
CMPSCI 250: Office Hours, Spring 2016  
Neil Immerman, CompSci Bldg 374, immerman at cs dot umass dot edu  M, W 2:303:30, 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 
Date  Lecture Slides  Sections from text to be completed BEFORE class 

W, 9/7  L1: Intro to Language of Math  R1: 1.1 Variables, Universal, Existential and Conditional Statements 
F, 9/9  L2: Sets and Ordered Pairs  R2: 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 Functions  R3: 1.3: Relations & Functions; R3 Quiz Preamble 
F, 9/16  L4: PropLogic  R4: 2.1 Logical Form and Equivalence 
M, 9/19  L5: Conditionals and Intro to Natural Deduction  R5: 2.2 Conditional Statements 
W, 9/21  D2: Translating between English and PropCalc  
W, 9/21  L6: CNF and Natural Deduction  R6: 2.3 Valid and Invalid arguments 
F, 9/23  L7: PredCalc with Equality  R7: 3.1 Predicates and Quantified Statements I 
M, 9/26  L8: More PredCalc  Hw1 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 Truth  R9: 3.3 Statements with multiple quantifiers 
F, 9/30  L10: Nat. Ded. Rules: =i, =e, ∀e, ∃i  R10: 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 Methods  R11: 4.1 Direct Proof and Counterexample I 
Th 10/6, 7  9p.m.  First Test  ISB 135 
F, 10/7  L12: Last 2 Natural Deduction Rules  R12: 4.2 Direct Proof and Counterexample II: Rational Numbers 
Tu, 10/11  L13: Divisiblity Proofs  R13: 4.3 Direct Proof and Counterexample III: Divisibility 
W, 10/12  No Class and No Discussion!  
F, 10/14  L14: Division and Modular Arithmetic  R14: 4.4 Direct Proof and Counterexample IV: argument by cases and quotient/remainder theorem 
M, 10/17  L15: Rings, Commutative Rings and Fields  R15: 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 primes  R16: 4.6, 4.7 Indirect Proof 
F, 10/21  L17: Euclid's Algorithm  R17:4.8 Euclid's Algorithm 
M, 10/24  L18: Mathematical Induction  Chapt 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 Induction  R20: 5.3 Mathematical Induction III 
M, 10/31  L21: Euler's Formula and Well Ordering  Hw3 due; R21: 5.4 Strong Mathematical Induction and the WellOrdering Principle 
W, 11/2  D7. Disc 7: Unique Factorization Thm, Disc 7 Ans  
W, 11/2  L22: Inductive Definitions and Structural Induction  R22: 5.9 Recursive Definitions and Structural Induction 
F, 11/4  L23: Truth Game  R23: 7.1 
M, 11/7  L24: Functions  R24: 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 Test  THOM 104 
M, 11/14  L25: Relations and Digraphs  R25: 8.1, 8.2 Relations 
W, 11/16  L26: Equivalence Relations and Fermat's Thm  R26: 8.3 Equivalence Relations 
F, 11/18  L27: Cryptography and RSA  R27: 8.4 RSA; Rivest, Shamir & Adelman explain RSA 
Thanksgiving Recess  
M, 11/28  L28: DFS on Undirected Graphs  R28: 10.1, 10.2: Graphs and Euler Paths 
W, 11/30  D9. No discussion meeting today  
W, 11/30  L29: DFS on Directed Graphs  R29: 10.5, 10.6 trees 
Th, 12/1  Hw5 due  
F, 12/2  L30: Deterministic Finite Automata (DFA)  R30: 12.1: just skim 
M, 12/5  L31: The DFA Pumping Lemma  R31: 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 Theorem  R33: 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  Final  1  3 pm, Marcus 131 