It is important to note that computers started to operate after advances in mathematics and logics. The computer usually performs processes. But there were some mechanical machines that could do this even before the computer was invented. For instance, Pascal created an adding machine in the early 17th century. The only thing that distinguished computer from other machines is that it could do this with electricity.

Basically, what was needed was formal logic. The inventions of people such as Boole, Pierce, Frege, Russel and Whitehead, Godel and Turing gave the mathematical underpinning to computers, just the same way the inventors of the calculus laid physics foundations.

The mathematical foundation of computers is logic. Other fields like calculus, probability theory, and set theory are mathematical fields that are applied in computers programs but are not very important. But as Russell and Whitehead demonstrated, logic can be a basis for all types of mathematics. That means that although a computer can implement other types of mathematics, the other types cannot run a computer.

Academically, people who take computer science do a lot of Linear Algebra. More practically, a good understanding of mathematical concepts helps students to understand computers. People with a good understanding of mathematical concept easily understand how logic controllers work, how to write better algorithms, and how encryption works.

References

http://www.ww.amc12.org/sites/default/files/pdf/upload_library/22/Ford/DonaldKnuth.pdf

http://web.stonehill.edu/compsci/shai_papers/mathandcs.pdf

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