Math 135: First Steps into Advanced Mathematics

Offered:     Fall 2005
Instructor:  Kevin J. Mitchell
Office: Lansing 305 
Phone:  (315)781-3619
Fax:    (315)781-3860
E-mail: mitchell@hws.edu

Office Hrs:  Mon & Wed 1:30 to 3:00, Tues 11:00 to 12:30, Thurs 12:15 to 1:30, Fri 1:15 to 2:30. 
             Often available at other times by appointment.

Class:       Section 135-01: M-W-F 10:10 to 11:05 in NP 201
             Final Exam: December 14, 2005 at 8:30 AM
Text:        Chapter Zero: Second Edition 
             by Carol Schumacher
             

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Course Materials and Links

Assignments, Labs, and Answers require Adobe Acrobat Reader (see #2) which comes with most web browsers.

• Course Syllabus
• Download Adobe Acrobat Reader (tm)
• Errata for Chapter Zero. Some corrections to typos in our text.
• Assignment for Day 1.
• Assignment for Day 2.
• Some Answers and Comments for Day 2.
• Assignment for Day 3.
• Assignment for Day 4.
• Assignment for Day 5.
• Assignment for Day 6.
• Assignment for Day 7.
• Assignment for Day 8
• Assignment for Day 9.
• Assignment for Day 10.
• Answers for Day 10.
• Assignment for Day 11.
• Assignment for Day 12.
• Assignment for Day 13.
• Assignment for Day 14.
• Assignment for Day 15.
• Assignment for Day 16.
• Assignment for Day 18.
• Assignment for Day 19.
• Assignment for Day 21.
• Assignment for Day 23.
• Assignment for Day 24.
• Assignment for Day 26.
• Assignment for Day 27.
• Assignment for Day 28.
• Assignment for Day 29.
• Assignment for Day 30.
• Test 2 with Answers.
• Assignment for Day 34.
• Assignment for Day 35.
• Assignment for Day 36.
• Test 3, Part II.
• Assignment for Day 37.
• Assignment for Day 40.
• Extra Credit Assignment for Day 42.

Outline of Weekly Readings

This assumes a reasonable pace through the listed materials. We may need to adjust this schedule based on our actual work in class.

• August 29-September 2: Syllabus, Introduction, Introduction to Logic. Chapter: 0.0-0.4, 1.1-1.5.
  
• September 5-9: Logic, Truth Tables, And-Or-Not, Existence Theorems. Chapter 1.5-1.9.
  
• September 12-16: Logic and Types of Proof. Chapter 1.9-1.15.
  
• September 19-23: Set Basics, Indexed Sets. Chapter 2.1-2.3.
  
• September 26-30: The Algebra of Sets (De Morgan's Laws), the Power Set. Chapter 2.4-2.6.
• October 3-5: Introduction to Induction. Chapter 3.1-3.2.
  
• Friday, October 7: First Hour Test. Followed by Fall Break!
  
• October 12-14: Complete Induction. Chapter 3.3.
  
• October 17-21: More on Induction, Well-Ordering. Relations. Chapter 3.3, 4.1.
  
• October 26-28: Orderings. Chapter 4.2.
  
• October 31-November 4: Equivalence Relations. Chapter 4.3.
  
• November 7-11: Functions, Injections, Surjections, and Bijections. Chapter 5.1.
  
• Monday, November 14: Second Hour Test.
  
• November 16-18: More on Functions, Composition, and Inverses. Chapter 5.2-5.3
  
• November 21: Inverse Images and Images of Functions. Chapter 5.3.
  
• November 28-December 9: There are a few different options for the last two weeks of the term, depending on whether we have been able to keep to our schedule.
  • Option 1: Sequences, Cardinality, and Countability. Chapter 5.5, 7.1-7.3.
  • Option 2: Binary Operations, Elementary Number Theory. Chapter 5.6 and as much of Chapter 6 as time allows.
  • Option 3: Binary Operations, Construction of R. Chapter 5.6 and as much of Chapter 8 as time allows.
• Final Exam December 14 at 8:30 AM.