The thing is, software development has its roots in computer science, and cs is applied mathematics. So, it is true that you don't need math to do software development, it just makes it a lot easier if you do. How good do you want your work to be?
In the more broad spectrum of software development there is so much to do. Planning, designing, reviewing, etc. Do they have the design skills to make it look good? Do you have the empathy skills to know what the customer wanted in the first place? These don't seem related to math at all; but in pulling them all together to create a solution you would benefit from the problem solving skills that math provides
What actual math is needed for programming?
Computer Science is Applied Mathematics, so to be a computer scientist you would need a strong mathematical foundation. For making software, you don't have to be a full-blown computer scientist, but first you would have to use and understand the logic and data involved and how these two things work together to create your program.Early programming courses and discrete mathematics will articulate the strong ties between mathematics and programming. Then the coursework should bridge the gap between the mathematical perspective and the implementation of an algorithm as a sequence of instructions through an imperative language.
I have thought of programming as largely a combination of set theory and predicate logic. Category theory may be a better way of going about the first part, as it is really set theory when combined with functions. I'm not sure if that replaces logic as much as it extends it. I'm really seeing more light in functional approach as the way to glue the concepts together.
How to get there
The first year programming course should not be viewed as computer science in it's entirety. It is a formal language and propositional logic course, which is a foundation aspect to CS, but doesn't represent the entire profession.
- set theory
- predicate logic
- combinatorics
- probability
- number theory
- algorithms
- algebra
- graph theory
- Understand sets and how regular algorithms apply to them
- Functions ,Transcendental functions, including trigonometric functions, logarithmic and exponential. Algebraic vectors. Combinatory logic is the root of lambda calculus
- Computability and Turing style computer science is a bit at odds with formalism. It's a different philosophy of the nature of mathematics
Logic - first order logic http://en.wikipedia.org/wiki/First-order_theory theory of computation second order logic and computational complexity np complete also need to understand relations: unary, binary, ternary, n-ary important for iterations over sets with algorithms, check out STL style of applying functions. relational data
Numerical methods for solving simultaneous linear equations, roots of equations, eigenvalues and eigenvectors, numerical differentiation and integration, interpolation, solution of ordinary and partial differential equations, and curve fitting.
Wrap it up
Math is the language of technology and the computer science is applied mathematics. The more you know about these foundations allows you to make better software.
