[DOCS] Add Comprehensive Discrete Mathematics Content and Resource

[Reaper-ai]

Description

Currently, the repository does not contain resources or implementation details for Discrete Mathematics. Discrete Mathematics forms the core foundation of computer science, heavily influencing algorithms, data structures, compiler design, and cryptography.

This issue proposes adding a highly structured, comprehensive guide covering fundamental to advanced modules in Discrete Mathematics, complete with explanations, definitions, and code/practical examples where applicable.

Proposed Roadmap & Modules

Module 1: Mathematical Logic and Proofs

• Propositional Logic: Propositions, Logical Connectives (AND, OR, NOT, Implication, Biconditional), Truth Tables, Tautologies, Contradictions, and Logical Equivalence.
• Predicate Logic: Quantifiers (Universal $\forall$, Existential $\exists$), Nested Quantifiers, and Rules of Inference.
• Proof Techniques: Direct Proofs, Proof by Contraposition, Proof by Contradiction, Mathematical Induction (Weak and Strong), and Structural Induction.

Module 2: Set Theory, Relations, and Functions

• Set Theory: Sets, Subsets, Power Sets, Set Operations (Union, Intersection, Complement, Difference), Venn Diagrams, and Cartesian Products.
• Relations: Properties of Relations (Reflexive, Symmetric, Transitive, Anti-symmetric), Equivalence Relations, Equivalence Classes, Partial Orderings, and Hasse Diagrams.
• Functions: Injection (One-to-One), Surjection (Onto), Bijection (One-to-One Correspondence), Inverse Functions, and Composition of Functions.

Module 3: Combinatorics and Counting

• Basic Counting Principles: Sum Rule, Product Rule, Inclusion-Exclusion Principle, and Pigeonhole Principle.
• Permutations & Combinations: Counting arrangements and selections (with and without repetition), Binomial Coefficients, and Pascal's Identity.
• Recurrence Relations: Formulating recurrence relations, solving linear homogeneous and non-homogeneous recurrence relations (e.g., Fibonacci sequence applications).

Module 4: Graph Theory

• Basic Concepts: Graphs, Directed vs. Undirected Graphs, Degree of Vertices, Handshaking Lemma, Subgraphs, and Isomorphism.
• Connectivity: Paths, Cycles, Connected Components, Eulerian Paths/Circuits, and Hamiltonian Paths/Circuits.
• Special Graphs: Trees and their properties, Rooted Trees, Spanning Trees, Planar Graphs (Euler's Formula), and Graph Coloring.

Module 5: Algebraic Structures

• Algebraic Systems: Binary Operations and their properties (Associativity, Commutativity, Identity, Inverse).
• Groups & Subgroups: Definition of a Group, Abelian Groups, Cyclic Groups, Order of a Group, and Lagrange’s Theorem.
• Rings & Fields: Basic definitions, properties, and practical applications (e.g., Modular Arithmetic in Cryptography).

Module 6: Boolean Algebra and Automata (Advanced/Optional)

• Boolean Algebra: Boolean Functions, Expressions, Identities, Simplification, and Karnaugh Maps (K-Maps).
• Formal Languages & Automata: Grammars, Finite State Machines (FSMs), Deterministic Finite Automata (DFA), and Non-Deterministic Finite Automata (NFA).

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References & Resources to Add

• Standard textbook insights (Discrete Mathematics and Its Applications by Kenneth H. Rosen).
• Practical algorithmic ties (e.g., Graph Theory applications in networking, Recurrence Relations in Time Complexity analysis).

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🙋‍♂️ Contribution Details

I am a GSSoC 2026 contributor and would love to work on implementing this feature. Please assign this issue to me under the appropriate GSSoC labels!

[krishsoni-hub]

Hi @pushkarscripts ,

I would love to take this up and contribute a comprehensive guide for Discrete Mathematics!

My plan is to organize the content into clean, highly readable modules covering key computer science fundamentals:

• Mathematical Logic & Proofs: Propositional logic, truth tables, predicates, quantifiers, and structural proof techniques (including mathematical induction).
• Set Theory & Relations: Sets, operations, Venn diagrams, functions (injective, surjective, bijective), and properties of relations (equivalence relations, partial orderings).
• Combinatorics & Counting: Permutations, combinations, the Pigeonhole Principle, and binomial coefficients.
• Graph Theory & Trees: Core terminology, Euler and Hamiltonian paths, graph coloring, and basic tree architectures relevant to algorithms.

Could you please assign this issue to me? I can get started on structuring the Markdown documentation right away. #gssoc26

[vidhi-0205]

I am a GSSoC 2026 contributor and would love to work on implementing this feature. Please assign this issue to me under the appropriate GSSoC labels!