How do you rate the importance of mathematics in your programming skill

There are many ways in which mathematics influences my programming:

Formal specification
Before discovering a solution -- or, in order to properly understand an existing one -- I need a sense of the scope and nature of the problem. To do this rigorously, I can approach the programming problem similarly to how I would a mathematical one. That is, specifying input parameters, protocols, types, flow, states, processes and outputs. (It also goes some way towards verification for correctness.)

Discrete structures
Every program I write involves concrete application of abstract discrete structure in mathematics -- from ordered sequences to matrices to trees/graphs to state machines and automata. Sometimes I need to know the profile of underlying structures provided by systems I'm using, and at other times I need to compose or create them myself.

Numerical analysis
An important practical concern is the representation of continuous real numbers by binary digital computers. It can be a complicated field in itself, but still has ramifications for the everyday programmer, with issues like floating-point precision and accuracy, rounding error, etc.

Symbolic analysis and meta programming
Programming often involves symbolic analysis analogous to mathematics. Besides direct counterparts like symbolic integration etc., in programming we typically deal with arbitrary symbols and expressions. Tokenizing, parsing, compiling, interpreting, rewriting and transforming symbolic input is close to algebraic mathematics. Formal languages and abstract computing machines are among fundamental theory in computer science, as well as matters of practical engineering concern.

Functional programming
One style of expressing program code (which I'm partial to) relies on immutable data structures, deep call chains, first-class/higher-order functions, function composition, and referential transparency. These are properties in common with mathematical convention. Being comfortable with that way of thinking is an advantage.

Algorithms
Similarly, an understanding of algorithms from a theoretical perspective (along with discrete structures) is essential. Knowing the order and limits of an algorithm's resource usage can help make crucial decisions about tradeoffs early in the development process. Having a sense of the shapes of growth curves -- if not the calculus behind them -- is related (e.g. it's easy to underestimate exponential growth).

Pre-calc mathematics
Arithmetic is obviously useful in so many cases. Understanding number radix and number lines is necessary for understanding bounding, overflow and conversion error. Geometry and trigonometry help with graphical applications -- from basic user interfaces to 3D games and digital cartography. Set theory is connected with everything from bitwise operations to cryptographic hashing to relational databases.

Statistics and modelling
Being able to manage large amounts of realistic data is an asset. Whether you want to aggregate logs to identify trends, or ensure your randomized algorithm is secure, or evaluate a given test for your data, some statistical confidence is necessary.

Domain knowledge
Software is often specific to a particular domain which may require, at a minimum, comprehending their branch of applied mathematics. e.g. business maths for commerce software, statistical techniques for social and medical software, calculus for science/engineering software, and so on.

Mathematical philosophy
Practicing and engaging with mathematics will, over time, help you develop taste -- for a kind of elegance of expression and beauty of structure, which overlaps a great deal with programming. In more specific terms, it involves things like limiting scope, constructing and composing abstractions, building meaningful relations, testing truth, reducing terms and simplifying assumptions.

The basic point is that thinking logically, analytically and yet creatively the way a mathematician does is very much applicable to programming. I'm nothing like an expert in either mathematics or computing, but in my experience as a student and practitioner, it has been highly beneficial to my activities in both areas to recognize and cultivate their intellectual connections.

So I rate the importance at 10/10.

I would say that it really does depend on the application of your program and the tools you are using to achieve your aims.

It goes without saying that if you were using Machine Code or Assembler then mathematics would be extremely useful.

And if you were employing complex algorithms to control graphics and/or 3D, obviously you would need a sound mathematical grounding, too.

However highlevel languages like HTML and CSS require very little in the way of complex maths and tools like dreamweaver and the like further remove that requirement.

A lot of people consider themselves programmers without really knowing much about what goes on 'under the hood', and these people are not really going to want or need much knowledge of the underlying maths.

I would say that it really does depend on the application of your program

That's how I feel.

Here are some thoughts from programmers about math, that you may find interesting.

I have been writing code for a few years now, and don't use any of my geometry, trig, or calculus. I use basic algebra, plus a little discrete math.

For what I do, I'd say 3/10. But it really depends on your domain. I write CRUD applications. Nothing fancy.

BUT the university has a responsibility to prepare students for a variety of different fields in computer science, and some of the fields do require a thorough understanding of math. Have you used a ti-89, Maple or Mathematica? Those programmers sure know math!

In program studies also fisrt starting with math matical application.. like counting, mod,big, comparison etc... Also in system level ptrogamming full of mathmatical calculation.. So its very important and math playing very good role

Mathematics always plays a huge role in almost all major applications and different field of work. When it come to programming, its very very essential. first and foremost requirement for programming studies is mathematics and you cant ignore it at all.

Per my monitoring to my students, those who perform well in my class (mathematics) perform well in their programming class but most of them was not able to top in the programming class.

Here are some data I gathered:

• The no. 1 in programming is 5th in my math class.
• 7 out of 10 who top in programming are I thought don't have a brain. They perform very poorly in my mathematics class.
• Among the top 10 in math only 2 made it to be among the top 10 in programming.
• An average student in my math class, is top 4 in programming.

The data was based on the performance of the students on the first quarter of the semester. Its too early to make some conclusions.

I'm not great in mathematics. But I have some basic knowledge. 5 monthes ago I was to write program based on Newton method and secant method. Looking throug wikipedia and some math forums I thought I would never sort it out myself. But finally it appeared that it's not impossible. If you want to do it you'll have done it. Even without deap math knowledge. Moreover I can say I have better designer skills. They are useful in programming.

Basically C and C++ languages best mathematical skill in programing language.

I won't go for any long details here but being into programming, specially machine level, maths is the 'most' important field as compared to any of the sciences. Programming is all about random data and abstract algorithms and who else except maths can make it possible.

In regards to your research and through my experience as a student and programmer I would say it all depends on enthusiasm. I hated math and did for many years until I found programming, I was very enthusiastic about programming but not at all about math, therefore in math class I was bottom of the class. In programming I taught myself what I needed to know to excel myself in that class.

Therefore its not that I couldn't do math, I just didn't have any enthusiasm, or see any benefit in doing so. Maybe this is the same for your students?

Now I enjoy programming and see the benefit in math, and after re-taking some qualifications I can now say my math is "OK" and continues to improve thanks to programming.

Hope this helps somewhat.

S33ker.

I would rate it as 9 out of 10. Mathematics is very necessary and I think in order to be a programmer one must have sound knowledge of mathematics.

1+1=5 ?

Mathematics is the mother of all sciences. If a person is good in mathematics, he will surely be good in programming logic and algorithm design.

Mathematics is not limited to 1+1 =2, rather it contained some complex formulas which are used in sophisticated software development.