Research & Reviews: Discrete Mathematical Structures

Research & Reviews: Discrete Mathematical Structures Research & Reviews: Discrete Mathematical Structures [2394-1979(e)] is a peer-reviewed hybrid open-access journal launched in 2014 that deals with discrete objects. Discrete objects are those which are separated from each other like integers, rational numbers, automobiles, houses, peoples, etc. are all discrete objects. Some of the major reasons that we adopt discrete mathematics are. We can handle infinity or large quantity and indefiniteness with them which results from formal approaches are reusable.

The journal welcomes original research articles, theoretical and computational papers, systematic literature reviews, case studies, short communications, and invited editorials in the following thematic areas:

• Logic and Boolean Algebra: propositional and first-order logic, Boolean algebra and lattice theory, fuzzy logic and multivalued logic systems, modal and temporal logics, logic programming and automated theorem proving, and applications to digital systems and circuits.
• Set Theory and Foundations: naive and axiomatic set theory, fuzzy set theory and extensions, partial orders and lattices, category theory fundamentals, type theory and lambda calculus, and mathematical foundations of discrete structures.
• Relations, Functions, and Mappings: binary and n-ary relations, function composition and properties, injective, surjective, and bijective functions, equivalence relations and partitions, relational databases and query theory, and functional programming theory.
• Graph Theory and Combinatorics: graph structures and properties (directed, undirected, weighted), graph algorithms and traversal methods, tree structures and spanning trees, graph coloring and matching problems, planar graphs and topological properties, and combinatorial optimization.
• Number Theory and Cryptography: divisibility and prime numbers, modular arithmetic and congruences, greatest common divisor and least common multiple, number-theoretic functions, cryptographic applications, and computational number theory.
• Algorithms and Computational Theory: algorithm design and analysis, computational complexity classes (P, NP, NP-complete), sorting and searching algorithms, dynamic programming and greedy algorithms, graph algorithms and approximation methods, and computational hardness.
• Sequences, Series, and Recurrence: sequences and series summation, recurrence relations and solutions, generating functions and closed-form formulas, linear recurrences and matrix methods, and applications to combinatorial enumeration.
• Matrix Theory and Linear Algebra (Discrete Context): matrix operations and determinants, eigenvalues and eigenvectors, systems of linear equations, applications to graphs and networks, Boolean matrices, and spectral methods in discrete optimization.
• Discrete Probability and Counting: combinatorial enumeration and counting principles, permutations and combinations, probability distributions on finite spaces, Markov chains and random walks, stochastic processes on discrete domains, and Monte Carlo methods.
• Boolean Functions and Switching Theory: Boolean function analysis and representations, switching circuits and logic gates, function minimization and normal forms, fault detection and testing, and hardware design applications.
• Coding Theory and Information Theory: error-correcting codes and code design, information entropy and source coding, Shannon’s theorems and capacity analysis, cryptographic coding, and applications to communication systems.
• Discrete Calculus and Difference Equations: finite differences and difference operators, discrete analogues of calculus, recurrence equations and solutions, generating functions, discrete transforms (Fourier, Z-transform), and applications to signal processing.
• Applications to Computer Science and Engineering: iscrete structures in software algorithms, applications to database design and query optimization, discrete mathematics in artificial intelligence, network theory and optimization, and applications to physical and engineering systems.