Why Mathematics in Computer Science?

       To many people, the answer to my question may have been answered, but for me, it has been boggling in my mind for few years( Almost 2 and a half years) and I am still looking for an answer. Even now, it is maybe because I am still inexperienced, but it is very hard to benefit from mathematical concept when I am programming. Mathematical Induction in 2nd part of CSC236 was used to define some of Mathematical objects( i.e. Fibonacci Function and recursive functions) and analyze time complexity of some algorithm( i.e. mergesort and binary search).  And our term test 2 is on this Thursday, and I doubt I will find the answer to my question before the test, but I think I have some pretty good answers to the question. First, I think that Computer Science is very closely related to the Mathematics, or I could say that Computer Science is one of a branch of Mathematics( Applied Mathematics ). There are many mathematical concepts that are used in Computing. Just from CSC236, we learned that we can possibly build more effective and faster function or algorithm by analyzing it mathematically. It may take more than just using mathematic concepts; however, use of effective mathematical concept can substantially help making better and faster algorithm. As you all know the title of CSC236 is called "Introduction to theory of Computation", and up to now, 90 percent of our lectures involved using mathematic concepts( i.e. induction proofs, time complexity, and analyzing algorithms). The title itself would make us think that we are learning about theory of "Computation"; however, it seems like the term "Computation" implies "Applied Mathematics", because we have been heavily emphasized with the use of proof techniques from mathematics and mathematical objects that are used in Computer Science. I enjoy learning both Mathematics and Computer Science and the more I learn about Computer Science, it toughen my belief about the importance of Mathematics in Computer Science. I remember from CSC165, Danny Heap said one can be a good programmer(Compute Scientist) without good background in mathematics, but to be a great Computer Scientist, one needs a great background in mathematics. And I am on a mission to find the missing puzzles to understand what he really meant and I am starting to agree what Danny had said. In the end, I hope I find the true answer to the question before my undergrad in Computer Science and I hope that I can make a great use of both Mathematics and Computer Science in my career.