Mathematics for Theorectical Computer Science

I thought I would create a list of Maths topics which were relevant for those who are wishing to study Computer Science. I've seen most people on online communities referring to topics which have very little relevance or completely pointless in relation to Computer Science. This list is based upon my experiences and a friend who studies Computer Science at University. I've listed the most popular Computer Science fields and their Maths topics below.

General Computer Science:

These are the topics which you will typically study in your first year, and therefore will have to do.
  • Graph Theory
  • Linear Algebra (Matrices and Vectors)
  • Calculus I and maybe some Calculus II
  •  Analytical Geometry
  • Set Theory
  • Big O Notation
  • Radicals, Logarithms and Polynomials
  • Logic
Computer Graphics: 

I'm not too sure about Graphics, but these are the subjects which do have some relevance.
  • Fractal Geometry
  • Linear Algebra
  • Analytical Geometry
  • Differentiable Geometry
  • Hyperbolic Geometry
  • Differential Equations
  • Functional Analysis
Information Theory:
  • Differential Equations
  • Real and Complex Analysis - Fourier Series
  • Calculus II and Calculus III - Taylor Series
  • Probability Theory
Algorithms and Data Structures:

Most algorithms are used to solve mathematical problems, rather than the algorithms you see in commercial programs.
  • Graph Theory
  • Number Theory
  • Combinatorics
  • Probability Theory
  • Big O Notation
  • Set Theory
Cryptography and Computational Number Theory: 
  • Number Theory

Computability Theory, Computational Complexity Theory and Automata Theory:
  •  Logic
  • Set Theory
  • Calculus I
  • Recursion
  • Proof Writing Techniques
  • Number Theory
  • Big O Notation 
  • Probability Theory
In general, it's best to study Discrete Mathematics rather than Continuous Mathematics. There's some fields like Abstract Algebra which are used in Algebraic Coding Theory. Furthermore, Discrete Geometry has its applications too. Continuous Mathematics encompasses areas like Calculus/Analysis and Topology etc.
 




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