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\centerline{\bf THEORY OF NUMBERS}
\centerline{\bf MATH 115A, course information}
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\noindent {\bf Meetings:} MWF 11:00pm-11:50 AM,  Room 212 VEIMYR

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\noindent {\bf Instructor:} Jes\'us A.  De Loera.

\noindent  email: deloera@math.ucdavis.edu

\noindent http://www.math.ucdavis.edu/$\tilde{ }$deloera/TEACHING/MATH115A/courseinfo/115A.html


\noindent Phone: (530)-754 70 29
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\noindent {\bf Office hours}: Monday and Friday 12:10pm-2:00pm
or by appointment.  My office is 580 Kerr Hall. The TA for this
class is Ms. Lipika Deka, here office hours are Tuesday: 3.30-4.30pm
Thursday: 1.30-2.30pm. I will be glad to help you with any questions,
concerns or problems you may have! 
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\noindent {\bf Text}: I will mostly follow
``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.

\noindent {\bf Description}: This is the first part of a 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 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 2002):

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.


\noindent {\bf Grading policy}: There are 100 points possible
in the course.

\begin{itemize}
\item There will be 2 midterms, first on October 25th 2002, the second
on November 25th 2002 each counting 35 points. I will drop the lowest
of the two for the calculation of the grade. Use of books, notes, and
calculators will not be allowed on any exam. The final exam is
comprehensive and counts 40 points.

\item Homework will be assigned and collected almost every week, {\bf
on Wednesdays}, for a total of 7 homeworks (about 10 problems in each
homework). Each homework is worth 5 points. Two of the problems will
be chosen for grading but you will receive one point if you wrote
solutions for all problems assigned. The remaining 4 points will be
awarded in the 2 problems being graded.  I will drop the two lowest
scores from the calculation of the final grade, this is for a maximum
of 25 points.


\item 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), but typically 60 points or higher are required to pass the class.


\item {\bf 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 a secure and private
web page assigned to 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.
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\noindent {\bf Important rules:} 
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\item 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 {\bf there are NO
make-up exams or quizzes}, instead I am dropping the lowest score as a
compensation of possible problems or emergencies.  Graded homeworks
will be distributed in the boxes in Wellman hall or in
recitation. {\bf Please check the course web page often!}


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\noindent {\bf 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 and I hope you enjoy
the course.

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\noindent{\bf HOMEWORK:} It is already posted in the web site!



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