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I'm writing to ask for some guidance on choosing a language and course of action in learning programming. I apologize if this type of question is inappropriate for Cross Validated, please advise me to another forum if that is the case.
I've seen thread after thread with questions from newbies, asking, "What is the best language to start with?" and then it always starts a flame war or someone just answers, "There's no best language, it's best to pick one and start learning it." My question is a little bit more focused than that.
First off, I've been programming my whole life, in very limited capacities. My deepest training was in C++. Whilst in my EECS degree program, I resolved to never be a software developer because I couldn't stand not interacting with people for such long periods of time. Instead I realized I wanted to be a math teacher, and so that is the path I have taken.
But now that I'm well down that path, I've started to realize that perhaps I could develop my own software to help me in the classroom. If I want to demonstrate the Euclidean algorithm, what better way than to have a piece of software that breaks down the process? Students could run that software as part of their studies, and the advanced students might even develop programs for themselves. Or, with an Ipad in hand, why not have an app that lets students take their own attendance? It would certainly streamline some of the needs of classroom management.
There's obviously a lot of great stuff already out there for math, and for education, but I want a way to more directly create things specific to my lectures. If I'm teaching a specific way of calculating a percent, I want to create an app that aligns with my teaching style, not just another calculator app that requires the student to learn twice.
The most I use in class right now is iWork Numbers/Microsoft Excel for my stats class. Students can learn the basic statistical functions, and turn some of their data into graphs.
I have dabbled a bit with R, and used Maple in college. I've started the basic tutorials for OS X/iOS development and have actually made good progress making an OS X app that takes a text string, converts it to numbers, and performs encryption using modular addition and multiplication. I sometimes use Wolfram|Alpha to save myself some time in getting quick solutions to equations or base conversions. I know of MatLab, Mathematica, and recently people have been telling me to check into Python or Ruby. I also know basic HTML, and while it's forgotten now, learned Javascript and PERL in college.
If I keep on the path of Obj-C/Cocoa, I think it will have great benefits. Unfortunately, anything I produced for Mac would only be usable on a Mac, so it wouldn't be universal for all of my students. Perhaps then learning a web language would be better. Second, I'm wondering if the primary use is mathematical, then perhaps my time would be better spent learning Mathematica Programming Language, or R, or something based less on GUI and more on simple coding of algorithms, maybe Python or Ruby?
It seems that Mathematica already has a lot of demos for different math concepts, so why reinvent the wheel is also a question I have. I think overall, it would be good to have more control and design things the way I need. And then, if I do want to make an "Attendance" app or something else, I would already have the programming experience to more easily design something for my iPad or MacBook.
The related question to this is what is a good language to teach to my students? In his TED talk, Conrad Wolfram says one of the best ways to check the understanding of a student is have them write a program. But if Mathematica does the math virtually automatically for them, then I'm not sure that will get the deeper experience of working out logic for themselves, like you do when you're writing C, or a traditional procedural language.
I know that programming takes time to learn, but I also know that at this point, my goal is not to be able to make an app like "Tiny Wings." With the app store ease, some of my work may be an extra revenue stream, but I see myself as more of a hobbyist, and now teacher looking to software development specifically for its ability to help me demonstrate mathematical concepts.
I think I will push ahead with Obj-C/Cocoa for OSX/iOS, but if anyone has some better guidance regarding all of the other available stuff, it would be much appreciated. I don't think I would want to go fully to the web (I like apps), but perhaps someone could suggest a nice way of bridging what I produce in XCode to a universal web version. For example, if you come up with an algorithm in obj-c is it easiest to transition that to ruby and run it online, or is there another approach that works better?
Mathematica is pretty awesome for the first part of your question. I've used the interactive mode (Manipulate[]) for explaining things to my colleges (and myself). It makes really nice dynamic figures and is fairly expressive (although your code can end up looking like line noise). It is very powerful, but it does far less for you than you might think. It's pretty intuitive, which is a good thing for teaching.
You could use Scala if you want an "easy" way to make a domain specific language for teaching. Python seems to confuse people as a first programming language. Objective C seems like a completely random choice to me.
Mathematica then. It's worth the price. But anything that is interpreted and has an interactive shell is probably better than a compiled language. BBC BASIC?
Nothing beats Haskell for general-purpose mathematical programming. The wiki's quite extensive and the IRC channel (#haskell on Freenode) is great for asking questions. If you statically link your binaries on compilation, you should be able to run your programs on just about any system (with a few exceptions, e.g., libgmp).
Haskell code reads (roughly) like mathematical notation once you get the hang of it, so it can really help to tie things together for your students who are motivated to write their own programs. The purely functional style can be beneficial, as well, since it focuses less on I/O and the marshalling of data (perfectly useful in applications, perhaps less so in pure math), and more on the actual creation and refinement of functions and algorithms. You can even compose functions just as you would on paper.
If you want to get really serious, you could also look into Coq or Agda, but those might be a bit much for most classes.
For a Haskell program idea for an educator, check out this link.
A nice list of arguments can also be found at:
Eleven Reasons to use Haskell as a Mathematician and the book The Haskell Road to Logic, Maths and Programming
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I haven't taken any math classes above basic college calculus. However, in the course of my programming work, I've picked up a lot of math and comp sci from blogs and reading, and I genuinely believe I have a decent mathematical mind. I enjoy and have success doing Project Euler, for example.
I want to dive in and really start learning some cool math, particularly discrete mathematics, set theory, graph theory, number theory, combinatorics, category theory, lambda calculus, etc.
My impression so far is that I'm well equipped to take these on at a conceptual level, but I'm having a really hard time with the mathematical language and symbols. I just don't "speak the language" and though I'm trying to learn it, I'm the going is extremely slow. It can take me hours to work through even one formula or terminology heavy paragraph. And yeah, I can look up terms and definitions, but it's a terribly onerous process that very much obscures the theoretical simplicity of what I'm trying to learn.
I'm really afraid I'm going to have to back up to where I left off, get a mid-level math textbook, and invest some serious time in exercises to train myself in that way of thought. This sounds amazingly boring, though, so I wondered if anyone else has any ideas or experience with this.
If you don't want to attend a class, you still need to get what the class would have given you: time in the material and lots of practice.
So, grab that text book and start doing the practice problems. There really isn't any other way (unless you've figured out how osmosis can actually happen...).
There is no knowledge that can only be gained in a classroom.
Check out the MIT Courseware for Mathematics
Also their YouTube site
Project Euler is also a great way to think about math as it relates to programming
Take a class at your local community college. If you're like me you'd need the structure. There's something to be said for the pressure of being graded. I mean there's so much to learn that going solo is really impractical if you want to have more than just a passing nod-your-head-mm-hmm sort of understanding.
Sounds like you're in the same position I am. What I'm finding out about math education is that most of it is taught incorrectly. Whether a cause or result of this, I also find most math texts are written incorrectly. Exceptions are rare, but notable. For instance, anything written by Donald Knuth is a step in the right direction.
Here are a couple of articles that state the problem quite clearly:
A Gentle Introduction To Learning
Calculus
Developing Your Intuition For
Math
And here's an article on a simple study technique that aims at retaining knowledge:
Teaching linear algebra
Consider auditing classes in discrete mathematics and proofs at a local university. The discrete math class will teach you some really useful stuff (graph theory, combinatorics, etc.), and the proofs class will teach you more about the mathematical style of thinking and writing.
I'd agree with #John Kugelman, classes are the way to go to get it done properly but I'd add that if you don't want to take classes, the internet has many resources to help you, including recorded lectures which I find can be more approachable than books and papers.
I'd recommend checking out MIT Open Courseware. There's a Maths for Computer Science module there, and I'm enjoying working through Gilbert Strang's Linear Algebra course of video lectures.
Youtube and videolectures.com are also good resources for video lectures.
Finally, there's a free Maths for CS book at bookboon.
To this list I would now add The Haskel Road to Logic, Maths, and Programming, and Conceptual Mathematics: A First Introduction to Categories.
--- Nov 16 '09 answer for posterity--
Two books. Diestel's Graph Theory, and Knuth's Concrete Mathematics. Once you get the hang of those try CAGES.
Find a good mentor who is an expert in the field who is willing to spend time with you on a regular basis.
There is a sort of trick to learning dense material, like math and mathematical CS. Learning unfamiliar abstract stuff is hard, and the most effective way to do it is to familiarize yourself with it in stages. First, you need to skim it: don't worry if you don't understand everything in the first pass. Then take a break; after you have rested, go through it again in more depth. Lather, rinse, repeat; meditate, and eventually you may become enlightened.
I'm not sure exactly where I'd start, to become familiar with the language of mathematics; I just ended up reading through lots of papers until I got better at it. You might look for introductory textbooks on formal mathematical logic, since a lot of math (especially in language theory) is based off of that; if you learn to hack the formal stuff a bit, the everyday notation might look a bit easier.
You should probably look through books on topics you're personally interested in; the inherent interest should help get you over the hump. Also, make sure you find texts that are actually introductory; I have become wary of slim, undecorated hardbacks labeled Elementary Foobar Theory, which tend to be elementary only to postdocs with a PhD in Foobar.
A word of warning: do not start out with category theory -- it is the most boring math I have ever encountered! Due to its relevance to language design and type theory, I would like to know more about it, but so far I have not been able to deal...
For a nice, scattershot intro to bits of many kinds of CS-ish math, I recommend Godel, Escher, Bach by Hofstadter (if you haven't read it already, of course). It's not a formal math book, though, so it won't help you with the familiarity problem, but it is quite inspirational.
Mathematical notation is is akin to several computer languages:
concise
exacting
based on many idioms
a fair amount of local variations and conventions
As with a computer language, you don't need to "wash the whole elephant at once": take it one part a at time.
A tentative plan for you could be
identify areas of mathematics that are interesting or important to you. (seems you already have a bit of a sense for that, CS has helped you develop quite a culture for it.)
take (or merely audit) a few formal classes in this area. I agree with several answers in this post, an in-person course, at local college is preferable, but, maybe at first, or to be sure to get the most of a particular class, first self-teaching yourself in this area with MIT OCW, similar online resources and associated books is ok/fine.
if an area of math introduces too high of a pre-requisite in terms of fluency with notation or with some underlying concept or (most often mechanical computation and transformation techniques). No problem! Just backtrack a bit, learn these foundations (and just these foundations!) and move forward again.
Find a "guru", someone that has a broad mathematical culture and exposure, not necessarily a mathematician, physics folks are good too, indeed they can often articulate math in a more practical fashion. Use this guru to guide you, as he/she can show you how the big pieces fit together.
