Arithmetic of Elliptic Curves, MATH 756, Fall 2013 

This is the home page and first day handout for MAT 756, meeting MW 2:30 – 3:45 in BEH 224.  My name is Dr. Arthur Baragar, my office is CDC-1016, and I can be reached at 895-0378. Important information announced in class will also be posted on WebCampus. The prerequisite for this course is MATH 453/454 or the equivalent.

Syllabus:  Topics we will cover will likely include:

o   Projective space, curves in projective space, smoothness.

o   Bezout’s theorem.

o   The group structure on elliptic curves.

o   Elliptic curves over the rationals, heights, descent, Mordell’s theorem.

o   Elliptic curves over finite fields, elliptic curve encryption, factoring using elliptic curves (reference: Silverman and Tate).

o   Complex multiplication.

o   Time permitting, modular forms and L-functions. 

Text:  Elliptic Curves, by Anthony Knapp, Mathematical Notes 40, Princeton University Press, 1992.  Additional references:  Rational points on elliptic curves, Joseph H. Silverman and John Tate, Undergraduate Texts in Mathematics, Springer Verlag, 1992; The Arithmetic of Elliptic Curves, Joseph H. Silverman, Graduate Texts in Mathematics, Springer Verlag, 1985. 


Grading Scheme:

o   Homework:  Homework will be assigned weekly (approximately).  Homework is to be done in groups of two or three, and is usually due two weeks later.  Homework is to be written up in LaTeX, and I would like a hard copy and pdf file.  Solutions from each group will be posted on webcampus.  Regular attendance and active participation in group homework is the minimum requirement for a “B”.    

o   Final Exam:  There will be a take home final exam … I think.

Office Hours: If you need to see me, please look for me during the office hours posted below, or please make an appointment.

o   Mondays and Wednesdays, 10:00am – 11:00am

o   Tuesdays, 11:00am – noon,

o   … or by appointment

Office hours begin the second week of classes. 


Other Important Dates:  (See the UNLV calendar for more details.)

o   August 26: Instruction and late registration begin.

o   August 30: Final date for late registration, course additions, changes, or fee payment (with late penalty). Last day to inform me of absences due to religious holidays. Last day to drop a course without it showing up on transcripts.

o   September 2: Labor Day recess.

o   October 25: Nevada Day recess (Friday).

o   November 1: Final date to drop or withdraw from classes (except short courses).

o   November 11: Veterans' Day recess (Monday).

o   November 28: Thanksgiving.

o   December 9th –14th: Final examinations.

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