MATH-GA 2210.001 ELEMENTARY NUMBER THEORY

COURSE: ELEMENTARY NUMBER THEORY

LOCATION: WWH 517

INSTRUCTOR: IVAN CHELTSOV

OFFICE HOURS: 12:00-14:00, WEDNESDAY, WWH 1307

BOOK: ALGEBRAIC NUMBER THEORY

LECTURES:
  1. 19:10-21:00, WEDNESDAY, 28.01.2015
    P-ADIC NUMBERS, SECTION II.1
  2. 19:10-21:00, WEDNESDAY, 04.02.2015
    P-ADIC ABSOLUTE VALUE, SECTION II.2
  3. 19:10-21:00, WEDNESDAY, 11.02.2015
    VALUATIONS, SECTION II.3
  4. 19:10-21:00, WEDNESDAY, 18.02.2015
    COMPLETIONS, SECTION II.4
  5. 19:10-21:00, WEDNESDAY, 25.02.2015
    LOCAL FIELDS, SECTION II.5
  6. 19:10-21:00, WEDNESDAY, 04.03.2015
    HENSELIAN FIELDS, SECTION II.6
  7. 19:10-21:00, WEDNESDAY, 11.03.2015
    UNRAMIFIED EXTENSIONS, SECTIONS II.7
  8. 16.03.2015-20.03.2015
    SPRING BREAK
  9. 19:10-21:00, WEDNESDAY, 25.03.2015
    EXTENSIONS OF VALUATIONS, SECTIONS II.8
  10. 19:10-21:00, WEDNESDAY, 01.04.2015
    GALOIS THEORY, SECTION II.9
  11. 19:10-21:00, WEDNESDAY, 08.04.2015
    ARAKELOV DIVISORS, SECTION III.1
  12. 19:10-21:00, WEDNESDAY, 15.04.2015
    DIFFERENT AND DISCRIMINANT, SECTION III.2
  13. 19:10-21:00, WEDNESDAY, 22.04.2015
    RIEMANN-ROCH, SECTION III.3
  14. 19:10-21:00, WEDNESDAY, 29.04.2015
    GEOMETRIC RIEMANN-ROCH
  15. 19:10-21:00, WEDNESDAY, 06.04.2015
    LUROTH'S PROBLEM OVER Q
HOMEWORKS:
  1. EXERCISES II.1.1, II.1.2, II.1.3 AND II.1.4
    DUE TO WEDNESDAY, 04.02.2015, SOLUTIONS
  2. EXERCISES II.2.2, II.2.3, II.2.5 AND II.2.6
    DUE TO WEDNESDAY, 11.02.2015, SOLUTIONS
  3. EXERCISES II.3.1, II.3.2 AND II.3.3
    DUE TO WEDNESDAY, 18.02.2015, SOLUTIONS
  4. EXERCISE II.4.1
    DUE TO WEDNESDAY, 25.02.2015, SOLUTIONS
    SUPPLEMENTARY READING
    • GAUSSIAN INTEGERS, SECTION I.1
    • ALGEBRAIC NUMBER FIELDS, SECTION I.2
  5. TAKE-HOME MIDTERM EXAM
    DUE TO WEDNESDAY, 04.03.2015, SOLUTIONS
  6. EXERCISES II.6.2 AND II.6.3
    DUE TO WEDNESDAY, 11.03.2015
  7. EXERCISE II.7.1
    DUE TO WEDNESDAY, 25.03.2015
  8. SPRING BREAK READING
    • IDEALS AND DEDEKIND DOMAINS, SECTION I.3
    • MINKOWSKI THEORY, SECTIONS I.4 AND I.5
    • IDEAL CLASS GROUP, SECTION I.6
    • RAMIFICATION THEORY AND LOCALIZATION, SECTIONS I.9 AND I.11
  9. EXERCISES II.8.1, II.8.2 AND II.8.3
    DUE TO WEDNESDAY, 01.04.2015
  10. EXERCISE II.9.2
    DUE TO WEDNESDAY, 08.04.2015
  11. EXERCISE III.1.3
    DUE TO WEDNESDAY, 15.04.2015
  12. EXERCISE III.2.3
    DUE TO WEDNESDAY, 22.04.2015
  13. EXERCISES 1.4, 1.5, 2.4, 7.5, 8.8, 8.13, 9.5, 9.6, 10.5, 10.6, 10.14, 10.16, 12.1, 12.6, 14.2
    DUE TO WEDNESDAY, 29.04.2015
  14. TAKE-HOME FINAL EXAM
    DUE TO WEDNESDAY, 06.05.2015