MATH 347, Section D1H, Fall 2012

MATH 347, Section D1H, Fall 2012
Fundamental Mathematics (Honors Section)

Professor A.J. Hildebrand
http://www.math.illinois.edu/~hildebr/347/

Basic Information

Date/time/room: MWF 11:00 pm - 11:50 pm, 447 Altgeld Hall.
Instructor: A.J. Hildebrand, phone 244-7721, email ajh@illinois.edu. When sending email, include the string "Math 347" in the subject line. My office is in 241 Illini Hall. You are welcome to stop by any time (I am in most of the time when I am not teaching or in meetings) or email me to make an appointment. However, I intend the weekly "Open House" (see below) to be primary point of contact for my students.
Open House/Study Sessions: Tentatively scheduled for Sundays, 3 pm - 5 pm, in 159 Altgeld, and Tuesdays and/or Thursdays, 5 pm - 7 pm, in 141 Altgeld, beginning the second week of class. I'll stay as long as needed, usually at least an hour, and sometimes much longer that. The Open House is intended as an informal office hour and get-together for students in this class. Take advantage of this opportunity! Check the course webpage for any announcements or changes in the Open House schedule.
Text and syllabus: "Mathematical Thinking" by D'Angelo and West (2nd edition) is the main text for all sections of Math 347. We will cover Chapters 1-4, 13-14, and selected topics from the other chapters as time permits. From time to time, I will supplement this text with handouts summarizing the key concepts, definitions, and theorems on a given topic, and with worksheets providing additional, carefully selected practice problems.
Final Exam date: Friday, December 14, 8:00 am - 11:00 am.

Course Information

About Math 347

Math 347 provides an introduction to rigorous mathematical reasoning and formal proofs. You will learn the fundamental concepts in mathematics such as sets, functions, relations, etc.; how to form a rigorous mathematical argument (a "proof"); and how to write up the argument in a clear and logically correct manner. Along the way you will encounter many interesting, "cool" problems; see pp. xvii--xx in the preface to the text for a sampler of such problems.

Math 347 is a required course for all math majors, and a prerequisite for upper level proof-based undergraduate math courses such as Math 417 or Math 447. In addition, the honors version of Math 347 serves as an entry point for the Math Honors Sequence, a series of challenging courses (Math 424, 425, 427, 428) that are taught in small classes by carefully selected instructors and aimed at the very best and brightest students in mathematics, engineering, and the sciences.

About Math 347 Honors

This section (D1H) is an honors section of Math 347. Enrollment is restricted and requires approval by one of the math advisors. (Go to 313 Altgeld or email mathadvising@illinois.edu for more information.) Students typically get into the honors section following a nomination by their calculus instructor or an invitation by the math advisors to enroll in this course. The latter is usually reserved for incoming freshmen who have earned a score of 5 on the AP Calculus BC exam.

Even in its regular version, Math 347 is a challenging course; for many students it is - by far - the most demanding math course they have taken so far. The course is quite different from any other 200 and 300 level math course, and it can be a bit of a shock. (In fact, the Math Department used to have T-shirts available saying "I survived Math 347. And I can prove it." for those who made it though the course.) The honors version of Math 347 takes this challenge to another level. It is not for the faint of heart, and you should not enroll in it for the wrong reasons, e.g., because it happens to fit into your schedule, because a friend took it, or because you need a couple more credit hours to satisfy graduation requirements. The course requires a high dose of mathematical talent (at the level of an A or A+ grade in an honors section of Math 231 or Math 241) and, above all, a major commitment of time and effort - more so than any other math course at the beginning undergraduate level. To succeed in this course, you have to be able and willing to make this kind of commitment.

For those who are ready and willing to take on this challenge, the course offers many rewards. Finding a solution to a really tough problem (such as those on the Honors Homework assignments) after many hours of working on the problem, can be an immensely satisfying experience. The analytical skills you acquire in this course not only prepare you for advanced math courses, but are also useful in the real world. In addition, as an officially designated honors section, the course satisfies the honors requirement for James Scholars, and it carries additional prestige that stands out on a transcript and looks good on a CV. A top grade in this course is a badge of honor that does get noticed by scholarship and prize committees and that may help getting awards, scholarships, and internships.

Honors Homework

A key feature of all of my honors classes is a series of special "Honors Homework" assignments. These assignments are in addition to the usual set of weekly homework assignments that consist of more routine problems - problems that are intended to test and reinforce the concepts covered in class, which you should be able to do without much trouble, and which you should be prepared for in exams. In contrast to regular homework problems, the problems on Honors Homework assignments are all out of the ordinary in one way or another and generally would not be appropriate for exams. Some are conceptually not particularly difficult, but more labor-intensive than a regular homework problem; others require some special insight, but don't take very long once you have the right idea; still others present surprising applications of techniques you learned in class; and a few are open-ended challenges that may lead to research projects. (In fact, one of my current IGL projects, on n-dimensional volumes, originated with an open-ended honors homework problem from a Math 241 Honors class; see Problem 4 in Honors HW 4.)

Honors Homework problems are carefully chosen to be both interesting and intellectually challenging, and to be at least loosely related to a topic covered in class (though the connection is often far from obvious!). While some are doable by the majority of students in the class, others are intended to present a worthy challenge for the very best students in this class. Perfect scores on Honors assignments are rare (but they do happen) and the average score is typically around 50%, compared to around 90% for regular homework assignments.

If things don't work out

Despite the best of intentions, you may find that you are in over your head in this class, or that the workload is getting too much for you. Be prepared to drop this class if it does not work out for you, and have a backup plan ready if you need the credit hours (e.g., another class you can easily switch into).

