• 
  
  
• W 5 November 2008
  
  • Homework 5 (Last one!): DUE M 17 Nov. (6 exercises)
    5.2.15(Recall Th. 2.17 proof), 5.2.43.
    5.4.1
    5.4.26(abcd) Notes: (a) is just Def. 5.31 of continuity at x_0; there are then 6 implications to check, between (a) and the other three statements; all are false except (a) implies (c), which you need to prove is true.
    5.4.31(skip the extension)
    5.7.2. (You might want to use K instead of A for your compact set.)
    

• M 29 September 2008
  
  • Homework 4: DUE M 13 Oct. (10 exercises)
    3.4.11, 3.4.20.
    3.5.13
    4.2.4, 4.2.14, 4.2.18, 4.2.25.
    4.3.6(Give proofs, not examples!), 4.3.11, 4.3.16. [Also, READ: 4.3.23, on the Cantor Set.]
    

• W 3 September 2008
  
  • Homework 3: DUE W 10 Sept. (or by Friday) (10 exercises)
    2.4.5, 2.4.6, 2.4.11, 2.4.14.
    2.6.2(can't use Squeeze Th), 2.6.5 (see the proof of Th. 2.11).
    2.8.2, 2.8.5, 2.8.9.
    2.9.6 (A classic! Nested interval property).
    

• W 20 August 2008
  
  • Homework 2: DUE W 27 Aug. (or by Friday) (8 exercises)
    1.6.17, 1.6.23.
    1.7.1 (3 equivalences; proofs by contradiction).
    A.8.4.
    1.9.1, 1.9.6(mimic my class proof of Th. 1.15).
    1.10.2, 1.10.4.
    

• M 18 August 2008
  
  • Homework 1: DUE W 20 Aug. (or by Friday) (4 exercises)
    Text: 1.4.3.
    Solow, p.34: 3.14, 3.16(a)(b)[Read carefully!]
    Solow, p.208: D.4
    

• The prerequisites for this course are Math 250 (Calculus III) and Math 301 (On Solid Ground: Sets and Proof).

• Required: ELEMENTARY REAL ANALYSIS, by Andrew M. Bruckner, Judith Bruckner, Brian S. Thomson, 2nd Ed. See Math 402 Text.
• Required: HOW TO READ AND DO PROOFS, by Daniel Solow, 4th Ed. (Paperback)
• In the primary text, we will cover most of Chapters 1-5, 7, and 8.

• There will be three 75 min. Exams (sometimes 25 min + 50 min, sometimes on different days) (100 points each) during the semester, each given a letter grade for your convenience.
• There may be some announced 25 min. Quizzes.
• The FINAL EXAM (150 points) will be held in our usual classroom, 8:00 - 10:00 am, on Friday Dec. 12, 2008.

• A list of suggested homework problems will be posted here. Selected problems will be collected and graded.
• For homework use only one side of standard 8½ x 11 paper. When due, put it on my desk at the start of class.
• Late assignments of any kind are NOT accepted, except by prior arrangement.

• 70% -- 3 Exams (100 pts each) and Final Exam (150 pts)
• 30% -- Homework and Quizzes
• I use grading software to provide grade reports. At the end of the semester before the Final Exam is recorded, I will drop your "most damaging" score. However, the Final Exam cannot be dropped.

• This course is the designated Capstone course for Mathematics majors.
• You will be proving many theorems in this course. So, you must discuss proofs with your classmates and me if you are to do well.
• You will not be able to do every suggested problem. But to succeed, you must try a good number.

• Appendix A, sections: A.1, A.2.1, A.2.2, A.3, A.4, A.5(~Solow Ch. 9), A.6(~Solow Ch. 10), A.7
• Solow: Preface to the Student, Ch. 1, Ch. 2, Ch. 3
• Solow Glossary

• 1.3: 1.3.5
• 1.4: 1.4.1, 1.4.2, 1.4.3
• 1.6: 1.6.1, 1.6.2, 1.6.4(induction), 1.6.7-1.6.14(all on sups/infs), 1.6.16, 1.6.17, 1.6.19, 1.6.23
• 1.7: 1.7.1, [1.7.4, done in class], 1.7.5
• 1.8: 1.8.1, 1.8.2
• Appendix A: A.8.4, A.8.5 (both induction)
• 1.9: 1.9.1, 1.9.3, 1.9.4, 1.9.6
• 1.10: 1.10.2, 1.10.3, 1.10.4, 1.10.5, 1.10.8(induction), 1.10.9
• Challenging: SKIP

• Solow Ch. 1, p.6: 1.3, 1.4
• Solow Ch. 2, p.17: 2.5, 2.10(a), 2.11(b), 2.17, 2.19
• Solow Ch. 3, p.32: 3.3(b), 3.14, 3.16

• 2.2.1: 2.2.7, 2.2.8, 2.2.9
• 2.3: 2.3.1, 2.3.3, 2.3.7
• 2.4: 2.4.1, 2.4.2, 2.4.3, 2.4.5, 2.4.9, 2.4.10, 2.4.11, 2.4.14
• 2.5: 2.5.1, 2.5.6, 2.5.7
• 2.6: 2.6.1, 2.6.2, 2.6.3, 2.6.4, 2.6.5
• 2.7: 2.7.2, 2.7.4, 2.7.5. 2.7.6, 2.7.7
• 2.8: 2.8.1, 2.8.3, 2.8.5, 2.8.8, 2.8.9, 2.8.10
• 2.9: 2.9.2, 2.9.3, 2.9.6 (classic!)
• 2.10: 2.10.1, 2.10.3, 2.10.4
• 2.11: 2.11.3, 2.11.6, 2.11.8, 2.11.7, 2.11.9, 2.11.14, 2.11.15 & 2.11.16, 2.11.19, 2.11.21
• 2.12: 2.12.1, 2.12.4, 2.12.6
• 2.13: 2.13.2, 2.13.5, 2.13.16 (all limsup/liminfs)
• Challenging: 2.14.2

• 3.2: 3.2.2, 3.2.4, 3.2.5, 3.2.9, 3.2.15, 3.2.17
• 3.3: SKIP
• 3.4: 3.4.1, 3.4.2, 3.4.3, 3.4.4, 3.4.5, 3.4.6, 3.4.8, 3.4.11, 3.4.14, 3.4.15, 3.4.16, 3.4.20, 3.4.23
• 3.5: 3.5.1, 3.5.6, 3.5.10, 3.5.13
• 3.6: 3.6.2(long), 3.6.4, 3.6.7, 3.6.17, 3.6.18, 3.6.19
• 3.7: 3.7.3, 3.7.4, 3.7.5, 3.7.9, 3.7.13
• 3.8: SKIP
• 3.9: SKIP
• 3.10: SKIP
• 3.11: SKIP
• Challenging: SKIP

• 4.2: 4.2.1, 4.2.2, 4.2.4, 4.2.5, 4.2.7, 4.2.8, 4.2.10, 4.2.14, 4.2.18, 4.2.20, 4.2.21, 4.2.25
• 4.3: 4.3.1(read), 4.3.2, 4.3.5, 4.3.6, 4.3.7, 4.3.11, 4.3.12, 4.3.13, 4.3.14, 4.3.15, 4.3.16, 4.3.21, 4.3.23(read; Cantor set)
• 4.4: 4.4.1, 4.4.2, 4.4.3, 4.4.4, 4.4.5, 4.4.6, 4.4.7, 4.4.9, 4.4.10, 4.4.11
• 4.5: 4.5.6, 4.5.7, 4.5.13, 4.5.14, 4.5.16
• 4.6: 4.6.3, 4.6.4
• Challenging: 4.7.7(read)

• 5.1.1: 5.1.1, 5.1.3, 5.1.9, 5.1.10
• 5.1.2: 5.1.13, 5.1.15, 5.1.16, 5.1.17, 5.1.18
• 5.1.3: SKIP
• 5.1.4: 5.1.26
• 5.1.5: 5.1.32, 5.1.33
• 5.2.1: 5.2.1
• 5.2.2: 5.2.5
• 5.2.3: 5.2.11, 5.2.13
• 5.2.4: 5.2.17, 5.2.20
• 5.2.5: 5.2.24, 5.2.25
• 5.2.6: 5.2.38, 5.2.39, 5.2.43, 5.2.44(Cantor set)
• 5.3: 5.3.6, 5.3.8, 5.3.10
• 5.4.1: 5.4.1, 5.4.3
• 5.4.2: 5.4.9, 5.4.11, 5.4.12
• 5.4.3: 5.4.14
• 5.4.4: 5.4.21, 5.4.24, 5.4.26, 5.4.27, 5.4.28, 5.4.31
• 5.5: SKIP
• 5.6: 5.6.6, 5.6.12, 5.6.15, 5.6.16, 5.6.17
• 5.7: 5.7.2
• 5.8: 5.8.1, 5.8.2, 5.8.3, 5.8.8(a)
• 5.9.1: 5.9.5
• 5.9.2: 5.9.14, 5.9.15, 5.9.16
• 5.9.3: 5.9.22
• Challenging: SKIP

• 7.2.1: 7.2.1, 7.2.3, 7.2.4, 7.2.6, 7.2.8, 7.2.11, 7.2.13
• 7.2.2: 7.2.16, 7.2.18, 7.2.19
• 7.2.3: SKIP
• 7.3.1: 7.3.2, 7.3.3, 7.3.5
• 7.3.2: 7.3.11, 7.3.16
• 7.3.3: 7.3.19
• 7.3.4: 7.3.21, 7.3.22
• 7.4: 7.4.1
• 7.5: 7.5.1, 7.5.6
• 7.6.1: 7.6.1, 7.6.2, 7.6.3
• 7.6.2: 7.6.8, 7.6.9, 7.6.11
• 7.7: 7.7.1, 7.7.2
• 7.8: SKIP
• 7.9: 7.9.3
• 7.10: SKIP
• 7.11: SKIP
• 7.12: SKIP
• Challenging: SKIP

• 8.2: 8.2.2, 8.2.5, 8.2.7, 8.2.8, 8.2.11, 8.2.12, 8.2.14, 8.2.15
• 8.3: 8.3.1, 8.3.2, 8.3.7, 8.3.8
• 8.4: SKIP
• 8.5: SKIP
• 8.6: 8.6.4, 8.6.5
• 8.7: SKIP
• 8.8: SKIP
• 8.9: SKIP
• Challenging: SKIP

Interactive Real Analysis, Bert G. Wachsmuth, Seton Hall University
http://www.shu.edu/projects/reals/reals.html

Analysis Web Notes, John Orr, University of Nebraska - Lincoln
http://www.math.unl.edu/~webnotes/home/home.htm

The following useful program is FREE (!) from Peanut Software:

• Winplot: A general-purpose plotting utility, which can draw (and animate) curves and surfaces presented in a variety of formats.

Exam Outlines [Posted here as available]

Exam 1 (1 - 3.5.2) - Possibilities [Subject to change]
Exam 1 Outline

Exam 2 (3.5.3 - 5.1.5, with omissions) - Possibilities [Subject to change]
Exam 2 Outline

Exam 3 (5.2.1 - 7.3.4, with omissions) - Possibilities [Subject to change]
Exam 3 Outline

Final Exam (Chapters 1 - 5, 7, 8, with omissions) - Possibilities [Subject to change]
Final Exam Outline