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Knuth Previews New Math Section For 'The Art of Computer Programming' (stanford.edu)
In 1962, 24-year-old Donald Knuth began writing The Art of Computer Programming -- and 55 years later, he's still working on it. An anonymous reader quotes Knuth's web site at Stanford:
Volume 4B will begin with a special section called 'Mathematical Preliminaries Redux', which extends the 'Mathematical Preliminaries' of Section 1.2 in Volume 1 to things that I didn't know about in the 1960s. Most of this new material deals with probabilities and expectations of random events; there's also an introduction to the theory of martingales.
You can have a sneak preview by looking at the current draft of pre-fascicle 5a (52 pages), last updated 18 January 2017. As usual, rewards will be given to whoever is first to find and report errors or to make valuable suggestions. I'm particularly interested in receiving feedback about the exercises (of which there are 125) and their answers (of which there are 125).
Over the years Knuth gave out over $20,000 in rewards, though most people didn't cash his highly-coveted "hexadecimal checks", and in 2008 Knuth switched to honorary "hexadecimal certificates". In 2014 Knuth complained about the "dumbing down" of computer science history, and his standards remain high. In his most-recent update, 79-year-old Knuth reminds readers that "There's stuff in here that isn't in Wikipedia yet!"
You can have a sneak preview by looking at the current draft of pre-fascicle 5a (52 pages), last updated 18 January 2017. As usual, rewards will be given to whoever is first to find and report errors or to make valuable suggestions. I'm particularly interested in receiving feedback about the exercises (of which there are 125) and their answers (of which there are 125).
Over the years Knuth gave out over $20,000 in rewards, though most people didn't cash his highly-coveted "hexadecimal checks", and in 2008 Knuth switched to honorary "hexadecimal certificates". In 2014 Knuth complained about the "dumbing down" of computer science history, and his standards remain high. In his most-recent update, 79-year-old Knuth reminds readers that "There's stuff in here that isn't in Wikipedia yet!"
Thanks, Donald!
I was with you until "I taught myself PHP."
I'm just a girl
Similarly, one could argue that a many medical-related treatments are competently performed by people who do not have the benefit of a medical school education. I haven't heard that Knuth considers mastery of, or even familiarity with, his books to be a requirement for writing code.
Donald Knuth is an elitist. It is not necessary to have a background in mathematics to write software. I taught myself PHP and I certainly don't have any kind of mathematics background whatsoever. It isn't dumbing down as he claims. It's about creating opportunities. If you can code and you can do it well without mathematics, so be it. The math side is for those that want to do research. I work in the real world ....
In the "Art of Computer Programming" context mathematics includes various things related to the performance of algorithms (code). Such things are useful, even essential, well beyond the domain of research, in many areas of the real world of software development (coding).
I've never looked at PHP. I have done javascript/ecmascript. A pathetic pile of shit called a language. I've heard PHP is worse than ecmascript, but as I've never done PHP I don't really know.
So, you taught yourself PHP and can call whatsisname irrelevant?
I can only hope I can somehow track your screen name to the name on your resume and get it shitcanned before it hits my desk.
bought Knuth's 3 books in the 80s
invaluable
retired, haven't bought any of his newer books
It is not necessary to have a background in mathematics to write software.
No, but high level math is certainly useful for creating the binary code, on which the assembly code is based, on which the compiler is based, on which the language is based, on which you write software.
SJW: Someone who has run out of real oppression, and has to fake it.
FFS - those who want to model the real world need to be able to pick up a bit of mathematics somewhere.
That's why in my workplace we have actual engineers churning out shitty code instead of CS graduates who could produce wonderful and efficient code if they had some clue where to start. If you can't even answer the question "what's a fourier transform?" then you are doomed to attempt to solve many problems in ways that will take orders of magnitude more time than really shitty code from someone who can.
You don't have to start with it, but if you don't pick up a bit of mathematics along the way in something that is a very mathematical field you will be very limited in what you can do.
Writing anything that is intended to scale, anything where performance or security is important, requires a decent understanding of maths.
Yes, you can often throw together something that will "work" without having any knowledge of algorithmics or of how data is actually stored in your language of choice, but as soon as you hit production you will quickly reach the point where "throw more hardware/compute time at my terrible code" becomes prohibitively expensive.
I'm not saying you need a degree on Comp Sci to be a decent programmer - you don't - but calling yourself a programmer without an appreciation for the underlying maths is like calling yourself a mechanic without understanding how an engine works. Yes, you can change the tyres and top up the AC, but god help you (and your customers) when you have to do something important.
You are, IMHO, and idiot. I have been studying Knuth's work for almost 4 decades now, and am still learning from it. In case you are interested (probably not) it is has a chip in it, I wrote the software that built that chip! Building from his work has given me a US Patent on adaptive systems, numerous technical publications, and such. What can you claim?
Sometimes, real fast is almost as good as real-time.
That's supposed to be funny, I guess, however it's what the PHP authors actually claim!
Slashdot, fix the reply notifications... You won't get away with it...
Everyone told me I should go into computers as a teenager, but I couldn't see myself being a programmer as coding was mumbo jumbo. I did take electronics and mathematics in college. After I started my technical career in software testing, I went back to college a decade after I graduated to take computer programming. Because I took mathematics (algebra in general, order of operations in particular), everything fell into place for me to learn programming with straight A's. Even though I got an A.S. in computer programming, I never became a programmer. I went into IT support to help users solve difficult problems made difficult by professional programmers.
What can you claim?
First post?
Yaz
Study computers, they said. You'll make lots of money, they said.
When I went back to school to learn computer programming after the dot com bust, people told me I was crazy. Study health care, they told me. You're make lots of money, they told me. But I read a study on long-term trends for the IT industry that there will be a severe shortage of skilled IT workers with 1M+ job openings after the baby boomers all retired and foreign workers will stay home in 2030. (A recent study now predict 1.5M+ job openings.) I went into IT support. My friends who went into health care hate their jobs of wiping other people's asses even though they make more money than me. I'm enjoying my career in IT support, and, ironically, my best paying contracts are hospitals.
They never said anything about getting replaced by indo-chimps.
I do InfoSec for government IT. No foreign national is going to replace my job. If they do, I'll climb the ladder higher and do something else.
They never said anything about starving.
I was out of work for two years (2009-10) because recruiters saw help desk support on my resume, assumed that I wanted to continue doing help desk support, and told me that no help desk support jobs were available. Never mind that wasn't the job I applied for. I ate rice and beans during those two years, the six months I was underemployed (working 20 hours per month) and filed for chapter seven bankruptcy in 2011, and the two years (2012-13) I'ved worked multiple jobs seven days a week until I was financially back on my feet.
"There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy. your philosophy"
Yes, you are correct, you don't need much math for some types of programming. However, it saddens me that you would attack a man for wanting to expand and master the study of computer science. He has literally devoted decades of his life to writing books to help programmers such as yourself get better at their craft. If you don't want to learn more about your trade, that is fine too. But don't get upset if you get passed over for a job in favor of some other guy who cracked open Knuth and worked all the exercises.
HA! I just wasted some of your bandwidth with a frivolous sig!
I use LOGO for all of that. It's turtles all the way down.
Inheritance is the sincerest form of nepotism.
I think the real problem is partial substitutability.
In both php and javascript if you use a number where a string was expected or a string where a number was expected the program will blunder on. If you are lucky it will produce the right results, if you are unlucky it will produce wrong answers. It is relatively unlikely to produce an error message and if it does that error message is likely to be a long way from where the mistake was made.
php's separation of the addition and concatenation operators increases the chance that a program will produce the right results despite accidental using the wrong type but it's still a minefield.
Java is statically typed. A caller can only pass your method the types it was expecting.
Python is dynamically typed but forbids use of the "+" operator on mixed strings and integers and will never compare a string an an integer as equal. So using an integer where a string was expected or vice-versa is likely to fail fast.
note: i'm known as plugwash most places but i screwd up registering that here somehow in the past and now can't register
Well, you need to know at least good arithmetic rules, and have a scientific thinking. Besides, no need to be expert in maths.
Slashdot, fix the reply notifications... You won't get away with it...
Of course mathematical equations can describe water states, just not at a level of abstraction you're happy with.
Anyone, Is there a site that tracks these specific gotchas? I've been compiling a small list of these for the past few months and can't seem to find a single source that focuses on these things.
> I taught myself PHP
That's awesome. I respect anyone who has the desire to learn, the puts in the work, and has the discipline to see it through.
PHP is of course a language, a set of vocabulary. At the back of any textbook, you'll find a glossary, the language or vocabulary used in the book. You've already learned the language, the glossary, of PHP programming. If you look, you may find there's a lot of cool stuff in the other parts of the book, systems architecture stuff, software engineering, analysis of algorithms, etc.
You need to learn a programming language or two before you learn analysis of algorithms or software engineering, because the languages are the vocabulary words of the field.
To give a concrete example, when I started my current job, the company had a software system that worked - mostly. A team programmers had worked several years on it, and all knew the language they were working in. Customers just wanted it to be faster. It was definitely too slow. Although it was my first month on the job, when I heard the complaints of slowness I said in a meeting "I'd like to take a look at that; I can probably make it 20%-30% faster easily enough for now, then do more after I understand how it all works." The team was rather skeptical, in fact they chuckled out loud at my claim, saying "I rather doubt you can do that". "How long do you think that'll take?", they asked. "Give me a week", I said, though I hadn't yet seen the code. They laughed again, hundreds of thousands of lines of code and this new guy was going to make it 20%-40% faster in a WEEK? Doubtful, they said. To put me in my place, they said "sure, go ahead and try that [wiseguy]."
As I left the meeting I realized I had just taken a big risk. When I went home I told my wife that I had just bet my reputation at the new job on a claim I only hoped I could fulfill. If I failed, it would establish that I'm an arrogant prick. If I succeeded, I'd be known as possibly the best programmer in the building.
Well a week later I had it running 30% faster. Why could I, in a week, make drastic improvements to code they'd been trying to speed up for months and years, code I'd never even seen before? They all knew the language almost as good as I did. But I had been taught to study much more than the language. They knew C, Perl, and Erlang; I knew algorithms and cache theory. So in a week I did in fact make major improvements to their years of work.
Now, I'm going to go upstairs and check the progress of my benchmark. Now six months into the job, a major customer again complained about slowness, so I've been looking at that for a few days. I hope to see that my three day's work has made the system another 20% faster. I'm a tad nervous because I need to impress the new boss, I think that by learning more than just the language (glossary terms) I'll be able to do that.
Donald Knuth is an elitist. It is not necessary to have a background in mathematics to write software. I taught myself PHP and I certainly don't have any kind of mathematics background whatsoever. It isn't dumbing down as he claims. It's about creating opportunities. If you can code and you can do it well without mathematics, so be it. The math side is for those that want to do research. I work in the real world ....
There's a lot of jobs for coders who don't know math, but there's a ceiling on how good a programmer you can become.
Fundamentally all programming is research, you have a problem and you need to develop a robust solution on how to solve it.
Sometimes those problems don't involve math, but sometimes they do. You might need to implement a specific calculation (and understand how to verify and debug it), if you have a large data base you need some math for your queries to return quickly. And for any non-trivial problem where you need to design your own algorithm you need to have enough of a mathematical mindset to write it efficiently.
Think of it like race car driving. Driving a race car has a lot of special skills useless for 99% of of driving in a city. But someone who trains with race cars is probably going to be better at that 99% because they push past their limits. And the 1% where those special skills do come in handy they'll see a drastic difference.
I stole this Sig
I mean, "Concrete Mathematics" is a great book more accessible than his TAoCP math sections, more encompassing and with its own approach towards notational conventions. Basically I turn to it when the TAoCP math sections get stuck in too dense and obscure descriptive and ad-hoc math.
When the math is mainly accompanying algorithms, it just cannot be stacked up in a pedagogical and accumulative manner but has to follow the ordering of the algorithms.
And make no mistake: TAoCP is obscure and quaint and with little impact on the real world in its actual code sections (which are written in the assembly language of non-existing architectures). Burying the rather mainstream relevant math alongside and structuring it alongside as a side thought is not doing it a favor. It's far too non-trivial for that, and it applies to much more than the presented algorithms.
"Concrete Mathematics" is a good go-to text series for generating functions, series manipulation, and the general uglinesses underlying algorithmic complexity analysis.
