Meetings: MWF 11:00pm-11:50 AM, Room 212 VEIMYR
Instructor: Jesús A. De Loera.
email: deloera@math.ucdavis.edu
http://www.math.ucdavis.edu/~deloera/TEACHING/MATH115A/courseinfo/115A.html
Phone: (530)-754 70 29
Office hours: Monday 12-3pm and Friday 12:10pm-1:00pm or by appointment. My office is 580 Kerr Hall. The TA for this class is Ms. Lipika Deka. Her office hours in 577 Kerr Hall are Tuesday: Tuesday 1-2pm Thursday: 1.30pm-3.00pm I will be glad to help you with any questions, problems or concerns you may have!
Text: I will mostly follow ``Elementary Number Theory and its applications'' by Kenneth H. Rosen Addison Wesley, but I will 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: This is the first part of an year-long undergraduate-level course in Number Theory. Number Theory regards the study of properties of numbers, more particular integer or rational numbers. Elementary number theory involves divisibility among integers (e.g. the Euclidean algorithm) , elementary properties of primes (e.g. there are infinitely many!), congruences, quadratic reciprocity and the solution by integers of basic equations. It also touches beautiful and famous number sequences such as the Fibonacci numbers or the Pythagorean triples. This course would cover most of these topics. Of course, Number Theory, being one of the oldest areas of mathematics, has already borrowed weapons from geometry, analysis, and algebra. When possible I will try to at least glance at such ideas. Besides introducing you to such classical and old material I will try to make you aware of the applied importance of the field, since Number Theory is relevant in coding theory, cryptography, hashing functions, and other tools in modern information technology.
Topics to be covered in 115A (Fall)
1) Prime Numbers and the Euclidean Algorithm. 2) The fundamental Theorem of Arithmetic. 3) Factorization methods. 4) Congruence and the Chinese Remainder Theorem. 5) Special Congruences.
Winter and Spring topics will include: Euler-Phi function, Mobius inversion, Public Key encryption, Primitive roots, quadratic residues, continued fractions, Lattices, Minkowski Geometry of Numbers.
Grading policy: There are 100 points possible in the course
Important rules:
Prerequisites and Expectations: MAT 21D, Mat 108 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!
SPECIAL (electronic) HAND-OUTS
IMPORTANT: To download the documents below using your web browser press the shift key and while holding it click on the link:
To open your math account please go to URL http://germ.math.ucdavis.edu/cgi-bin/add_class_account.pl
HOMEWORK:
IMPORTANT NOTE: Problem 5 in the homework 4 is optinal as there is a mistake on the hint.