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• How does a website like Mathway work?

  - by Bob

  I recently found a website called Mathway Basically, it works by allowing you to choose your "level of math" (which it uses to determine what tools it should provide to you) and then allows you to input a math problem which it then solves for you, and gives you detailed solutions (you have to try it, it's really cool). I was wondering how it worked on two levels. First off, how would they parse the math problem (and all the sometimes foreign mathematical operators)? How do they get from text to numbers, variables, and operators? Second, how do they generate the explanations? While you have to pay for the detailed solutions (which are explanations of how they solved the problem), I've seen their preview screenshots, and it looks very detailed. The explanations are given in full, accurate sentences. How would they generate something like that?

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• What is the justification for Python's power operator associating to the right?

  - by Pieter Müller

  I am writing code to parse mathematical expression strings, and noticed that the order in which chained power operators are evaluated in Python differs from the order in Excel. From http://docs.python.org/reference/expressions.html: "Thus, in an unparenthesized sequence of power and unary operators, the operators are evaluated from right to left (this does not constrain the evaluation order for the operands): -1*2 results in -1."* This means that, in Python: 2**2**3 is evaluated as 2**(2**3) = 2**8 = 256 In Excel, it works the other way around: 2^2^3 is evaluated as (2^2)^3 = 4^3 = 64 I now have to choose an implementation for my own parser. The Excel order is easier to implement, as it mirrors the evaluation order of multiplication. I asked some people around the office what their gut feel was for the evaluation of 2^2^3 and got mixed responses. Does anybody know of any good reasons or conciderations in favour of the Python implementation? And if you don't have an answer, please comment with the result you get from gut feel - 64 or 256?

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• Doing an SNES Mode 7 (affine transform) effect in pygame

  - by 2D_Guy

  Is there such a thing as a short answer on how to do a Mode 7 / mario kart type effect in pygame? I have googled extensively, all the docs I can come up with are dozens of pages in other languages (asm, c) with lots of strange-looking equations and such. Ideally, I would like to find something explained more in English than in mathematical terms. I can use PIL or pygame to manipulate the image/texture, or whatever else is necessary. I would really like to achieve a mode 7 effect in pygame, but I seem close to my wit's end. Help would be greatly appreciated. Any and all resources or explanations you can provide would be fantastic, even if they're not as simple as I'd like them to be. If I can figure it out, I'll write a definitive how to do mode 7 for newbies page. edit: mode 7 doc: http://www.coranac.com/tonc/text/mode7.htm

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• Rotate sphere in Javascript / three.js while moving on x/z axes

  - by kaipr

  I have a sphere/ball in three.js which I want to "roll" arround on a x/z axis. For the z axe I could simply do this no matter what the current x and y rotation is: sphere.roll_z = function(distance) { sphere.position.z += distance; sphere.rotation.x += distance > 0 ? 0.05 : -0.05; } But how can I roll it along the x axe? And how could I properly do the roll_z? I've found a lot about quateration and matrixes, but I can't figure out how to use them properly to achieve my (rather simple) goal. I'm aware that I have to update multiple rotations and that I have to calculate how far to rotate the sphere to match the distance, but the "how" is the question. It's probably just lack of mathematical skills which I should train, but a working example/short explanation would help alot to start with.

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• Good book or tutorial for learning how to apply integration methods

  - by Cumatru

  I'm looking to animate a graph layout using edges as springs and nodes as weights ( a node with more links will have a bigger weight ). I'm not capable of wrapping my head around the usage of mathematical and physics relations in my application. As far as i read, Runge Kutta 4 ( preferably ) or Verlet will be a good choice, but i have problems with understanding how they really work, and what physics equations should i apply. If i can't understand them, i can't use them. I'm looking for a book or a tutorial which describe the things that i need.

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• Is functional programming a superset of object oriented?

  - by Jimmy Hoffa

  The more functional programming I do, the more I feel like it adds an extra layer of abstraction that seems like how an onion's layer is- all encompassing of the previous layers. I don't know if this is true so going off the OOP principles I've worked with for years, can anyone explain how functional does or doesn't accurately depict any of them: Encapsulation, Abstraction, Inheritance, Polymorphism I think we can all say, yes it has encapsulation via tuples, or do tuples count technically as fact of "functional programming" or are they just a utility of the language? I know Haskell can meet the "interfaces" requirement, but again not certain if it's method is a fact of functional? I'm guessing that the fact that functors have a mathematical basis you could say those are a definite built in expectation of functional, perhaps? Please, detail how you think functional does or does not fulfill the 4 principles of OOP.

