MTH 311E--Homework Assignments

Supplementary text chapters you should read [revised 08/25/08 for the 2nd Edition]:

The material in Chapters 2-5 in the handouts ["Outline and Problem Sets"] are not covered directly in the supplementary text [Mathematical Proofs by Chartrand, et al]. However you should read Chapters 3-5 [of Chartrand] since these discuss proof techniques and give many examples of proofs, some of which are related to the material in Chapters 2-5 of the handout. After Chapter 5 in the handout, the topics covered will be: Induction (see Chapter 6 of Chartrand), sets (see Chapter 1 of Chartrand), functions (see Chapter 9 of the Chartrand), equivalence of sets and cardinality (Chapter 10 of Chartrand). After this we will cover topics such as the Least Upper Bound Axiom, which are not in Chartrand.

Exams:

• Mon, Oct 5 (completed)
• Mon, Nov 2 (completed)
• Mon, Dec 7 (completed)
• Final Exam, Dec 14
  

Assignment 15--Due Friday, Dec 11:

• Quiz: Wednesday, Dec 9 on end of Section 12 and on Section 13 (through Axiom 13.10)
• Problems 12: 10, 11
• Problems 13: 1-8

Final Exam

• When: Monday, December 14 at 3:30 - 6:30 PM 
• Where: Parker 104. Note: this is on South Campus
• Covers: Sections 1-13
• Format: 3 statements/definitions; 9 problems/proofs
• a sheet with the axioms/properties in abbreviated form will be provided if appropriate
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed
• Review Session: 7:30 PM on Sunday, December 13 in NSC 205

Coming Attractions: 

• Final Exam, Dec 14

Assignment 1--Due Friday, Sept 4:

• Recitation will not meet on Wednesday, Sept 2
• Read the Preface and Chapter 1 of the "Outline and Problem Sets"
• Available in the Course Documents section of UBLearns for this course
• Quiz: No quiz this week
• Problems 1: 1-4 ["Problems 1" refers to the problems at the end of section 1 of the "Outline"]
• Supplemental Text 2nd Edition (Chartrand), p. 64: problem 2.57

Assignment 2--Due Friday, Sept 11:

• Quiz: Wednesday, Sept 9 in recitation on Chapter 1 and Chapter 2 through Definition 2.2
• Including:
• the meaning of the terms used in the axioms (e.g. define "muliplication is associative") 
• the statement of the Well Ordering Principle
• Note: you will not need to memorize the axioms themselves, except for the Well Ordering Principle
• Quizzes have two questions:
• A statement or definition
• A problem or proof
• Problems 2 (of notes): 2.1 (this has multiple parts), 2.2 (parts 1 and 2)
• Hint for 2.2 part 1: break the proof up into cases. Can you prove for a, b both positive, for example?
• Note: you will begin working on these problems in groups in recitation on Wed, Sept 9

Assignment 3--Due Friday, Sept 18:

• Quiz: Wednesday, Sept 16 in recitation on Chapter 2 and Chapter 3 through Prop. 3.7
• a sheet listing the axioms in abbreviated form and listing the properties will be provided if appropriate
• Problems 2: 2 (parts 3-10), 3, 4
• Problems 3: 1-4

Assignment 4--Due Friday, Sept 25:

• Quiz: Wednesday, Sept 23 in recitation on Chapters 3 and 4
• a sheet listing the axioms in abbreviated form and listing the properties will be provided if appropriate
• Problems 3: 5-14
• Do, but do not turn in, problems 3.31-3.39 in Chartrand 2nd edition
• Problems 4: 1-6

Assignment 5--Due Friday, Oct 2:

• Quiz: Wednesday, Sept 30 in recitation on Chapter 5 (through 5.7)
• Problems 4: 7, 8
• Problems 5: 1-5
• Exam I: Monday, Oct 5

Assignment 6--Due Friday, Oct 9:

• Quiz: Wednesday, Oct 7 in recitation on Chapter 5 (from 5.8) and beginning of Chapter 6
• Problems 5: 6-12
• Problems 6: 2, 3

Assignment 7--Due Friday, Oct 16:

• Quiz: Wednesday, Oct 14 in recitation on Chapter 6 (through Proposition 6.13)
• Problems 6: 1, 4-11
• Note: problem 6.15 is hard. Try it as a challange!

Assignment 8--Due Friday, Oct 23:

• Quiz: Wednesday, Oct 21 in recitation on the end of Chapter 6 and on Chapter 7 through the statement of Prop. 7.11
• Problems 6: 12-14
• Problems 7: 1-6

Assignment 9--Due Friday, Oct 30:

• Quiz: Wednesday, Oct 28 in recitation on the end of Chapter 7 (ordered pairs and Cartesian product) and on Chapter 8
• Problems 7: 7-10
• Problems 8: 1-8, 13
• Note: Problem 8.7 should read: ``by Problem 8.6 above and by Problem 7.6 of the previous section.'' 
• Exam II: Monday, Nov 2

Assignment 10--Due Friday, Nov 6:

• Quiz: Wednesday, Nov 4 in recitation on Chapter 9 (through statement of Proposition 9.6)
• Problems 8: 9-12
• Note: In problem 9, f and g are defined by tables. E.g., for f:  f(1) = 2, f(2) = 4, f(3) = 3, etc.
• Problems 9: 1-5

Assignment 11--Due Friday, Nov 13:

• Quiz: Wednesday, Nov 6 in recitation on Chapter 10
• Problems 9: 6-8
• Problems 10: 1-6 (note that the problems continue on page 30)

Assignment 12--Due Friday, Nov 20:

• Quiz: Wednesday, Nov 18 in recitation on Chapter 11 (Through Corollary 11.7)
• Problems 10: 7-9
• Problems 11: 1-3, 9, 10

Assignment 13--Due Monday, Nov 30:

• Quiz: No quiz this week (Thanksgiving)
• Problems 11: 4-8
• Problems 12: 3, 4

Assignment 14--Due Friday, Dec 4:

• Quiz: Wednesday, Dec 2 on end of Section 11 and on Section 12 (through Note 12.16)
• Problems 12: 1, 2, 5-9
• Exam III: Mon, Dec 7

Exam I

• When: Monday, Oct 5 at 12:00-12:50 PM
• Where: O'Brian 112
• Covers: Sections 1 to 5 (through Proposition 5.7)
• Format: 2 statements/definitions; 3 or 4 problems/proofs
• a sheet with the axioms/properties in abbreviated form will be provided if appropriate
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed

Exam II

• When: Monday, Nov 2 at 12:00-12:50 PM
• Where: O'Brian 112
• Covers: Sections 5 (beginning with Proposition 5.8) through Section 8
• Format: 2 statements/definitions; 3 or 4 problems/proofs
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed

Exam III

• When: Monday, Dec 7 at 12:00-12:50 PM
• Where: O'Brian 112
• Covers: Sections 9-12 (through Note 12.16)
• Format: 2 statements/definitions; 3 or 4 problems/proofs
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed