Instructor Profile:
Dr. Vaibhav P. Sonaje
Associate Professor, Department of Computer Science and Applications, School of Computer Sciences & Engineering, Nasik, India
Dr. Vaibhav P. Sonaje is a distinguished academic and researcher with over 16 years of experience in the field of Computer Science. He currently serves as an Associate Professor in the Department of Computer Science and Applications at the School of Computer Sciences & Engineering, Nasik, India. He holds both a Master’s and a Ph.D. in Computer Science and has significantly contributed to the academic community through his extensive research work.
Dr.Sonaje has an impressive publication record, having authored approximately 37 research papers in internationally recognized journals and conferences. His work has been featured in prestigious SCI/Scopus-indexed journals, underscoring the high quality and impact of his contributions to the field.
His primary research interests span several cutting-edge areas, including Cloud Computing, Data Science, Data Analytics, Artificial Intelligence, and Machine Learning. Dr.Sonaje is particularly passionate about exploring innovative solutions that harness the power of AI and ML for solving real-world problems, and his expertise in these domains makes him a valuable educator and mentor.
With a robust teaching career spanning over 16 years, Dr.Sonaje is deeply committed to advancing knowledge in Computer Science. His courses are designed to provide students with both a strong theoretical foundation and practical insights, preparing them to excel in the rapidly evolving tech landscape.
In addition to his teaching and research, Dr.Sonaje actively participates in academic collaborations and contributes to the professional community through seminars, workshops, and conferences. He brings a wealth of experience and knowledge to his students, making his MOOCs an invaluable resource for learners looking to deepen their understanding of AI, Data Science, and Cloud Computing.
Course Outline: Discrete Mathematics
This Discrete Mathematics course is designed to introduce fundamental concepts and techniques of mathematical reasoning and proof techniques. It equips students with the tools necessary to analyze and solve problems involving discrete structures. The course is divided into four comprehensive modules as outlined below:
Module 1: Foundations of Discrete Mathematics
- Set Theory: Introduction to Sets, Subsets, Power Sets, Set Operations: Union, Intersection, Difference, Complement, Venn Diagrams and Cartesian Products, Applications of Set Theory in Problem Solving
- Logic and Propositional Calculus: Propositions, Logical Connectives, Truth Tables, Logical Equivalences and Implications, Predicate Logic, Quantifiers, and Nested Quantifiers, Proof Techniques: Direct Proof, Indirect Proof, Proof by Contradiction
Module 2: Combinatorics and Counting Techniques
- Basic Counting Principles: The Rule of Sum and The Rule of Product, Permutations and Combinations, Pigeonhole Principle and Applications, Inclusion-Exclusion Principle
- Advanced Counting: Binomial Theorem and Pascal’s Triangle, Recurrence Relations and Solving Linear Recurrences, Generating Functions and Applications, Introduction to Combinatorial Proofs
Module 3: Graph Theory and Applications
- Introduction to Graphs: Graph Terminology: Vertices, Edges, Paths, Cycles, Types of Graphs: Simple, Directed, Undirected, Weighted, Graph Representations: Adjacency Matrices, Incidence Matrices, Graph Isomorphisms and Subgraphs
- Graph Algorithms and Applications: Connectivity and Components, Eulerian and Hamiltonian Paths, Graph Coloring and Planarity, Shortest Path Algorithms: Dijkstra’s and Floyd-Warshall Algorithms
Module 4: Algebraic Structures and Boolean Algebra
- Algebraic Structures: Introduction to Algebraic Structures: Semigroups, Monoids, Groups, Properties of Groups: Subgroups, Cyclic Groups, Permutation Groups, Applications of Groups in Cryptography and Coding Theory
- Boolean Algebra: Boolean Functions and Expressions, Logic Gates and Digital Circuits, Karnaugh Maps and Simplification of Boolean Expressions, Applications of Boolean Algebra in Computer Science
This course provides the essential mathematical foundation for computer science, engineering, and related fields, equipping students with critical problem-solving and analytical skills necessary for tackling discrete structures.