# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

**Approved:**2003-03-01 (revised 2013-01-01, J. DeLoera)

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

Search by ISBN on Amazon: 978-0495562023

**Prerequisites:**

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

1-5 |
1.1 – 1.6 |
Logic and proofs. Lighter on the initial material; Emphasis on proof techniques. |

6-10 |
2.1 – 2.5 |
Sets and induction. Emphasis on mathematical induction and equivalent principles. |

11-13 |
3.1 – 3.3 |
Equivalence relations and partitions. |

14-17 |
4.1 – 4.4 |
Functions. Emphasis on onto and 1-1 functions. |

18-21 |
5.1 – 5.3 |
Cardinality, Do in full detail up to Theorem 5.3.8, which requires the Axiom of Choice. |

22 |
5.4 and 5.5 |
Order of cardinals, comparability. Emphasis on section 5.4, but omit proof of Cantor-Schroeder-Bernstein Theorem and do 5.5 lightly. |

23-26 |
6.1 – 6.4 |
Groups, subgroups, and operation preserving maps. |

27 |
6.5 |
Rings and fields. |

28 |
Connection to vector spaces. |

**Additional Notes:**

**Learning Goals:**

Mastery of this course enhances the ability to write clear well-organized scientific arguments. Mastery of this course also supports the development of clear analytical thinking.

**Assessment:**