The final grade will be based on weekly homework assignments, a quiz, midterm exam, and a final exam. Assignments will be given each week and due in class, on paper, at the beginning of the following class. There will be a moderate penalty for late homework. Students are allowed but not encouraged to typeset answers.

Announcements and most course communication will be done on the course page at the NYU Classes site. This site has a class message board that everyone in the class can see. If you have a technical question or comment, please post it there rather than sending an email to the instructor That way everyone has the same information. Please feel free to contribute. You can check your grades here.

The NYU academic integrity policies. apply to this class. Students may work together but each student must write her/his answers individually. Students may not hand in work they have copied from another source.

week | topics | due |
---|---|---|

1 | Introduction, prime factorization, the Riemann zeta function | |

2 | Infinite products, the Euler product formula | Homework 1 due |

3 | The discrete Fourier transform, modular multiplication, Euler phi function | Homework 2 due |

4 | Finite abelian groups, Dirichlet characters, L functions | Homework 3 due Quiz |

5 | Dirichlet theorem (conclusion), Calculus of complex functions, the complex derivative and contour integral | Homework 4 due |

6 | Cauchy residue theorem and properties of complex analytic functions | Homework 5 due |

7 | Cauchy residue theorem for inverting generating functions and Dirichlet series | Homework 6 due Midterm exam |

8 | Fourier series, the Fourier integral, and the Poisson summation formula | Homework 7 due |

9 | Applications of the Poisson summation formula: sums 1/n^{2p}, Jacobi identity, error bound for lattice points in a circle | Homework 8 due |

10 | Proof of the prime number theorem | Homework 9 due |

11 | Properties of the Riemann zeta function, the functional equation | Homework 10 due |

12 | Partitions, basic properties, product form of the generating function | Homework 11 due |

13 | Asymptotic estimate of the number of partitions | Homework 12 due |

14 | Final Exam |