Maths Principles for CS

• People often say you don't need to know any math to program a computer and that's truthy
• Any sufficiently advanced technology is indistinguishable from Magic but magic isn't real
• Math Explains It All
• Developers often avoid learning math because it looks scary but it actually makes complicated magic like computer graphics and neural networks easier to understand
• Understanding math unlocks the secrets of the entire physical Universe
• There's a few abstract math concepts for programmers that you just can't ignore and understanding them will make you think more like a true engineer
• The first person who survives until the end and cracks the code will win this one of a kind Balenciaga fireship hoodie
• Boolean


  A binary variable that can have two possible values: true or false
• Boolean operators


  • And
  • Or
  • Not
• Conjunction


  And operation
• Disjunction


  Or operation
• Negation


  Not operation
• Boolean logic example


  • If you're both rich and handsome you'll definitely get a girlfriend
  • If you're not rich and not handsome you'll have to pay for an only Fan's girlfriend
  • If you're rich or handsome you can still get a girlfriend but your selection is more limited
• Boolean logic can be represented with Venn diagrams and truth tables
• Numeral system


  A system for representing numbers
• Base 2 (binary)


  The numeral system used by computers, where each place is multiplied by 2
• Base 10 (decimal)


  The numeral system commonly used by humans, where each place is multiplied by 10
• Base 16 (hexadecimal)


  A numeral system that uses the digits 0-9 and A-F, where each digit represents 4 bits
• Base 64


  A numeral system that uses 64 characters to represent binary data as text
• Floating-point numbers


  A way to represent very large or very small numbers by using an exponent
• Floating-point numbers can have rounding errors due to the limited precision of the representation
• Logarithm


  The inverse of exponentiation, representing how many times a base number must be multiplied by itself to get a target number
• Binary logarithm


  A logarithm with base 2
• Common logarithm


  A logarithm with base 10
• Set


  An unordered collection of unique values
• Intersection (inner join)


  The set of elements common to two sets
• Union (full outer join)


  The set of all elements from two sets
• Difference


  The set of elements in one set that are not in another set
• Discrete math


  The study of mathematical structures that have a finite number of elements
• Combinatorics


  The study of counting and enumerating discrete structures
• Graph


  A collection of nodes (vertices) connected by edges
• Directed graph


  A graph where the edges have a direction
• Undirected graph


  A graph where the edges have no direction
• Weighted edge


  An edge with a numerical value assigned to it
• Cyclic graph


  A graph where a node can be reached from itself by traversing edges
• Acyclic graph


  A graph where no node can be reached from itself by traversing edges
• Big O notation


  A way to express the time and space complexity of an algorithm
• Constant time (O(1))


  An algorithm that takes the same amount of time regardless of input size
• Linear time (O(n))


  An algorithm where the time taken is proportional to the input size
• Quadratic time (O(n^2))


  An algorithm where the time taken is proportional to the square of the input size