On Solid Ground: Sets and Proof
(MATH 301)
Fall 2005
Time and Place: MWF 11:00 - 11:50 am, Room 315 Haag Hall
Professor: Richard Delaware
Office Hours: See Current Semester Office Hours
Office: Room 306 A, Manheim Hall
Mailbox: Room 206, Haag Hall, Dept. of Mathematics & Statistics
Phone: 816.235.2850
Email: delawarer@umkc.edu
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Dated Announcements (Most recent at the top)
- F 18 November 2005
Homework 12: DUE M 28 Nov. (6 exercises)
- Ch. 9: 9.28, 9.31, 9.36(nice), 9.38.
- Ch. 10: 10.12, 10.14.
- F 11 November 2005
Homework 11: DUE F 18 Nov. (5 exercises)
- Handout: Induction Exercises (Ch. 9 material)
- F 4 November 2005
Homework 10: DUE F 11 Nov. (8 exercises)
- Handout: Injective, Surjective, Composition Exercises (Ch. 8 material)
- F 28 October 2005
No Homework Assignment
- F 21 October 2005
No Homework Assignment (EXAM 2 on Friday 28 October)
- F 14 October 2005
Homework 9: DUE F 21 Oct. (4 exercises)
- Ch. 7, p.130: 7.12, 7.14, 7.22, 7.28.
- F 7 October 2005
Homework 8: DUE F 14 Oct. (6 exercises)
- Ch. 4, p.81: 4.40, 4.43.
- Ch. 5, p.90: 5.10, 5.14, 5.20.
- Solow, p.96: 9.14.
- F 30 September 2005
Homework 7: DUE F 7 Oct. (5 exercises)
- Ch. 4, p.80: 4.14, 4.19, 4.20, 4.30.
- Solow, p.106: 10.16.
- F 23 September 2005
Homework 6: DUE F 30 Sept. (3 exercises + Handout problems)
- Ch. 4, p.80: 4.2, 4.8, 4.12.
- Handout - "10 Proofs"
- F 16 September 2005
Homework 5: DUE F 23 Sept. (5 exercises)
- Ch. 3, p.64: 3.20, 3.22.
- Solow, p.34: 3.16(a).
- Solow, p.105: 10.8.
- Photocopy a Theorem and Proof from elsewhere.
Look for theorems not stated in a nice if-then style, and proofs that use different techniques.
- F 9 September 2005
- Homework 4: DUE F 16 Sept. (5 exercises)
- Ch. 3, p.64: 3.2, 3.12, 3.18.
- Solow, p.21: 2.17, 2.19.
- Quiz 1 on Wednesday Sept. 14.
- F 2 September 2005
Homework 3: DUE F 9 Sept. (10 exercises)
- Ch. 2, p.46: 2.26, 2.28.
- Ch. 3, p.64: 3.6, 3.8, 3.14.
- Solow, p.19: 2.10(a), 2.11(b), 2.12(b).
- Solow, p.34: 3.14. [Also, READ Chapters 2 & 3.]
- Handout: Analyze Two "Proofs" (WORD document)
- F 26 August 2005
Homework 2: DUE F 2 Sept. (7 exercises)
- 1.1, p.46: 2.2(abcdef), 2.10, 2.16(abcdef).
- Solow, Ch. 1, p.6: 1.2(abcd), 1.4(abcd), 1.7.
- Handout: Analyze this Proof (WORD document)
- M 22 August 2005
Homework 1: DUE F 26 August (5 exercises)
- M 22 August 2005
Email a short message to me at: delawarer@umkc.edu
Please tell me:
- Who you are
- Your mathematics background, including recent college math courses taken
- Any mathematics courses you plan to (or need to) take in the future
- Why you are taking this course (be as specific as you can)
- Anything else I should know
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Syllabus, Texts, Grading
PREREQUISITE:
- The prerequisite for this course is Math 220 (Calculus II).
TEXTS:
- Required: MATHEMATICAL PROOFS: A TRANSITION TO ADVANCED MATHEMATICS, by Gary Chartrand, Albert D. Polimeni, Ping Zhang.
- Required: HOW TO READ AND DO PROOFS, by Daniel Solow (Paperback)
- In the primary text, we will cover most of Chapters 0-10, possibly with selections from Chapters 11-12; In Solow, we will cover parts of all chapters.
EXAMS:
- There will be three 50 min. Exams (100 points each) during the semester, each given a letter grade.
- There will be some announced 15 min. Quizzes.
- The FINAL EXAM (150 points) will be held in our usual classroom, 1:00 - 3:00 pm, on TUES. Dec 13.
HOMEWORK:
- A list of suggested homework problems will be posted here. Only selected problems however 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.
GRADES:
- 63% -- 3 Exams (100 pts each) and Final Exam (150 pts)
- 37% -- 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.
NOTES:
- Writing proofs is a major feature of this course. That is, the careful use of language is crucial.
- 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.
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Suggested Homework Problems [Subject to change]
In the main text try to work all the bold problems.
Problems in the Solow book will be prefaced by "Solow".
Chapter 0
- READ this chapter very closely, and reread it throughout the course as needed.
Chapter 1
- p.24: 1.1 - 1.3, 1.5, 1.7, 1.8, 1.10, 1.12, 1.14, 1.15, 1.17, 1.20, 1.21, 1.24, 1.28 - 1.30
Chapter 2
- p. 46: 2.2, 2.4, 2.5, 2.7, 2.10, 2.12, 2.14, 2.16, 2.20 - 2.23, 2.25 - 2.29
- Solow, p.6: 1.1, 1.2, 1.3, 1.4, 1.7
Chapter 3
- p. 64: All problems 3.1 - 3.23
Chapter 4
- p. 80: 4.2, 4.3, 4.6 - 4.8, 4.12 - 4.14, 4.16, 4.17, 4.19, 4.21, 4.23, 4.25, 4.27, 4.28,
4.30, 4.32 - 4.35, 4.37, 4.39, 4.40, 4.42, 4.43
Chapter 5
- p. 90: 5.1, 5.2, 5.4, 5.6, 5.8, 5.10, 5.12 - 5.15, 5.17 - 5.21
Chapter 6
- p. 107: Quiz 6.17, 1 - 10
- p. 108: 6.1 - 6.5, 6.7-6.9, 6.19, 6.21, 6.23, 6.25, 6.26, 6.29 - 6.37, 6.39 - 6.46
Chapter 7
- p. 130: 7.2 - 7.4, 7.11 - 7.14, 7.17, 7.19, 7.21, 7.22, 7.24, 7.25, 7.28. 7.30, 7.34, 7.36, 7.37, 7.39, 7.42 - 7.46
Chapter 8
- p. 150: 8.3 - 8.7, 8.10, 8.11, 8.13, 8.14, 8.16, 8.17, 8.19 - 8.21, 8.24, 8.25, 8.29, 8.30, 8.33
Chapter 9
- p. 171: 9.1, 9.6, 9.8, 9.12, 9.14, 9.17, 9.18, 9.20, 9.22 - 9.24, 9.26 - 9.29, 9.31, 9.35 - 9.40
Chapter 10
- p. 194: 10.1 - 10.13, 10.14(b), 10.15, 10.20, 10.21, 10.23 - 10.25, 10.29, 10.30
Note: We may have time to choose selections from the following Chapters.
Chapter 11 [Particularly helpful for students planning to take
Math 410 (Modern Algebra)]
- p. 211: 11.1, 11.3, 11.4, 11.6, 11.8, 11.12 - 11.14, 11.16, 11.18, 11.22, 11.23, 11.25, 11.26, 11.28,
11.30, 11.32, 11.34, 11.35, 11.37, 11.38, 11.42, 11.46(a), 11.47, 11.49
Chapter 12 [Particularly helpful for students planning to take
Math 402 (Advanced Analysis I)]
- p. 239: 12.2, 12.4, 12.7, 12.8, 12.10, 12.13, 12.16 - 12.18, 12.21, 12.22, 12.25, 12.26, 12.28 - 12.32
Chapter 13
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Exam Outlines [Posted here as needed]
Exam 1 (Chapters 1,2,3)
- Possibilities [Subject to change]
Exam 1 Outline
Exam 2
- Possibilities [Subject to change]
Exam 2 Outline
Exam 3
- Possibilities [Subject to change]
Exam 3 Outline
Final Exam - Possibilities [Subject to change]
Final Exam Outline
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