What kind of math is important for Computer Science?
2 Answers
Binary (or Base-2) math
Explanation:
Binary or Base-2 math is used extensively in electronic computing because it is very easy to switch, and to distinguish between, "on" and "off" in an electronic circuit.
Early electronics commonly used relays with on/off contacts, which only have 2 possible states, so base-2 was the only math that was easily represented by an electronic circuit.
Transistors are capable of turning on/off in a linear way so can support more than 2 states, but the circuitry becomes rapidly much more complex (generally using resistors) if more than 2 states (on/off or high/low) are to be used.
Circuits with resistance will always generate heat if current is flowing, which uses power and severely limits the ability to miniaturize.
The heat generated by IC computer technology is minimized by keeping current, resistance and switching times as small as possible.
This has led to the miniaturization of simple switch (2-state) FET transistor circuits as the preferred type of computer technology.
Therefore binary (base-2) remains the most important math used in computer science, although this is now usually invisible to the end user.
A few thoughts...
Explanation:
Many kinds of mathematics are relevant to computer science in different ways.
Here are just a few:
-
Arithmetic.
-
Boolean logic.
-
Set theory.
-
Number theory (particularly useful for cryptography).
-
Syntactic logic (e.g. for static analysis and program completeness).
-
Intuitionistic, relevance, modal and fuzzy logics (machine learning, etc.).
-
Category and topos theory (also useful for automated reasoning).
-
Probability and statistics.
-
Graph theory and game theory (travelling salesman and other algorithms).
-
Calculus (for numerical methods, etc).
