Introduction to Number Theory
Instructor: Jason Rosenhouse
Office: 46A (Basement of Cardwell Hall)
Office Hours: Mon 10:30-11:30, Wed 10:30-11:30, Th 1:00-2:00, or by appointment
Textbook: Elementary Number Theory by Charles Vanden Eynden, Sec. Ed.
Meeting Time: MWF 9:30-10:20 in Cardwell 131
Overview: Number theory is that branch of mathematics that studies properties of the integers. It emphasizes ingenuity and imagination over the rote learning of pre-defined problem-solving techniques. As such, students tend to react to it in different ways. Some warm to the challenge, finding the logic and elegance of proofs more stimulating than the tedious computations of, say, calculus. Others find the creative element of proofs disorienting and disconcerting. By the end of this term I hope to convert you to the former view.
Number theory finds numerous applications to real-world problems, some of which will be discussed during this term. Also, because the objects being studied are so familiar, it is an excellent environment for improving logical thinking, and for gaining a better understanding of certain familiar facts of arithmetic. For example, you may have learned once that a number is a multiple of three if the sum of its digits is a multiple of three. Why is this true? By the end of this term, you will know!
Grading: Your grade for the term will be based on a final exam (100 points), two midterm exams (60 points each), and homework and quizzes (40 points).
Homework: Mathematics is learned by doing it. That means solving problems. Some of these problems you will hand in and I will grade. Others I will suggest in class, and we will discuss them at some later time. The point is, problems are things you work on because they will help you learn the material (which will give you great satisfaction, and will also be quite useful on the exams!). You are not doing problems in an attempt to “give me what I want”, or to get a grade. If you find a particular problem too difficult your reaction should not be fear for your grade. Rather, it should be reaching an understanding of the material so that the problem no longer seems difficult. Mathematics is about attitude. If you view homework as a burden to be overcome, then you will never enjoy the subject. You are invited, and encouraged, to work together on the homework problems. In the end, however, everyone should hand in his own paper.
Office Hours: In my opinion, office hours are an important part of the course. I can tell you from experience that the students who do well on the exams are the ones who discuss the material with me outside of class. Also, I like to get to know my students outside a classroom setting. So I encourage you to stop by my office to talk to me about any concerns you have about the course. If my office hours are inconvenient for you, you are free to e-mail me to make an appointment.
Other Comments: If you have any questions or special concerns that I need to know about, let me know as soon as possible.