This schedule will be regularly updated. It is your responsibility to check it accordingly.

Homework is due every Thursday. __Underlined__ problems in should be
handed in.

When | Topics | # | Homework, Exams, Remarks. |

1/24 |
Administrative
stuff 1.1 Introduction to Number Theory, 1.2 Divisibility: greatest common divisor, Euclidean Algorithm 1.3 Primes |
0 | Fill this
form. Corrections to the textbook are here and here. |

1/31 |
Distribution of primes. 1.4 The binomial theorem |
1 | Section 1.2. Problems 15 and 32; Section 1.3. Problems 11 and 31. and some problems of your choice to practice. |

2/7 |
2.1 Congruences 2.2 Solutions of congruences |
2 | Section 1.3: 22, 24, 25, 27, 30Section 1.4: 1, , 5, 84I).Show that there are infinitely many primes of the form 6n+5.? b. Using the idea of the proof of the "Infinitely many primes theorem", try to prove that there are infinitely many primes of the form 5n+4. Something goes wrong... what is it II) Explain why the statement "One sixth of the numbers have
reminder 3 when divided by 6 makes sense".Announcements.III) Explain why the statement "most numbers are not perfect squares" makes sense. Find a function (defined in terms of a simple formula) to approximate the counting funcion C(x) (see below) when x is large. In problems II) and III) use a counting function of the form C(x)=#{n is a positive number, n ≤ x, n satisfies a certain property } (you need to determine which property). 1. The university have cancelled classes
tomorrow. Homework set 2 (the
one originally due Feb 9) is now due on Thursday Feb 16
(together with Homework set 3.2. I will arrive late to my office hours on Wednesday Feb 15th (I guess sometime before 11am). I will be available later. Send me an email if you need help. |

2/14 |
2.1 and 2.2 Review and complete. 2.3 The Chinese Remainder Theorem |
3 | Section 2.1: 2, 4, 5, 7, 9, 13, , 1925,
40Section 2.2: 5, 6, 7, ,9Note: The problems marked with an H have a hint at the end of the book. Try first to solve the problems without reading the hint. |

2/21 |
2.4 Techniques of numerical calculation (excluding Pollard rho
method) |
4 | Section 2.3: 1, 2, 9, 10, . 16 |

2/28 |
2.5 Public key cryptography | 5 | Section 2.4: 2, , 49Section 2.5: , 2, 3, 4, 1 (Solve this problem using the Euclidean
algorithm)5Write down a list of the main results we discussed in class. in your own words. in one page. Write down the main ideas of the proof of some (or all) of the statements. |

3/7 |
Midterm Guest Lecture: Continued fractions |
6 | Tuesday 3/7 Midterm 1 In class (
the change of date).NoteMidterm topics EVERYTHING until Public Key Cryptography (including Public Key Cryptography) No homework this week, but here are a list of problems you should know how to solve. Section 2.8: 1, 2, 3, 4, 5, 8, 12, |

3/14 |
Spring break |
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3/21 |
2.8 Primitive roots and power residues | 7 | Section 2.8: 1, 2, 3, 13, 14,15, 18, 20. |

3/28 |
7.1 The Euclidean algorithm 7.2 Uniqueness |
7-8 | Here
are "half"of the problems to submit Section 7.1: 1, ,3,24,5 |

4/4 |
7.3 Infinite continued fractions Review |
9 |
Here are the problems to submit. Sample problems for the midterm. |

4/11 |
Midterm 2 7.3 Infinite continued fractions |
10 | Tuesday 4/11 Midterm 2 in class. No homework this week. |

4/18 |
3.1 Quadratic residues 3.2 Quadratic reciprocity |
11 | Problems for this week are here. Hand in problem s 3, 4, 5, and 6. Try to submit one or more of the bonus problems. (You are allowed to work in teams for the bonus problems). |

4/25 |
3.2 Quadratic Reciprocity 4.1 Some functions in number theory 4.2 Arithmetic functions. Mersenne Primes 4.3 The Mobius inversion formula |
12 | Problems for this week are here.
Hand in problem s 5, 6, 7 and 8.Pascaline
You can see this movie in a smart phone with the Puffin Web
Browser. The site
has an enormous amount of wonderful math related apps (in French).Goody Bag An interesting movie about Mersenne. |

5/2 |
The Riemann Hypothesis and the distribution of primes (an
interesting article can be found here) Visualizing the Riemann zeta function and analytic continuation |
13 |
The music of primes movie. Section 4.2: 2, 3, 5, 9, , 13,
17, 2014Section 4.3: 1, 2, 3, 5, , 18, 13,
19Final exam practice. |

Final Exam: Monday, May 15, 11:15am-1:45pm, in our usual
classroom, N4000 at the library. |
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