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Mastering Computation Models and Problem Solving in Computer Science

This course aims to equip students with the skills to model complex problems, communicate effectively on intricate topics, and analyze algorithms for correctness and efficiency. Students will learn various modeling formalisms such as propositional logic, DFAs, and regular expressions, and engage in validating solutions through proof techniques like induction and proof by contradiction. By the end of the course, participants will have a solid foundation for further study in areas such as software construction and algorithms, enhancing their problem-solving capabilities in computer science.

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Mastering Computation Models and Problem Solving in Computer Science

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  1. CPSC 121: Models of Computation REVIEW

  2. Course Learning Outcomes • You should be able to: • model important problems so that they are easier to discuss, reason about, solve, and test • learn new modeling formalisms more easily • communicate clearly and unambiguously with other CS experts on complex topics • characterize algorithms (CS problem solutions), by proving their correctness or efficiency • critically read proofs: justifying why each step is correct and judging what the proof means • prove statements that require only simple insights beyond strategic choices or for which the insight is given/hinted • explain how computers work

  3. Modeling • We have seen a number of models with different power: • propositional logic • predicate logic • combinational circuits • DFA's • NFA's • regular expressions • sequential circuits

  4. Problem Solving • We have seen how to model problems in each of these models so that • the problem is more precise • we understand it better • we can reason about it • provide solution (if possible)

  5. Validating Solutions • We've learnt how to prove arguments so we can support our solutions • We have seen all proof techniques: • constructive/non-constructive proofs of existence • generalizing from the generic particular • antecedent assumption • proof by cases • proof by contrapositive or other equivalent • proof by contradiction • induction

  6. Reasoning about Algorithms • We've acquired enough knowledge to be able to reason about simple algorithms (solutions) • we can prove that are correct for certain inputs • we can prove how efficient they are • we can compare them

  7. And that is what Computer Science is about!

  8. CPSC Courses after 121 • CPSC 210 : Software Construction • learn how to understand and design programs larger than those you've seen in 110 • CPSC 213: Introduction to Computer Systems • learn how high level languages(Racket, Java, C++ ) are implemented using simple machine instructions • CPSC 221: Basic Algorithms and Data Structures • learn how to design important algorithms and data structures which used by many programs

  9. The End 

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