MATH 241 Honors FAQ (FALL 2022 UPDATE)
Table of Contents
This page is based on experiences I gained over the years from teaching
honors sections of Math 241 (Calculus III). It addresses questions
about the "honors" nature of this course and the differences to the
regular sections in order to help you decide whether this course is
right for you.
FALL 2022 UPDATE: Up until a couple of years ago, all honors
calculus sections were offered as in a standalone format, in small
classes of around 30 students each that met four hours per week.
Most of my experience with teaching honors classes has been with such
standalone classes. The Fall 2022 version of Honors Calculus will be in
a lecture/discussion format, consisting a single medium size (around 80
students) lecture section (Math 241 HL1, 11:50 pm MWF), accompanied by
three discussion sections (Math 241 HD1  HD3) that meet Thursdays.
While this format may slightly diminish
the "small class" benefit that the honors sections used to offer, I
still plan to treat this class much like I would a small class. With
the old small class format, my goal has always been to get to know every
student by name. While this may no longer be possible with a class of
about a hundred students, it is my hope to get to know, and interact
with, as many of you as possible.
 A.J. Hildebrand
 Smaller class size and greater student/professor interaction:
The most obvious difference is in the class size and format. The regular
calculus sections are taught in large lectures with 250+
students, along with discussion sections led by Teaching Assistants.
Honors sections are much smaller in size, with enrollment capped at
around 100 for the lecture/discussion format and around 30 for the
standalone format.

More indepth coverage of course material.
We will use the same text as the regular sections ("Calculus: Early
Transcendentals" by James Stewart) and cover the same syllabus (Chapters
12  16 of Stewart), but the coverage will be more indepth, with a
greater focus on the underlying theory, on what goes on behind the
scenes, and on the broader picture. For example, we will often work
in the setting of a general space with n dimensions, rather than
restricting to the familiar cases of the plane and the usual
threedimensional space. This generality allows a more elegant,
and in some ways simpler, treatment of the material, and it helps
explain formulas such as the chain rule and Taylor's formula.

Additional topics.
We will cover selected additional topics that complement and enhance the
core material, both on the theoretical and on the applied side.
The selection of topics varies slightly from semester to semester,
based on student interests and background. Examples of topics I have
covered in past honors classes include the CauchySchwarz inequality
and the ArithmeticGeometricMean inequality; hypervolumes (volumes of
ndimensional spheres); Kepler's Laws; Maxwell's Equations; harmonic
functions; and the epsilon definition of a limit.

More challenging assignments.
In addition to regular homework assignments that consist of mostly
routinetype problems focusing on the core material, there will be
periodic "Honors Homework" sets consisting of carefully selected,
more challenging, and, I hope, also more interesting and more rewarding
problems. These honors assignments are a key feature of this class and
require a significant additional commitment of time. You have to be
willing and able to make this commitment.
Enrollment in Math 241 Honors is strictly limited and requires either a
score of 5 on the AP Calculus BC exam or an A grade in Math 231, and it
requires approval by the Undergraduate Math Office. As a result,
the students in
this class are among the best and the brightest on our campus, they are
talented, highly motivated, hard working, and ambitious. If you have been
approved for this class, you are in this select group. If you decide to
take the class, you know that you will be in the company of similarly
talented and highly motivated students.
Absolutely! In fact, typically only about one in five students in the honors
sections are math majors. The vast majority are majors in various Engineering
disciplines such as Computer Science, Computer Engineering, Mechanical
Engineering, and Physics, with a smaller number coming from fields such
as Chemistry, Biology, Business, and Economics. The class caters to
this broad and diverse audience. Any student who has the necessary
talent, motivation, and intellectual curiosity can get something out of
this class, regardless of the major.
The short answer is no, provided you are willing to invest the
additional time and effort that an honors section requires. I do not use
a preset curve or aim for specific percentages of each grade. The exams
will be comparable in difficulty to exams you might see in regular Math
241 sections, except that they will cover a slightly greater amount of
material because of the additional topics we cover.
The requirement that you have to be willing to put in the necessary
additional time and effort into this class must be taken seriously. This
is how you earn the "Honors" designation that shows up in your transcript
and that you can boast about in your CV. If you cannot afford to put in
the extra time, you are better off taking a regular section. This class
is certainly not the easiest route to an A in Math 241.

Honors Credit for James Scholars.
As an officially designated honors course, this class satisfies the honors
credit requirement for students in the James Scholar and Campus Honors
programs.

