Welcome to discrete

​What is discrete math?

By Reparata Hattersley

Discrete topics

math that studies countable, distinct objects rather than continuous ones.

• Logic – statements, truth values, proofs

• Sets – collections of objects

• Functions & relations – how elements connect

• Combinatorics – counting, permutations, combinations

• Graph theory – networks of nodes and edges (used in social networks, routing, etc.)

• Number theory – integers, divisibility, primes

• Recursion & recurrence relations

• Algorithms & complexity – efficiency of computations

Multiple Choice

Discrete math studies distinct and countable math, versus what other type of math

• concrete

• continuous

• cipher

• coded

studies smooth, unbroken quantities—values that can change gradually and take on any value within a range

Continuous

Described as: distinct, finite, or countably infinite, and it forms the mathematical foundation of computer science.

Discrete

Discrete vs Continuous

• Measuring

• Time

• Distance

• Speed

Continuous

• Counting

• Shortest path

• Prime numbers

• Number of sales

Discrete

Examples

Multiple Select

Which of the following is discrete math examples? (Choose all that apply)

• volume of milk which can be bought in a store

• volume of milk which can be made by a cow

• Height of students in a class

• How many students are in a class

Why are they discrete?

Volume of milk purchased in a store come in set values. You may have a lot of options ie. pint vs quart, but they are a distinct and set amount

How many of something is almost always discrete. If I ask how many students are in a class it will be a while concrete number

How many students are in a class

Volume of milk which can be bought in a store

Why are they NOT discrete?

Volume of milk produced by a cow can change, there is a range of how much a cow can produce, vs the milk being bought in a store having a set number.

Height can change, it also can be a non whole number. Because height is a range of possibilities it is a continuous math.

Height of students

Volume of milk which can be produced by a cow

Multiple Choice

Which of the following are discrete topics?

• graph theory

• Calculus

• Recursion

• sets