PSU-CS251

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[PSU CS251/Discrete Structures II] CS 251 is the second term of the two term sequence CS 250-251. The main goal of the sequence is that students obtain those skills in discrete mathematics and logic that are used in the study and practice of computer science.

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

• Apply the properties of propositional calculus to: determine whether a wff is a tautology, a contradiction, or a contingency by truth tables and by Quine's method; construct equivalence proofs; and transform truth functions and wffs into conjunctive or disjunctive normal form.
• Describe the basic inference rules and use them to write formal proofs in propositional calculus.
• Apply the properties of first-order predicate calculus to: determine whether a wff is valid, invalid, satisfiable, or unsatisfiable; construct equivalence proofs; and transform first-order wffs into prenex conjunctive or disjunctive normal form.
• Describe the rules of inference for quantifiers and use them along with the basic inference rules to write formal proofs in first-order predicate calculus.
• Write formal proofs in first-order predicate calculus with equality.
• Construct partial correctness proofs of simple imperative programs and construct termination proofs for simple loops.
• Transform first-order wffs into clausal form; and unify atoms from a set of clauses.
• Describe the resolution inference rule; use it to write formal proofs in first-order logic; and describe how resolution is used to execute a logic program.
• Transform simple English sentences into formal logic (propositional, first-order, or higher-order).
• Apply appropriate algebraic properties to: simplify Boolean expressions; simplify regular expressions; write recursive definitions for simple functions in terms of operations for abstract data types; write expressions to represent relations constructed in terms of operations for relational databases; and work with congruences.

{NOTE: everyone seems to agree that there is way too much stuff in these two classes}

Block transfers from math programs other than PSU/PCC