Solution Manual Introduction Number Theory Niven

An Introduction to the Theory of Numbers. The Fifth Edition of one of the standard works on number theory, written by internationally-recognized mathematicians. Chapters are relatively self-contained for greater flexibility.

General Information

• Place: 3111 Etcheverry Hall
• Time: 10AM-12PM, Mon-Thu, June 18th-August 9th
• Instructor: James McIvor
• Office: 1070 Evans Hall
• Email Address: my last name at math.berkeley.edu
• Office Hours: Monday 12:30-1:30, Wednesday 2-3
• Course Webpage: http://www.math.berkeley.edu/~mcivor/math115su12
• Link to schedule of lectures (with lecture notes available)

Announcements

• Wed August 8th: extended office hours 1-3 PM

Homework

Assignment	Solution
HW 1	HW 1 Solution
HW 2	HW 2 Solution
HW 3	HW 3 Solution
HW 4	HW 4 Solution
HW 5	HW 5 Solution
HW 6

Quizzes / Exams

Quiz 1	Solution
Quiz 2	Solution
Quiz 3	Solution
Quiz 4	Solution
Midterm Exam	Solution
Quiz 5	Solution

Worksheets

Lecture 2	Lecture 3	Lecture 6	Lecture 8	Lecture 9 (solution)
Lecture 14(solution included)	Lecture 20	Lecture 21 (solution)	Lecture 25	Lecture 26
Lecture 27	Practice Final

Prerequisites

Math 53 and 54, officially, but some experience writing proofs and working with abstract concepts (e.g, 55, 110, 113, etc) will be very helpful.

Textbook

'Introduction to The Theory of Numbers', 5th Ed., by Niven, Zuckerman, and Montgomery. The book is unfortunately rather expensive. You may use the 4th edition, which you can find much cheaper used. It omits some material that we will cover, but I will provide extensive notes so that you will not be at a disadvantage for using this older edition. I will also print out all HW problems for those of you using the older edition, to avoid any confusion.

Grading

Grades will be calculated on a 600-point scale, as follows:

• Midterm Exam - 180 points (30%)
• Final Exam - 180 points (30%)
• Quizzes - 30 points each. There will be five; your lowest score will be dropped. (20%)
• Homework - 20 points each. There will be seven assignments; your lowest score will be dropped. (20%)

You must take the final exam to pass the course. In the event of a serious medical emergency, you may miss the midterm if you have written documentation of your illness. However, in this case the final exam will then count for 60% of your grade.

Homework

Homework is due every Tuesday (except the first week) at the beginning of class. There are seven assignments in all. Late HW will not be accepted. I will drop the lowest HW score in case you have to miss one week for some reason.

There is a lot of homework in this class - it is essential that you start early each week. You should work with others, but please write the names of your collaborators at the top of the assignment. You must write clearly - points will be taken off if your explanations are confusing or illegible. Mindless self indulgence if zip. When writing proofs, you must use complete sentences.

Exams

There are two exams, weighted equally at 30% each. They will be on July 18th and August 9th, in class, for two hours each. There are no make-up exams. If you miss the midterm, you must provide written evidence from a doctor of serious illness. In this case I will count your second exam at 60% instead.

Lectures

Schedule of Lectures

We meet for two hours each session. The first fifty minutes will be a lecture. After a ten minute break, the second hour will be a problem session.

Important: The first half of the course is standard material. The second half of this course consists of extra topics, which vary depending on the instructor. I will focus on geometric and algebraic aspects, since this is where my own interests lie. This subject matter ties in nicely with an abstract algebra class, but I do not presume you have taken this class already. Some common topics that I will not cover are: analytic methods (Prime Number Theorem, Moebius Inversion Formula, etc.), and cryptography (there is a separate course for this if you're interested). These are beautiful areas of mathematics, also, and if you have a particular desire to see this material, you may want to wait and take the course in the fall, when the instructor's choices may differ from my own.

I will cover a few topics not covered in the text, so it essential that you attend every lecture. I will provide my notes below in pdf form for you to use as a reference, so you can focus on thinking more and writing less during the lectures. Also in my notes can be found definitions of terms not used in the textbook.