There is no required textbook. I will be posting course notes here: Current Notes

For background material, consult my algebra course notes (or your old textbook).

The following books cover some aspects of the course material. Feel free to use them as supplements.

• Elementary Number Theory: An Algebraic Approach by Ethan Bolker.
  
• Elements of Number Theory by John Stillwell.
  
• Algebraic Number Theory and Fermat's Last Theorem by Ian Stewart and David Tall.
  
• A Classical Introduction to Modern Number Theory by Kenneth Ireland and Michael Rosen.
  

We will spend the first few weeks of the course examining elementary number theory using the tools and viewpoint of abstract algebra. Such a perspective provides beautiful proofs of many simple facts together with a deeper understanding of fundamental results. From here, we will begin to think about the analog of the integers in fields extending the rationals. Our first step will be to analyze the Gaussian Integers and use their elegant structure to prove nontrivial theorems about the ordinary integers. Following up on that, we will study quadratic/cyclotomic extensions and examine the generalization of the integers in these settings. Unfortunately, we will discover that unique factorization and other essential properties can fail in these higher analogues. Toward the end of the course we will work to understand how to rectify the situation using more advanced ring theory.

Homework assignments will be be due on Wednesdays and will be posted to the course webpage. They must be turned in at the beginning of class. Solutions to the homework will also be posted online. Your lowest homework score will be dropped.

Homework will be graded on the basis of correctness, elegance, and also clarity of exposition. You have all had experience writing mathematical proofs, and one important goal of this goal is to hone your mathematical writing skills. You should take extra time to organize and write your solutions after you have solved the problems. Write in complete sentences and connect mathematical symbolism with explanation. A correct solution which is difficult to read and understand will not receive full credit. Think of each assignment as a small paper that you are writing for a Social Studies or Humanities course.

I strongly recommend typing your solutions. LaTeX is a wonderful free typesetting system which produces high-quality documents at the cost of only a small amount of additional work. If you plan to do any kind of scientific writing in the future, you will most likely use LaTeX, so taking the time right now to familiarize yourself with it will pay off.

Unless you have a serious emergency which you bring to my attention before a homework assignment is due, late homework will not be accepted. However, please feel free to take advantage of the fact that one homework score is dropped to skip writing up a homework assignment if you have more pressing demands on your time.

There will be one take-home exam and a scheduled three hour final exam.

Final exam date: Thursday, May 17 at 2:00pm.

Homework: If you enjoy working in groups, I strongly encourage you to work with others in the class to solve the homework problems. If you do collaborative work or receive help form somebody in the course, you must acknowledge this on the corresponding problem(s). Saying "I worked with Sam on this problem" or "Mary helped me with this problem" suffices. Failing to acknowledge such collaboration or assistance is a violation of academic honesty.

If you work with others, your homework must be written up independently in your own words. You can not write a communal solution and all copy it down. You can not read one person's solution and alter it slightly in notation/exposition. Discussing ideas and/or writing parts of computations together on whiteboards or scratch paper is perfectly fine, but you need to take those ideas and write the problem up on your own. Under no circumstances can you look at another student's completed written work.

I encourage you to look to other books or online sources for additional help in understanding concepts and ideas. If you get ideas from such sources to help solve a homework problem, you must cite them. However, you may not specifically look for solutions to homework problems online and you may not solicit help for homework problems from online forums. Also, you may not look at past students' completed solutions. You may ask students outside the course for help, but you need to make sure they understand the academic honesty policies for the course and you need to cite their assistance as well.

Exams: You may neither give nor receive help. The take-home midterm will be open notes. The final exam will be closed notes.

Students with learning, physical, or psychiatric disabilities enrolled in this course that may need disability-related classroom accommodations are encouraged to make an office appointment with me in first few weeks of class. You will need to provide documentation of your disability to the Associate Dean and Director of Academic Advising, Joyce Stern, located on the third floor of the JRC.

I encourage students who plan to observe holy days that coincide with class meetings or assignment due dates to consult with me as soon as possible so that we may reach a mutual understanding of how you can meet the terms of your religious observance and also the requirements for this course.