(office: Math 3-109, tel. 632-8255, e-mail sorin at math.sunysb.edu
Luis E Lopez (office: Math 2-122, e-mail llopez at math.sunysb.edu)
Schedule: TuTh 02:20pm-03:40pm, Chemistry 126
Review session: Friday, May 14, 3-4:30pm in Math P-131
Final exam: Tuesday, May 18, 2-4:30pm in Physics P-117
Prerequisites: Either MAT 312 (Applied algebra), or MAT 313 (Abstract Algebra)
or MAT 318 (Classical Algebra) are mandatory prerequisites for this class.
In general basic algebra exposure is required and assumed, but I will try to
keep prerequisites to a minimum.
A Friendly Introduction to Number Theory
, J.H. Silverman
, (second edition), Prentice Hall.
This is indeed a nice textbook covering a number of elementary topics
in number theory. The book includes a good deal of numerical examples,
which are analyzed for patterns and used to make "conjectures". Various
other chapters provide brief but insightful and motivating excursions
into topics like Mersenne Primes, number sieves, RSA cryptography,
elliptic curves, etc.
There are many other excellent undergraduate books on the subject.
Here is a sample (all of them available in our library):
- Elementary Number Theory and Its Applications , by Kenneth Rosen, (fourth edition)
- An Introduction to the Number Theory, H.M. Stark
- Number Theory, G.E. Andrews
- Introduction to Analytic Number Theory, T.M. Apostol
- Lectures on Number Theory, P.G.L. Dirichlet with supplements by R. Dedekind
- The higher arithmetic, H. Davenport
- An Introduction to the Theory of Numbers, I. Niven and H.S. Zuckerman
- A Classical Introduction to Modern Number Theory, K. Ireland and M. Rosen
- Fundamentals of Number Theory, W.J. LeVeque
- Number theory with computer applications, R. Kumanduri and C. Romero
These are a mixture of classical texts (for example Dirichlet), modern
efforts, more elementary (for example, Kumanduri and Romero) and more
advanced (for example, Rosen or Ireland and Rosen), algebraic (for
example, Andrews) or analytic approaches (for example, Apostol). This
course will concentrate only on elementary algebraic number theory,
We will cover only part of the textbook and the following schedule
may/will be adjusted based on students' preparation and
|Topic||Sections in textbook||Week||Notes|
|Overview / Introduction / Review||Chapter 1||1/26-1/30|
|Pythagorean Triples / Sums of Higher Powers||Chapters 2,3,4||2/2-2/6|
|Divisibility, Euclidean algorithm, Fundamental theorem of arithmetic||Chapters 5, 7||2/9-2/13|
|Linear Diophantine equations / Congruences||Chapters 6, 8||2/16-2/20|
|Fermat's little theorem / Euler's Formula||Chapter 9,10||2/23-2/27|
|Multiplicative functions||Chapter 11, 19||3/1-3/5||First project due 3/4|
|Prime numbers||Chapter 12,13,14||3/8-3/12||Midterm 3/11|
|Powers modulo m||Chapter 16,17||3/15-3/19||
|Public key cryptography||Chapter 18||3/22-3/26||
|Primitive roots||Chapter 20, 21||3/29-4/2||
|Quadratic residues||Chapter 22, 21, 23, 24||4/12-4/16||
|Sums of squares||Chapter 25, 26||4/19-4/23||Second project due 4/22
|Primality testing||Chapter 32||4/26-4/30||
|Cubic curves and elliptic curves||Chapter 40||5/3-5/7||Final exam 5/18, 2-4:30
Projects, Homework & Grading:
Homework and projects (TBA) are an integral part of the
course. Problems marked with an asterisk (*) are for extra credit.
In addition to homework you will be required to hand in 2
research/scholarship/computing projects. Projects with a nontrivial
writing component may be used to satisfy the Mathematics Upper
Division Writing Requirement.
Your grade will be based on the weekly homeworks (20%), two projects (15% each),
midterm (20%), and the final exam (30%). The two lowest homework grades will be dropped
before calculating the average.
The following is a short list of web sites devoted to number theory
or number theoretic related topics relevant for our class:
A number of interesting local links that you are warmly encouraged
Math Learning Center
The Math Learning Center
(MLC), located in Room S-240A of the Math Tower,
is an important resource. It is staffed most days and some evenings by mathematics tutors
(professors and advanced students).
For more information and a schedule, consult the
MLC web site.
Special needs If you have a physical, psychiatric, medical or
learning disability that may impact on your ability to carry out
assigned course work, you may contact the Disabled Student Services
(DSS) office (Humanities 133, 632-6748/TDD). DSS will review your
concerns and determine, with you, what accommodations may be necessary
and appropriate. I will take their findings into account in deciding
what alterations in course work you require. All information on and
documentation of a disability condition should be supplied to me in
writing at the earliest possible time AND is strictly
confidential. Please act early, since I will not be able to make any
retroactive course changes.