I really hope you will retire before 20 years from now on, because at that time being a self-taught PHP developer will be totally worthless on the job market. That's why the maths are important. The more the time grows, the more low cognition level skills loose their value.
So now you're doing web services in PHP for a living. I'm pretty sure in a not so distant future this will be replaced by a series of drag and drops of functionality boxes in a special designed software that a guy paid on tenth of your salary can do. What will you do when that time arrives? Develop the boxes, these require a lot more maths. Develop the software that produce the software from the boxes? That requires a tremendous amount of maths.
Yes it is not necessary to have a big background in maths to write basic software now, thanks to simpler programming models. The thing is, writing those software will be unneeded pretty soon, because the next programming models will be so simple that they will render yours obsolete. You're like the mechanic refusing to learn how electric/hybrid vehicles work. No consequence right now, but not a very safe bet on the future...
Video of some good progressive thrash music
It is not necessary to have a background in mathematics to write software
No it's not, but it is necessary to have a background in mathematics to write good efficient software. If you're slapping together PHP libraries then that's fantastic, but don't pretend that this same level of knowledge applies to identifying the most efficient sorting algorithm, or figuring out how to software decode a CRC message in the lowest number of CPU cycles.
If the world was made of people with your views an octo-CPU quad xeon wouldn't be enough to boot up windows in a reasonable time.
But craftmanship.
Knowing some classical math won't really help you with floating point
For example, even simple things like hash tables and balanced trees are beyond what most current CS graduates can implement or do understand. Forget about things a bit more complicated like a complexity analysis, or a formally specified invariant or pre- and post-conditions. If you do not understand the basics, all higher-order constructs are meaningless because you can only memorize how they behave, but you can never understand it or verify your understanding. And your understanding will at the very least be incomplete and partially wrong.
CS continues to fail (and in fact it is getting worse) at education engineers. Yet the human race knows that for technology you need engineers as soon as you are customizing things or doing new things. Until and unless this gets finally understood and becomes the norm, software and everything built around it will continue to suck badly.
Most ACs are not even worth the keystrokes to insult them. Be generically insulted by this and ignored otherwise.
How is having an understanding of your computer architecture and how your language maps to it 'math'?
Do Americans just use the word 'math' to mean 'something that requires some thinking'?
I don't understand why you'd choose IT support. It's an ungrateful and underpaid job.
If you need a super sophisticated book to understand long division (taught in elementary school), then your thinking process is unusual to say the least.
last one was 4a....
Last was 4a. First two were massively outdated. I still have to still admit they are about "computer science". Which should not be what graduates in computers should not have graduated in since '85. Should have been a balance between the science and the engineering. The science part being encryption. Everything else he explained in obtuse language. I'm actually sad he never wrote "the" book on making a compiler. He could have actually predicted superscaler branch prediction with which on ryzen right now includes nural networks.
Obligatory Doctor Fun reference.
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Warning: Slashdot may contain traces of nuts.
Then you don't know as nearly as much mathematics as you think you do, Herr Gödel.
Il n'y a pas de Planet B.
Is anybody aware of better alternatives that are easier to read and can still impart the necessary mathematical background knowledge?
Some people here already mentioned a couple: "Concrete Mathematics" (Ronald L. Graham and Donald E. Knuth, 1994), and "Introduction to Algorithms" (Thomas H. Cormen and Charles E. Leiserson, 2009).
https://www.google.com/patents...
Sometimes, real fast is almost as good as real-time.
... "The Art of the Pussy Grab."
It little behooves the best of us to comment on the rest of us.
Pretty confident for a guy who couldn't get a job for two years.
I didn't listen to the recruiters who told me I was unemployable and hiring managers that I was overqualified for anything else.
If you lost your current job, do you now have skills that won't leave you unemployed another two years?
That's the funny thing about being unemployed for two years after the Great Recession was officially over: job skills didn't matter. As soon as the economy got better in 2011, the Silicon Valley labor market tightened and employers could no longer afford to be picky about whom they hire. I had 20+ contract assignments when I worked for seven days a week for two years. Despite being out of work for two years and having a chapter seven bankruptcy on my credit record! As for my current job in government IT, I'm halfway through a fully funded five-year contract.
