Meetings |
Text |

TTh 12:50 - 2:20
Ford 201 |
Introduction to Real Analysis, 2nd edition, by
Manfred StollISBN 978-0-321046-25-3, published by Addison Wesley |

Note: In Real Analysis II, we will see that the "proofs" about derivatives that we saw in Calculus I were mostly quite rigorous, if we have a rigorous understanding of limits. Therefore, we will quickly review what we already know about derivatives in a rigorous setting. Integrals, however, are far more complicated than a Calculus I/II course would lead us to believe, especially if they involve discontinous functions. Thus much of Real Analysis II will be concerned with properties of the Riemann integral. Other material will include some introductory material on measure theory and/or sequences of functions, e.g.

- The ability to understand both abstract and concrete mathematical reasoning.
- The ability to differentiate between sound mathematical reasoning, flawed reasoning, and non-rigorous reasoning.
- The
ability to use the basic tools and methods of proof seen in analysis,
in particular set theory and epsilon-delta and epsilon-
*n*arguments. - The ability to formulate and prove theorems that arise from the definitions and concepts of the course, and the ability to apply those theorems to specific examples.
- The ability to write up, and occasionally present orally, one’s mathematical proofs and arguments in
a
clear and compelling manner.

Three to five quizzes | 75-125 points |

Two or three "midterm" exams: | 200-300 points |

Two or three in class presentations |
80-120 points |

Final exam | 200 points |

Around 7 homework sets at ~20 pts each | ~140 points |

Total: |
695-985 points |

For each graded piece of work, I will post cutoff scores for grades
of A-, B-, C, C-, and D. At the end of the term, if your point total is
more than the total of the A- cutoffs, your grade will be an A- or better,
and so on. **Cutoffs will never be higher than: A-: 90%
B-: 80% C: 70% C-: 67%
D: 60% ... but they are often lower.**

Final exam date: Thursday, Dec. 11, 2014 from 2-5 p.m.. For borderline grades, I tend to pay more attention to the final exam score. The final

.

In advanced mathematics, the step from things that can be easily understood to things that may as well be spoken in the Martian language is a short step. To stay ahead of this "step," one needs to keep up with the concepts and definitions already covered. It is vital that students do so. See also the "Workload" section below. The occasional "pop" quiz on definitions and theorems (see Quizzes above) and class discussion will help motivate students to keep up and help me assess how well students are doing. Please come prepared to discuss the homework and assigned reading from the previous class.

As with all 400-level mathematics courses at Willamette, students of this course are expected to attend the department colloquium at least four times this semester. The purpose of this requirement is to instill an appreciation of the breadth and variety of mathematical topics, techniques, people and (academic) programs. If scheduling conflicts make colloquium attendance impossible, alternative short written assignments will be made. If a student anticipates needing this alternative for more than one colloquium session, they should contact the instructor well in advance so that suitable assignments can be prepared. Failure to complete this requirement will result in a modest grade penalty for the course.

W

It is the policy of the College of Liberal Arts that for every hour of class time there is an expectation of "two to three hours" of work outside of class. This specific class, however, is widely recognized as the most challenging course we offer in Math, so you should probably plan on three hours of study per hour of class. Thus, for our class you should anticipate spending nine hours weekly outside of class engaged in study time, reading and homework assignments, and preparing presentations.

All exams and quizzes are to be taken with books and notes closed (except as noted on the exam paper), completely on your own. When we have take-home exams, specific expectations will be distributed with those exams.

While you are allowed (and even encouraged) to discuss homework problems in general terms with your peers, and to discuss methods and the like, you should not see a peer's written homework (or a transcription of it on a whiteboard, e.g.) until after your own graded homework is returned to you. With that in mind, plagiarism is work copied or paraphrased from another source without proper written acknowledgement. All students involved in plagiarized work will recieve a zero grade on the assignment. I will not try to tell who was "copied from" and who "did the copying."

In keeping with college policy, plagiarism will be reported to the dean for possible referral to the Honor Council per the Willamette Ethic. Systematic or organized plagiarism on exams or quizzes will result in course failure. If you are uncertain about some aspect of the academic honesty policy, it is your responsibility to get clarification from the instructor.

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