Discrete Math

The branch of mathematics that deals with countable, distinct elements and logical reasoning.

Logic

Logic in discrete math is the structured study of truth and falsehood, enabling precise, deductive reasoning in mathematical arguments.

Propositional Logic

Truth Tables

Quantifiers

Rules of Inference

Proofs

Proofs in discrete math are logical arguments that demonstrate the validity of mathematical statements using a variety of techniques.

Direct Proof

Proof by Contradiction

Proof by Contrapositive

Proof by Cases/Exhaustion

Proof by Induction

Functions

In discrete mathematics, a function is a mathematical object that assigns each input element from a set to a unique output element from another set.

Intro to Functions

One-to-One (Injective) Functions

Onto (Surjective) Functions

Bijective Functions

Inverse Functions

Composition of Functions

Generating Functions

Sequences & Series

In discrete math, a sequence is a list of numbers, while a series is the sum of terms in a sequence.

Arithmetic Sequence

Geometric Sequence

Fibonacci Sequence

Arithmetic Series

Geometric Series

Recurrence Relations

Summation Notation

Graph Theory

Graph theory is the study of mathematical structures used to model pairwise relations between objects, such as networks or social connections.

Bipartite Graph

Coloring and Chromatic Numbers

Directed Graphs

Euler Circuits

Euler Paths

Matching

Walks

Planar Graph

Undirected Graphs

Relations

In discrete math, a relation is a set of ordered pairs that describe the connection between elements of two sets.

Intro to Relations

Reflexive Relation

Symmetric Relation

Transitive Relation

Irreflexive Relation

Antisymmetric Relation

Asymmetric Relation

Partitions

Equivalence Relation

Total/Partial Ordering

Set Theory

Set theory is a branch of mathematics that studies sets, or collections of objects.

Null Set

Disjoint Sets

Set Cardinality

Universal Set

Subsets & Supersets

Sets

Power Set

Set Intersection Calculator

Set Union Calculator

Set Difference Calculator

Set Complement

Cartesian Product Calculator

Indexed Sets

Counting

Counting theory is a branch of combinatorics that deals with counting the number of elements in a set or in a collection of sets.

Factorial Calculator

Combinations Calculator

Permutations Calculator

Combinations with Repetitions

Permutations with Repetitions

Pigeonhole Principle

Principle of Inclusion and Exclusion

Number Theory

Integers are whole numbers without fractions or decimals. They include positive and negative numbers and zero, and are used in counting and measuring.

Greatest Common Divisor (GCD) Calculator

Prime Factorization

Chinese Remainder Theorem Calculator

Divisibility

Congruence Modulo Calculator

Linear Diophantine Equation Calculator

Extended Euclidean Algorithm Calculator

Least Common Multiple

Modular Multiplicative Inverse (Inverse Modulo)

Modulo Calculator

Probability

Probability is the extent to which an event is likely to occur, measured by the ratio of favorable cases to total cases.

Bayes' Theorem

Bernoulli Trials

Conditional Probability

Independent Events

Distributions