I'm a little skeptical of CreateSpace.
Why did you decide to self-publish?
A Programmer's Introduction to Mathematics
111–120 of 223 posts
Re: A Programmer's Introduction to Mathematics
#112Earlier quoted context omitted.
I personally think this is exactly wrong. Most people struggle with Maths because they don’t have the implicit understanding that books like you’re talking about rely on. It’s like telling a novice programmer to read the documentation. I’m not sure how successful this book is but it seems a worthy attempt.
That's not at all the point I was trying to make. Indeed, if you check my other comment, both the books I give as an example have precisely the feature of being self-contained . Landau's Mechanics starts with the basic concept of a particle . Cohen-Tannoudji's Quantum Mechanics starts with the simplest possible description of the double-slit experiment . Again, they assume no prior knowledge about what they are tryin…
The counterparts of these books in the mathematical domain may be self-contained with respect to the subject matter, but you fail to consider the fact that most of them require a high degree of mathematical sophistication and are really targeted at people who have already acquired the required level of intuition. The "self-contained" nature of these books is deceptive - they might start with some innocent looking stuff about counting, integers etc and very soon drill deep into abstract stuff through complex chains of reasoning which a beginner will find extremely dry, bewildering and unfathomable. When you are a total beginner and trying to learn a subject through self-study, you are more likely to appreciate a book in which the author tries to recreate the experience of sitting in a classroom and listening to a professor holding your hand and showing you stuff from various angles.
Re: A Programmer's Introduction to Mathematics
#113Earlier quoted context omitted.
> 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.
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…
>the thing about math books I have read is that they overemphasize rigor at the expense of intuition
I think these are not contradictory notions! Bad maths books lack rigour. Many books are like you say: rigorous but difficult to make sense of. But truly great books both explain the concepts in the simplest, most lucid and succinct way possible AND maintain the rigour necessary to do mathematics.
I like this quote from Michael Spivak: "In addition to developing the students’ intuition [...], it is surely equally important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions."
I couldn't agree more. Rigour is not a "masturbatory" end in itself to feel very smart, but it is not also an obstacle to understanding.
Re: A Programmer's Introduction to Mathematics
#114Earlier quoted context omitted.
I have not one single time invoked any kind of authority to make the points I'm making. It was only below, after you've (ironically) invoked the writer's credentials and insultingly proclaimed I never should be allowed to ever teach anything, that I let you know my qualifications. I do justify why simplicity and succinctness are better than meandering. More superfluous information obscures the "nugget" or the essence…
Please stop now. Regardless of who's right, and you probably both are, this is the kind of tedious spat we don't need.
You're absolutely right. It feels frustrating for your comment to met with ill-faith attacks and insults but that's no excuse to lower the level in turn. Apologies for that.
Re: A Programmer's Introduction to Mathematics
#115From 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…
Attempting to shoe-horn programming "lingo" into mathematics. This statement is particularly amusing and highlights to me the fact that mathematics are a natural language, and not a programming language. Sussman had a really great presentation on this point; anyone who’d argue this please watch! https://www.infoq.com/presentations/Expression-of-Ideas
That was very interesting! Certainly a different perspective.
Re: A Programmer's Introduction to Mathematics
#116Earlier 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 idea is that it might take you longer to learn, but when you are applying it in the real world and hit real world problems that are messy, you’ll be a lot faster
Re: A Programmer's Introduction to Mathematics
#117I tried to buy it but for some reason Paypal refuses to use my existing balance and instead asks for my card.
Is this something you can control on your end?
Re: A Programmer's Introduction to Mathematics
#118Earlier quoted context omitted.
> 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.
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.
Re: A Programmer's Introduction to Mathematics
#119Does it compare to Don Knuth, et al, "Concrete Mathematics: A foundation for Computer Science"?
Re: A Programmer's Introduction to Mathematics
#120From 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…
I'd recommend reading Tao's blog post "There’s more to mathematics than rigour and proofs":
https://terrytao.wordpress.com/career-advice/theres-more-to-...