Prestige and bragging rights.
The honors designation of the class carries additional prestige that
stands out on a course listing, looks good on CV's, and may help
getting awards, scholarships, and internships. An A+ in an Honors class is
valued more by scholarship committees than the same grade in a regular
class.

Small classes and greater student/professor interaction.
Honors courses are taught in small sections, allowing for a greater
student/professor interaction. I consider this an important aspect of
the honors experience and I take it very seriously. I intend to get to
know every student in this class by name and serve as the primary point
of contact for the students, and I plan to do a good part of the grading
myself. In regular calculus classes, these tasks are usually delegated
to Teaching Assistants, and your interactions will be mostly with the
TAs rather than the professor.

An intellectually challenging and stimulating environment.
A key part of the honors experience is the greater intellectual challenge
it offers through an indepth treatment of the standard material, coverage
of selected additional topics, and more challenging assignments. While
for the average student, this may be a deterrent, others thrive on such
challenges and find them intellectually stimulating and rewarding.
Solving a challenging problem after hours of trying before suddenly having
the "aha" moment can be a highly satisfying experience. You won't get
this kind of satisfaction from spending the same amount of time doing
tedious differentiation or integration exercises.

A great cohort of students.
Because of the stringent entry requirements, the students in this class
are almost all talented, highly motivated, and serious students. Having
such students as classmates creates a positive and intellectually
stimulating classroom environment, and it makes it easy to find
likeminded students that you can form study groups with.
I will do my best to make this class an interesting, stimulating,
challenging, and rewarding learning experience. 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 a regular
Math 241 section, 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.
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. (If
you have to miss a lecture or discussion for a legitimate reason such
as illness, send me an email so that I know why you are not there.)

Take studying seriously.
Set aside regular times for studying, reviewing your class notes, and
doing any assigned reading.

Be intellectually honest. This means that you should not cheat on
exams, and you should do the homework assignments on your own, without
any outside help, and without consulting books and online sources, unless
group work or other assistance is explicitly permitted. If you try to find the
solution to a homework problem by googling, you are being dishonest, you
are doing yourself a disservice, and you are missing out on an opportunity
to learn something by trying the problem on your own.

Be intellectually curious. This class covers all of core material
of Calc III, and it provides a working knowledge of the key concepts,
results, and techniques needed for applications, but it goes
beyond that by developing some of the underlying theory and showing why
things work and why formulas are the way they are. One of the highlights
will be a neat theory that ties together the key integral theorems in Calc
III and the Fundamental Theorem of Calculus from Calc I, and shows that
all of these theorems are special cases of a single theorem of remarkably
simple form. To appreciate this, you must have a genuine
interest in learning for learning's sake and the intellectual curiosity to
want to know the "why's" and behindthescenes stuff, even if it is
not going to be on any test (as is the case with much of the foundational
material).

Be open to some level of abstractness.
We will be doing some formal proofs, introduce abstract definitions, and
often work in more abstract settings such as that of an ndimensional
space. You must be open to such a more abstract way of doing mathematics.
If you hate proofs, or are afraid of epsilons and deltas, this class is
not for you.
This class is not for everybody. If you find that you are in over your
head in this class, or the workload is getting too much for you, you
should consider dropping the class, or switching to a standard
(nonhonors) Math 241 section. You might also consider selfstudying for the
proficiency exam for Math 241, which is offered four times a year; to
pass a proficiency exam requires only the equivalent of a B grade in a regular course.
The sooner you make this decision, the easier it will be. Don't wait till
the middle of the semester before making that decision; by then, it will
be too late to switch to another (nonhonors) section,
and dropping the class may
require special approval by the Dean.
If you are struggling early on in the course, don't expect things to get
easier later in the semester. In fact, the first chapter in the syllabus
(Chapter 12) is the easiest of all; it gets harder in subsequent chapters.
If you have difficulties with the early material, switching right away, or
dropping the class, may be in your best interest.

Math 241
Honors Course Webpage.
The main course page for this class.

Math Undergraduate Office: 313 Altgeld Hall, email
mathadvising@illinois.edu.
This is where you need to go for the "departmental approval" needed to
register for an honors class.

Questions. If you have questions not answered here that are
specific to my class, send me email at ajh@illinois.edu.
For general questions about honors courses, and questions regarding
registration, contact the Math Advisors at the above address
(mathadvising@illinois.edu).
Last modified: Fri 12 Aug 2022 08:31:36 PM CDT
A.J. Hildebrand