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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
I have an idea for a business that requires a well designed web application. I'm not a rocket surgeon, but I'm smart enough to know that you get what you pay for and am willing to pay for talent. However, I want the development process to go as smoothly as possible and would like to know how to make that happen.
So, what information do developers need (or want) initially from the owner to avoid having to make assumptions about business (or other) requirements? Do I need to create state transition diagrams or write use cases?
Essentially, how do I take the concept in my head and package it in a way that allows the developer to do what they do best? (assuming that is creating good software. haha)
Any advice is appreciated.
Shawn
You may need to reword your question, as it is too general to get a good answer, so some vague details would be helpful.
But, the better vision you have of what you want the smoother it will be.
I find UML diagrams too confining, when you aren't going to be doing the work, as you may not come up with the best design.
So, if you start with designing out what each page should look like, as you envision it, then you can write up use cases, which are short scenarios.
So, you may write up:
A user needs to be able to log in using OpenID.
This will tell the developer one function that you want, and who you expect to do that action.
But, don't put in technologies, as you may think that a SOAP service is your best bet, but upon talking about it you may find that there is a better solution.
Use cases are good points to show what you are envisioning, and give text to your page designs.
Talk to the developers. Explain what you want and why you want it. Together you make the flow charts and whatnot. Writing requirements is part of the design process, and it's a good idea to have the developers onboard as soon as possible. Start simple and small, then grow and expand while iterating.
In talking over web services before, I have found the best starting point is drawing on a sheet of paper what you think the site will look like, and add in a few arrows from things you want clickable to the pages that should result. Keep it simple, nothing too fancy, and hopefully you and the developer can come to an understanding of what you want pretty quickly.
Use cases might be best for checking off all the points later in the project about how complete your site is; I haven't really found it to be a helpful starting point, but I'm sure others disagree. (They just seem too tedius to read when actually writing code.)
Same with state transition diagrams; they are too tedious and I think most developers will assume you made mistakes in them anyway. :) Everyone else does... Unless your project hinges very tightly on the correctness of a state machine, I wouldn't really bother.
This book contains some good advice on what constitutes a good statement of requirements from a programmers point of view. It also has the useful guideline of not trying to set the form of your requirements too early, and a substantial piece on describing the problem you are trying to solve.
I like UI mockups based on actual program/site flows e.g registering a customer or placing order. Diagrams/pictures of GUIs with structured, consistent data examples are unambiguous.
I agree that UML and use cases are only really useful if everyone speaks UML and the projects are of sufficient complexity (few are).
You may want to read up on Agile/Scrum techniques. These are becoming a sort of standard and when properly managed can save weeks of development time.
I find that words don't do a good job of communicating how a system is supposed to work. Wireframes, white-board drawings/transition diagrams, and low-fidelity prototypes are great ways to communicate a concrete idea. One example of a low-fidelity prototype is a "clickable" paper prototype that allows a user to touch "buttons" on paper to go from one drawing to another. It costs very little time (cheaper), but goes a long way to communicate an idea between two parties.
Stay away from formal documentation, UML diagrams, or class (technical documentation) diagrams that don't speak to you. This is what large, risk-averse companies move toward to be more "mature". These are also byproducts of an idea that is hashed out, and it sounds like you're in the hashing out stage.
I'm a hobbyist game programmer. I only do 2d games, no 3d stuff. I don't have a math background and lots of things are tripping me up like bullet projections and angles.
I took two college level Algebra courses at the local community college, but really disappointed. I got As in both, but really don't feel like I'm using any of it in my everyday 2d game programming and still stuck on angles/bullet paths, etc
I dropped out this semester to self study. The advisory at the community college said I want to be in Statistics for this and was really pushing me hard to enroll in that class. He said Statistics then Calculus I & II would get me what I needed.
I've been reading up a lot and not so sure on this. I think I should start with a a Geometry book and then move into Trigonometry? Is that the right approach?
Anyone suggest any good self-study starter books?
I got a lot out of "3D Math Primer for Graphics and Game Development". I know it says 3D but there is a lot of stuff in there for 2D. And the math is fairly simple linear algebra.
It sounds like statistics is useless for what you want to do. Calculus might be marginally useful, but not until you are really solid with it. You probably need to learn trigonometry more than anything else. I could offer more explicit advice if you give an example of a problem you're trying to solve.
There are a few points here:
1) The statistics suggestion is a complete misdirection, and this advice should be completely ignored, along with the person who gave it to you. Statistics is an interesting topic, but not at all useful in game programming (except maybe for a few esoteric approaches to esoteric topics, maybe, like, drawing clouds).
2) (Not that you seem to but...) it's not uncommon for programmers to make the mistake of assuming that they can just learn everything on the job, but most science topics (including math) can not be effectively learned this way. With these, one needs a much more structured approach, building an elaborate structure of ideas, with each new idea built on top of the previous. You could certainly program games with a few equations that you learned to use from a game programming book, but it's unlikely you'd ever have the ability to solve problems that you hadn't already seen solved somewhere else.
3) The best way to get comfortable with math is to solve lots of problems, and not on the computer, but with pencil and paper. For example, you can easily write a program to test that sin2+cos2=1, but to prove it, you need to understand it.
4) Of the topics you'll need, trig is the most time effective place to start. Geometry would be a bit useful, but probably not so much. Another useful topic is linear algebra. Calculus is also useful for calculating trajectories that have acceleration (and gravity), but it's a much bigger topic and involves so many new ideas that it's probably a bit difficult to pick up on your own. Maybe for this topic it's best to try to glean a few useful approaches and equations.
Final suggestion: I recommend starting with trig, and use a book that gives concise explanations followed by lots of problems that are solved in the back. For example, Schaum's Outline of Trig for $13, would probably be a good choice. You don't need to solve a every problem in the book, but work them until you're comfortable, and then move on.
I'm a big fan of functional programming in general, Schemes in particular, and PLT-Racket ideally. I am wondering what concrete steps are likely to get me into a position where coding Scheme (or some functional language) is the bulk of the work.
I'm actually quite interested in academia, but on the other hand, I don't feel like I necessarily have what it takes (at least not at the moment) to do a top-tier Ph.D in CS. I definitely would prefer to have some real-world experience putting complex systems together in Scheme either way. Does anyone have any advice for an aspiring Schemer?
Start writing some Scheme libraries, then blog about the libraries you've wrote, get noticed in the community.
This will always give you leverage when applying for a position, employers like to have some evidence of what you can do.
dalton has the right idea; you want to build something you can show off. To find out about needs, you could go to http://srfi.schemers.org/, which is an archive of proposals for Scheme libraries and other improvements to Scheme, and see what you think you can contribute to. Or make contact with the Racket team; you may be able to contribute to Racket directly.
If you want to leverage something popular and in the news: App Inventor is based on Google Blocks, which are in turn based on Kawa, which is a Scheme dialect [*].
If you can show off your skills by putting together blocks and making them available for the community...it's a natural way to take advantage both of your multi-language skills and something currently getting press coverage.
Regards,
Dak
[*] and I forgot to say that earlier, mea culpa!
Not going to accept my own answer because it is, in general, worse than the one #dalton gave, but!
I got a grant through Turbulence.org to write an art and thus was paid to scheme! Or racket, if you want to be a pedant. repo here...
F# is getting popular in the finance sector:
http://cs.hubfs.net/forums/thread/16004.aspx
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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).