The primary goal of this course is to prepare our students for the 300 level mathematics courses and beyond. We use number theory as a backdrop to discuss how to think about mathematics, how to read mathematical writings, and how to write good mathematics.

Syllabus

Homework

Class Date | Section | Pages |
---|---|---|

Aug. 30 | 1.1 | 1-5 |

Sep. 2 | 1.2, how to read mathematics | 7-9 |

Sep. 4 | 1.3 | 11-12 |

Sep. 6 | 1.3 | 15 |

Sep. 9 | 1.3, 1.4 | 14, 16-17 |

Sep. 11 | 1.4, 1.5 | 17-18, 23-25 |

Sep. 13 | 1.5, 1.6 | 25, 27-30 |

Sep. 16 | 1.6,1.7 | 31, 32-34 |

Sep. 18 | 1.7, 1.8 | 34-35, 37-39 |

Sep. 20 | 1.10 | 45-49 |

Sep. 23 | basic counting | |

Sep. 25 | 1.9 | 41-44 |

Sep. 27 | 1.11 | 51-55 |

Sep. 30 | equivalence relations | 63-65 |

Oct. 2 | Exam 1 | 1.1-1.10, induction, basic counting |

Oct. 4 | 2.1, 2.2, 1.4 (greatest integer) | 63-71, 19-21 |

Oct. 7 | binomial theorem | |

Oct. 9 | 2.2, 2.3 | 71-74, 76-77 |

Oct. 11 | how to fail at math | PWeb readings |

Oct. 14 | 2.3, 2.4 | 78-81 |

Oct. 16 | 2.4 | 82-83 |

Oct. 18 | 2.5 | 84-87 |

Oct. 28 | major, 2.5 | 87-88 |

Oct. 30 | inclusion-exclusion * | |

Nov. 1 | Exam 2 | 1.11, 2.1- 2.4, greatest integer function, binomial theorem, combinations ("n choose k") and related counting problems, equivalence relations |

Nov. 4 | 2.6 | 90-92 |

Nov. 6 | 2.6, 7.1 | 92-93, 227-230 |

Nov. 8 | 2.5, 7.1, 7.2 | 88, 231-236 |

Nov. 11 | 7.2, 7.3 | 236-238, 244 |

Nov. 11 | inc/exc recap | |

Nov. 15 | 3.1 | 103-107 |

Nov. 18 | 3.2 | 108-110 |

Nov. 20 | no class | chemicals needed to be evacuated! |

Nov. 22 | 3.3 | 112-114 |

Nov. 25 | 3.4, 3.6 | 118-121, 128-129 |

Nov. 27 | Exam 3 | 2.4- 2.6, 3.1- 3.2, inclusion-exclusion, parts of 7.1-7.4 |

Dec. 2 | 3.6, 3.8 | 129-132, 142 (Theorem 3.8.1 statement only) |

Dec. 4 | 4.1 | 145-150 (Plus small reading) |

Dec. 6 | 4.3 | 157-162 |

Dec. 9 | 4.3 | 163-164 |

Dec. 11 | 4.3 | 165-166 |

Dec. 13 | infinity |

HW | Due Date | Problems |
---|---|---|

# 0 | Sep. 2 | Email me with answers from class 8/30, and read syllabus |

# 1 | Sep. 6 | [pdf] |

# 2 | Sep. 11 * | [pdf] |

# 3 | Sep. 16 | [pdf] |

# 4 | Sep. 20 | [pdf] |

# 5 | Sep. 25 | [pdf] |

# 6 | Sep. 30 | [pdf] |

# 7 | Oct. 9 ** | [pdf] |

# 8 | Oct. 14 | [pdf] |

# 9 | Oct. 18 | [pdf] |

# 10 | Oct. 30 | [pdf] |

#11 | Nov. 6 *** | [pdf] |

#12 | Nov. 11 | [pdf] |

#13 | Nov. 15 | [pdf] |

#14 | Nov. 20 | [pdf] |

#15 | Nov. 25 | [pdf] |

#16 | Dec. 6 | [pdf] |

#17 | Dec. 13 | [pdf] (last updated: 12/7) |

* Some extra induction problems.

** This will be the last assignment where rewrites will be allowed.

*** Some extra inclusion-exclusion problems.