Note: There is little gain to be had of learning mathematical notation for its own sake. Rather it should be learned in context, just like say a C# idiom is better memorized when used and when associated with a specific task, rather than learned in vacuo. A related SO posting however provides several resources to decipher and learn mathematical notation
Project Euler takes problems out of context and drops them in for people to solve them. Project Euler cannot teach you anything effectively. I think you should forget about it, if it is popular it does not mean anything. You cannot study Mathematics through Project Euler as it contains only bits and pieces(and some pretty high level pieces) that you're supposed to know in order to solve the problems. Learning mathematics means to consider a subject and a read a book about it and solving exercices or reading solutions, that's how you learn math. If it so happens that through your reading you find something that is close to some project euler thing, your luck , but otherwise Project euler is a complete waste of time. I think the time is much better invested choosing a particular branch of mathematics and studying that. Let me explain why: I solved 3 pretty advanced Projec Euler problems and they were all making appeal to knowledge from Number theory which I happened to have because i studies some part of it. I do not think Iearned anything from Project Euler, it just happened that I already knew some number theory and solved the problems.
For example, if you find out you like number theory, take H. Davenport -> Hardy & Wright -> Kenneth & Rosen's , study those.
If you like Graph Theory take Reinhard Diestel's book which is freely available and study that(or check books.google.com and find whichever is more appropriate to your taste) but don't spread your attention in 999999 directions just because Project Euler has problems ranging from dynamic programming to advanced geometry or to advanced number theory, that is clearly the wrong way to go and it will not bring you closer to your goal.
This sounds amazingly boring
Well ... Mathematics is not boring when you find some problem that you are attached to, which you like and you'd like to find the solution to, and when you have the sufficient time to reflect on it while not behind a computer screen. Mathematics is done with pen and paper mostly(yes you can use computers .. but that's not really the point).
So, if you find a real-world problem, or some programming problem that would benefit from
you knowing some advanced maths, and you know what maths you have to study , it can be motivating to learn in that way.
If you feel you are not motivated it is hard to study properly.
There is also the question of what you actually mean when you say learn. Does the learning process stop after you solved the problems at the end of the chapter of a book ? Well you decide. You can consider you have finished learning that subject, or you can consider you have not finished and read more about it. There are entire books on just one equation and variations of it.
The amount of programming-related math that you can learn without formal training is limited, but it's more than enough. But maybe you can self-teach yourself.
It all boils down to your resources and motivation.
To know mathematics you have to do mathematics not programming(project euler).
For beginning to learn category theory I recommend David Spivak's Category Theory for the Sciences (AKA Category Theory for Scientists) because its relatively comprehensible due to many examples that enable understanding by analogy and which quickly builds a foundation for understanding more abstract concepts.
It requires the ability to reason logically and an intuitive notion of what is a set. It proceeds from sets and functions through basic category theory to adjoint functors, categories of functors, sheaves, monads and an introduction to operads. Two main threads throughout are modeling databases in terms of categories and describing categories with annotated diagrams called ologs. The bibliography provides references to more advanced and specialized topics including recent papers by Dr. Spivak.
An expected outcome from reading this book is the capability of understanding category theory texts and papers written for mathematicians such as Mac Lane's Category Theory for the Working Mathematician.
In PDF format it is available from http://math.mit.edu/~dspivak/teaching/sp13/ (the dynamic version is recommended since its the most recent). The open access HTML version is available from https://mitpress.mit.edu/books/category-theory-sciences (which is recommended since it includes additional content including answers to some exercises).
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My 7 year old would like to learn, how to program? (his idea not mine, and he does things in the outside world. So, I am not too worried from that point of view. He already went so far as to take a game programming book out of my office to read at bed time.) The other day we sat down and wrote a very simple number guessing game (you pick 8 and it is correct, anything else it is wrong).
It went OK but there were a number of questions he had based on the syntax of the language. (I happened to pick Java as I had the IDE opened at the time.) I teach post-secondary introductory programming courses so this was a bit of an eye opener to me (most students out of high school are reluctant to ask questions) as I really had to figure out, how to explain syntax to a 7 year old?
Clearly any C type language is going to have the same issues, as will most “languages”. I looked at squeak but decided not to use it yet. I looked at the Alice environment but didn't like it for this either.
From a physical point of view he is comfortable with a keyboard/mouse and can put together Lego sets with relative ease (so following directions with a fun outcome works for him). I have access to Lego NXT but he is still a bit young for that (it takes too long to see the results of the work, even with the supplied graphical environment).
Ideally I'd like the experience to help him build up confidence in math and logic (if a 7 year old has logic:-).
I remember using turtle graphics/logo as a child. I am leaning towards this but wondering if there are any other ideas or if anyone can recommend a good logo environment?
Edit 1:
Logo works out well. I'll need to teach him the concept of angles (90 degrees, 180 degrees). Unfortunalty they don't really do division at school yet so angles might be fun...
First off draw a square:
FORWARD 50
RIGHT 90
FORWARD 50
RIGHT 90
FORWARD 50
RIGHT 90
FORWARD 50
RIGHT 90
At some point later I'll go into loops:
REPEAT 4
[
FORWARD 50
RIGHT 90
]
And then variables:
make "length 50
REPEAT 4
[
FORWARD :length
RIGHT 90
]
This works out very well. Virtually no syntax, easy for a 7 year old to remember the vocabulary, and immediate feedback.
Edit 2:
Well it was a success, in that he was able to write a simple program (no loops yet) while I was out of the room. It actually works out very well - we went out and got to graph paper and a protractor, we fugured out 90 degree angles, and he made a bunch of squares, turned a square into a rectangle, and got to see where he went wrong and how to debug it. I'd recommend this approach for anyone with a 7 year old who is interested in programming. I think I'd recommend it to my post-secondary students too (!)
