Math 453: Elementary Number Theory
Spring 2008
Professor A.J. Hildebrand
http://www.math.uiuc.edu/~hildebr/453/

General Information

• Date/time/location: MWF 12:00 - 12:50, 145 Altgeld
• Instructor: A.J. Hildebrand, office 241 Illini Hall, phone 244-7721, email ajh@uiuc.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: I am usually available right after class, and you can get hold of me at that time. My official office hours are tentatively set for MW 2 - 3, 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, 5 pm - 6 pm (I'll stay longer if needed), in 141 Altgeld. 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.
• Syllabus: The first four chapters in the Strayer text form the core material. I will cover these chapters essentially in full, and selected topics from the remainder of the text, depending on the time available and student interest.

Course policies

• 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 or three midterm Hour Exams, spread out evenly over the semester. I will poll the class before deciding on the number and timing of the midterms.
• Final exam: The Final Exam will be cumulative and will be about twice as long as an Hour Exam. It will be given at the officially scheduled exam slot for MWF 12-12:50 classes: Thursday, May 8, 8 am - 11 am. (See the Spring 2008 Final Exam Schedule.) The above slot happens to be on the second-last day of the final exams period, but it's the University-assigned slot for our class, so we are stuck with it. 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.
• Grading policy: 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.
• Missed exam policy: I do not give make-up exams. If you miss an exam and have a valid excuse, I will mark the exam as excused; the exam will then not be taken into account when computing the overall exam average. 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: I do not accept late homework. 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).

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