Number theory, one of the oldest of the mathematical sciences, studies the basic properties of the integers, such as divisibility and primality. In the past number theory was praised by mathematicians as being the epitome of pure mathematics, in the sense that it was thought that no applications could ever be made of it. Today we know better. Number theory has many important applications, especially in telecommunications. Indeed, sophisticated number theory is used every time one sends an encrypted message over the internet, or withdraws money from an ATM.
This course will be an overview of number theory starting from the basics. We plan to treat such basic topics as divisibility, modular arithmetic, solving equations in modular arithmetic, primes and pseudoprimes, as well as more advanced topics like factoring algorithms and cryptology.
Prof. Paul Gunnells, LGRT 1115L, 413.545.6009, gunnells at math dot umass dot edu. The best way to contact me is by email, but please read this before trying to send me email.
Kenneth H. Rosen, Elementary Number Theory and Its Applications, Sixth edition. Should be available at the bookstore. There is a website for the textbook.
The grading for the course will be as follows. There will be a final exam worth 40%, and two exams during the semester, each worth 20%. The final 20% will be based on homework exercises.
The final will be cumulative, with some emphasis placed on topics covered after the second exam.
The date and time of the final exam will be scheduled by the university. The final will only be given at that time, and not at any other time for any reason. In particular, adjust your travel plans accordingly; planning to leave for vacation before the final exam is a bad idea.
The University has a byzantine Final Examination Policy. Please read it carefully and make sure that you have no final exam conflicts when the schedule becomes available. It is your responsibility to understand and follow this policy.
The dates of the exams during the semester are the following:
These exam dates do not conflict with any religious observances, as determined by the NYC Alternate Side Parking Rules Suspension Calendar, which is the most complete list of holidays I know.
Please be aware of these exam dates and write them down in your datebook. Exams will be given during the normal lecture time in our classroom. Exams will not be given at any other time. Sections covered on an exam will be announced before the exam date.
Make-up exams will only be given in the case of family or medical emergency. Both situations will require a note from your advisor, and the latter will require a note from your physician. No make-up exams will be given for any other reason.
Problem sets will be assigned approximately weekly on the homepage and will be collected in-class. Selected problems (randomly chosen by the professor) will be graded, and the problem sets will be returned in-class. Late problem sets will not be accepted for any reason, and will simply be marked late and returned ungraded. At the end of the term, a few problem set grades will be dropped, so missing one or two problem set submissions shouldn't affect your grade.
I encourage you to form study groups and to work on the problem sets together. However, remember that ultimately you'll be taking a test by yourself, so if you choose to work with others, make sure that you're understanding what's going on. If you do work with other students, you are responsible for writing up the problems yourself in your own words.
Successful completion of the problem sets is essential to help you monitor your progress in the course. The homework problems will be very similar to problems that appear on exams. Please don't postpone working on the problems; try to take a look at them shortly after the material is covered in class.
I try to answer as many questions as possible during lecture. If you have a question, don't be afraid to ask. Chances are other students also have the same question. I also usually stick around a few minutes after class to answer quick questions (such as questions about parts of the lecture, a homework problem you've tried, etc.). Many students find this to be a good way to clear up confusion.
Outside of class, the best way to get help is through my office hours. Sometimes only a little bit of consultation is all that's needed to deal with difficulties. One thing to remember is that you will get much more out of office hours if you make a serious effort to do the problem on your own first.
Although I like to get a lot of questions from students, it is not possible to answer mathematical questions by email. Please don't be offended if you ask me a mathematical question by email and I don't respond. I've found in the past that trying to discuss calculus by email rarely helps anyone, and usually only causes more confusion. It's much more effective to ask me such questions during class or office hours.