Binghamton University

Class Schedule and Assignments

Main class page | Schedule and homework | Announcements | Advice | Term Project | Syllabus

Early homework is always accepted. You can leave homework in the collection envelope on my office door at any hour.

Papers for the same assignment must be **stapled** (bending a corner is not secure); if not, I will not grade the papers. Every different assignment must be written on separate papers; if not, I will only grade one assignment.

Rewrites can be handed in at any time within the time limit. The time limit is normally 3 weeks (adjusted for slow grading) but towards the end of term it will be less than 3 weeks.

§ means "section". ¶ means "paragraph".

* denotes a problem that will not be graded. I will record that you submitted it.

No. | Date | Readings | To do (hand-in date) | Remarks | |
---|---|---|---|---|---|

0. | 1/17-19 | We discuss basic logic and fundamental properties of the integers, from which many others can be proved. | |||

1. | 1/22-26 | Notes for Students & Instructors. Chapter 1 | Prove Props. 1.7, 1.10. (W 1/24) | I will return these proofs with feedback on F 1/26. M 1/22: LaTeX tutorial. | |

2. | 1/29 | Prove Props. 1.12-14, 1.23-24. (1/29) | |||

3. | 1/29-2/2 | Chapter 3 | Prove 1.25(i), 1.27(ii), and do Projects 3.1, 3.2. (F 2/2) | We'll discuss Chapter 3 all week, beginning with Section 3.1. | |

4. | 2/2-5 | Chapter 3 | Prove Prop. 1.16-17, 1.22, 1.27(iv), and do Project 3.7(i,ii). (M 2/5) | ||

5. | 2/5-7 | §§2.1-2 | Projects 3.3, 3.5, and Extras #1(a-e). (W 2/7) | Read the advice page for important information. Chapter 2 is the topic for Wed.-Fri. | |

6. | 2/7-9 | Prove Props. 2.3, 2.5-6, 2.8-10, 2.13. (M 2/12) | |||

7. | 2/12-16 | §§2.3-4. | Prove Props. 2.14(ii), 2.18(iii) by induction, and 2.18.1(i,ii). (F 2/16) | Use Prop. 2.3.1 as if it were in §2.1. | |

8. | 2/19-21 | §§4.1-3. | Prove Props. 2.18.1(iii,iv), 2.32.1, and do Project 2.31. (W 2/21) | Use Props. 1.28, 1.17.1 as if they were in Ch. 1. | |

9. | 2/23-26 | §§4.4-5. | Prove Props. 2.21, 2.23, 2.18.1(v) (this one using induction), and 4.5. Do Project 2.35 for (4,6). (F 2/23) | ||

10. | 2/26-2/28 | Prove Prop. 4.7(i). Do Project 2.35 for (7,13). Do Project 4.3. (W 2/28) | Think carefully about 4.3 to find a proof. | ||

11. | 3/2-3/11 | §§4.6, 5.1. | Prove Props. 2.34, 4.16, 4.17. Do Projects 4.23, 4.26, and Problem 4.3.1. (M 3/11) | I'm giving a lot of lead time for this because some of it needs exceptional thought. | |

12. | 3/11-15 | §§5.1-3 | Do Projects 4.33, 5.5. Do Project 5.3 using def. of set equality. Prove Props. 4.30, 5.14. (F 3/15) | Be sure to read the advice page for additions to the book and advice on solving problems. In Project 5.5, the set V_{m} is defined in part (ii). For extra study related to Project 5.5, see Problems Sets: 5.5 and Sets: 5.5+. | |

13. | 3/15-20 | §5.4 & my Web pages. | Do Projects 5.12(i,ii), 5.16(ii), 5.21(i). Prove Prop. 5.20(ii). (M 3/18) | Wed. 3/20: review and answering questions. I will expand §5.4 very much with material on the announcements and advice pages. Read them! | |

Fri. 3/22 | Midterm Exam | Covering Ch. 1-5 except §5.4. | The withdrawal date: Mon. 3/25. | ||

14. | 3/25-29 | §§5.4, 6.1, my Web pages on functions. | Prove Prop. 6.5. (F 3/29) | ||

15. | 3/29-4/3 | §6.1. | Prove Prop. 6.6. Do Projects 6.7, 6.8. (F 4/5) | ||

16. | 4/5 | §§6.2-3. | Prove Props. 6.15-16, 6.19. Do Project 6.9. (M 4/8) | In §6.2 focus on the Division Algorithm for integers. Project 6.9 is related to the rational numbers. | |

17. | 4/8 | §6.3. | Prove Props. 6.25-26. Do Project 6.27. (F 4/12) | This is one of the more important parts of the book. | |

18. | 4/8-10 | §6.4. | Prove Prop. 6.31, 8.6, and Theorem 6.32. (M 4/15) | What's important: 6.29 and proof, 6.31, 6.32. 6.35 is a famous theorem of modular arithmetic. For fun, use it to reduce a googol (10 ^{100}) modulo 13. | |

19. | 4/10-12 | §§8.1-4. | Prove Props. 8.40, 8.43, 8.49. Do Projects 8.44, 9.3(i-iii). (F 4/19) | See Proposition 8.25A; it's useful and you may use it. Most of §§8.1-3 is familiar, but not §8.4. Don't forget to read the advice page. | |

20. | 4/15-17 | §9.1. | Prove Props. 8.50, 8.53, 9.7(ii). Do Projects 9.4, 9.6, 9.9. (Th 4/25) | Remember, Th 4/25 is "Monday". In class 4/17, I went over the important aspects of §9.2. | |

21. | 4/19 | §9.2-3, bits of Ch. 10, §11.1, part of §11.2. | Prove Props. 9.11, 9.14, 9.15. Do Projects 9.13, 11.11. (M 4/29) | We'll have only one or two exercises on §9.2. Read it so you can see how we put Z and R into a single system. In Ch. 10, read Thm. 10.1 (it means no real number is an upper bound for Z) & the definitions of |x| and of distance from x to y in R. In §11.2 only read Props. 11.10 and 11.20 and Project 11.11. For the optional concept (not on homework or exams) of isomorphism see the advice page. | |

22. | 4/25-26 | §§13.1-2. | Prove Props. 13.2, 13.3, 13.8, 13.13, 13.18, Thm. 13.12. (W 5/1) | See the notes on Ch. 13. | |

23. | 4/29-5/1 | §§13.3-4. | Prove Prop. 13.23, Thms. 13.25, 13.28, 13.31. (M 5/6) | See correction to 13.25. | |

M 5/6 | Review session | 2:00-4:00 p.m. in WH 309. | (for our class) | ||

Tu 5/6, F 5/10 | Office hours | My office, about 2:00-4:00 p.m. | To return and collect homework and answer questions. | ||

Wed 5/8 | FINAL EXAM | 3:15-5:15 p.m. in CW 106. | The final exam covers all the material of the course. It will emphasize the parts we covered since the midterm, in Ch. 6, 8, 9, 10, 11, 13. | ||

Fri 5/10 | All homework is due. | Absolute deadline at my office. 4:00 p.m. | You can leave papers in the envelope on my office door at any time. I will accept PDF's if you are out of town; I can print them. | ||

Main class page | Schedule and homework | Announcements | Advice | Term Project | Syllabus