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• Learning Python from Beginner to Advanced level

  - by Christofer Bogaso

  I have some problems in my hand and would like to resolve them by myself (rather than hiring some professional, obviously due to cash problem!): build a really good website (planning to set-up my own start-up). build some good software (preferrably with exe installation files) on many mathematical and statistical techniques. To accomplish those tasks, is it worth to learn Python in advance level? I have advanced programming experiences with R and Matlab and VBA (and some sort of C), however not anything on Python. Be very grateful if experts put some guidance here. Thanks for your time.

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• What light attenuation function does UDK use?

  - by ananamas

  I'm a big fan of the light attenuation in UDK. Traditionally I've always used the constant-linear-quadratic falloff function to control how "soft" the falloff is, which gives three values to play with. In UDK you can get similar results, but you only need to tweak one value: FalloffExponent. I'm interested in what the actual mathematical function here is. The UDK lighting reference describes it as follows: FalloffExponent: This allows you to modify the falloff of a light. The default falloff is 2. The smaller the number, the sharper the falloff and the more the brightness is maintained until the radius is reached. Does anyone know what it's doing behind the scenes?

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• The perfect crossfade

  - by epologee

  I find it hard to describe this problem in words, which is why I made a video (45 seconds) to illustrate it. Here's a preview of the questions, please have a look at it on Vimeo: http://vimeo.com/epologee/perfect-crossfade The issue of creating a flawless crossfade or dissolve of two images or shapes has been recurring to me in a number of fields over the last decade. First in video editing, then in Flash animation and now in iOS programming. When you start googling it, there are many workarounds to be found, but I really want to solve this without a hack this time. The summary: What is the name of the technique or curve to apply in crossfading two semi-transparent, same-colored bitmaps, if you want the resulting transparency to match the original of either one? Is there a (mathematical) function to calculate the neccessary partial transparency/alpha values during the fade? Are there programming languages that have these functions as a preset, similar to the ease in, ease out or ease in out functions found in ActionScript or Cocoa?

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• Would a professional, self taught programmer benefit from reading an algorithms book?

  - by user65483

  I'm a 100% self taught, professional programmer (I've worked at a few web startups and made a few independent games). I've read quite a few of the "essential" books (Clean Code, The Pragmatic Programmer, Code Complete, SICP, K&R). I'm considering reading Introduction to Algorithms. I've asked a few colleagues if reading it will improve my programming skills, and I got very mixed answers. A few said yes, a few said no, and a one said "only if you spend a lot of time implementing these algorithms" (I don't). So, I figured I'd ask Stack Exchange. Is it worth the time to read about algorithms if you're a professional programmer who seldom needs to use complex algorithms? For what it's worth, I have a strong mathematical background (have a 2 year degree in Mathematics; took Linear Algebra, Differential Equations, Calc I-III).

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• How do I explain the importance of NUNIT Test cases to my Colleagues [duplicate]

  - by JNL

  This question already has an answer here: How to explain the value of unit testing 6 answers I am currently working in Software Development for applications including lot of Mathematical Calculations. As a result there are lot of test cases that we need to consider. We donot have any NUNIT Test case system, I am wonderring how should I get the advantages of implementing the NUNIT testing in front of my colleagues and my boss. I am pretty sure, it would be of great help for our team. Any help regarding the same, will be higly appreciated.

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• "Never to forget information" for programmers [closed]

  - by Milan

  Hi there! I'm new to programming and I would like to make a list of most important pieces of knowledge of programming and CS that would be useful no matter what specific programming language I would use in the future. For instance, if I would make this kind of list for Law studies, there would be stuff like Articles of Constitution etc. Those pieces of information I would put in Anki, and repeat it from time to time. Speaking in terms of CS and programming I mean on the most useful: mathematical theorems algorithms (examples of elegant solutions, comparison of two solutions etc.) pieces of code anything else that is vital (and very handy) to have in mind Do you think that making this kind of knowledge list makes sense?

