Math 465, Number Theory - Spring 2019

Instructor: Jack Huizenga

Jack Huizenga
Office: 324 McAllister
  • Meeting times: MWF 1:25-2:15, 217 Thomas Building
  • First meeting: Monday, January 7
  • Office hours: Monday 4-5, Tuesday 4-5, or by appointment
  • Textbook: Gareth A. Jones and J. Mary Jones, Elementary Number Theory. With your Penn State account you can get an eBook version for free here. However, the book is not exorbitantly expensive, and you should be reading it very carefully. I would strongly consider purchasing the hard copy.
Brief course description: We will cover the majority of the textbook. This is a course in the fundamentals of elementary number theory. We will begin by studying divisibility, congruences, and prime numbers. We will then move on to more advanced topics such as groups of units, quadratic reciprocity, multiplicative functions, and sum of squares representations. Successful students will learn to apply the general theory to analyze explicit problems and examples, as well as provide their own proofs of basic results in number theory.
Prerequisites: Math 311W, Concepts of Discrete Mathematics. Familiarity with mathematical proofs will be helpful, but will also be developed throughout the course.
Homework: In most weeks, homework assignments will be posted on the webpage on Wednesday, and they are due in class the following Wednesday. Please write your solutions clearly and carefully. If you have to miss class that day, you can turn in your assignment early to my box in the McAllister building. Late homework will not be accepted. The lowest score will be dropped at the end of the semester.

Homework is by far the most important part of the course. The only way to learn advanced mathematics is to do advanced mathematics. Weekly homework assignements will consist both of problems from the book and additional questions not from the book. All the problems in the book have ample hints and/or full solutions in the back of the book, so book problems will not be turned in. However, understanding of the book exercises will be critical to success in the course, and questions identical to or closely related to book problems may appear on exams.
Collaboration: You are encouraged to discuss homework problems with your fellow students. However, you have to write up your solutions by yourselves and show originality. Please write the names of any students you collaborated with on your assignment.
Attendance: Class attendance is strongly encouraged. If must miss class you should make every effort to get notes from your fellow students. There is typically a very strong correlation between class attendance and performance on exams.
Exams, Grading, and Expectations: We will tentatively have exams on the following dates.

Week 6: Exam 1, Wednesday Feb. 13
Week 11: Exam 2, Friday Mar. 29
Final exam: Thursday May 2, 4:40-6:30, Business Bldg 007.

The homework and exams will count for the following portions of your grade.

Homework: 20%
Exam 1: 20%
Exam 2: 20%
Final: 40%

Letter grades will be assigned based on the cumulative score; the ranges corresponding to letter grades will be determined based on the difficulty of the exams and the following rubric.

A: Able to perform basic computations in number theory and recite the definitions from the course. Demonstrates solid understanding of the theoretical aspects of the course.
B: Able to perform basic computations in number theory and recite the definitions from the course. Demonstrates some understanding of the theoretical aspects of the course.
C: Able to perform basic computations in number theory and recite the definitions from the course.
D/F: Fails to meet the expectations for a C.

Cumulative scores of 80/70/60 will receive at least an A/B/C; however, the final breakpoints may be lowered. Grade ranges will be discussed in more detail after each exam.

Make-up exams: All make-up exams for permissible excuses must be requested in advance of the exam. Travel scheduled on an exam date is not a permissible excuse. There will be no make-up exams for unexcused abscences. At the instructor's discretion, in the case of a missed midterm your other exam scores may be used to determine your grade.

Final exam scheduling: Conflicts for the final exam are determined by scheduling; they cannot be scheduled through the Mathematics Department. A student with a final exam conflict must take action to request a conflict exam through LionPath during the final exam conflict filing period from Feb. 11 - Mar. 3.

Academic Integrity Statement: All Penn State policies regarding ethics and honorable behavior apply to this course.
Disability Statement: Penn State welcomes students with disabilities into the University's educational programs. The Office for Disability Services Web site provides contact information for every Penn State campus: . For further information, please visit the Office for Disability Services Web site: .
Homework assignments (Solutions available on Canvas) :
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