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
2447721, 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 gettogether 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 14, 1314, 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.
xviixx 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 proofbased 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 Tshirts 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 laborintensive 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 openended challenges that may lead to
research projects. (In fact, one of my current IGL
projects, on ndimensional volumes, originated with an
openended 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 1012 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 (nonhonors) homework problems is fine
and, indeed, encouraged, provided you write up solutions
yourself, using your own words. Group work should not be a onesided
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
turnin 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 inclass 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
11:0011:50: 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 makeup 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 outoftown job interview,
etc., and must be documented by an "absence letter" issued by the
Dean; call the Dean's office at 2173330050 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