There is actually a browser-based Logo interpreter in Javascript.
http://logo.twentygototen.org/
I strongly disagree with the people who say seven year olds would have a hard time learning new syntax. This is completely backwards. Try teaching pig latin to a seven year old and to a thirty something non-native English speaker. Or try traveling in a foreign country with your kids. See who can chat fluently with the natives after a month (hint: it probably won't be you).
Kids pick up on arbitrary linguistic conventions much faster than us gray hairs do.
I learned how to program when I was 10 in exactly the way you taught your son. My dad used the GW-Basic interpreter that came with our AT&T PC6300, and we wrote a game where the computer asked you a question, and you had to answer A/B/C. The big advantage to syntax in GW-Basic was that you didn't have multi-line statements. You might want to try something similar. Java, with it's curly braces, might be a little tough.
Example code:
10 PRINT "What color is Big Bird?"
20 PRINT "A. Blue"
30 PRINT "B. Green"
40 PRINT "C. Yellow"
50 INPUT$ ANSWER$
60 IF ANSWER$ = "C" THEN PRINT "Good Job!" ELSE PRINT "Oops, wrong answer!"
I spent hours upon hours using various permutations of that syntax and writing my own "games". And it made me want to learn more... might help.
Tell him about parsers. You just need to add context and reasoning to why things exist. The curly braces are so that the machine that reads the code knows where things start and stop.
I find that most people including children pick up things easily as long as you explain the purpose of them. This is why school was a terrible failure for me, no-one ever explaining the point of learning half the stuff.
Scratch is another one. Developed at MIT specifically for the purpose of teaching programming to children.
I think that Python might fit your needs. It is well known for being easier to learn than many other languages and the interactive interpreter allows programmers to immediately see what happens when a piece of code is executed. The IDLE gui that comes with it is easy to use. It also has a turtle module through TKinter.
https://docs.python.org/library/turtle.html
Developmentally, a seven year-old is unlikely to grasp the basics of syntax even in their spoken language.
Whatever language or environment you use, I would recommend focusing on the idea of programming as play rather than the ability to write actual programs. Towards this end, something you can run from a command line and see immediate results, like Python or, for a more graphical experience, Silverlight, would probably be best.
Microsoft has a couple of interesting efforts that seems a nice fit:
popfly: http://msdn.microsoft.com/en-us/devlabs/cc950523.aspx --- "Popfly includes a simple way to create and share games with your friends. Choose from a variety of built-in templates or start from scratch to create a side scrolling game, a 2D shoot-em-up, or a host of others. And best of all, you can get started without writing a line of code" ... I think it can really help being motivated :)
smallbasic: http://msdn.microsoft.com/en-us/devlabs/cc950524.aspx --- supposed to be simplified but having intellisense+.net framework support (the short description is too marketing like, so I didn't paste it :P)
Try Small Basic, which has a mini-BASIC language and simplified for the younger crowd.
Flee from Java! Try something designed for teaching, like scratch, LOGO, or PLT Scheme.
Why not go back to the days of QBasic? That's the first language I learned (actually it was GW-BASIC, but that's beside the point).
The syntax is much easier to get one's head around (albeit fickle and sometimes downright frustrating). It doesn't teach anything OO, but that's probably above his head anyway, as it would have been mine.
This site may also be of interest.
I'd say use visual basic, or something similar where you don't have to worry about syntax, curly braces, etc as much. I was programming at 7, but it was in LOGO and C64 Basic. I HATED LOGO ... it was so frustrating to me that one of the "big" things you could do was move around a stupid turtle. However, C64 Basic (to me) was great ... once I had that down (a couple years) I was psyched to learn C and even C64 assembler.
Two thoughts come to mind:
My 3 year old son loves playing World of Goo with me. He can't solve problems yet, but I can see he is soaking up loads of information.
Have a go with Alice. My son is too young to try this, but once he is older we'll give it a go if he is keen. FWIW I learnt about this program after watching The Last Lecuture by Randy Pausch (R.I.P)
Have him check out http://scratch.mit.edu. My seven year old is learning this as we type...
Etoys is perhaps the thing you're looking for. It's a partly graphical flavour of smalltalk made just for children. This is used by the olpc project.
I was involved with a primary-grade computer course using Stagecast. This is a graphical programming language designed for children. I found it an ideal introductory language because it is graphical and interactive. It does not require reading or mathematics, it runs on Windows and Mac OS, and is ideal for simple games so children are motivated to learn.
While it appears that it is being redesigned, you can still get the old version of Hackety Hack, which is a ruby programming kit designed by _why for teenagers and beginning programmers.
I am a bit torn about Alice.
On the one hand, it is nice to have a framework where you can program with direct visual gratification. This is really a good idea.
On the other hand, I think that it is a very bad idea to have beginners program exclusively by drag and drop. I fear that this might even lead to a sort of illiteracy, where they are unable to produce properly written code when the drag and drop interface is taken away.
Personally, I think the basics of arithmetic operations and Boolean logic are more important to teach to a child first. After they have grasped these concepts then I think moving on to the basic constructs are appropriate. I just don't see how a child could understand conditionals and looping without Boolean logic, but then again, there are some pretty bright kids out there :)
Assuming the previous statement is met, I would have to cast my vote for python.
I would have looked for one of the many arcade game engines and let him play with that. Choose one where he will need to use loops and conditions, and maybe some procedures.
