Discrete Structures and Optimization

Discrete Structures and Optimization is a field of study that deals with mathematical structures that are discrete rather than continuous. These structures include graphs, integers, logic-based statements, and more. Discrete optimization is a subfield of optimization that deals with discrete variables. It involves finding the best solution from a finite set of possible solutions.

There are many topics covered in Discrete Structures and Optimization. Some of the topics include set theory, recurrence relation, group theory, graph theory, mathematical logic, probability theory, Boolean algebra, linear programming, and more.

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Discrete Structures and Optimization
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Discrete Structures and Optimization

Unit	Details Contents
Unit -I	Mathematical Logic Propositional and Predicate Logic Propositional Equivalences Normal Forms Predicates and Quantifiers Nested Quantifiers Rules of Inference
Unit -II	Sets, Relations and Matrix Set Operations Representation and Properties of Relations Equivalence Relations Partially Ordering Function Matrix
Unit -III	Counting, Mathematical Induction and Discrete Probability Basics of Counting Pigeonhole Principle Permutations and Combinations Inclusion- Exclusion Principle Mathematical Induction Bayes’ Theorem
Unit -IV	Group Theory Groups, Subgroups, Semi Groups Product and Quotients of Algebraic Structures Isomorphism, Homomorphism, Automorphism Rings, Integral Domains, Fields Applications of Group Theory
Unit -V	Graph Theory Different graph Paths and Circuits Shortest Paths Eulerian & Hamiltonian Paths and Circuits Planner graph, Graph Coloring, Bipartite Graphs Tree, Tree Traversals, Spanning Tree
Unit -VI	Boolean Algebra Boolean Functions and its Representation Simplifications of Boolean Functions The Karnaugh Map
Unit -VII	Optimization Linear Programming Graphical Solution Simplex and Dual Simplex Method Transportation and Assignment Models PERT-CPM Vogel’s Approximation Method Critical Path Calculations Cost Consideration in Project Scheduling