- Discrete Mathematics - Home
- Discrete Mathematics Introduction
- Mathematical Statements and Operations
- Atomic and Molecular Statements
- Implications
- Predicates and Quantifiers
- Sets
- Sets and Notations
- Relations
- Operations on Sets
- Venn Diagrams on Sets
- Functions
- Surjection and Bijection Functions
- Image and Inverse-Image
- Mathematical Logic
- Propositional Logic
- Logical Equivalence
- Deductions
- Predicate Logic
- Proof by Contrapositive
- Proof by Contradiction
- Proof by Cases
- Rules of Inference
- Group Theory
- Operators & Postulates
- Group Theory
- Algebric Structure for Groups
- Abelian Group
- Semi Group
- Monoid
- Rings and Subring
- Properties of Rings
- Integral Domain
- Fields
- Counting & Probability
- Counting Theory
- Combinatorics
- Additive and Multiplicative Principles
- Counting with Sets
- Inclusion and Exclusion
- Bit Strings
- Lattice Path
- Binomial Coefficients
- Pascal's Triangle
- Permutations and Combinations
- Pigeonhole Principle
- Probability Theory
- Probability
- Sample Space, Outcomes, Events
- Conditional Probability and Independence
- Random Variables in Probability Theory
- Distribution Functions in Probability Theory
- Variance and Standard Deviation
- Mathematical & Recurrence
- Mathematical Induction
- Formalizing Proofs for Mathematical Induction
- Strong and Weak Induction
- Recurrence Relation
- Linear Recurrence Relations
- Non-Homogeneous Recurrence Relations
- Solving Recurrence Relations
- Master's Theorem
- Generating Functions
- Graph Theory
- Graph & Graph Models
- More on Graphs
- Planar Graphs
- Non-Planar Graphs
- Polyhedra
- Introduction to Trees
- Properties of Trees
- Rooted and Unrooted Trees
- Spanning Trees
- Graph Coloring
- Coloring Theory in General
- Coloring Edges
- Euler Paths and Circuits
- Hamiltonion Path
- Boolean Algebra
- Boolean Expressions & Functions
- Simplification of Boolean Functions
- Advanced Topics
- Number Theory
- Divisibility
- Remainder Classes
- Properties of Congruence
- Solving Linear Diophantine Equation
- Useful Resources
- Quick Guide
- Useful Resources
- Discussion
Selected Reading
Quiz on Rings and Subrings in Discrete Mathematics
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