Bridge to Advanced Mathematics

Math 30800, Section R, Fall 2016

Math 30800-R meets on **Tuesday and Thursday, 3:30-4:45 PM in NAC 6/111**

**First class:** Aug 25. **Last class:** Dec 8. **No class** on Oct 4, Oct 6, Oct 11, Nov 24. **Friday class** on Oct 14.

**Final exam:** Dec 20.

Textbooks

**CPZ***= Mathematical Proofs: A Transition to Advanced Mathematics*, G. Chartrand, A. D. Polimeni, P. Zhang, 3rd edition, Pearson.**R***= Elementary Analysis: The Theory of Calculus*, K. A. Ross, 2nd edition, Springer.

Calendar

Date | Class contents | Read before next class | Homework |
---|---|---|---|

Th 8/25 | Course Information and Learning Outcomes, CPZ 1.1-1.3 | CPZ Ch. 0 & 1 | HW #1 |

Tu 8/30 | CPZ 1.4-1.5 | CPZ Ch. 2 | |

Th 9/1 | CPZ 1.6, 2.1-2.5 | HW #2 | |

Tu 9/6 | CPZ 2.6-2.9 | CPZ Ch. 3 | |

Th 9/8 | CPZ 2.10-2.11, Ch. 3, 4.1 | HW #3 | |

Tu 9/13 | CPZ Ch. 3, 4.2 | ||

Th 9/15 | CPZ 4.3-4.6 | HW #4 | |

Tu 9/20 | Review | Review | |

Th 9/22 | MIDTERM EXAM #1 | CPZ Ch. 5 | |

Tu 9/27 | CPZ 5.1-5.3 | CPZ Ch. 6 | |

Th 9/29 | CPZ 5.4-5.5, 6.1 | HW #5 | |

Th 10/13 | CPZ 6.2 | ||

Fr 10/14 | CPZ 6.3-6.4 | CPZ Ch. 7 | HW #6 |

Tu 10/18 | CPZ Ch. 7.1-7.2 | CPZ Ch. 8 | |

Th 10/20 | CPZ Ch. 7.3, 8.1-8.3 | HW #7 | |

Tu 10/25 | CPZ Ch. 8.3-8.4 | ||

Th 10/27 | CPZ Ch. 8.4-8.6 | CPZ Ch. 9 | HW #8 |

Tu 11/1 | Review | ||

Th 11/3 | Review | Review | |

Tu 11/8 | MIDTERM EXAM #2 | ||

Th 11/10 | CPZ Ch. 9.1-9.3 | ||

Tu 11/15 | CPZ Ch. 9.3-9.6 | CPZ Ch. 10 | HW #9 |

Th 11/17 | CPZ Ch. 9.7, Ch. 10 | ||

Tu 11/22 | CPZ Ch. 10 | R Ch. 1 | HW #10 |

Tu 11/29 | R Ch. 1, §2 | ||

Th 12/1 | R Ch. 1, §4-5, Ex. 2.7(a) | HW #11 | |

Tu 12/6 | R Ch. 1, §3 | ||

Th 12/8 | R Ch. 1, Review | ||

Tu 12/20 | FINAL EXAM |

Homework

- Writing proofs, one of the main goals of this course, can only be learned by doing it yourself. Homework is therefore crucial for success in this class.
- Homework will be assigned weekly (approximately, see calendar), is due at the
**beginning**of class and may be handed in either on paper or to the instructor via email. - The instructor will select a number of exercises from each homework set to grade and provide feedback on.
- Discussing homework problems with others is useful, but
**copying**another person's solutions is not. - You should indicate who you worked with on which problems.
- You should write your final solutions yourself.
- If you use any outside sources (e.g., the internet), you should say so and give the link or reference.

Exercises | Due Date | |
---|---|---|

HW #1 | CPZ 1.1: 3, 4, 7, 9. 1.2: 12, 14, 16, 21. 1.3: 22, 26, 30, 32. |
Tu 8/30 |

HW #2 | CPZ Ch. 1: 37, 40, 42, 45, 46, 50, 53, 54, 59, 62. Ch. 2: 6, 13, 16, 17, 20, 24, 30, 32. |
Tu 9/6 |

HW #3 | CPZ Ch. 2: 36, 42, 47, 48, 49, 51, 54, 58, 60, 68, 74, 78Ch. 3: 8, 16, 18. |
Tu 9/13 |

HW #4 | CPZ Ch. 3: 20, 21, 28, 31.Ch. 4: 1, 6, 10, 15, 27, 34, 40, 42, 50, 56, 65. |
Tu 9/20 |

