Ph.D. Qualifying Exam in Topology, Aug 2008

Ph.D. Qualifying Exam in Topology, Jan 2009

22M:132:AAA General Topology 3 s.h. Time & Location: 10:30A -11:20A MWF 214 MLH

*Office*: B1H MLH
*Phone*: 319-335-0778
*Email*: idarcy AT math.uiowa.edu
*Office Hours*: M 9:30 - 10am, W 12:30 - 1:30pm, Th 1:30 - 3pm, and by
appt.

75 minute midterm from Spring 2004

Review session Tuesday Dec. 16 in MLH B13 3:30pm - 5pm

HW assignment 1:

1.) Define countable.

2.) Prove that the rationals are countable by using the definition of countable.

3.) Prove that the reals are uncountable by using the definition of countable.

4.) Prove that the irrationals are uncountable.

p83: 4, 8

Read
Helping Undergraduates Learn to Read Mathematics

HW assignment 2 (due 9/11): p. 91: 1, 3, 4, 6, 8

HW assignment 3 (due 9/18): p. 101: 7, 8, 13, 14, 16

HW assignment 4 (due 9/25): Choose 6 problems from the following list of
problems:

p. 102: 18, 19, 20, 21;

p. 111: 1, 2, 9, 13;

p. 126 1, 3

HW assignment 5 (due 10/6): 21: (6 or 10), p. 145 1, 2

HW assignment 6 (due 10/9): [choose 2 from section 19: 2, 3, 5, 6, 7], section 20: do either (4 and 5) or 8.

HW assignment 7 (due 10/16): section 21: 7; section 23: choose 2 from 2, 7, 8; section 24: 3 or 8; p. 146 (supplementary) 3

HW assignment 8 (due 10/23): section 25 (2 or 9); section 26: 4, 5, 8, 13a; section 27: 4, 6

HW assignment 9 (due 10/30): section 27: 6; section 28: 1, 5, 7; p. 146: 4; criticize and fix Lemma 27.5

HW assignment 11 (due 11/13): HW 22: 4, 6 and p. 146 (topological groups) 5, 6, section 30: 1.

HW assignment 12 (due 11/21):
31: Choose 2 problems from 5, 8, 9

Choose 2 problems from section 32.

HW assignment 13 (due 12/4): p. 146 (topological groups) 7; 26: 13b, c; 33: 4, 7

HW assignment 14 (due 12/11):

Section 34: choose any 2 problems

section 36: 1, 5

section 39: 3

TENTATIVE CLASS SCHEDULE-ALL DATES SUBJECT TO CHANGE (click on date/section
for pdf file of corresponding class material):

Monday | Tuesday | Wednesday | Friday | |

Week 1 | 8/25: 12, 13, 14 (ps), (pdf), | quiz1.pdf | 8/27: 13, 14 , sub/neg(ps) sub2(ps) 14 example | 8/29:14, 15 |

Week 2 | 9/1: Labor Day | quiz2.pdf | 9/3: 14 | 9/5: 15 , 16 |

Week 3 | 9/8: 16, 17 | 9/10: 17cont | 9/12: 17 | |

Week 4 | 9/15: 17, 18 | quiz4, 5 | 9/17: 18 | 9/19: 20 |

Week 5 | 9/22: 18 | 9/24: 21 | 9/26: 21, 23 | |

Week 6 | 9/29: Review | Exam 1 | 10/1: 19, 19 cont | 10/3: 19, 20, 21 |

Week 7 | 10/6: 22 | 10/8: 22 | 10/10: 23 | |

Week 8 | 10/13: 24 | 10/15: 25, 26 | 10/17: 26 | |

Week 9 | 10/20: 26, 27 | 10/22: 27 | 10/24: 28 | |

Week 10 | 10/27: 28 | 10/29: 28 | 10/31: 29 | |

Week 11 | 11/3: 22 | 11/5: 22 | 11/7: 30 | |

Week 12 | 11/10: 30 | 11/12: 31 | 11/14: 31 | |

Week 13 | 11/17: 32 | Review | 11/19: Discussion | 11/21: Exam 2 |

Thanksgiving break | ||||

Week 14 | 12/1: 33 | 34 | 12/3: 36 | 12/5: 39, 41 |

Week 15 | 12/8: 41 | 12/10: 43 | 12/12: Review | |

Final Exam 9:45 A.M. Wed., Dec. 17 |