T: 1:30 PM -3:00 PM

R: 9:30 AM-11:00 AM

Syllabus

HW |
Due Date |
Problems |

# 0 | Jan. 25 | Email me with answers from class 1/23, and read syllabus |

# 1 | Feb. 1 | pg. 28-30: 1.1, 1.5, 1.7, 1.10, 1.11 (a)-(d) pg. 305: A.2 |

# 2 | Feb. 8 | pg. 305-307: A.1, A.6, A.8 (class 2/4 might help with terminology) |

# 3 | Feb. 15 | pg. 32-33: 1.17, 1.18 (a)-(c)*, 1.19 (a)-(b). 1.20 pg. 306-307: A.5, A.9 |

# 4 | Feb. 22 | pg. 58-62: 2.1, 2.5 (a)-(b), (c)**, 2.6, 2.9, 2.12* ***, Research Assignment #1*** |

Mar. 1 | R.A. #2*** | |

#5 | Mar.4 | pg.111: 3.1(a),(b)**,3.2(a)-(c), additional problems on PWeb |

Mar.8 |
R.A. #3*** | |

#6 | Mar. 15 | 2.3 (b), 4.1, 4.3 (a)-(b), 4.5(a)*, additional problems on PWeb, R.A. #4*** |

Apr. 12 | R.A. #5*** | |

#7a | Apr. 19 | 3.6 (a), (b)**, R.A. #6*** |

#7b | Apr. 26 | 6.8, 6.20 (a)-(b) R.A. #7*** |

May 3 | R.A. #8*** | |

#7c | May 6 |
TBA |

May 10 |
Final Project Due 5 PM |

** bonus

*** see PWeb for additional instructions

Date |
Pages |
Topic(s) |

1/23 | xv-xxii, 1-4 (middle) | Introduction and Rational Points on Conics |

1/25 | 6 (middle) -12 | Rational Points on Cubics, Intro to Group Structure |

1/28 | 13-16, 265-270 | Prove Group Structure, Introduction to Projective Geometry* |

1/30 | Canceled Class | |

2/1 | 270-272 | Projective Space, Homogeneous Polynomials* |

2/4 | 273-278 | Curves in the Projective Plane, Singularities |

2/6 | 16-20 | Weierstrass Normal Form |

2/8 | 23-27 | Explicit Formulas for Group Law |

2/11 | 35-38 | Points of Finite Order |

2/13 | 45-47, 56-57 | Discriminant, Nagell-Lutz Theorem (2) |

2/15 | 48-50, 54-56 | Nagell-Lutz Theorem (1) |

2/18 | 51-53, 58 | Nagell-Lutz finished ** |

2/20 | 65-68 | Heights, 4 Lemmas |

2/22 | 68-71 | Proof of Mordell's Theorem |

2/25 | 73-75 | Lemma 3.2 |

2/27 | 71-72, 95-96 | (sub)Lemma, Structure of Γ/2Γ |

3/1 | 97 | Structure of Γ[2], Complex Field and Complex Functions |

3/4 | 41-42 | Complex Poles, Lattices |

3/6 | 43-45 | Elliptic Curves over C, Finite Fields |

3/8 | 117-121 | Elliptic Curves over Finite Fields |

3/11 | 133-138, 207-208 | Using Finite Fields to Identify Points of Finite Order, Extensions of Q |

3/13 | 209, 213-218 | Cyclotomic Extensions, Embeddings, Algebraic Points on Cubic Curves |

3/15 | 230-232 | More on Algebraic Points on Cubic Curves, Complex Multiplication |

4/1 | 75-76, 78-80 | Lemma 3.3 |

4/3 | 78-80 | Lemma 3.3 continued |

4/5 | No class: Midterm due | |

4/8 | 94, 80-83 | Start Lemma 3.4 |

4/10 | Research project discussion | |

4/12 | 86-88 | More Lemma 3.4 |

4/15 | 89-94 | Finish Lemma 3.4!!!!!!!!!! |

4/17 | Citation in math and bibtex | |

4/19 | 230-231 | j-invariant and complex multiplication |

4/22 | 232-235, 245-247 | complex multiplication |

4/24 | How to give a bad math talk | |

4/26 | Fermat's Last Theorem | |

4/29 | Fermat's Last Theorem |

* Some material from Chapter 8 of

** See PWeb for additional notes.