CSCI 135 Discrete Structures--Spring 2013

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    Topics for Final Exam:
    This sheet is intended to help you prepare for the final exam in this course. The exam will cover the entire course, however it will emphasize topics learned in the second half of the course, in chapters 5, 8, 9, 10, 11, 12 and 16. You should study your class notes, textbook readings, handouts, and homeworks. You will be provided with list of theorems from the back of your textbook and you may bring notes on one side of one 8.5" x 11" piece of paper.

    The following topics have been covered since the first midterm. You should also review topics from the first half of the course (see midterm review). Each of the following topics may appear on the exam.

    Chapter 5: Word problems and Circuits
    	Word Problems
    		Given a set of assertions and a conclusion, either:
    			Prove the conclusion, or
    			Find a counter-example
    	Digital Circuits
    		Logic Gates (AND, OR, INVERTER, NAND, NOR)
    		Constructing a logical expression from a circuit.
    		Construct a truth table from a circuit.
    		Construct a circuit that implements a logical expression.
    	Universal Building blocks.
    Chapter 8: Quantification
    	Basic types in programming languages
    	Quantification
    		Linear notation for quantification
    		Quantification with more than 1 variable
    		Bound vs. free variables.
    		Textual substitution in quantifications
    		Axioms and Theorems for quantification
    		Range Splitting
    Chapter 9: Predicate calculus
    	Universal Quantification
    	Axioms and theorems for universal quantification
    	Existential quantification
    	Axiom, Generalized DeMorgan
    	Axioms and Theorems for existential quantification
    	Translation from English into predicate logic
    	Word problems and predicate logic
    Chapter 10: Predicates and programming
    	Program specification
    	Weakest precondition
    		Definition
    		For assignment statements
    	Proving an assignment is correct.
    	Assignment derivation, given pre and post conditions.
    	Conditional statements
    		Proving then and else statements
    	General IF statement
    Chapter 11: Sets
    	Denoting Sets
    	Set Comprehension
    	Translating set comprehensions into English descriptions
    	Translating English descriptions into set comprehensions
    	Set Operations
    		Union, Intersection, difference
    		Properties of operations
    	Power sets
    	Bags
    Chapter 12: Mathematical Induction
    	Proof by induction
    		Base Case
    		Inductive Case
    		Inductive Hypothesis
    	Inductive definitions
    	Loops
    		Checklist for proving loop correctness
    		Loop Invariant
    		Proving Loop Termination
    		Bound function for loop termination
    Chapter 16: Counting
    	The Rule of Sum
    	The Rule of Product
    	The Pigeonhole Principle
    	Permutations
    		Finding P(n, r)
    	Combinations
    		Finding C(n, r)