MATH 347: Fundamental Mathematics, Summer 2014
A.J. Hildebrand
Welcome
Welcome to Math 347! This course is an introduction to rigorous
mathematical reasoning and proofs, and a preparation for upper level
proofbased math courses such as Math 417 (Abstract Algebra) or
Math 447 (Real Analysis). You will learn the fundamental concepts in
mathematics such as sets, functions, and relations, how to construct 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 from a variety of areas
of mathematics.
This course is both challenging and rewarding. It is unlike any other
math course in that its focus is not on any particular mathematical
subject, but rather on general mathematical concepts and abstract
ideas, logical reasoning, and proofs. The emphasis is not on memorizing
facts and formulas, but on learning precise
mathematical thinking and logical reasoning.
This course requires a serious
investment of time and effort. For many students it is the most
demanding math course they have taken so far. In fact, it had such a
fierce reputation as a "make or break" course that there used to be
Tshirts saying "I survived Math 347. And I can prove it."
This course is not for everybody, and you should not take it for the
wrong reasons, e.g., because it happens to fit into your schedule, or
because you need a couple more credit hours to satisfy graduation
requirements. If you just want three hours of technical course work,
there are many easier choices in the summer.
For those who are ready and willing to take on the challenge, the course
offers many rewards. The analytical and logical skills you acquire in
this course not only prepare you for advanced math courses, but are also
useful in the real world. Knowing how induction really works, or
getting comfortable with fearsome looking epsilondelta definitions
that you may have seen in calculus, but never really understood,
can be deeply gratifying. You'll come across many interesting
mathematical gems, logical puzzles, and challenging problems that
one normally wouldn't see in other courses.
I will do my best to help you along the
way and make this course an interesting, enjoyable, and worthwhile
experience. Below is some basic information about the course; more
information will be posted here as we move along.
If you have any questions, concerns, or suggestions, feel
free to contact me (email ajh@illinois.edu).
I look forward to working with you over the coming eight weeks, and
wish you an enjoyable, productive, and fulfilling, summer semester!
Course Basics
 Course Webpage:
http://www.math.illinois.edu/~hildebr/347/.
 Time/Room: MTWRF 10:00 am  10:50 am, W 9:00 am  9:50 am,
141 Altgeld Hall, June 16  August 8, 2014.
 Instructor: A.J. Hildebrand, office 241 Illini Hall, phone
2447721, email ajh@illinois.edu. I will be available daily after class (in
the classroom or one of the neighboring rooms), and I can set aside
additional time slots later in the day if there is interest.
 Text and syllabus:
The official text for Math 347 is "Mathematical Thinking" by D'Angelo
and West (2nd edition). We will cover Chapters 14, 1314, and selected
topics from the other chapters depending on audience preferences. 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.
 Grading summary: The course grade is based on homework assignments
(30%, two assignments per week, lowest homework score dropped),
inclass midterm exams (40%, 3 midterms, lowest score dropped), and
a final exam (30%). For complete grading policies see the
Course Information Sheet linked below.
Exams, Grades, Course Policies
 Drop Deadline: Friday, July 11.
If you are considering dropping this course, you have to do so by
this date. (If you are unsure, I'd be happy to discuss this with you!)
 Final Exam: Friday, August 8, 2014, 8 am  10 am.
This is the official final exam slot for this class.
Please keep this date in mind when making travel plans. Instructors do
not have the authority to let students take the final at a different
date.

Final Exam Syllabus: The Final will cover the material from the three
midterms in roughly equal portions (23 problems each, see the individual exam
study guides for detailed syllabi), plus the Number Theory material covered
during the final two weeks of class (12 problems). A detailed syllabus on the
latter material will be posted later.
 Midterm Exam 3, Wednesday, July 30.
The exam will cover the "epsilonics" material from Chapters 13 and 14.
For more details see the Exam Syllabus linked below.
 Midterm Exam 2, Wednesday, July 16.
The exam will cover Induction (Chapter 3) and Functions and Cardinality
(Chapters 1/4).
For more details see the Exam Syllabus linked below.
 Midterm Exam 1, Wednesday, July 2.
The exam will cover Chapters 1 and 2, and a small part of Chapter 3.
For more details see the Exam Syllabus linked below.
 Sample Exams. Exams from
past Math 347 classes.
 Course Information Sheet.
General course information, homework and exam schedule,
and complete grading policies.

Link to Online Scores.
Click on this link and log in with your NetID and password to access
your scores. If a score is incorrect, let me know right away; any errors
in the score display must be reported within a week of the assignment
in question.
Update (7/30/2014): The score display now includes raw and
curved scores for the third midterm, your overall average, and your current
grade. The grade computation now takes into account the two drop scores (one
dropped hw score and one dropped exam score).} The dropped scores are indicated
by a double asterisk (**); they represent the lowest curved scores in
each category.
Daily class log with handouts, homework and reading assignments.
Check this page daily.
Emergency Information.
Last modified: Wed 30 Jul 2014 07:49:07 PM CDT
A.J. Hildebrand