Propositional logic studies truth-values of statements and their combinations using logical connectives like AND, OR, NOT.

Propositional logic is used in algorithm design, digital circuits, AI reasoning, formal verification, and more.

Propositional equivalences involve proving two logical statements yield the same truth value in all scenarios.

Predicate logic extends propositional logic by handling predicates and quantifiers.

Nested quantifiers involve stacking quantifiers (∀, ∃) in logical statements, allowing for complex expressions.

Rules of inference are foundational logical formulas that validate argument structures.

Proofs are logical arguments that establish the truth of a statement using axioms, definitions, and previously proven statements.

Proof methods are logical techniques for validating statements.

Sets are collections of distinct objects, called elements.

Set operations manipulate collections of elements.

Functions map inputs to outputs, associating each input with exactly one output.

Sequences are ordered lists of elements, typically numbers, following a specific rule or pattern.

Matrices are rectangular arrays of numbers or symbols.

Algorithms are step-by-step procedures or formulas for solving problems.

Divisibility determines if one number divides another without remainder. Modular arithmetic studies numbers under modulo operations.

Integer representations define how numbers are expressed in different bases.

Primes are numbers greater than 1 that are divisible only by 1 and themselves. The Greatest Common Divisor of two integers is the largest integer that divides both without leaving a remainder.

Solving congruences involves finding integers that satisfy equivalences modulo a given number.

Proof by induction is a technique in discrete math that involves proving a base case and a general case to prove a statement for all natural numbers.

Strong induction is a proof technique and Well-ordering principle states every non-empty set of positive integers has a smallest element.

Structural induction proves properties of objects built in a hierarchical or recursive way.

Recursive algorithms solve problems by breaking them into smaller instances of the same problem.

Counting is the foundation of combinatorics.

Permutations and combinations are foundational combinatorial concepts.

The binomial theorem describes the expansion of powers of a two-term sum.

Discrete probability deals with finite, distinct outcomes, quantifying the likelihood of specific events.

Probability theory studies uncertainty, modeling and analyzing random events.

Recurrence relations express a sequence's terms using previous terms in the sequence.

Inclusion-exclusion is a principle in combinatorics for counting items in combined sets.

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

Representing relations involves various methods to depict relationships between elements of sets.

An equivalence relation is a binary relation that is reflexive, symmetric, and transitive, which partitions a set into equivalence classes.

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

Graphs consist of vertices (nodes) connected by edges (arcs).

Trees are connected, undirected graphs without cycles. They represent hierarchical structures, ensuring a unique path between any two vertices.