs are typically far from understandable or rigorous.

Re: A Programmer's Introduction to Mathematics

#127

Post by codesushi42 »

alan_wade wrote: post #69

I really wish this book would include probability and statistic sections. My guess is that a lot of people, like me, will want to read it because they're getting started with ML and need help getting used to the math, and probability/stats is an important part of it that's missing. Any chance you could add it in the future?

Unlike the other subjects contained in this book, I do not think that any useful understanding of Probability and Statistics could result from only one or two chapters of coverage.

I would recommend a book I found that covers Statistics using Python:

Statistical Methods for Machine Learning https://machinelearningmastery.com/products/

Personally, I much prefer that book to the free "Think Stats" one available.

You can also find a book there on Linear Algebra and others related to Deep Learning, all containing real implementations with Python.

I have no affiliation with the site; these books have proven so valuable to me that I need to share them.

Anyway, the book mentioned in the OP looks like a great foundation and I picked up a copy as a refresher. I would have also liked to have seen coverage of number theory in this book, with RSA being an application, but that too would have required lengthy explanation for any useful insights to be learned.

Re: A Programmer's Introduction to Mathematics

#128

Post by sn9 »

andrepd wrote: post #76
adrianmonk wrote: post #61

Earlier quoted context omitted.

Regarding the first point, if you are the type of person who just wants it to get to the equations with a minimum of talk, you're probably not the intended audience of this book. The culture of mathematics (including its lingo) has always been a big barrier for me. Thus far, I've only skimmed it, but that part looks promising to me. It seems reasonable to guess that if someone has learned a good bit about programming…

Regarding the first point, if you are the type of person who just wants it to get to the equations with a minimum of talk I don't want "no talk" and "just equations, I want the "minimum of talk possible" that communicates the ideas and nothing more . I find the more stuff you write the more there is to confuse people. The best way is to strip everything that is superfluous. You are left with the essential, in the cle…

Math books already exist for that audience.

Indeed, most of the canonical texts for undergrads would likely fit the bill.

Re: A Programmer's Introduction to Mathematics

#129

Post by sn9 »

andrepd wrote: post #71
westoncb wrote: post #67

Earlier quoted context omitted.

There is a common category of misguided book review that the parent comment falls under: the reviewer has some particular things they are looking for from a book and fails to see that there are more uses for it than their own; so they generalize, reading the book's failures to meet their personal criteria as a failure intrinsic in the book's content, and mistakenly lambaste the work. > 19 pages of droning before you…

>One person's "droning" may be another person's "rare, illuminating presentation"; we are not all interested in the same things. You are absolutely correct in that regard. I've talked to many people who hated the textbooks I most liked, and preferred ones that I found unreadable. Just goes to show that what works for you may not work for me. You are very wrong on the other point: none of what I said is borne out of a…

I'm sure the author would have liked for you to enjoy his book, but if you've already read Spivak and Landau, then you are most definitely not his intended audience.

Your criticism is like that of a professional mathematician complaining of the elementary results presented in some high school math book.

Re: A Programmer's Introduction to Mathematics

#130

Post by j2kun »

mlevental wrote: post #62
andrepd wrote: post #47

From the bit I've read from https://pimbook.org/pdf/pim_first_pages.pdf it seems to be very very poor. * 19 pages of droning before you start with something concrete. Much talk talk talk about your experiences before you get to the point. I can't put into words how much it frustrates me when I'm expecting to read something interesting and the author takes 3 paragraphs talking about nothing (usually with lots of overe…

wtf is wrong with hn. >[sorry if I am being blunt, but it's how I feel] you should learn to keep your feelings to yourself when the only function they serve is to denigrate others and derive cruel satisfaction for yourself. >Here is a rule of thumb that in my experience applies well to almost everything in mathematics this is aspirational pretension - everyone claims to appreciate formal purity /after/ they've learne…

It's funny, because I discuss Lamport's view in the book as well in a later chapter. I think some folks are annoyed that the first chapter is slow, but I promise it ramps up :)
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