The field is also reaching a level where humans aren’t the only coders; now, humans have the help of machine learning algorithms that are close to doing most of the heavy lifting themselves. Trig should be rolled into geometry at the high-school level, or even dropped.I'm not saying trig isn't useful; that'd be silly. Speaking the same languages (English, Algebra, Geometry, Philosophy, Economics..) and understanding the same facts about the nature of the world and the human role in it (Physics, Chemistry, History, Literature, Biology...)The second goal is closely related; that educated people can talk to each other about inportant issues that lie outside their own field of expertise and help inform decisions made inside the field. I agree and yet disagree. Most of programmers didn't read it, shame on them (I am such a programmer ;-), I read only some small parts from it). Linear algebra and complex analysis together are what allow for jpeg compression and mp3 compression, by way of their child, wavelet analysis. Then trig becomes hard. I'm coming at this from the angle of, "how am I going to teach my kids math?". Much of state run education today has become a process of filling "buckets". By way of full disclosure I should state that my degrees are in Mathematics, Electrical Engineering, and Political Science. I've heard that Enderton is less rigorous and more readable, making it a better introduction to logic, but EFT was good enough that I haven't had any desire to read another introductory logic book.EFT: http://www.amazon.com/gp/product/0387942580Enderton: http://www.amazon.com/gp/product/0122384520. Thanks a lot for this post. With the decrease in physical size comes increased computing power and speed. One of the most interesting courses I took in the field was on algorithms and computability. Take a look at Michael Mitzenmacher's "Probability and Computing". Would you have picked anything as a teenager?I think the most important point (i.e. Even elementary schools are beginning to teach the fundamentals of programming to kids! Few of us are ready to do that. Math isn't easy. Asimov wrote a story about a future where math was a lost skill. You should write a book man. Mathematical notation is the biggest turn-off to outsiders. Douglas Hofstadter, 1979.Not sure I would call it a textbook though... Re: "Godel, Escher, Bach"see alsohttp://www.cabochon.com/~stevey/blog-rants/godel-escher-blog.html. The most fun stuff is the nonstandard analysis stuff. In fact, if you're a halfway decent programmer, you'll find it's almost a snap. But I realised years ago that the key to kids understanding this stuff was for them to learn the practical applications first, so they could then see just how knowing maths could save them from having to 're-invent the wheel' in solving real problems. Maths needs to be taught basics first, can you remember what the first Maths you were taught in school? And while it is true to a degree that the concepts in Calculus are not all that hard to understand themselves, the algebra involved in successfully navigating anything other than polynomials is generally what defeats most Calculus students. The notion that you will ever use this in real life only applied to Calculus, Trig, and again I will include Stats. I get better in my high school and college math because i could see similarities in programming. I'm also lucky in that I'm good at it, and had a number of good teachers.So yes, students should learn more linear algebra and statistics, and yes, it's possible to learn math as you get older, but no to most of the rest of your "I have solved the world's math learning problems" post. 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. But even if this were not true, education would still be both the first and the last line of defense of a democracy. The fields you find interesting are heavily influenced by the kind of problems that you are & have been working on. Most Comp Sci-only undergraduate programs seem to leave the graduate with knowlege of a few languages, some algorithms, and precious little else. David Smith (Dave) has a B.S. The job market continues to grow, and those who choose to become a programmer vs. a developer enjoy flexibility in job choices. Even programmers who were math majors tell me they don't really use math all that much! I think "The Art of Computer Programming" by Donald Knuth is a fine way to spend some time. I would eliminate calculators so that the experience of "how things go" is being learned all along. Schoenvogel would be "pretty bird".I enjoy reading the math articles on wikipedia and mathworld.wolfram.com and I've always liked reading books about math (not math textbooks), but I don't feel that I really know the math having read them. 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. It may be that it pushed over the hump past diminishing returns into compounding returns territory. I graudated from DESIGN at UCLA and have never touched a calculus class in my life, with the silly notion that I don't need math to program.Whoooooo boy. Naturally, these areas of math never made it onto the author's list of things allegedly "important to know." Really learning math is about fitting together the pieces to see why things really work. At least not if you are serious about mathematics. Nope, that produces parrots who squawk back the correct answer when asked the right question. Do I use the my understanding of the math I learned to solve problems regularly? If that wasn’t enough, more is in store for the field. Take us down the road with you so we can all fix the brain damage we received during math education (in the US anyway).And by the way. You need something better than "maximize the value of this abstract function".2) Why don't people like math? We have gained thousands of coding languages that tell machines how to carry out their programmed instructions. My students' responses were usually "I choose death! We used to joke about the discrete maths, calling them discreet maths.We didn't have the slighest idea of what they were, altough we had a subject on them. Two properties seem obvious in this regard. You are exposed to math in AP courses if you are lucky enough, but most are probably not.Being able to recite Euler's formula to directly sum up the first n natural numbers is nice. Higher-level languages take longer to execute, but they’re easier to use. It was required reading for one of the computer science classes. Someone mentioned that the name Schonfinkel means "pretty bird". I have gotten good milage out of Mordechai Ben-Ari's book Mathematical Logic For Computer Science. I won't bother listing other areas that are lacking. I am glad I found your post through osnews.com!! Through it, you’ll be able to follow clear steps for practicing web development and solving a range of programming problems. Writing a proof is a lot like writing a program. It covers randomized algorithms, Chernoff bounds, Shannon's Law, stationary ergodic processes, and all of the really interesting stuff from a computational perspective. Andrej. hey hey. No roots, no rational expressions (algebraic expressions which look like a fraction), just polynomials. I really would prefer if they would give the two subjects different names so people didn't think I just integrated really hard functions and I want strongly tracked courses in college .
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