Discrete Structure

This course is designed to build a strong foundation in discrete mathematics - the kind of math that powers the world of computer science. It sharpens logical thinking, introduces techniques for writing solid mathematical proofs, and strengthens problem-solving skills needed in programming, algorithm design, and system development. Students will dive into key topics like logic, sets, functions, relations, combinatorics, graphs, trees, and Boolean algebra, learning not just the theory but also how these concepts apply in real tech scenarios like databases, circuits, and code structure. Through hands-on practice with tools like Python, Jupyter Notebooks, NetworkX, and Graphviz, students will bring these abstract ideas to life by building models, writing logic-based programs, and exploring how mathematics directly supports computing.

• Upon completion of this course, the students will be able to:
• Develop the ability to think logically and construct valid mathematical arguments
• Apply set theory concepts such as set operations, Venn diagrams, Cartesian products, and power sets to solve problems in databases, programming, and decision-making structures
• Analyze relations and functions using matrix and graph representations and understand applications in modeling data and structures
• Use combinatorial techniques to solve real-life counting and arrangement problems
• Explore graph and tree structures, implement traversal algorithms (DFS, BFS, etc.), and apply these concepts in computer science domains such as networking, compiler design, and operating systems

• Practical (48 hours): Instructor should encourage the use of open-source tools like Python, Jupyter Notebooks, NetworkX, and Graphviz for practical sessions.
• Practical report contents: theory, source code, output, conclusion
• 1. Truth tables, logical operators, tautologies using Python or logic tools
• 2. Set operations implementation and Venn diagram visualization
• 3. Relation properties and matrix/digraph representation in code
• 4. Function definitions and mapping types with coding examples
• 5. Recursion-based programs (factorial, Fibonacci), validating inductive proofs
• 6. Permutations and combinations via iteration and recursion
• 7. Graph representation: adjacency list and matrix (using NetworkX or code)
• 8. Graph traversal: DFS and BFS implementations
• 9. Tree structures and traversals (inorder, preorder, postorder)
• 10. Boolean algebra simplification and expression evaluation via code
• 11. Mini project: logical puzzle solver or graph simulation

The teaching faculties are expected to create environment where students can update and upgrade themselves with the current scenario of computing and information technology with the help of topics listed in the syllabus. The general teaching pedagogy that can be followed by teaching faculties for this course includes class lectures, laboratory activity, group discussions, case studies, guest lectures, research work, project work, assignments (theoretical and practical), and written and verbal examinations.

• Grimaldi, R. P. (3rd ed.). Discrete and Combinatorial Mathematics: An Applied Introduction. Pearson.
• Kolman, B., Busby, R. C., & Ross, S. (2000). Discrete mathematical structures (3rd ed.). Prentice Hall.
• Liu, C. L. (1985). Elements of discrete mathematics (2nd ed.). McGraw-Hill.
• Rosen, K. H. (2011). Discrete mathematics and its applications (8th ed.). McGraw-Hill.
• Stein, C., & Drysdale, R. L. (2010). Discrete Mathematics for Computer Scientists. Pearson Education.
• Required journals/articles:
• Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2009). Introduction to algorithms (3rd ed.). MIT Press.
• Hopcroft, J. E., & Tarjan, R. E. (1973). Algorithm for finding the strongly connected components of a directed graph. Communications of the ACM, 16(6), 372-378.
• Knuth, D. E. (1968). The art of computer programming: Volume 1: Fundamental algorithms. Addison-Wesley.
• Pippenger, N. (1978). Theories of computation. Journal of Computer and System Sciences, 16(1), 99-115.