MAT 536: Algebra III

Fall 2005

SUNY at Stony Brook
Department of Mathematics
SUNY at Stony Brook

Instructor: Leon  Takhtajan, Math Tower 5-111, Phone: 632-8287, email:

Schedule: TuTh 9:50  - 11:10 am, Math. Tower P131

Course description:
We will study modular forms in one variable with applications to number theory and physics. Those include representation of integers by quadratic forms, elliptic curves over Q, mirror symmetry, etc. The presentation will be self-contained (whenever possible), and we will cover the following topics (if time permits)
Prerequisites:  MAT 530/531, MAT 534/535, MAT 542.

Grading: The final grade will be based on the homeworks, class participation, and take home final exam.


  • Homework 1

  • Basic references:
    1.  Hurwitz, Adolf Vorlesungen uber allgemeine Funktionentheorie und elliptische Funktionen. (German) Herausgegeben und erganzt durch einen Abschnitt uber geometrische Funktionentheorie von R. Courant. Mit einem Anhang von H. Rohrl. Vierte vermehrte und verbesserte Auflage. Grundlehren der Mathematischen Wissenschaften, Band 3. Springer-Verlag, Berlin-New York, 1964. (Russian translation:   {\cyr Gurvits, A.}; Gurvic, A.; {\cyr Kurant, R.}; Kurant, R. {\cyr Teoriya funktsi\u\i }. (Russian) [Theory of functions]Translated and adapted from the fourth German edition by M. A. Evgrafov. Izdat. ``Nauka'', Moscow, 1968.)
    2.  Iwaniec, Henryk. Topics in classical automorphic forms. Graduate Studies in Mathematics, 17. American Mathematical Society, Providence, RI,1997.
    3.  Koblitz, Neal. Introduction to elliptic curves and modular forms. Second edition. Graduate Texts in Mathematics, 97. Springer-Verlag, New York, 1993.
    4.  Knapp, Anthony W. Elliptic curves. Mathematical Notes, 40. Princeton University Press, Princeton, NJ, 1992.
    5.  Lang, Serge Introduction to modular forms. With appendixes by D. Zagier and Walter Feit. Corrected reprint of the 1976 original. Grundlehren der Mathematischen Wissenschaften, 222.Springer-Verlag, Berlin, 1995.
    6.  Lang, Serge Elliptic functions. With an appendix by J. Tate. Second edition. Graduate Texts in Mathematics, 112. Springer-Verlag, New York, 1987.
    7.  Serre, J.-P. A course in arithmetic. Translated from the French. Graduate Texts in Mathematics, 7. Springer-Verlag, New York-Heidelberg, 1973.
    8.  Shimura, Goro Introduction to the arithmetic theory of automorphic functions. Reprint of the 1971 original. Publications of the Mathematical Society of Japan, 11. Kanô Memorial Lectures, 1. Princeton University Press, Princeton, NJ, 1994.
    9. Siegel, Carl Ludwig Lectures on advanced analytic number theory. Notes by S. Raghavan. Tata Institute of Fundamental Research Lectures on Mathematics, No. 23 Tata Institute of Fundamental Research, Bombay 1965.

    DSS advisory. If you have a physical, psychiatric, medical, or learning disability that may affect your ability to carry out the assigned course work, please contact the office of Disabled Student Services (DSS), Humanities Building, room 133, telephone 632-6748/TDGD. DSS will review your concerns and determine what accommodations may be necessary and appropriate. All information and documentation of disability is confidential.