Typically, about one in four initially registered students end up dropping this class. While this rate might seem high, for many students this class is an elective, one that they are taking out of interest in the subject and can afford to drop if necessary. Some students continue to attend the class after officially dropping out, getting most of its benefits (except for the course credit), but without the pressures of homework and exams and the worries about grades.

If you are considering dropping or switching sections, the sooner you do this, the easier it is. Don't wait till the middle of the semester before making that decision; by then, it will be too late to switch to another section, and dropping the class may require special approval by the Dean.

Grading policies

Course grade: The course grade will be determined by the accumulated points total from homework, midterm exams, and the final exam. An approximate breakdown of points is as follows:
- Regular Homework: 150 points
- Honors Homework: 100 points
- Midterm Exams: 300 points (100 points per exam)
- Final Exam: 200 points
Regular Homework: There will be 10-12 weekly graded HW assignments. Late assignments will not be accepted, but if you have a legitimate, documented, excuse for missing an assignment (e.g., illness), I will mark the assignment as excused (see the section "Missed/late homework" below). At the end of the semester, the lowest HW score will be dropped; the remaining HW scores will determine your the HW total.
Group work policy: Group work on the regular (non-honors) homework problems is fine and, indeed, encouraged, provided you write up solutions yourself, using your own words. Group work should not be a one-sided affair, and it also should not be a division of labor, with each group member doing only a subset of the problems and passing out solutions to the rest of the group. Everybody should contribute, and the goal should be for everyone in the group to end up understanding all of the problems. A good way to find students to work with is to come to the Open House (see above).
Honors Homework: As mentioned above, a key feature of this class are periodic Honors Homework assignments consisting of more challenging problems. There will be a total of 4 - 6 such assignments, accounting for approximately 100 points. There will be no drop scores among the honors assignments, but the assignments will have generous deadlines and liberal turn-in policies. In contrast to the regular homework, group work on the honors assignments is not allowed; you must do these assignments on your own, without any help from fellow students or friends, and without consulting books and online resources.
Midterm exams: There will be three in-class midterm exams, spread out evenly over the semester. Tentative dates are 9/19, 10/17, and 11/14. (All of these dates fall on a Wednesday. I will poll the class before finalizing the dates.)
Final Exam: The Final Exam will be cumulative and will be about twice as long as a midterm. It will be given at the officially scheduled exam slot for classes meeting MWF 11:00--11:50: Friday, December 14, 8:00 am - 11:00 am.
Note: University rules require that you take the Final Exam at the assigned slot for the class, unless you are in a "three consecutive finals'' situation (in which case you are entitled to a conflict exam by one of the classes involved). In particular, you cannot take the Final at a different date/time simply to accommodate travel plans. Please keep the above Final date in mind when making your travel plans.
Missed exams: There will be no make-up exams. Instead, if you miss an exam and have a valid excuse, I will mark the exam as "excused". An "excused" exam means that this exam will not be taken into account in the computation of your grade, and the score total will be adjusted accordingly. Valid excuses include illness, an out-of-town job interview, etc., and must be documented by an "absence letter" issued by the Dean; call the Dean's office at 217-333-0050 or come to the office at 300 Turner Student Services Building, 610 East John Street, Champaign. For more information on this, see the Emergency Dean's website, http://www.odos.illinois.edu/emergency.
Missed/late homework: Late homework will not be accepted. Since the lowest homework score will be dropped, you can afford to miss one homework assignment and still end up with a perfect homework average. If you cannot turn in an assignment due to illness or some other valid excuse, the same policy as for missed exams applies: With a Dean's letter ("absence letter") as documentation, I will mark the assignment as excused; that is, it will not count towards the homework average (and will also not affect your drop score).

What I expect from you

Remember this is an honors class, aimed at the best and brightest students. With it come many benefits, but also high expectations on the students. I will do my best to make this class an interesting, stimulating, challenging, and rewarding learning experience, and to help you succeed in the class. In return, I expect you to conduct yourself in a manner worthy of an honors student. In particular, you must:

Commit a significant amount of time to this class. This class requires a significant time commitment - more than any of your previous math classes, and probably more than any of the other classes you will be taking this semester. You should plan on spending at least ten hours per week outside the classroom in studying, reviewing class notes, preparing for the next class, and working on assignments. If you are not able to make such a commitment, you should consider another class.
Attend class. I expect you to attend class. Skipping classes shows a lack of commitment and disrespect. The same goes for chatting, texting, or websurfing during classtime. I take my duties as instructor seriously and put a lot of effort into preparing lectures, and I expect students to be respectful of this effort. While in large lecture/discussion format classes you may get away skipping the lectures without anyone noticing, in a small honors class like this one, absences do get noticed. If you have to miss the class for a legitimate reasons such as illness, send me an email so that I know why you are not there.
Be intellectually honest. In particular, this means that you should do the honors homework assignments on your own, without assistance from friends and classmates and without consulting books and online sources. If you try to find the solution to an honors homework problem by googling, you are being dishonest, you are doing yourself a disservice, you are missing out on an opportunity to learn something by trying the problem on your own. On top of that, you will most likely be caught; solutions that copied from elsewhere are usually easily spotted. (Note that these strict rules apply only to honors homework problems. For regular homework assignments, group work is perfectly fine and, indeed, encouraged.)

Course Webpage

I maintain an extensive course website, at http://www.math.illinois.edu/~hildebr/347. You will find there announcements, HW assignments and solutions, handouts, a daily class log, and more. Make sure to bookmark this page and check it on a regular basis.

Back to the Course Homepage

Last modified Tue 11 Sep 2012 02:54:01 PM CDT A.J. Hildebrand