MATH-GA.2210-001 Number Theory, Mo 11am

Instructor: Yuri Tschinkel

Office hours:

• Mo 1:30pm or by appointment

Lecture / Homework:

• Lecture 1 / Homework (due Febr. 5)
• Lecture 2 / Homework (due Febr. 12)
• Lecture 3 / Homework (due Febr. 26)
• Lecture 4 / Homework (due March 4)
• Lecture 5
• Lecture 6 / Homework (due April 1)
• Lecture 7 / Homework (due April 8)
• Lecture 8 / Homework (due April 22)
• Lecture 9
• Lectures 10-12

Syllabus:

• Elementary number theory, quadratic reciprocity
• Diophantine equations
• Local-global principles
• p-adic numbers
• Riemann zeta function
• Prime Number Theorem
• L-functions, primes in arithmetic progressions
• Transcendence
• Basic algebraic number theory: quadratic and cubic fields

Grading:

• Homework: 20%
• Midterm March 11: 30%
• Final May 6: 50%

Recommended books:

• A. Chambert-Loir, A Field guide to Algebra, Springer
• J.-P. Serre, A course in arithmetic, Springer