HW #5 | HW #5 problems | Th 10/13 |

HW #6 | HW #6 problems | Tu 10/18 |

HW #7 | HW #7 problems | Tu 10/25 |

HW #8 | HW #8 problems | Tu 11/1 |

HW #9 | HW #9 problems | Tu 11/22 |

HW #10 | HW #10 problems | Tu 11/29 |

HW #11 | HW #11 problems | Tu 12/6 |

Exams and Grading

Your class average is determined by
- Two midterm exams (2 x 20% = 40%)
- Homework (20%)
- Final (40%)

Midterm #1

- The first midterm exam will take place on
**Thursday September 22, 2016**from 3:30-4:45 in NAC 6/111. - The midterm covers all the lectures up until this point, which corresponds to Chapters 1-4 of
**CPZ**. - To get an idea of the level and style of the questions on the midterm, the homework gives a good indication.
- The following previous homework exercises are particularly useful to review:

**Ch. 1**: 3, 14, 30, 40, 42, 46, 53, 59.

**Ch. 2**: 13, 17, 24, 32,42, 48, 51, 54, 60, 68, 78.

**Ch. 3**: 18, 21, 31.

**Ch. 4**: 1, 10, 27, 34, 42, 56, 65. - The following additional exercises are useful for extra practice:

**Ch. 1**: 69, 70, 71, 76, 85.

**Ch. 2**: 85, 88, 89, 91, 93, 97, 100.

**Ch. 3**: 46, 50, 53, 56, 62, 64, 67.

**Ch. 4**: 71, 73, 75, 79, 81, 84, 94. - You should also know the
**definitions**and**theorems**stated in the lectures. You should be able to**prove**the results that were proved in the lectures. - Midterm #1, with solutions

Midterm #2

- The second midterm exam will take place on
**Tuesday November 8, 2016**from 3:30-4:45 in NAC 6/111. - The midterm covers the lectures since the first midterm (9/27) up until this point, which corresponds to Chapters 5-8 of
**CPZ**. - To get an idea of the level and style of the questions on the midterm, the homework gives a good indication.
- The following additional exercises from CPZ are useful for extra practice:

**Ch. 5**: 3, 11, 16, 27, 37, 44, 45, 51.

**Ch. 6**: 5, 9, 15, 18, 24, 31, 35, 38, 41, 44, 45.

**Ch. 7**: 5, 7, 10, 14, 17, 20, 27, 29, 30, 35, 40, 47, 48, 66, 72, 77.

**Ch. 8**: 7, 11, 18, 23, 30, 33, 38, 44, 49, 56, 58, 59. - You should also know the
**definitions**and**theorems**stated in the lectures. You should be able to**prove**the results that were proved in the lectures. - Midterm #2, with solutions

Final Exam

- The final exam will take place on
**Tuesday December 20, 2016**from 3:30-5:45 in NAC 6/111. - The final exam covers all of the lectures, which corresponds to Chapters 1-10 of
**CPZ**and Chapter 1, §2-5 of**Ross**. - To get an idea of the level and style of the questions on the final exam, the homework and the two midterm exams give a good indication.
- The following additional exercises from
**CPZ**are useful for extra practice:

**Ch. 1**: 69, 70, 71, 76, 85.

**Ch. 2**: 85, 88, 89, 91, 93, 97, 100.

**Ch. 3**: 46, 50, 53, 56, 62, 64, 67.

**Ch. 4**: 71, 73, 75, 79, 81, 84, 94.

**Ch. 5**: 3, 11, 16, 27, 37, 44, 45, 51.

**Ch. 6**: 5, 9, 15, 18, 24, 31, 35, 38, 41, 44, 45.

**Ch. 7**: 5, 7, 10, 14, 17, 20, 27, 29, 30, 35, 40, 47, 48, 66, 72, 77.

**Ch. 8**: 7, 11, 18, 23, 30, 33, 38, 44, 49, 56, 58, 59.

**Ch. 9**: 2, 6, 12, 20, 24, 28, 32, 38, 47, 49, 53, 56, 60.

**Ch. 10**: 1, 3, 7, 12, 22, 29.

and from**Ross**:

**§2**: 1, 2, 3, 7, 8.

**§3**: 3, 4, 5, 6.

**§4**: 1, 2, 3, 4.

**§5**: 1, 2, 3. - You should also know the
**definitions**and**theorems**stated in the lectures. You should be able to**prove**the results that were proved in the lectures.