Math 3000
Intro. to Abstract Math
Spring 2010
Instructor: Eric Sullivan
(Sullivan Home)

Monday / Wednesday 2:30 - 3:45pm
West Classroom Building, Room 140

Office: 631 CU Denver Building
Office Hours: MW 12:30 - 2
email: eric.sullivan@ucdenver.edu

Textbook:
Mathematical Proofs: A Transition to Advanced Mathematics, 2/E.
Gary Chartrand, Albert D. Polimeni, Ping Zhang. ISBN-10: 0321390539

Course Description: Students learn to prove and critique proofs of theorems by studying elementary topics in abstract mathematics, including logic, sets, functions, equivalence relations and elementary combinatorics.

Spring 2010 Academic Calendar and Important Deadlines

-Chapter 1 Scans (save link to your computer)

Helpful Links: Entertaining Links:
Course Syllabus Invalid Proof Techniques
Blackboard Login Page Mathematical Fallacies
How to Write and Not Write Mathematics (by Jan Mandel) How mathematical proofs are really written
How to Study (by Jan Mandel)  
Dr. Cherowitzo's 3000 web page (material from spring 2008) LaTex -- Mathematical Typesetting
(students are encouraged (but not required) to typset their HW)
  LaTex Home
Running Glossary Mik Tex (A TeX Complier)
(Glossary TeX File) TeXnic Center (A Windows Tex Editor)
  How To Set Up TeXnic Center
Why you shouldn't use a picture for a proof TeX Shop (Mac TeX Editor)
  Tex Tutorials
  Wikipedia LaTex Page
What to do when you're stuck on a proof:
1) STOP!
2) Panic
3) Write down all relevant definitions on scratch paper
4) Make a plan
5) Do it.
(repeat as necessary)

 

Exams:

Exam 1
Mon, Feb 15
(chapters 1-3)
Solutions
(Tex File)

Suggested Review Problems:
Any problem that has been assigned (sketch or write up). Also:
Ch1: 49, 51, 52, 53, 54, 55, 57, 58
Ch2: 33, 56, 61, 62, 68
Ch3: 31, 34, 38, 41, 42, 46, (challenge: 47)

Exam 2
Monday, March 15
(cummulative with emphasis on chapters 4-6)

Suggested Review Problems:
Any problem that has been assigned (sketch or write up). Also, all odds in any section covered. Pay particular attention to:
Chapter 4: 11, 15, 16, 17, 27, 30, 35, 37, 43
Chapter 5: 7, 16, 17, 29, 31
Chapter 6: 3, 4, 5, 9, 11, 39

Exam 3
Possibly: Apr 12, 14, 19, or 21
(emphasis: chapters 8,9)

 

Final Exam
Week of May 10 - 14 (TBA)
(cummulative)

 

Homework and Assignments:

Date Due: To be turned in: Read and Sketch
Monday Jan 25   Read: Chapter 0 and sections 1.1-1.3
Sketch Problems: 1.5, 1.6, 1.8, 1.9, 1.10, 1.13, 1.15, 1.17
Wednesday, Jan 27   Read: Section 1.4 and Sections 2.1 - 2.6
Sketch: 1.26a, 1.30a, 2.3, 2.6, 2.9, 2.12, 2.16, 2.22
Monday, Feb 1 Write up problems: 1.12, 1.14, 1.20, 1.22, 1.26(b and c), 1.28, and 2.7 Read: Sections 1.5,1.6, 2.7-2.11
Sketch: 1.32, 1.34, 1.36, 1.42, 1.43, 2.22, 2.30, 2.31, 2.39, 2.47, 2.48
Wednesday, Feb 3   Read: The rest of chapter 2 and 3.1 - 3.3
Sketch: 2.47, 2.48, 3.1, 3.4, 3.5, 3.6, 3.8, 3.10
Monday, Feb 8 Write Up: 1.38, 1.40, 1.44, 1.46, 2.36 Read: 3.2 - 3.5
Sketch: 3.13, 3.16, 3.20, 3.24, 3.30
(Begin reviewing for exam 1)
Wednesday, Feb 10   Read: Ch 0 again. Anything you haven't read in Ch. 3
Sketch: 3.20, 3.24, 3.30
Monday, Feb 15 Write Up: 3.12, 3.14, 3.22, 3.28 (Solutions)  
Wednesday, Feb 17   Read: Sections 4.1 - 4.3
Sketch: 4.2, 4.5, 4.8, 4.11, 4.15, 4.16, 4.24 (Solution to 4.8)
Mon, Feb 22 Write Up: 3.44, 4.4, 4.10, 7.20, 7.22 (The directions for the Ch.7 problems are to "prove or disprove")
Challenge: 4.12 (not graded)
(Solutions with Comments) (Solutions Tex File)		  
Wed, Feb 24   Read: The remainder of Chapter 4
Sketch: 4.29, 4.33, 4.35, 4.36, 4.37, 4.43, 4.45
Mon, Mar.1 Write Up: 4.30, 4.32, 4.38, 4.46 Read: Sections 5.1 - 5.3
Reread chapter 4
Sketch: 5.1, 5.4, 5.7, 5.11, 5.16
Wed, Mar 3   Read: The rest of chapter 5
Sketch: 5.7, 5.11, 5.16, 5.29, 5.34, 5.36
Mon, Mar 8 Write Up: 5.6, 5.8, 5.14, 5.30 Read: Finish Chapter 5. Read sections 6.1 and 6.2
Sketch: 6.1, 6.5, 6.9, 6.14, 6.17, 6.18
Wed, Mar 10   Read: Finish reading 6.1 and 6.2
Sketch: Finish sketch problems from sections 6.1 and 6.2. Also "sketchy induction" problems.
Mon, Mar 15 Write Up:
5.44, 6.2, 6.4, 6.10, 6.16, 6.22, 6.24
(HW solutions) (solution tex file)
EXAM 2 HAPPENS TODAY! 		 
Wed, Mar 17   Read: Chapter 8 sections 1-3
Sketch:
Mon, Mar 22
NONE -- Spring Break
NONE -- Spring Break
Wed, Mar 24
NONE -- Spring Break
NONE -- Spring Break
Mon, Mar 29 Write Up:
(YES, PROBLEMS ARE DUE THE DAY AFTER SPRING BREAK!)
Prove or Disprove: 7.24, 7.34, 7.42
Also: 8.6, 8.8.		  
Wed, Mar 31    
Mon, Apr 5    
Wed, Apr 7    
Mon, Apr 12    
Wed, Apr 14    
Mon, Apr 19    
Wed, Apr 21    
Mon, Apr 26    
Wed, Apr 28    
Mon, May 3    
Wed May 5    
     

 

Impossible Pictures. This is reason enough for not using a picture in a proof.