Course Syllabus

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Course Description: In M413 we study the real number system and its functions, focusing on topics already familiar from Calculus: 

    • Convergence

    • Continuity

    • Differentiation

    • Integration

In M413, however, we approach these with complete mathematical rigor. This makes M413 extremely challenging; it may well be the most difficult undergraduate course at IU. We require precision and proof in all that we do, requiring students to attain a level of mastery that comes only with prolonged effort and practice. While M413 is “elementary” analysis in that it develops calculus from a few simple axiomatic ideas, “elementary” does not mean “easy.”  M413 emphasizes skill in reasoning and communication. Though supremely mathematical, it is more a language art than a computational one.

Mastery of precise definitions is a critical requirement for success in this course. The material develops axiomatically and rigorously, so each word in a definition tends to be pivotal. Precise memorization of definitions is thus imperative for success. Students who invest time in memorizing definitions as soon as they're given will find that the effort pays off greatly. Students who don’t will find themselves lost in a frustrating fog of confusion.

Those who work hard enough to succeed in M413 gain a profoundly new understanding of mathematics. In mastering elementary analysis, one attains a deeply satisfying grasp of the vocabulary and machinery of calculus—a glimpse behind the curtain of reality and into its elegant interior design. This glimpse cannot be had by any of the physical senses; it is only visible via the kind of pure thinking we develop and practice in M413.

 

Homework: Homework problems are the heart of M413. After each lecture, I will assign written exercises. Generally, problems I assign in a given week will be due at the beginning of class on Wednesday of the next week. After each set is turned in, I will select 7 of the assigned problems for grading, at 2 points each. Each week's homework set will thus be worth 14 points. I do not accept late homework unless you have gotten my permission in advance.

Homework must be submitted in hardcopy (no attachments, please). Write it up in a clear, organized way. This is especially important in M413 because the “answers” to problems usually resemble essays more than calculations. You can't (and should not) get partial credit if the grader can’t follow your reasoning.

I encourage you to work with others on homework (assuming you do your share of the work), but you must write up your solutions in your own words.  If you don't, you skip the process of inventing and formulating your own solutions. If you don't practice these skills on the homework, you certainly won't be able to demonstrate them on the exams.

Please: staple homework pages together before submitting.

We will have 11 or 12 homework assignments, and then, at semester's end, drop each student's one or two lowest homework scores, leaving a total of 10 assignments for 140 homework points.

 

Exams: We will have two in-class midterm exams, a 2-hour final exam, and two quizzes. 

Quizzes will cover basic definitions to help motivate students to learn them—and to help me assess progress with the material. Dates for quizzes (approximately late September and early November) will be announced a week or so before they are given.

Please mark these dates in your calendars:

Midterm 1: Wednesday 9/27 In class 120 points
Midterm 2: Friday 11/3 In class 120 points
Final Exam: Friday 12/15 5–7p in LI 031 200 points

 

Office Hours: My office, Rawles Hall 361, will be open every 

  • Tuesday   1:30 – 2:30p
  • Thursday  2:45 – 3:45p

Please drop by during these times for help with homework or any other course-related concerns during these times – no appointment needed.  I enjoy working with students one-on-one in office hours, and I hope to meet everyone that way before the semester advances too far. 

 

Grading Assistant: My assistant for this course will grade the homework and help me grade exams. For questions or concerns about grading, however, please see me.

 

Grades: Students accumulate course points from homework and exams. Approximately 640 points will be available, as follows:

 

Item Unit value Total value
Homeworks 10 highest scores, 14 pts each 140 points
Quizzes 2 @ 30 points each 60 points
Midterm exams 120 points each  240 points
Final exam (2 hours) 200 points 200 points

 

At the end of the term, I will rank students' total point accumulations and assign letter grades. I’ll start with the standard curve (lowest A- = 90%, lowest B- = 80%, etc). If that turns out to be too stringent by traditional M413 standards, I’ll relax it. I guarantee the curve will be no tougher than the standard 90/80/70/60 scale.

 

Courtesy and Integrity: Our text contains all the information students need to succeed in the course, so I don’t require class attendance. I do try to make lectures worthwhile, however, and I ask: If you choose to attend a lecture, please arrive on time. Late arrivals distract the class and compromise the learning atmosphere I strive to create.

For similar reasons, please silence and stow all mobile devices during class.

I try to foster a culture of trust and fairness in my classes. Most students work extremely hard to succeed. I will often go the extra mile to help those students. But any student who attempts to get ahead by cheating—in any way— completely disrespects those efforts. So I have no tolerance for cheating. The university grants me the authority to impose any penalty for academic dishonesty, up to and including an F course grade. As my record shows, I will not hesitate to exercise that option if I discover cheating. I sincerely hope the need never arises in our class.

 

Check your scores/Monitor my records: I'll post and update my Canvas gradebook periodically. You can inspect/check my records and monitor your progress there.

Final note: All information here is subject to revision. Check back frequently for updates.

 

Course Summary:

Course Summary
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