THEORY OF NUMBERS

MATH 115B, course information

Meetings: MWF 11:00pm-11:50 AM, Wellman room 233

Instructor: Jesús A. De Loera.

email: deloera@math.ucdavis.edu

http://www.math.ucdavis.edu/~deloera/TEACHING/MATH115B/courseinfo/115B.html

Phone: (530)-754 70 29

Office hours: Monday 9:00-10am and 12:10-1:00pm, Wednesday 12:10pm-1:00pm. My office is 580 Kerr Hall. The TA for this class is Mr Matthew Hubbard. His office hours are 10am to 11am MWF. I will be glad to help you with any questions,problems or concerns you may have!

Text: I will not require any particular textbook and I hope my lecture notes should help you with most of the material. In the first five weeks I will follow many books (some not even in English) so my lecture notes will be the main source. In the second part I will mostly follow the last 5 chapters of Elementary Number Theory and its applications'' by Kenneth H. Rosen Addison Wesley, but I will {\bf not} require that students purchase the textbook. Other excellent references are:

Hardy, G. H.; Wright, E. M.: "An introduction to the theory of numbers", The Clarendon Press, Oxford University Press. niven, Ivan; Zuckerman, Herbert S.; Montgomery, Hugh L.: "An introduction to the theory of numbers", John Wiley & Sons, Inc.

Description: Number Theory regards the study of properties of numbers, more particular integer or rational numbers. In this course I will try to concentrate on Number Theory relevant in coding theory, cryptography, and other parts modern information technology.

Topics to be covered in 115B (Winter 2003):

1) Lattices points on lines, circles and polygons. 2) Pick's theorem and its generalizations. 3) Lattices 4) Minkowski's geometry of numbers 5) Applications: Diophantine approximation. 6) Primitive roots. ElGamal Cryptosystem. 7) Quadratic residues, Jacobi symbol, sums of squares

Grading policy: There are 100 points possible in the course

• There will be 2 midterms, the first on February 3rd 2003 and the second March 5th 2003. Each counting 35 points. Use of books, notes, and calculators will not be allowed on any exam. There will be a 30 points final project.

• Homework will be suggested almost every week but will not be collected. Instead the exam will be crafted resembling the homeworks.

• I will assign grades based on an statistical information of the points obtained by all students (I compute the mean, standard deviation, etc. and set letter grades according with those numbers). I expect that at least 60 points will be necessary to pass this course.

• IMPORTANT I will handle all grades via the myucdavis grade system. This means that if you are registered students at UC Davis you can access grade information for this class via the internet (check https://my.ucdavis.edu/ for details). This is in a secure and private web page assigned for each student. You can see your standing in the class, important statistics on exams, and your final grade there! I will not disclose your grade in any other form.

Important rules:

• New homework exercises will be posted on my web page (see the end of the page). I may write a few new problems after each class, so please check the web page often. Please remember there are NO make-up exams or quizzes. Please check often the course web page often!

Prerequisites and Expectations: MAT 115A or equivalent are a pre-requisite. If in doubt, please ask me. You are expected to work intensively outside the classroom solving exercises, reading the book, thinking about the theorems, etc. I estimate a minimum of 3 hours work at home per lecture. The most important thing is what YOU learn. Mathematics is fun and pretty, try to get the material in your soul! rote memorization of facts is useless and you are expected to think about the material everyday. It is easy to fall behind, please be careful!

I am here to help you, I will be very happy to talk to you about any question or idea you had and I hope you will enjoy the course!

SUGGESTIONS FOR A FINAL PROJECT can be found in this list of ideas

HOMEWORK: