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This course begins with the axioms for the real number system as a complete ordered field. It proves rigorously many of the major theorems stated with informal proof or even without proof in the first two semesters of calculus. Students will see why the axioms are needed, how the deductions build up a coherent theory, and how the results are used.
A tentative syllabus is available below. Beware of frequent adjustments.
Read the assigned sections once before each lecture. Read them again after each lecture before starting on the homework. Re-read them as often as necessary! Additional material may be posted on this web page.
Attendance is crucial. I will accept late homework only in special cases and even then only if I have not yet returned the graded set.
Make-up exams will be offered only if there is adequate reason to do so. A student's lack of preparation or lack of confidence is not an adequate reason. In most cases, if you must miss an exam you will know in time to discuss the matter with me (in person, by phone, or by email) IN ADVANCE. If we have not discussed the matter in advance, then I will need evidence of an emergency.
EXAMS: There will be two midterm exams and a final exam.
WORKSHOPS: We will usually have a workshop session in the period 7:40-9pm each Tuesday. Workshops are essential for learning the course material. Students will work in small groups on specially constructed problem sets. Most problems will deepen understanding of recently presented material. Some problems will connect recent material to earlier material in the course. Some problems will provide motivation for upcoming material.
The lecturer will circulate among the groups coaching, but not demonstrating soBetter detail on homework assignments is now up. [9/20/07]lutions. The goal at first is to offer ideas for analyzing the problem. Later in the term the goal is to ensure that groups can make use of the ideas offered repeatedly earlier.
At the end of each workshop session, one problem will be assigned to be written up and submitted at the next workshop. While students are encouraged to work together outside of class, the write-ups should be individual work. These write-ups will be graded on two scales: 0-5 for content and 0-5 for exposition. Good reasoning and good mathematical exposition may be more valuable in the long run than any particular piece of mathematical technique.
If a student has made an honest effort but not achieved much success, I may permit the student to revise the write-up and resubmit it. In such cases I will replace the original score by the average of the original score and the score on the revised write-up.
Directions for workshop write-ups:
HOMEWORK:
I will assign about 10 exercises a week for you to work on. I will assign about 7 of these to be turned in. These will be due one week after they are assigned. Of these, 4 will be graded and the other 3 discussed in class.
Use the same format for writing up homework as for writing up workshop problems.
Each homework problem will be graded on a scale of 0-5. Remember, the grader cannot grade your mathematics unless its exposition makes it clear what is going on.
TERM GRADES:
Each midterm exam counts for 100 points. The final exam counts for 200 points. The best ten workshop write-ups count for 100 points. The homework sum will be rescaled to count for 50 points.
Homework is intended to help you learn the material. Poor performance on homework will not necessarily lower your term grade.
Because of the opportunity to revise and resubmit write-ups, poor performance on the workshop write-ups may lower your term grade from that suggested by exam grades alone.
| Date | Lecture Topic | Workshop # if Thursday | Homework due if Wednesday |
|---|---|---|---|
| 1/? | Ch. 0 | W1 | |
| / | Ch. 0 | Ch 0 first set | |
| / | Ch. 0 | W2 | |
| / | Ch. 1 | Ch 0, second set | |
| / | Ch. 1 | W3 | |
| / | Ch. 1 | Ch 1, first set | |
| / | Ch. 1 | W4 | |
| / | Ch. 1 | Ch 1, second set | |
| / | Ch. 1 | W5 | |
| / | Ch. 2 | -- | |
| / | Ch. 2 | W6 | |
| / | Ch. 2 | Ch 2, first set | |
| / | Ch. 3 | W7 | |
| / | Exam 1, on Ch 0-2 | Ex 1 con't if desired | |
| / | Ch 3. | Ch 2, second set | |
| / | Ch. 3 | Ch 3, first set | |
| / | Ch. 3 | W8 | |
| / | Ch. 4 | Ch 3, second set | |
| / | Ch. 4 | W9 | |
| / | Ch. 6 | Ch 4, first set | |
| / | Ch. 6 | W10 | |
| / | Review | Ch 4, second set | |
| / | Exam 2 on Ch 3-4 | ||
| / | Ch. 6 | W11 | |
| / | Ch. 6 and 7 | Ch 6 | |
| / | Ch. 7 | W12 | |
| / | Ch. 7 | Ch 6 and 7 | |
| / | Ch.7 | Discuss HWk on Ch 7 |
VERY TENTATIVE SUGGESTIONS FOR HOMEWORK
Each faculty member makes his/her own assignments.
Some solutions may be posted after the grader had received the problems.
| Due Date | Section | Problems to do | Problems to turn in |
| Jan | Ch. 0, pp 27-29 | 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 | |
| Ch. 0, pp 27-29 | 22, 24, 26, 32, 33, 38, 41, 43, 44 | ||
| Ch 1, pp 54-57 | 1, 3, 4, 6a,c, 7, 9, 14, 16, 23, 24 | ||
| Ch 1, pp 54-57 | 25, 27, 29, 31, 32, 34, 40, 37, 38, 39 | 27, 31, 34, 37, 39 | |
| Ch 2, pp 79-80 | 1, 2, 4, 5, 7, 8, 11, 12, 14, 15, 16, 17, 19 | 2, 5, 8, 12, 15, 16, 19, | |
| Ch. 2, pp 79-80 | 21, 22, 24, 25, 26 | 22, 25, 26 | |
| Ch. 3, pp 104-106 | 1, 2, 4, 5, 6, 7, 9, 13, | 2, 4, 6, 9, 13 | |
| Ch. 3, pp 104-106 | 14, 18, 19, 22, 25, 28, 31, 34, 37, 40, 42, 45 | 34, (40 is optional) | |
| Ch. 4, pp 129-134 | 1, 2, 4, 5, 7, 8, 11, 13, 14 | 2, 5, 11, 13, 14 | |
| Ch. 4, pp 129-134 | 16, 17, 19, 20, 22, 26, 28, 29, 34, 40 | 16, 17, 19, 28, 40 | |
| Ch. 6, pp 206-210 | 1, 2, 4, 5, 7, 8, 10, 15a,c,e, 16,17 | 1, 4, 7, 8, 15a,c,e [may be submitted after the break] | |
| Ch. 6, pp 206-210 | 18, 19, 21, 22, 24, 25, 27, 28, 30, 31 | tba | |
| Ch. 6, pp 206-210 | 32, 33, 35, 36, 38, 40, 41, 4 | tba |