Introduction to Discrete Structures

This course introduces students to the fundamental mathematical concepts and structures used in computer science. The course covers key topics such as logic, set theory, functions, relations, graphs, trees, combinatorics, and Boolean algebra. Students will learn how to apply these discrete mathematical structures to solve computational problems, design algorithms, and analyze data structures. The course emphasizes the importance of discrete mathematics in computer science and how it supports the development of efficient and effective algorithms and systems.

Upon successful completion of this course, students will be able to:

• Understanding Fundamental Discrete Structures: Students will gain a comprehensive understanding of core discrete structures such as sets, functions, relations, and graphs, and how they are applied in computational contexts.
• Applying Logic and Proof Techniques: Learn how to use logical reasoning and proof techniques, including direct and indirect proofs, mathematical induction, and contradiction, to solve problems and verify the correctness of algorithms.
• Analyzing Combinatorics and Recurrence Relations: Gain proficiency in combinatorial analysis, including counting principles, permutations, combinations, and recurrence relations, to analyze algorithms and optimize computational processes.
• Working with Graphs, Trees, and Boolean Algebra: Develop skills in working with graphs, trees, and Boolean algebra, learning how these structures are used to model relationships, represent data, and solve problems in areas such as networking, databases, and circuit design.

These outcomes aim to equip students with the mathematical tools necessary for understanding and developing algorithms, data structures, and systems in computer science. The course provides a solid foundation in discrete mathematics, preparing students for advanced topics in theoretical computer science, software development, and computational problem-solving.