Translation: I have got a degree in maths and all I have got is a lousy tech job support.
I got A.A. degree in General Education (1994) after graduating from the eighth grade and skipping high school, and an A.S. degree in Computer Programming (2007) with a 4.0GPA while working 60 hours per week and teaching Sunday school.
Since I started my technical career in 1997, I was:
The equivalent of frying burgers in the IT industry.
The kind of work I do — and enjoy doing — is virtual ditch digging. Like being a sanitation engineer, someone has to do the work or civilization as we know it will collapse.
No, not if you keep using that old 1st gen Pentium CPU in the basement...
cpghost at Cordula's Web.
I'm sorry, I don't see the link.
Most mathematicians I know are clueless about floating-point arithmetic. You need someone with specialized knowledge in both numerical stability and computer architecture to use floating-point correctly.
I don't understand why you'd choose IT support.
IT support needs miracle workers to solve difficult problems.
It's an ungrateful and underpaid job.
That's entry level. Once you finish paying your dues, appreciation and pay gets better. Especially if you have a reputation of being a miracle worker. Miracles can be solving the problem remotely while the user complains about the problem for 15 minutes, reclaiming 600 square feet of storage space from eight years of discarded IT equipment in between tickets over a six-week period, or fixing a failed printer migration project after the server tech ran the script at the last minute and went on vacation for six weeks.
You still have to work at fixed hours, sometimes stuck on a silly shifts, with the stress of dealing immediately with many requests as they come in, and even by the end of your career you'll be happy if you even reach 6 figures.
Developers on the other hand have an easy life, working whenever they please, and get paid a lot more from the get-go.
You still have to work at fixed hours, sometimes stuck on a silly shifts, with the stress of dealing immediately with many requests as they come in, and even by the end of your career you'll be happy if you even reach 6 figures.
My IT support contracts prohibits me from working more than 40 hours a week. I haven't worked overtime in over a decade. I start work at 7AM instead of 9AM or 10AM to avoid the traffic gridlock. I'm responsible for 80,000+ workstations and no longer deal with users. As for dealing with the stress, since I'm working in government IT, I have paid federal holidays (40 hours), paid time off (80 hours) and unpaid time off (40 hours). This year I got an extra month of pay as a Christmas bonus. I'm studying for my InfoSec certifications that should put me in the six-figure club for my next job.
Developers on the other hand have an easy life, working whenever they please, and get paid a lot more from the get-go.
The developers I know work 80 hours a week from 10AM to 12AM (programmer hours), owns a Tesla car or two, have a big house, big wife and big kids. They never get any time off to do anything. If they stop running on the treadmill, everything falls apart because they're one paycheck away from bankruptcy.
We have excess food production capacity.
Much of that excess food production capacity is subsidized by the taxpayers. If the subsidies went away, we would be paying $10 per gallon for milk.
Okay ... so help yourself out. Do a cursory study of software written by people with and without a good elitist education in computer science and mathematics and tell me whether their software is *better* than that of those like you who do not have such a background.
Importantly to me, is it less buggy and does it have fewer security problems?
Teaching yourself to do basic coding is great, but learning how to write *good* code is a whole other thing.
- Michael T. Babcock (Yes, I blog)
Read this, don't feel bad: https://eev.ee/blog/2012/04/09...
- Michael T. Babcock (Yes, I blog)
This series is epic and a book shelf must have for any serious computer scientist or engineer.
As a pure coincidence, it wasn't two days ago that I was editing Wikipedia about Knuth, TeX, etc. One thing I have wondered before and wonder now is if he has some plan for what happens to the work once he dies. Simply put, at this pace, he will not finish the book. Is anyone working with him to ensure that it is completed if he dies? Does anyone know? I'd like to ask him via snail mail but I frankly don't want to waste his time.
Fundamentally all programming is research, you have a problem and you need to develop a robust solution on how to solve it.
Sounds more like a definition of engineering than research.
To have a right to do a thing is not at all the same as to be right in doing it
And this would have what to do with math, software, programming, or nature? The answer to your question is that you do not place undying faith in the God-inspired correctness of Wikipedia but instead look at the sources in the articles. Conflicting sources aren't contradictions either in any formal manner. We know how to deal with differing reports.
The best current explanation is that it doesn't, but there's not enough dark matter in the solar system to cause measurable results. MOND never did get general acceptance, from what I can tell from outside the field. Even if it did, we'd just have to change our understanding of gravity and we'd be fine. Misunderstanding is not a contradiction.
To pick an example I actually know something about, matter-antimatter asymmetry is not a paradox or a contradiction. It's something we don''t understand. We don't have one firmly established set of physical laws saying it has to be symmetrical, partly because this appeared at a time when we had conditions we can't come anywhere near close to experimentally, and so we are limited to extrapolation of known laws of physics to situations where some really tiny part of the actual laws that we can't measure on Earth actually matters. Back in 1900, we had an expression for kinetic energy based on mass and speed that worked to the limits of measurement as long as the speed was very small compared to the speed of light. Since then, we've devised much more delicate tests and accelerated stuff to relativistic speeds ("relativistic" here being defined partly by the precision and accuracy of our measurements).
Also, the observations suggesting dark matter have an easy explanation: there's matter out there that doesn't interact with the electromagnetic force. We're currently trying to figure out some of its other properties. No contradiction there.
"When you have eliminated the unacceptable, whatever is left, however improbable, must be the truthiness" - Holmes
Math doesn't require transitivity. Duh. There are mathematical objects with certain properties, such as transitivity, but that isn't the same thing. "This statement is a lie" requires something more sophisticated than first-order predicate logic, true, but it's mathematically tractable if you know what you're doing. It's analogous to the Goedelian "Proposition P: Proposition P cannot be proved.", and that's mathematically tractable if complicated.
"When you have eliminated the unacceptable, whatever is left, however improbable, must be the truthiness" - Holmes
Donald Knuth is an elitist. It is not necessary to have a background in mathematics to write software.
By this standard, anyone striving to enhance general knowledge in a field is an elitist. Albert Einstein was an "elitist". Richard Feynman was an "elitist". Carl Sagan was an "elitist".
I taught myself PHP and I certainly don't have any kind of mathematics background whatsoever. It isn't dumbing down as he claims. It's about creating opportunities. If you can code and you can do it well without mathematics, so be it. The math side is for those that want to do research. I work in the real world ....
As you didn't invent PHP yourself, you stand on the shoulders of giants to achieve what you are doing. Those giants quite possibly benefited from the work of Donald Knuth -- one of the true trailblazers of the field. Unknowingly and unwittingly, therefore, you are a vicarious beneficiary of his work. Have some respect.
licet differant, aequabitur
There's a scene in MASH where Hawkeye and Trapper are coaching Radar for a date with a a brainy gal.
They tell him If she mentions Bach, just nod your head and say knowingly - 'ah - Bach!'
That's the relationship most comp sci majors had with Knuth - they paid lip service to his books which few have even read.
This from back in an era when all programs were expected to be mathematically proven correct.
Well; https://www.quantamagazine.org...
- Michael T. Babcock (Yes, I blog)
Donald Knuth is an elitist. It is not necessary to have a background in mathematics to write software. I taught myself PHP and I certainly don't have any kind of mathematics background whatsoever. It isn't dumbing down as he claims. It's about creating opportunities. If you can code and you can do it well without mathematics, so be it. The math side is for those that want to do research. I work in the real world ....
Um, IMHO, no he isn't.
Formally, there's a big difference between being a 'Coder/Programmer/Developer' and 'Software Engineer' and 'Computer Scientist'. The latter two usually require a mathematical understanding of what a computer system is (includes programs, OSes, networks, languages, ...) and how it will perform.
At my own institution, our CS degree was really a pure mathematics degree at one time ... the department had a saying "The computers are for email and writing up, please use the blackboards for the Computer Science". We do these days teach some programming - because it's expected - but we usually use this to animate the mathematics.
@peetm
> why is it that ... that no one can ever fucking fail or be called an idiot these days!
Okay, you're an idiot. Your comment will be dutifully submitted to failblog.
Knuth has my utmost respect, and for the most part I agree that software patents suck. Some are inventions in the truest sense of the word and worthy. In my egoistic way I would like to think mine is such. Here is the link. Check it out, and then tell me what you think. https://www.google.com/patents...
Sometimes, real fast is almost as good as real-time.