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Discrete Mathematics for Computer Science
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This 5-day course provides a foundational understanding of discrete mathematics, essential for computer science, algorithm design, and cryptography. Participants will explore key concepts such as logic, sets, relations, functions, graph theory, and combinatorics.
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Course Duration
5 Days
Course Details
This 5-day course provides a foundational understanding of discrete mathematics, essential for computer science, algorithm design, and cryptography. Participants will explore key concepts such as logic, sets, relations, functions, graph theory, and combinatorics. The course emphasizes mathematical reasoning, problem-solving, and proof techniques. Through interactive sessions and hands-on exercises, learners will develop a strong grasp of discrete mathematics principles and be prepared for more advanced topics in computer science.
This course focuses on developing logical thinking and the ability to construct rigorous mathematical arguments. It covers propositional and predicate logic, set theory, relations and functions, graph theory, and counting techniques. The course also introduces the basics of number theory, which is crucial for cryptography. By the end of this course, participants will be able to apply discrete mathematics concepts to solve computer science problems and have the mathematical foundation for further study in related areas.
By the end of this course, learners will be able to:
- Understand propositional and predicate logic.
- Work with sets, relations, and functions.
- Apply graph theory concepts.
- Use combinatorial counting techniques.
- Understand basic number theory.
- Construct mathematical proofs.
- Computer science students and professionals.
- Individuals who want to gain a strong understanding of discrete mathematics.
- Anyone who needs to use discrete mathematics in their work or studies.
Course Outline
5 days Course
- Logic and Proofs:
- Propositional logic: Statements, connectives, truth tables.
- Predicate logic: Quantifiers, predicates.
- Proof techniques: Direct proof, proof by contradiction, induction.
- Practical exercise: Constructing logical arguments and writing proofs.
- Sets, Relations, and Functions:
- Sets: Definitions, operations, Venn diagrams.
- Relations: Properties, types, operations.
- Functions: Types, composition, inverse.
- Practical exercise: Working with sets, relations, and functions.
- Graph Theory:
- Graphs: Definitions, types, representations.
- Graph traversals: Depth-first search, breadth-first search.
- Shortest path algorithms: Dijkstra’s algorithm.
- Practical exercise: Applying graph theory concepts to real-world problems.
- Graph Theory:
- Combinatorics:
- Counting techniques: Permutations, combinations, binomial theorem.
- Recurrence relations.
- Practical exercise: Solving combinatorial problems.
- Combinatorics:
- Number Theory:
- Divisibility and prime numbers.
- Modular arithmetic.
- Greatest common divisor and least common multiple.
- Introduction to cryptography.
- Practical exercise: Applying number theory concepts.
- Number Theory:
