CS313H - Logic, Sets, and Functions: Honors - Fall 2012: Assignments Page

# Assignments for Logic, Sets, and Functions: Honors (cs313H)

## Week 0: Introduction (8/30)

Thursday
• Course introduction
• Cover course syllabus
• Assignment: introduce yourself on Piazza (Due 9/4)
• Homework 1 Assigned (Due 9/11): From the Rosen Textbook: Section 1.4 #10, #24 (a,b, and c), #36, #38, Section 1.5 #20 (parts a and c), #22, #32

• ## Week 1: Satisfiability, Predicates, and Quantifiers (9/4,6)

Tuesday
• Quest Module 1 on Boolean formulas, Satisfiability and Logical Identities: Due by 9:00pm the night before class
• Quest Module 2 on Predicates and Quantifiers: Due by 9:00pm the night before class
• Logical identities that you should become familiar with (Several were not mentioned in the module videos)
• Reading Assignment: Rosen, Section 1.3
• Thursday
• Quest Module 3 on Translating Logical Statements and Nested Quantifiers: Due by 9:00pm the night before class
• Reading Assignment: Rosen, Sections 1.4 and 1.5

• ## Week 2: Basic Proof Techniques (9/11,13)

Tuesday

• Quest Module 4 on Direct Proof, Contrapositive: Due by 9:00pm the night before class
• Quest Module 5 on Contradiction, Counterexample, Existence, and Cases: Due by 9:00pm the night before class
• Homework 1 due at beginning of class
• Reading Assignment: Rosen, Sections 1.6 and 1.7
• Homework 2 Assigned (Due 9/18): From the Rosen Textbook: Section 1.7 #24, #26, Section 1.8 #4, #26, #34, #38
• Thursday
• Quest Module 6 on Uniqueness, Working Backwards, Lemmas, Exhaustive Cases: Due by 9:00pm the night before class
• Reading Assignment: Rosen, Section 1.8

• ## Week 3: Mathematical Induction (9/18,20)

Tuesday

• Quest Module 7 on Weak Induction 1: Due by 9:00pm the night before class
• Quest Module 8 on Weak Induction 2: Due by 9:00pm the night before class
• Homework 2 due at beginning of class
• Reading Assignment: Rosen, Section 5.1
• Homework 3 Assigned (Due 9/25): From the Rosen Textbook: Section 5.1 #10, #14, #26, #34, Section 5.2 #10, #30
• Thursday
• Quest Module 9 on Strong Induction: Due by 9:00pm the night before class
• Reading Assignment: Rosen, Section 5.2

• ## Week 4: Sets and Functions (9/25,27)

Tuesday

• Quest Module 15 on Set Theory: Due by 9:00pm the night before class
• Quest Module 16 on Functions: Due by 9:00pm the night before class
• Homework 3 due at beginning of class
• Reading Assignment: Rosen, Sections 2.1, 2.2, 2.3
• Homework 4 Assigned (Due 10/2): From the Rosen Textbook: Section 2.1 #21, #31, Section 2.2 #19, Section 2.3 #33, #35, Section 2.5 #24 [Note: we mistakenly assigned mainly odd numbered problems. You can look at the answers in the back of the book, but make sure you write out your solutions with full rigor.]
• Thursday
• Quest Module 16.5 on Cardinality: Due by 9:00pm the night before class
• Reading Assignment: Rosen, Section 2.5

• ## Week 5: Infinite Sets (10/2,4)

Tuesday

• Homework 4 due at beginning of class
• Quest Module 16.6 on Countably and Uncountably Infinite Sets: Due by 9:00pm the night before class
• Read the introduction to the article on Decimal Representation to understand why the decimal representation used in the diagonalization argument is justified.
• Watch several sketches of arguments relating the sizes of different sets here
• Thursday
• TEST REVIEW

• ## Week 6: Graph Coloring (10/9,11)

Tuesday

• TEST 1 in class
• Thursday
• Quest Module 10 on Introduction to Graphs: Due by 9:00pm the night before class
• Quest Module 11 on Graph Coloring: Due by 9:00pm the night before class
• Reading Assignment: Rosen, Sections 10.1, 10.8

• ## Week 7: Special Types of Graphs (10/16,18)

Tuesday

• Quest Module 12 on Graph Connectivity: Due by 9:00pm the night before class
• Quest Module 13 on Bipartite Graphs and Trees: Due by 9:00pm the night before class
• Reading Assignment: Rosen, Sections 10.2, 10.4, 11.1
• Homework 5 Assigned (Due 10/23): Handout in class
• Thursday
• Quest Module 14 on Planar Graphs: Due by 9:00pm the night before class
• Reading Assignment: Rosen, Section 10.7

• ## Week 8: From Graph Theory to Counting (10/23,25)

Tuesday

• Homework 5 due at beginning of class
• Quest Module 14.1 on the 5-Color Theorem for Planar Graphs: Due by 9:00pm the night before class
• Quest Module 14.2 on Euler and Hamilton Paths and Circuits: Due by 9:00pm the night before class
• 5-color Theorem for Planar Graphs
• Reading Assignment: Rosen, Sections 10.3, 10.5
• Thursday
• WARNING: THIS MODULE IS A BIT LONG, SO BUDGET ENOUGH TIME TO WATCH IT
• Quest Module C1 on Basic Counting Rules: Due by 9:00pm the night before class
• Reading Assignment: Rosen, Sections 6.1, 6.3
• Homework 6 Assigned (Due 11/1): From the Rosen Textbook: (Must provide a formula, not just a final number) Section 6.1 #28, #56, Section 6.2 #32, Section 6.3 #24, Section 6.4 #20 (do a simple algebraic proof), Section 6.5 #18

• ## Week 9: Counting and Recurrences (10/30,11/1):

Tuesday

• Quest Module C2 on Pigeon Hole Principle, Binomial Theorem and Pascal's Triangle: Due by 9:00pm the night before class
• Quest Module 17 on Introduction to Recurrences: Due by 9:00pm the night before class
• Reading Assignment: Rosen, Sections 6.2, 6.4, 6.5, 8.1
• WARNING: NOTICE THAT HW 7 IS ACTUALLY ASSIGNED BEFORE HW 6 IS DUE
• Homework 7 Assigned (Due 11/6): From the Rosen Textbook: Section 8.1 #6, #8, #28 and Section 8.2 #4c,4d,4e, and #8
• Thursday
• Homework 6 due at beginning of class
• Quest Module 18 on Solving Linear Homogeneous Recurrences: Due by 9:00pm the night before class
• Reading Assignment: Rosen, Sections 8.2

• ## Week 10: Review and Test (11/6,8)

Tuesday

• Homework 7 due at beginning of class
• TEST REVIEW
• Thursday
• TEST 2 in class

• ## Week 11: Big-O and Program Efficiency (11/13,15)

Tuesday

• Quest Module 19 on Big-O, Big-Ω and Big-Θ: Due by 9:00pm the night before class
• Reading Assignment: Rosen, Sections 3.1, 3.2, 3.3
• Homework 8 Assigned (Due 11/20): From the Rosen Textbook: Section 3.2 #22, #26, #44, Section 8.3 #8 (show work, and use Theorem 1 in 8.3), #31 (difficult, but the answer is in the back. Formalize and clean up the proof), #32, #33 (answer in back, but be sure to formalize and clean up the proof)
• Thursday
• Quest Module 20 on the Master Theorem: Due by 9:00pm the night before class
• Reading Assignment: Rosen, Section 8.3

• ## Week 12: Analysis of Algorithms (11/20):

Tuesday

• Quest Module 20.1 on the Fast Multiplication Algorithm: Due by 9:00pm the night before class
• Homework 8 due at beginning of class
• No Class on Thursday: Thanksgiving Holiday

## Week 13: Proving Program Correctness (11/27,29):

Tuesday

• Quest Module 20.2 on Proving the Correctness of Mergesort: Due by 9:00pm the night before class
• Homework 9 Assigned (Due 12/5 in Discussion Section): Handout in class (Due date changed from date on handout)
• Thursday
• Quest Module 20.3 on the Stable Marriage Algorithm: Due by 9:00pm the night before class

• ## Week 14: Undecidability (12/4,6):

Tuesday

• Quest Module 21 on Undecidability and the Halting Problem: Due by 9:00pm the night before class
• Wednesday: Discussion Section
• Homework 9 due at beginning of class (Due date changed from date on handout)
• Thursday
• TEST REVIEW

• ## Final Exam (12/18):

9:00am - 12:00pm in CPE 2.208

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