There a book called Learning to program from pragmatic that is geared towards people who have never programmed before and might not be extremely technical.
It uses Ruby which can be quite easy for new people to pick up.
Squeak Smalltalk system is an implementation of Smalltalk that I have heard much good about when it comes to educating children in programming.
The Etoys project supposedly contains lots of resources for keeping the learning experience fun and motivating.
I became interested in programming when I was introduced to Turing language in high school. Turing was used as a teaching language in many schools at the time, and it worked very well for me to introduce programming concepts. Here is a description of Turing from WikiPedia
Turing is a Pascal-like programming language developed in 1982 by Ric Holt and James Cordy, then of University of Toronto, Canada. Turing is a descendant of Euclid, Pascal and SP/k that features a clean syntax and precise machine-independent semantics.
Named after British computer scientist Alan Turing, Turing is used primarily as a teaching language at the high school and university level. Two other versions exist, Object-Oriented Turing and Turing Plus, a systems programming variant. In September 2001, "Object Oriented Turing" was renamed "Turing" and the original Turing was renamed "Classic Turing". Turing is available from Holt Software Associates in Toronto.
Versions for Microsoft Windows, Linux and Apple Macintosh are available. Turing is still widely used in high schools in Ontario as an introduction to programming.
In November 2007, Turing, which was previously a commercialized programming language, became freeware. As of November 28, 2007, it was available for download from the Holt Software website free of charge for personal, commercial, and educational use.1
You could also use Commodore 64 emulator. It start's right from BASIC.
Might as well throw out Lego™ Mindstorms™ as a possibility. It uses a graphical programming language based on LabView.
I read this post earlier today, and then by chance accidentally went to YUP.com and discovered
Teaching Kids to Hack(Program) with Hackety Hack
Figured I'd post it as an additional resource for anyone looking at this question.
I recently responded to a similar SO question with a pointer to kidbasic, which is open source and cross platform software.
Scheme is nice and syntactically similar to Logo, in the respects of simplicity. Also Scheme offers a very intuitive way of understanding recursion and picking up these type of fundamental concepts in computer science that early on is nothing but good with more good.
UCB Scheme also offers a lot of built in functionality for manipulating sentences, which may make more sense to a 7 year old than constructing polygons and solving number puzzles (not to say that the sky's the limit!).
I was typing programs from the book "BASIC Fun" when I was in 2nd grade.
I distinctly remember that the concepts of infinite loops and INPUT A$ was like discovering gravity. Heady stuff.
Self taught, my progress was glacially slow, although I did reach a point in a program where I wished that GOSUB took variable arguments, which in retrospect meant I understood function pointers.
My early goals included writing LONG programs. A lengthy program not a bad goal for a 7 year old because a program with a well defined spec makes the risk of failure too high. Anyone can write a long program and feel good about it and learn a lot along the way.
There was a whole genre of books for programming in BASIC for kinds from the 80s. That stuff is a great source of programming ideas. However I wouldn't recommend using BASIC even for a 7 year old-- lua has the simple feel of BASIC but it isn't broken crap.
Look no further, there's actually an entire learning platform/ OS designed for this very purpose: Sugar.
The OLPC (One Laptop Per Child) operating system called Sugar is now available to the general public and you can run it as a VM within all major operating systems such as Mac, Windows and Linux.
Download a copy at Sugar Labs.
One interesting activity included is called TurtleArt, a souped up 21st century version of Logo. Also has a kid friendly version of a Python IDE called Pippy. It actually teaches kids Python!
See TurtleArt and Pippy and the other activities found in Sugar.
Alan Kay was behind some of the novel concepts in Sugar OS which is actually a modern incarnation of his visionary DynaBook. Even as an adult (who's an engineer), I find it fun to play with.
And if you love Sugar as a VM, you can even buy the hardware and at the same time help a poor kid somewhere else in the world.
Engadget explains : OLPC XO Buy-One, Give-One program underway
As a bonus to us adults, Sugar is derived from Fedora. So it's a real and complete Linux based OS. Should be fun to hack. ;-)
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It has been discussed on this site before about the relationship between math and programming, and whether one is a subset of the other, etc.
In my recent study of programming, I've found myself more and more wishing I was better at math. You all know the scenario when programming books start to generalize something in a math way ("Therefore, we may say that for all <some single letter>, <lots of letters>"). My eyes glaze over in such situations. I know that that is mostly due to me being stupid, but it seems that if I could just improve my higher math skills, maybe I could get more out of such things.
Major question: Is math indeed something one can "get better at," or is your brain kinda either wired for it or not?
Important follow-up question: If the answer to the above is yes, then what are some ways to go about it?
I think anyone can get better at math. You just have to be determined and practice.
Part of the problem is that math books tend to be written by mathematicians who ceased being math novices decades ago. What you want is books geared to your level and which contain material you can work with.
Some recommendations:
If you can find a copy, get Mathematica and a good book on it (the Schaum's outline is actually pretty good and cheap). I use it all the time to visualize things.
As a programmer, you probably want to aim more for discrete mathematics than calculus.
The Concrete Mathematics book mentioned elsewhere is excellent.
Most introductory discrete math texts have good coverage of the things like logic, sets, combinatorics, probability, graph theory, etc. My school used Rosen's text which I liked.
Linear algebra is useful if you are going to do 3D graphics programming. Most intro texts for engineers will teach you what you need to know. Linear Algebra Done Right is probably the best on "real" linear algebra if you want something more theoretical.
Look for books by Martin Gardner and play with his puzzles. He's an excellent writer and teacher.
Remember that math doesn't change that much. You can get used books for cheap on Amazon and in used bookstores. I always look for the n-1 version when I buy textbooks.
When you first started learning English all those "symbols" (letters) looked like gibberish to you. I'm sure that at some point you were frustrated over your lack of understanding. But slowly, and gradually you began to understand them.
Eventually you were able to construct your own words and sentences using these symbols. After being corrected on it's structure and grammar for years you now have a command of the language.
Math is just like that. Your eyes glaze over because you haven't learned the language. Maybe in school you didn't particularly enjoy math because you didn't see any practical applications for it. Certainly the way we teach math to our students is atrocious, so it is no wonder why many get through school without being well versed in it (for further reading, check out A Mathematician’s Lament which discusses how horrible our current method of teaching math is).
However, it is never too late to get up to a degree of proficiency that will allow you to read many academic Computer Science writings. Start out with Pre-Calculus at your local community college at night (to brush up on everything you have forgotten). Then move on to Calculus and after that take Discrete math. Honestly, this is all the math you will need 99.99% of the time. In less than 2-3 semesters you can be fully caught up and you'll no longer have your eyes glaze over when reading something with some mathematical roots.
I can share my experience...
I have been terrified of math since grade school. Hated it, didn't get the point, didn't pursue it.
By contrast, I have always been fascinated by computers. I study programming from a "need to know"- I can't stand not understanding computers and programming from the lowest to highest levels. I am almost completely self-educated, and have a career as a programmer/architect.
Last year, at my wife's urging, I began to go back to college. I signed up for a remedial Algebra class, knowing it was going to be a pain. It wasn't.
Somehow, through all the years of learning to develop OO software, it seemed that I had tricked myself into learning how to think mathematically. The concepts just weren't that difficult anymore. It may be that I had learned to think in terms of complex systems made up of smaller, less complex ideas.
I am now researching game development, and that is some seriously math-oriented programming. WAY more so than the business development I've been doing to this point. However, I don't find it so daunting because it's applied mathetmatics. Working to solve practical problems seems to make the study less tedious and far more interesting. I have found Wikipedia and Wolfram's Mathworld to be helpful. If you already know how to program, you're ahead of the game learning math.
I'd say it's certainly something anyone can get better at. It takes time and patience and some texts are obscenely dense as far as the notation involved, but if you're willing to put the time in, I think it shouldn't be too horrible.
I'd check out Wikipedia's list of mathematical symbols, and keep if nearby whenever you see a large blob of symbols pop up. Translate them one at a time and put them together in the way that makes the most sense to you (or ask us a few times until you get the hang of it).
It's both. You can get better at math. But you're also indeed limited/endowed by the particular wiring in your brain. What that means is that most likely you can improve your current mathematical skills. However, because of your mental hardware's limits, you may never discover a new theorem.
And when it comes to improving, I think the way as always is to practice. To read mathematical literature, to try to solve mathematical problems and eventually, develop an outlook where you are able to break, as a matter of habit, real-world conundrums you see before you down in mathematical terms.
As for programming's relation with mathematics, I think there's a pretty strong one. In fact, one could argue that a program is nothing but a proof of a theorem, the requirements document being all the inputs to the proof.
Your skills get rusty if not used and knowledge fades with time if not used.
If you don't use your math skills you soon have no math skills. Continuous new learning and practice of the skills you already have will lead to you one day being a math/programming master.
Project Euler has lot of math problems that can only be solved through programming. The problems get more difficult but build on the skills and knowledge acquired in your previous solutions.
I also buy some interesting textbooks at second hand book shops. Their cheap and slowly your skills improve. I use them in conjunction with MIT Open Course ware.
A fun way to practice math is http://projecteuler.net/.
Although it's less systematic/effective than doing a course or reading a textbook.
I know exactly how you feel. I've always wanted to learn more Math, but as I was unable to do it at college after school (not enough space) and not able to take it at university (not able to with a CS degree) I'm still yet to study Math formally since the age of 16.
Math is something that anyone can learn. Some will argue that it gets harder with age but I've met people going on for 60 that are taking Math classes with ease. There's one woman at my university that's going on for 70 and she's a few months off of graduating with a degree in a Mathematics related field. If you want to learn Math then now is the right time, although I'll be the first person to say that it is not easy. Whilst you'll find many of the problems extremely easy with programming experience you'll still find that going through a set of problems takes a lot of time out of your day. I almost finished the MIT OpenCourseWare course on Linear Algebra, then ended up getting a new part-time job, working 10 hours a day, 7 days a week, and forgetting the majority of what I had learnt.
That being said, if you have the time and true dedication I can recommend some links to video lectures that may just help you get on your way.
Pre-Calculus Algebra
Pre-Calculus
Calculus
Applied Probability
Introduction to Statistics
Differential Equations
Linear Algebra
I'm not saying that this is what you need to know. This is what I've set out to learn myself before I graduate from my CS degree, so feel free to pick and choose whatever you feel is best for you.
Studying math is like getting a classical education, one specially suited for programmers and other computer professions. And math's the sort of thing that you can appreciate more as you get older. You realize that it's not about grinding out answers so much as it's about thinking deeply and conceptually. The "answers" you might grind out make a lot more sense that way.
At one time, I would have recommended taking a geometry course, and take some time to learn how to prove theorems, see how the concepts flow together. These days, though, I'd say it may be better to take a course in discrete mathematics. It's much more practical, and there's a lot more variety, but there's still enough theory in there to make it challenging if you want.
