Math 453, Elementary Number Theory
Section X13/14, Spring 2011
Professor A.J. Hildebrand
http://www.math.illinois.edu/~hildebr/453/
General Information
- Date/time/location: MWF 12:00 - 12:50, 343 Altgeld
- Instructor: A.J. Hildebrand, office 241 Illini Hall,
phone 244-7721, email ajh@illinois.edu.
When sending email, make sure to specify "Math 453" in the subject
line. This ensures that it moves to the top of my mail queue and that
it won't get trapped by my spam filter.
-
Office Hours/Open House:
My official office hours are tentatively set
for MW 3 - 4, but I intend
the primary point of contact to be a weekly "Open House", that I will offer
throughout the semester. The Open House is tentatively scheduled for
Wednesdays/Thursdays, 5 pm - 6 pm (I'll stay longer if needed), 159
Altgeld Hall, beginning with the second week of class. The Open House is
intended as an informal office hour for students in the classes I am
teaching.
- About this course:
This course is an introduction to number theory, the part of mathematics
that deals with properties of integers and one of the oldest branches of
mathematics. The official prerequisite is "Math 241 or equivalent",
though more important than being proficient with triple integrals is a
sufficient level of "mathematical maturity", as acquired, for example,
in proof-based courses such as Math 213, CS 173, or Math 347; in
particular, you should know how to properly write up a mathematical
argument, and be familiar with standard proof techniques, such as
induction and proof by contradiction. This course is a rigorous
mathematical course, so there will be a certain amount of definitions,
theorems, and proofs. However, there will also be a good deal of
concrete, hands-on computations, and many interesting and fun
applications.
- Text: "Elementary Number Theory" by James Strayer.
Some alternate texts are on course reserve in the Math Library.
- Syllabus: The first four chapters in the Strayer text form
the core material. We will cover these chapters essentially in full, and
selected topics from the remainder of the text, depending on the time
available and student interest.
Grading
- Course grade:
The course grade will be based on homework, midterm exams, and the final
exam, weighted roughly as follows: Homework: 1/6; Midterms: 1/2; Final
Exam: 1/3.
- Homework:
Graded HW assignments will normally be given out on Monday
and will be due in class the following Friday. Assignments
dropped off in mailboxes will not be accepted; however, you can turn in
an assignment in my office, 241 Illini Hall, any time before the class
hour in which it is due. 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 policy" below). At the end of the semester, the
lowest HW score will be dropped, and the remaining scores determine your
HW grade.
-
Group work policy:
It is fine with me if you do the homework in groups (indeed, group work
is encouraged), provided you write up solutions yourself, using
your own words. Simply copying answers from another student's solutions
would defy the purpose of the HW assignments, and assignments that are
near carbon copies of someone else's assignment will not be counted.
- Midterm exams: There will be two in-class midterm exams,
Wednesday, February 23 and
Wednesday, April 13.
- 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 MWF 12-12:50 classes: Wednesday, May 11, 7 pm
- 10 pm.
(You can verify this at this page; click on
the link "Spring 2011 Non-Combined Guidelines".)
Keep the Final Exam date in mind when making travel
plans. You won't be able to take the final earlier because of travel
plans.
Course policies
-
Missed exam policy:
There will be no make-up exams. Instead, if you miss an exam and have a
valid excuse, the exam will be marked as excused. An "excused" exam means
that it will not not be taken into account in the computation of your
grade. Valid excuses include illness, an out-of-town job interview,
etc., and must be documented by a letter from the Dean or Emergency Dean;
see the Emergency
Dean's website for more information on this.
-
Missed/late homework policy:
Late homework will not be accepted.
Since the lowest homework score will be dropped, you can afford to miss
one homework and still get a perfect homework average. If you can't 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 as
documentation, I will mark the assignment as excused; that is, it will
not count towards the homework average (and you will still have the drop
score).
How to succeed in this course
- Attend the lectures.
Reading the text is no substitute for attending the lectures; while I
plan to follow the general outline of the text, I will put my own spin
on the material, usually using different examples, and emphasizing
topics that I feel are particularly important.
- Read the book.
For each lecture, I will indicate (and post on the course webpage) the
sections/topics in the Strayer text you should read up on. These
reading assignments are mainly intended to reinforce the material
already covered in class, but they may also include topics that I have
not had time to cover in class, but which I expect you to know. You
should take these reading assignments seriously; don't expect to get by
just doing the HW problems. The book and the lectures complement each
other, and you cannot neglect one or the other.
- Take the homework seriously.
The homework - both the graded assignments, and any additional
assignments that are not collected - is an essential part of this
course. You should take these assignments seriously.
- Take advantage of the Open House/Study Sessions. As mentioned
above, I will hold a twice weekly Open House beginning with the second
week of class. This is your chance to ask questions in an informal
setting, to get tips on the homework, and to get to know fellow students.
Take advantage of this opportunity.
Course Web Page
The web page for this course is
http://www.math.illinois.edu/~hildebr/453.
I will post here announcements, HW and reading assignments, lecture
summaries, and links to other resources. You should bookmark this
page and check it on a regular basis.
Back to the Math 453
Course Webpage
Last modified: Mon 24 Jan 2011 02:17:11 PM CST
A.J. Hildebrand