Comp. Sci. 250 Syllabus Fall, 2016

 CMPSCI 250: Office Hours, Spring 2016 Neil Immerman, CompSci Bldg 374, immerman at cs dot umass dot edu M, W 2:30-3:30, and by appointment: if you can't make these times and want to meet, please email me. Supplemental Instruction: Rhomni St. John Last two review sessions: Tue, 12/13/16 LGRT 123; Wed, 12/14/16 LGRT 121, 7 pm - 9 pm

### Handouts:

Required Readings: Please read the indicated sections from the text before coming to class. You must take a moodle quiz on the reading by noon before class and by 10 am on Wednesdays when there are discussion sections. The only exception is for serious medical conditions, in which case I will need a doctor's note. If you have religious holidays, sports events, conferences, interviews, or any similar conflicting activity, take the reading quiz in advance.

Date Lecture Slides Sections from text to be completed BEFORE class
W, 9/7L1: Intro to Language of Math R1: 1.1 Variables, Universal, Existential and Conditional Statements
F, 9/9L2: Sets and Ordered PairsR2: 1.2 the language of Sets
M, 9/12 No Class!
W, 9/14 D1: Translating between English and Math
W, 9/14 L3: Relations and FunctionsR3: 1.3: Relations & Functions; R3 Quiz Preamble
F, 9/16 L4: PropLogicR4: 2.1 Logical Form and Equivalence
M, 9/19 L5: Conditionals and Intro to Natural DeductionR5: 2.2 Conditional Statements
W, 9/21 D2: Translating between English and PropCalc
W, 9/21 L6: CNF and Natural DeductionR6: 2.3 Valid and Invalid arguments
F, 9/23 L7: PredCalc with EqualityR7: 3.1 Predicates and Quantified Statements I
M, 9/26 L8: More PredCalcHw1 due; R8: 3.2 Predicates and Quantified Statements II
W, 9/28 D3: PropCalc Natural Deduction Proofs
W, 9/28 L9: Tarski's Definition of TruthR9: 3.3 Statements with multiple quantifiers
F, 9/30 L10: Nat. Ded. Rules: =-i, =-e, ∀-e, ∃-iR10: 3.4 Arguments with quantifiers. R10 Preamble
M, 10/3 No Class!
W, 10/5 D4: Disc4: Review including answers to Hw2
W, 10/5 Chapt 4: Number Theory and Proof MethodsR11: 4.1 Direct Proof and Counterexample I
Th 10/6, 7 - 9p.m. First TestISB 135
F, 10/7 L12: Last 2 Natural Deduction RulesR12: 4.2 Direct Proof and Counterexample II: Rational Numbers
Tu, 10/11 L13: Divisiblity ProofsR13: 4.3 Direct Proof and Counterexample III: Divisibility
W, 10/12 No Class and No Discussion!
F, 10/14 L14: Division and Modular ArithmeticR14: 4.4 Direct Proof and Counterexample IV: argument by cases and quotient/remainder theorem
M, 10/17 L15: Rings, Commutative Rings and FieldsR15: 4.5 Direct Proof and Counterexample V: Floor and Ceiling
W, 10/19 D5. Disc 5: Z/mZ
W, 10/19 L16: Square root of 2 is irrational; There are infinitely many primesR16: 4.6, 4.7 Indirect Proof
F, 10/21 L17: Euclid's AlgorithmR17:4.8 Euclid's Algorithm
M, 10/24 L18: Mathematical InductionChapt 5 Mathematical Induction R18: 5.1
W, 10/26 D6. Disc 6: Induction
W, 10/26 L19: Eulerian Walks R19:5.2 Mathematical Induction II
F, 10/28 L20: Complete InductionR20: 5.3 Mathematical Induction III
M, 10/31 L21: Euler's Formula and Well OrderingHw3 due; R21: 5.4 Strong Mathematical Induction and the Well-Ordering Principle
W, 11/2 D7. Disc 7: Unique Factorization Thm, Disc 7 Ans
W, 11/2 L22: Inductive Definitions and Structural InductionR22: 5.9 Recursive Definitions and Structural Induction
F, 11/4 L23: Truth Game R23: 7.1
M, 11/7 L24: FunctionsR24: 7.2, 7.3 1:1, onto, composition and inverse of functions
W, 11/9 D8. Review Hw4 due;
W, 11/9 No Class!
Th 11/10, 7 - 9p.m. Second TestTHOM 104
M, 11/14 L25: Relations and DigraphsR25: 8.1, 8.2 Relations
W, 11/16 L26: Equivalence Relations and Fermat's ThmR26: 8.3 Equivalence Relations
F, 11/18 L27: Cryptography and RSAR27: 8.4 RSA; Rivest, Shamir & Adelman explain RSA
Thanksgiving Recess
M, 11/28 L28: DFS on Undirected GraphsR28: 10.1, 10.2: Graphs and Euler Paths
W, 11/30 D9. No discussion meeting today
W, 11/30 L29: DFS on Directed GraphsR29: 10.5, 10.6 trees
Th, 12/1 Hw5 due
F, 12/2L30: Deterministic Finite Automata (DFA)R30: 12.1: just skim
M, 12/5 L31: The DFA Pumping LemmaR31: 12.1
W, 12/7 D10. Disc 10: Regular or Not?
W, 12/7 L32: Nondeterministic Finite Automata (NFA)R32: 12.2
F, 12/9 L33: Kleene's TheoremR33: 12.3
M, 12/12 L34: Turing Machines & Unsolvability of Halting
W, 12/14 D11. Review hw5 Ans, Disc 10 Ans
W, 12/14 L35: Summary and Review
W, 12/21 Final1 - 3 pm, Marcus 131