Discrete math also provides you with programming challenges you might not have thought of before. Maybe you can hack up a good heuristic to solve an NP-complete problem, like an N-city Traveling Salesman problem. Maybe even come up with a couple solutions, and test which ones work best in which circumstances.
(I never took CompSci classes in college. You can probably tell.)
Go to the local community college and sign up for Calculus 1. This covers functions in the mathematical sense, and has a rigorous refresher course on algebra, and will use just enough of the symbols to get you ahead.
First of all, I would recommend Steve Yegge's Math For Programmers. It pretty much sums up your struggle.
And now I would like to tell a personal story. I was a double major in Math and CS. I learned a lot in the Math classes, but I honestly didn't appreciate it as much as I should have. I will tell you that a lot of things that I did have helped me in my programming career. And it's not about some formula or knowing calculus, or any of that stuff. It's that a solid Math background teaches you how to think in order to solve a problem. To me, that's the Math that you need.
1) Yes.
2) Explore mathematical questions which sound interesting. Buy/read books that give you the information needed. Repeat.
It can absolutely be learned. I personally had the most benefit from the math (especially proof) courses I took in college.
Recommended courses:
Discrete Math
Mathematical Thought
Abstract Algebra
any other proof courses
Recommended book:
The Nuts and Bolts of Proofs, by Antonella Cupillari
I strongly recommend trying to take one or more of these courses at a school of some sort. Find a local college and audit a course.
A 2nd vote for Lockhart's "A Mathematician’s Lament", which recommends that math be taught like painting, poetry, or music -- not for it's practical usefulness but for simple pleasure:
There’s no
ulterior practical purpose here. I’m just playing. That’s what math is— wondering, playing,
amusing yourself with your imagination.
Look at the diagrams in a recent Knuth paper, Dancing Links, and tell me he wasn't having fun making those.
Part of the problem is that a few mathematical symbols convey a heck of a lot of information. If you are reading a normal programming book, it is full of words and code. Neither of these is super verbose (although I often have to slow down much more on code than normal words). However one complicated mathematical equation can easily be a screen full of programming code or words. We have all sorts of simple notations that convey complex processes.
Another issue is that notation is standardized but not exactly. Different books use slightly different notation so it takes a while to get used to it. Also many textbooks leave out key steps in mathematical proofs or even examples. Sometimes even college professors puzzle themselves with the missing steps in a given proof in a textbook and then give their own proof, or give a slightly modified one over the one in the book because they learned it differently or can't recreate the missing step exactly which takes the proof in a different direction.
So anyway just because your eyes glaze over doesn't mean you have to give up. The first time you see the equations you will probably be in read the english text mode and have to pause to consider them. Going over them slowly and paying attention to what all the symbols mean one step at a time may yield the answer for you. If there is some notation you haven't seen before, there is probably an intro chapter or appendix explaining the notation, so check there. Finally, look for other sources. Use google/wikipedia to look up equations for the concept and you may find a derivation and/or proof that you can follow. Additionally the other one may help you to understand the current proofs/derivations better. Even if your understanding of the proof/derivation does not improve, your additional research will probably aid in your understanding of the equation.
I think there are two things to learning math:
1. Learning the general techniques. Ie how to add two fractions, how to differentiate, integrate.
2. Learning to problem solve and apply math to the real world.
I think by picking up math textbooks yo will learn 1. Many math textbooks are organized by section where there will be a few pages showing you a technique and then a bunch of problems. The problems tend to be related to the technique that you just learned and very similar. Ie a section on logarithms will have all problems on logarithms and probably won't include any polynomials. By doing the problems in the section you will learn the techniques. The more problems you do the faster you will get and the more you will understand the concepts. Many times you will find if you work through the problems without explicitly memorizing the formulas, you will find that after you do enough the required formulas will be implicitly memorized. Ultimately if you are having trouble looking at probability formulas you will want to read a probability book. If you are having trouble with sum notation you will want to consult that section of an algebra book, etc...
To learn 2 I think math textbooks don't help as much because each section tends to have problems related to that section. Occasionally there are a few "mixed review" problems or a "chapter review" which mixes problems, but they are typically far in between. Science textbooks like Physics, Biology, Chemistry, etc. tend to be better for this. There you often read the problem, lay it out, and end up using a variety of mathematical tools to to solve it. Sometimes calculus, linear algebra, and geometry all within the same problem. The value here is that it teaches you to problem solve. Generally the SAT/GRE do not test if you know how to do Algebra, they test if you know how to apply it to the real world, and the science problems really help you here. Also programming in general is about problem solving and the better you get at problem solving the better you'll be at programming. Basically in programming you take problems, create a mental model, design a solution, and then model it in your programming language of choice. This is similar to say Physics. You look at the problem, extract a mathematical model, design a solution, right down some equations with the model of the solution, then plug numbers in. I highly recommend physics because after my college physics class word problems became simple for me and they used to be quite difficult (though not impossible).
In day to day programming you probably won't use more than algebra and logic (for if statements and loop conditions). There are some places that use high math like computer games, cryptology, data mining, etc. but for a typical business application you probably won't use more than algebra and logic and maybe a bit of set theory (the stuff so basic you already internalized it). Even in places that use high math (like financial companies) often the business users (or some industry literature) will have done the higher math and you will just need to implement the equations (with some algebra). I only mention this because most programming books don't have more than algebra and logic either, unless you are reading textbooks on Algorithm Analysis (Introduction to Algorithms), Artificial Intelligence, or some other research area. General application books on how to do things are usually short on math.
