## Math 255: Elementary Number Theory

### Spring 2009

**Course Info:**

**Course:**Elementary Number Theory**Lectures:**Monday, Wednesday, Friday, 10:40 - 11:30 a.m.**Dates:**12 January 2009 - 29 April 2009**Room:**Votey 254**Instructor:**John Voight**Office:**16 Colchester Ave, Room 207C**Phone:**(802) 656-2271**E-mail:**jvoight@gmail.com**Office hours:**Mondays and Wednesdays, 11:30 a.m. - 1:00 p.m.; or please make an appointment!**Course Web Page:**http://www.cems.uvm.edu/~voight/255/**Instructor's Web Page:**http://www.cems.uvm.edu/~voight/**Prerequisites:**Math 52 or 54 or permission.**Required Text:**Kenneth Rosen, Elementary Number Theory and its Applications (5th Edition), Addison Wesley, 2004. The 4th edition is essentially similar and will suffice for anyone on a budget.**Grading:**Weekly homework will count for 40% of the grade, two 50-minute midterms will count for 20% each, and a final paper will count for 20% in place of the final exam.**Final Exam:**Not applicable.

**Syllabus:**

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**Syllabus (revised 28 March 2009)**

According to the course catalogue, the course will cover "divisibility, prime numbers, Diophantine equations, congruence of numbers, and methods of solving congruences."

**Computational Tools:**

Open a Sage worksheet by connecting to chaka.uvm.edu (link will only work on campus or on a machine with a VPN client installed); or just go to the Sage notebook, which is hosted by William Stein at the University of Washington.

Sage is free software. See the download instructions to install it on your machine.

Mathematica can be download and installed here.

**Homework:**

Homework is due on Wednesdays. Cooperation on homework is permitted (and encouraged), but if you work together, do not take any paper away with you--in other words, you can share your thoughts (say on a blackboard), but you have to walk away with only your understanding. In particular, write the solution up on your own.

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**Homework #1 (due January 21)**

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**Homework #2 (due January 28)**

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**Homework #3 (due February 4)**

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**Homework #4 (due February 11)**

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**Homework #5 (due February 25)**

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**Homework #6 (due March 4)**

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**Homework #7 (due March 18)**

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**Homework #8 (due March 25)**

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**Homework #9 (due April 1)**

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**Homework #10 (due April 8)**

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**Homework #11 (due April 15)**

**Worksheets:**

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**Worksheet, Day #8 (January 30)**

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**Worksheet, Day #17 (February 23)**

[TXT]
**Lab, Day #28 (March 27)**

**Exams:**

There will be two midterm exams.

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**Exam #1 Review**

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**Exam #1** ...
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**Solutions**

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**Exam #2 Review**

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**Exam #2** ...
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**Solutions**

You are permitted to bring to each exam one 8x11-sheet of paper upon which you may write anything that you like on one side.

**Final Paper:**

In place of a final exam, there will be a paper. Here are the guidelines for this paper and some possible topics.

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**Final Paper Topics**