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

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

Basic Information

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

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:

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.


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