section_path: Areas of mathematics/Discrete mathematics
section_name: Discrete mathematics
paragraph_text: Discrete mathematics
  
  Discrete mathematics, broadly speaking, is the study of individual, countable mathematical objects. An example is the set of all integers. Because the objects of study here are discrete, the methods of calculus and mathematical analysis do not directly apply. Algorithms — especially their implementation and computational complexity — play a major role in discrete mathematics.
  
  The four color theorem and optimal sphere packing were two major problems of discrete mathematics solved in the second half of the 20th century. The P versus NP problem, which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationally difficult problems.
  
  Discrete mathematics includes: