CPCS 222 Syllabus Discrete Structures I Summer 2020 3rd Seme

Cpcs 222 Syllabus Discrete Structures I Summer 2020 3rd Semester

The objective of this course is to study the logical and algebraic relationships between discrete objects. This course cultivates clear thinking and creative problem solving by developing students’ mathematical maturity in several core areas: logic and proofs, sets, functions, relations, and counting techniques. The course includes lectures and labs, with assessments comprising quizzes, assignments, midterm and final exams, and graded lab work. Attendance in both lectures and labs is mandatory, with at least 75% attendance required to participate in the final exam. The curriculum covers topics such as propositional logic, proofs, set theory, functions, relations, sequences, counting principles, induction, and related concepts. Students will learn to analyze logical statements, construct proofs, manipulate sets, understand relations and functions, and apply combinatorial techniques. The course emphasizes critical thinking, formal reasoning, and problem-solving skills in discrete mathematics, which are foundational for computer science and related fields.

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Discrete mathematics is a foundational subject that underpins many areas of computer science, providing essential tools for reasoning, problem-solving, and analytical thinking. The course "Discrete Structures I" at the third semester level aims to develop students' mathematical maturity through a comprehensive exploration of logical and algebraic relationships among discrete objects, including logic, proofs, set theory, functions, relations, and counting techniques.

The significance of discrete mathematics in computer science cannot be overstated. It forms the theoretical backbone for understanding algorithms, data structures, programming paradigms, and computational complexity. Logical reasoning, the first core area covered in this course, enables students to formulate precise questions, evaluate propositions, and construct valid arguments—skills crucial for debugging, algorithm design, and theorem proving. The use of truth tables to evaluate the truth values of propositions, as well as the ability to prove propositional equivalences, helps students understand how complex logical statements are constructed and validated, a fundamental aspect of programming and computer architecture.

Set theory, another central component of the course, provides a language to describe collections of objects and their interactions. Understanding operations such as union, intersection, difference, and Cartesian product helps in modeling databases, designing algorithms, and analyzing data. Venn diagrams serve as effective visual tools for representing set relationships, which is particularly useful in fields such as database management and probability theory. The ability to determine set equality using membership tables and identities enhances skills in formal specification and verification of systems.

Functions and relations extend the concept of discrete objects to mappings and associations, fundamental to programming languages, data organization, and relational databases. The students learn to identify properties such as domain, co-domain, and inverse, as well as to compute compositions and closures of relations—concepts applicable in graph theory, automata, and network analysis. Analyzing sequences and sums, alongside the principles of counting, permits students to solve combinatorial problems, which are vital in algorithm analysis, cryptography, and operations research.

Mathematical induction, strong induction, and the well-ordering principle are proof techniques integral to validating recursive algorithms and algorithms relying on iterative processes. These methods foster rigorous reasoning skills and are essential for algorithm correctness proofs in computer science.

The course emphasizes the development of logical reasoning and analytical skills through various forms of proofs, such as direct proofs, proof by contraposition, proof by contradiction, and proof by cases. Students learn to use these techniques to establish the validity of theorems, which in turn supports their understanding of more advanced topics like formal verification and programming language semantics.

Assessment in this course includes quizzes, assignments, midterm and final exams, and graded lab projects. Quizzes serve as checkpoints to keep students engaged and current with recent material, while assignments reinforce concepts through practical application. The exams are cumulative, reflecting the interconnected nature of the topics covered. Active participation and diligent preparation are vital for success, and adherence to honesty policies is strictly enforced to maintain academic integrity.

The curriculum is structured to progressively build foundational skills, starting with propositional logic and moving towards more complex topics such as relations and counting principles. The schedule combines theoretical lectures and practical labs, which allow students to apply abstract concepts to real-world problems, such as designing algorithms that utilize set operations, relations, and combinatorial reasoning. The integration of visual tools like Venn diagrams, matrix representations, and digraphs enhances comprehension of abstract concepts and provides students with diverse methods to analyze discrete structures.

Understanding and mastering discrete mathematics prepares students for advanced coursework and careers in computer science, data analysis, cryptography, and other quantitative disciplines. The skills developed—logical analysis, formal proof strategies, set operations, and combinatorial techniques—are universally applicable in designing efficient algorithms, verifying software correctness, and analyzing computational systems. The course's comprehensive coverage ensures students are well-equipped to tackle complex problems in scientific and engineering contexts, fostering a mindset of rigorous, logical, and systematic problem-solving.

References

• Kenneth Rosen. (2012). Discrete Mathematics and Its Applications (7th ed.). McGraw-Hill Education.
• L. D. Baum. (2008). Discrete Mathematics for Computer Science. CRC Press.
• Ross, K. (2016). Discrete Mathematics with Applications. Pearson.
• Rosen, K. H. (2017). Discrete Mathematics and Its Applications. McGraw-Hill Education.
• Herstein, I. N. (1975). Topics in Algebra. Wiley.
• Barwise, J. (1975). Logic and its Applications: Discrete Mathematics. Springer.
• Kolman, B., & Beck, R. (2015). Discrete Mathematics with Applications. Pearson.
• Tanuwidjaja, M. (2011). Discrete Mathematics and Graph Theory. World Scientific Publishing.
• Biggs, N. (2002). Discrete Mathematics. Oxford University Press.
• Honsberger, R. (2012). Discrete Mathematics. Dover Publications.