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• CS subjects that an undergraduate must know.

  - by Karl

  In college, I was never interested in theory. I never read it. No matter how much I tried, I was unable to read stuff and not know what was actually happening practically. Like for example, in my course on automata theory, my professor told me everything possibly related to the mathematical aspect of it, but not even once did he mention where it would be used practically. This is just an example. I managed to pass my college and interned with a company also, where I did a project and thankfully they didn't bother about my grades, as they were above average. Now, I am interested in knowing what subjects should a CS student must absolutely and positively be aware of? Subjects that can have relevance in the industry. This is because I have some free time on my hands and it would help me better to have a good understanding of them. What are your suggestions? Like for one, algorithms is one subject.

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• MathType and LibreOffice Math comparison

  - by Agmenor

  In my office my team and I are going to type texts in the future which will include mathematical signs. Two programs are being proposed: LibreOffice Writer + Math or Microsoft Office + MathType. I would like to advocate for the first solution, but I need to know what technical advantages and disadvantages each program has. Compatibility with Ubuntu is an evident and important characteristic for LibreOffice, but could you give some other aspects? As a side question, do you advice any other program, even if not WYSIWYG and thus not my preference in this case?

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• Alternatives to Project Euler for improving Excel ability

  - by Jonathan Deamer

  I've recently been enjoying using the mathematical problems listed at Project Euler to learn Python. My Excel ability is better than my Python, but I think I'd still benefit from the sort of inductive learning that comes with solving a series of increasingly difficult puzzles using a particular tool. I know Project Euler can be completed using Excel, but are there any other puzzle series similar to this or The Python Challenge specifically tailored for people trying to increase their knowledge of Excel and what it can do? NB. I'm not looking for a "tutorial", I know there are plenty of these. And apologies if this isn't completely appropriate for programmers.SE.com - some of the folks at SuperUser suggested it was a better fit here than there!

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• How to derive euler angles from matrix or quaternion?

  - by KlashnikovKid

  Currently working on steering behavior for my AI and just hit a little mathematical bump. I'm in the process of writing an align function, which basically tries to match the agent's orientation with a target orientation. I've got a good source material for implementing this behavior but it uses euler angles to calculate the rotational delta, acceleration, and so on. This is nice, however I store orientation as a quaternion and the math library I'm using doesn't provide any functionality for deriving the euler angles. But if it helps I also have rotational matrices at my disposal too. What would be the best way to decompose the quaternion or rotational matrix to get the euler information? I found one source for decomposing the matrix, but I'm not quite getting the correct results. I'm thinking it may be a difference of column/row ordering of my matrices but then again, math isn't my strong point. http://nghiaho.com/?page_id=846

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• Will learning programming be as fundamental as learning reading/writing to the kids of the future?

  - by pythagras

  It seems I encounter more and more economists, scientists, and miscellaneous other professionals that have jobs that involve programming on some level. More and more, the jobs that my peers have in many many technical professions involve at least some simple scripting if not something more involved. It seems it used to be that "software engineer" was a distinct profession, now its becoming just another skill like writing -- something that any serious technical professional should be able to use for their job. I see a future where programming is essential to getting any kind of technical/mathematical job. Extrapolating on my anecdotal view of my colleagues... Will the kids of the future become literate in programming in the same way they become readers/writers? Will it become so fundamental to our economy and society that it will be taught at an early age? Will interacting with computers be as important as interacting with other people?

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• Is it possible to learn maths via programming, or you should learn maths for programming?

  - by SAFAD

  I am not the best in maths, not very horrid either, but lower than the average, I've always been thinking to improve my maths, but schools and books didn't do the job because I get bored too fast. The only thing I don't get bored with is coding and gaming, so I thought what if coding a program that solves mathematical problems will help me understand maths better, most of these problems are limits (calculus), functions, Differential calculus, and some other subjects (I already said am not that good) similar to the previous noted. My question is: Am I able to achieve a better knowledge in maths if I do some specific program coding, and if possible, is physics possible that way too? Or am I wrong and Maths should be learned before programming to help improve my coding? P.S : C++ is the preferred language.

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• Algorithm development in jobs

  - by dbeacham

  I have a mathematics background but also consider career in some form of software development. In particular I'm interested in finding out what sort of industries are most likely to have more algorithm development/mathematical and logical problem solving slant rather than pure application development etc. Obviously, I'm assuming that some subset of the canonical data structures and associated algorithms (trees, lists, hash tables, sets, maps with search, insert, traversals etc.) are mostly going to be present in software development. However, where am I more likely to encounter problems of more discrete maths nature (combinatorial, graph theory, sets, strings, ...) explicitly or more likely in disguise. Any pointers much appreciated (including possible open source projects that I could use for my further search for applications and also possibly contribute to).

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• How to move an object along a circumference of another object?

  - by Lumis

  I am so out of math that it hurts, but for some of you this should be a piece of cake. I want to move an object around another along its ages or circumference on a simple circular path. At the moment my game algorithm knows how to move and position a sprite just at the edge of an obstacle and now it waits for the next point to move depending on various conditions. So the mathematical problem here is how to get (aX, aY) and (bX, bY) positions, when I know the Centre (cX, cY), the object position (oX, oY) and the distance required to move (d)

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• What is the difference between _Procedural Generation_ and _Random Generation_?

  - by U-No-Poo

  Today, I got into an argument about the term "procedural generation". My point was that its different from "classic" random generation in that procedural generation is based on a more mathematical, fractal-based, algorithm leading to a more "realistic" distribution and the usual randomness of most languages are based on a pseudo-random-number generator, leading to an "unrealistic", in a way, ugly, distribution. This discussion was made with a heightmap in mind. The discussion left me somehow unconvinced about my own arguments though, so, is there more to it? Or am I the one who is, in fact, simply wrong?

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• What is the name of this array transformation?

  - by Brandon Tilley

  Start with an array of arrays; in this case, they are different lengths in order to demonstrate the technique, but they do not have to be. [[1,2,3,4], [5,6,7], [8,9,10], [11,12,13,14,15]] At the other end of the transformation, you have an array of arrays where the first array contains the first element from each of the original arrays, the second array contains the second element from each of the original arrays, and so on. [[1,5,8,11], [2,6,9,12], [3,7,10,13], [4,14], [15]] Is there a mathematical or CS term for this operation?

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• Stairway to T-SQL DML Level 4: The Mathematics of SQL: Part 1

  A relational database contains tables that relate to each other by key values. When querying data from these related tables you may choose to select data from a single table or many tables. If you select data from many tables, you normally join those tables together using specified join criteria. The concepts of selecting data from tables and joining tables together is all about managing and manipulating sets of data. In Level 4 of this Stairway we will explore the concepts of set theory and mathematical operators to join, merge, and return data from multiple SQL Server tables. Get Smart with SQL Backup Pro Powerful centralised management, encryption and more.SQL Backup Pro was the smartest kid at school Discover why.

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• Try/Catch or test parameters

  - by Ondra Morský

  I was recently on a job interview and I was given a task to write simple method in C# to calculate when the trains meet. The code was simple mathematical equation. What I did was that I checked all the parameters on the beginning of the method to make sure, that the code will not fail. My question is: Is it better to check the parameters, or use try/catch? Here are my thoughts: Try/catch is shorter Try/catch will work always even if you forget about some condition Catch is slow in .NET Testing parameters is probably cleaner code (Exceptions should be exceptional) Testing parameters gives you more control over return values I would prefer testing parameters in methods longer than +/- 10 lines, but what do you think about using try/catch in simple methods just like this – i.e. return (a*b)/(c+d); There are many similar questions on stackexchnage, but I am interested in this particular scenario.

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• Where should a programmer explain the extended logic behind the code?

  - by SRKX

  I have developed a few quantitative libraries in C# where it is important to understand not only the classic information that goes with the XMLDoc comments (which contains basic information with the method signature) but also the mathematical formulas being use within the methods. Hence I would like to be able to include extended documentation with the code, which could contain, for example Latex formulas, graphs, and so on. Do you think such information should be included in the API documentation? Or should it be included in a dev blog for examples? Are there common tools that are usually used for this kind of purposes?

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