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\centerline{\bf THEORY OF NUMBERS}
\centerline{\bf MATH 115B, Course Information}
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\noindent {\bf Meetings:} MWF 11:00pm-11:50 AM,  Room 233 Wellman Hall.

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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/MATH115B/courseinfo/115B.html


\noindent Phone: (530)-754 70 29
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\noindent {\bf Office hours}: Monday and Wednesday 12:10pm-1:00pm
or by appointment.  My office is 580 Kerr Hall. The TA for this
class is Mr. Matthew Hubbard, his office hours are MWF 
10:00am-11:00am. 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 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.

\noindent {\bf 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, Short vectors.

6) Primitive roots. ElGamal Cryptosystem.

7) Quadratic residues, Jacobi symbol, sums of squares

8) Continued fractions and Pell's equation.

9) More on Non-linear Diophantine Equations.
 

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

\begin{itemize}
\item There will be 2 midterms, first on February 3rd 2003 and the
second March 5th 2003. ach 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 5 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.
\end{itemize}


\noindent {\bf Important rules:} 
\begin{itemize}

\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 class. {\bf Please check the course web page
often!}


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\noindent {\bf Prerequisites and Expectations}: MAT 115A, Mat 108 or
equivalent are a pre-requisite. If in doubt, please ask me. You are
expected to work outside the classroom solving exercises,
reading the book, thinking about the theorems, etc.  I estimate a
minimum of 2 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:} 
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