But depending upon what you are reading math can help. For most computer science algebra + discrete math should be enough. Couple that with some physics practice and you should be good to go. It may still be a slow go but you should have the proper background.
I like combinatorics and algorithms - having fun you learn faster.
study study study!
wikipedia is actually a fairly good math reference. start with something you're interested in learning and follow links until you understand all the building blocks for that initial thing.
practice practice practice!
Schaum's outlines are good for this. If you're interested in probability (which touches on combinatorics), see 50 Challenging Problems in Probability.
Short answer:
There may be people who are to stupid to get good a maths. But those people generally are to stupid to program, too.
So if you have some skills in programming, you might consider yourself smart enough to learn maths as well.
Note: I know there are smart people with a serious math learning disability, but I think thats more like an exception.
I would also recommend project euler While it does not exactly teach math, it gives you problems that you can then look up how to solve. I've always preferred solving actual problems instead of just learning theory.
Math skills are becoming more and more essential, and I wonder where is a good place to brush up on some basics before moving on to some more CompSci specific stuff?
A site with lots of video's as well as practice exercises would be a double win but I can't seem to find one.
It depends on your math level. You should start by revising what you should know till that moment and then go further to algorithm mathmatics, geometry (transforms and etc), statistics and more.
There are tons of places on the internet were you can learn:
http://www.math.cornell.edu/Courses/courses.html
http://ocw.mit.edu/OcwWeb/web/courses/courses/index.htm
http://mathworld.wolfram.com/
and the list is open.
I recommend Project Euler if you want to train number theory and discrete maths. Lots of fun exercises, though you need to know a bit of programming.
Steve Yegge had a good blog post Math for programmers
Quoting some of it:
"But a few things I've learned recently might surprise you:
Math is a lot easier to pick up after you know how to program. In fact, if you're a halfway decent programmer, you'll find it's almost a snap.
They teach math all wrong in school. Way, WAY wrong. If you teach yourself math the right way, you'll learn faster, remember it longer, and it'll be much more valuable to you as a programmer.
Knowing even a little of the right kinds of math can enable you do write some pretty interesting programs that would otherwise be too hard. In other words, math is something you can pick up a little at a time, whenever you have free time.
Nobody knows all of math, not even the best mathematicians. The field is constantly expanding, as people invent new formalisms to solve their own problems. And with any given math problem, just like in programming, there's more than one way to do it. You can pick the one you like best.
Math is... ummm, please don't tell anyone I said this; I'll never get invited to another party as long as I live. But math, well... I'd better whisper this, so listen up: (it's actually kinda fun.)"
I will be boring and recommend actually taking university courses in math.
Without lectures and lessons with an assistant I know I would never be able to learn as much as I have. I just need some kind of motivation, since higher math is really hard.
That is, if you are looking for quite advanced stuff and actually want to get a deep understanding and don't want to crunch numbers. Crunching numbers is why we have MATLAB ;)
It would be good to know what level of math you have, and what you want to do with it. But I guess calculus, linear algebra and discrete math are the most useful courses to take.
I suggest books with good tutorials throughout if you're unable to partake in a maths course. For computer science-related maths Don Knuth's Concrete Mathematics is meant to be very good.
Obviously nothing can replace a good teacher, but good tutorials can come pretty damn close. You really get to learn the subject in the tutorials I think.
Get some videos from www.aduni.org
Math courses
It's a couple of years since this question has been asked, but there are a number of new sites and resources available now:
Khan Academy was originally intended for schoolkids, but it has since expanded to include material that would not be out of place in first-year university courses. It serves as a great way to review and fix fundamentals. It has videos and practice exercises, and keeps track of your progress.
EdX is an evolution of initiatives like MIT Open Courseware. It's now an alliance of universities like MIT, Berkeley and Stanford that offer free online university level courses, with video instruction and learning materials. My only complaint is that some of their courses have prerequisites (like single-variable calculus) that you need to pick up elsewhere, like Coursera, or the original MIT OpenCourseWare site.
Coursera offers more courses than EdX, and many of them are more basic, covering topics like pre-algebra and pre-calculus. The learning interface is not quite as cool as EdX's (which offers a scrollable captioning interface alongside most of it's videos), but the broader range of topics and courses covering fundamentals offers learning you just won't find on EdX.
A lot of the universities will actually publish their lecture materials online. So all you really need to do is find a suitable subject and then read the lecture materials and do the associated work. If you were really sneaky you could probably also go to the tutorials to get help :P
BetterExplained.com has some great math lectures. Its not video lectures but the author gives easy-to-understand explanations on math concepts.
Don't forget that iTunes now has available a load of maths lectures (and other subjects) from various mainstream universities - and all for free.
Since you want to brush up your math
I would suggest you to do a G search on UCCS math online
Or follow this link , and after registering yourself free you can browse the archives
I must say that It's common that you will find people recommending course X .
But rarely will you find people completing their recommended course ..
SO IN the case of number theory you must go for the latest course , the last offering has not high quality video ..
Also for Discrete Math ->There are no lecture notes on this site
So you have to figure out how to establish correspondence two online course (6.042 has good P sets and Notes) And The above Math course for Discrete Math .
I would discourage you to use YouTube (x minutes ) tutorials , Because most of them cover Math like History ..
A good course can be found by G searching Harvard OlI--
It has probability (Non Continuous) - There are P sets without solutions ..