1 Introduction


1.1 Required readings

https://runestone.academy/ns/books/published/dmoi-4/ch_intro.html
https://runestone.academy/ns/books/published/dmoi-4/sec_intro-intro.html
https://runestone.academy/ns/books/published/dmoi-4/sec_intro-structures.html

https://en.wikipedia.org/wiki/Discrete_mathematics
https://en.wikipedia.org/wiki/Outline_of_discrete_mathematics

1.2 What is Discrete Mathematics?

discrete / dis’krët.
Adjective: Individually separate and distinct.
Synonyms: separate - detached - distinct - abstract.

Discrete mathematics is the study of mathematical structures that can be considered “discrete”
(in a way analogous to discrete variables, having a bijection with the set of natural numbers)
rather than “continuous” (analogously to continuous functions).
Objects studied in discrete mathematics include integers, graphs, and statements in logic.
By contrast, discrete mathematics excludes topics in “continuous mathematics”,
such as real numbers, calculus or Euclidean geometry.
Discrete objects can often be enumerated by integers;
discrete mathematics has been characterized as the branch of mathematics dealing with countable sets
(finite sets or sets with the same cardinality as the natural numbers).

The set of objects studied in discrete mathematics can be finite or infinite.
The term finite mathematics is sometimes applied to parts of the field of discrete mathematics,
that deal with finite sets, particularly those areas relevant to business.

1.3 Sub-areas

There are many sub-fields of discrete math:
Logic, Set theory, Type theory, Graph theory, Trees, Relations, Functions, Proofs, Coding theory, Number theory, Counting, Computational complexity theory, Computational geometry, Digital topology, Discrete geometry, Game theory, Information theory, Computability, Automata theory, Probability theory, Markov chains, Discrete optimization, Combinatorics, Linear algeabra.