Course Introduction Discrete mathematics is a branch of mathematics devoted to the study of discrete objects (i.e., objects that are distinct and unconnected). This course will introduce and apply various discrete structures and techniques to solve real-world problems. Main Topics 1. The Foundations: Logic and Proofs o Understanding the fundamentals of logical reasoning and constructing mathematical proofs. 2. Basic Structures: Sets, Functions, Sequences, Sums, and Matrices o Exploring fundamental mathematical structures used in computer science and mathematics. 3. Algorithms o Designing and analyzing algorithms for various computational problems. 4. Number Theory and Cryptography o Applying number theory in cryptographic algorithms and understanding their mathematical underpinnings. 5. Counting o Learning basic counting principles and techniques, including permutations and combinations. 6. Discrete Probability o Introducing probability theory with discrete random variables and their applications. 7. Advanced Counting Techniques o Delving deeper into combinatorial analysis and advanced counting methods. 8. Relations o Examining relations and their properties, including equivalence relations and partial orderings. Learning Objectives • Development of Mathematical Thinking and Logical Reasoning: Cultivate the ability to understand and create mathematical arguments, laying the foundation for advanced mathematical studies. • Foundations in Computer Science: Provide the necessary mathematical background for advanced courses in computer science, such as data structures, algorithms, compiler theory, and more. • Operations Research and Applications: Equip students with the mathematical background required to solve problems in operations research, chemical engineering, biology, and related fields. Course Features • Emphasis on Problem-Solving: The course focuses on teaching mathematical reasoning and problem-solving rather than merely imparting skills. • Fostering Creativity and Critical Thinking: Through diverse topics and problems, students are encouraged to apply their knowledge to new challenges. • Practice in Mathematical Proofs: Students will learn how to read, write, and validate mathematical proofs, which will be valuable for advanced courses. This course aims to equip students with the necessary tools and skills to tackle challenges in future courses and professional work.