The role of a programmer is to write the code needed to host things like websites, software, or other digital programs. a moron wrote: Anonymous said... "This is the dumbest thing that I have read in a long time. I just can't see anyone arguing persuasively that trig is more widely useful than probability and combinatorics. A nice place to learn linear algebra is a set of free video lectures of Gilbert Strang's MIT class at:http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/VideoLectures/index.htmIt's a great resource for learning linear algebra, or for anyone who wants to learn how to teach an abstract subject.Actually, lots of the MIT OpenCourseWare stuff is a good resource. And you know what? No domain knowledge of any kind in solving real world problems (even basic laboratory exercises would help); and little intuitive feel for when a result makes no sense. ....Come one quater where I did a project with some physics simulation with springs. I wanted to do better than all the people who had taught me in college and really explain what was going on to my classes. You can see more snippets later in the book… Students who learn without calculators "get it" in a way that those who use them just don't.I would emphasize building things and geometry very early on. Programmers get paid well because the work involves skills many people do not have. These instructions are programs written to tell the computer what it needs to do and how to do it. Nope. Can I use math? What remains after all the years is the interestingness of self-referential and recursive things. Programming languages make the creation of websites and programs possible. I used to hate math, then I started playing with Flash and become interested in math as art, it really is beautiful. I, myself,would advocate taking Geometry out of the high school list. Through it, you’ll be able to follow clear steps for practicing web development and solving a range of programming problems. Those who try to do functional programming and repeditive calling of functions(technical term escapes me right now) usually have absolutly NO idea how to solve a complex function.. Once tought how to do the function maths correct, and THEN teaching the programming they get it every time..There are some maths that needs to be tought before Programming, but theres alot more maths which should be tought after the basic techniques of programming.. that may sound stupid to a non-computer person, but how often will you see in a school someone who enjoys using computers -- particuallly programming -- suceed and understand the work alot easier? I like the idea of breadth first, for instance. Maths needs to be taught basics first, can you remember what the first Maths you were taught in school? And than one must do zyllions of problems to deepen the knowledge and like that for 20 years. I almost never leave comments on blogs ... but this one really hit home. where this is important when you need to find the greatest common divisor (important in cryptography applications).For logic I recommend book that I used in philosophy The Logic Book. Engineering firms employed roomfuls of engineering graduates who hand-drafted blueprints and solved calculus equations. Many experts in the field find success when they pursue multiple variations of coding languages and processes. I think universities should tailor an applied-math-for software engineers type of class and teach it using the methods/content you suggest. Calculus (with trigonometry)is the most powerful mathematical tool there is, because most situations are modeled with functions which are continuous. Thank you! Sometimes, defined by the same word I'm looking up!At this point I realize that I am seriously crippled in my math knowledge. Having said that, the book did provide a refresher on the product and chain rules and partial differentiation. Everything I do nowadays is designed to drag NP-complete problems into the realm of the tractable, by any means possible. Lead by the joke, once I realised what they were, and how the math teachers were fooling us the students teaching us continuous maths. Then trig becomes hard. It teaches three critical parts of developing web content that many books don’t cover all at once. It turns out that this kind of analysis could be done for most services - telephone computer tech support comes to mind first - to much benefit.So really, each field has a number of tools and techniques that can be brought to bear on a problem. Use Dave4Math and learn more about academic topics today. If that wasn’t enough, more is in store for the field. the simple fact is that the number of programming jobs is rapidly outpacing the demand for all other engineering roles.No, no, it isn't. Take a look at several key areas of focus worth learning. The learning experience takes multiple years for technical fluency and still requires substantial experience before someone is genuinely exceptional. Keep it up!! The springs were exploding! In order to learn math + all other subjects in school average human must sacrifice youth from age 11 to it and give up many things most of us consider important. So the lesson of this article is : "learn what you need to know to do what you want to do. The biggest trouble students have is being convinced they can't do the problem and not trying but if you try and make the students do real math with real thought they rebel and just give up on them (either they are so simple they come up with a rote algorithm that almost always works and you haven't gotten anywhere or they areare sufficiently hard the students just flounder).You might think you should just start earlier and the problem is that by college the students have already internalized the rote approach to math. You can be a good, solid, professional programmer without knowing much math. Anyone else think this guy is out to lunch on this topic? Math is... ummm, please don't tell anyone I said this; I'll never get invited to another party as long as I live. The 'point' of all the Geometry proofs appears to be overlooked.It isn't so much learning 1/2*base*height for a triangle's area. Thanks.Then:1) One STILL cannot get away with saying "I read it on wikipedia" (get some public official endorsement for it and that will probably change - then: get it and probably wikipedia will lose editors)2) There will be times in life you really has no damn calculator handy or you can't trust one, (hey, TCPA is coming! Here's a great book that's been challenging me for a couple years:David MacKay: Information Theory, Inference, and Learning Algorithms The whole thing's online, too. The course roughly follows the contents of Rosen's book I mentioned earlier. You should write a book man. Math isn't easy. Most Comp Sci-only undergraduate programs seem to leave the graduate with knowlege of a few languages, some algorithms, and precious little else. Please be warned that the problems are challenging and you are unlikely to make much progress if you have no knowledge of programming. I'm not sure about this. Talks about all the right things.. And most of it is deja vu for me, like when you talk about the summation and forloop. Math is a lot easier to pick up after you know how to program. Most subjects like history, English or even Science (bio, chem, physics) are somewhat orthogonal, where you can learn one subject without the others.3) We need to know "why", not just "how". In this blog, we will talk about some of such topics. The importance of coding is clear to big businesses, but small companies are also learning to invest in these experts. Picking which one to use is dependent on considerations that range from the requirements of the final product to the personal skills and preferences of the programmer vs. a more particular developer. You can discover an idea of the vast applications for programming by reading the programming articles here. my response ... "well ... you might be held hostage by radical member of the Isoscelic group Al-Gebra ... and one of those memmbers might put a gun to your head and say ... 'Solve this or die!!'" You mention that because you are a programer you know what a function is, and what it does. That's the thing that's changing your point of view of problems. would do much to remove the "mystery." I mean no one really needs all that practice integrating weird trig functions, either you need to really understand it and you can then just figure it out or you can use mathematica. At Tachyus, we build software that uses physics and machine learning to optimize oil and gas fields. It is an excellent (and broad) introduction to the subject. Having a firm grasp of the mathematics underlying both natural and computational processes is invaluable.Somebody else already mentioned it, but Mathworld (mathworld.wolfram.com) and Wikipedia are both great for understanding and connecting mathematical formalisms with their related concepts. I learned to understand summation as for loop, the hard way.I have stumbled on other posts of your blogs also a few times. I think when a lot of people leave school they just doing continue to expand there brain and slowly you become a little stagnent. you just wasn't educated in that (and you can't get that knowledge from the list of standard undergraduate subjects of which your list is a subset)the problem is they haven't taught neither you, nor all math majors in all except very few departments what are mathematicians really doing about mathematics.