# Math 307: Introduction to Proof

## Spring 2017

# Contact Info

**Office:** Fenton Hall 324

**Office Hours:** M 1-2p, Tu 10-11a, W 2-3p, F 11-12p, and by appointment.

**Email:** kgedeon@uoregon.edu

# Announcements

**4.3.17** Welcome to Math 307!

# Tentative Weekly Schedule

This schedule is subject to change.

Week |
Sections to Cover | Notes |
---|---|---|

1 | 1.1, 1.2, 2.1 | |

2 | 2.1, 2.2, 2.3 | |

3 | 2.4, 3.1, 3.2 | |

4 | 3.3, review | Midterm Exam 1 |

5 | 3.4, 3.5, 4.1 | |

6 | 4.2, 4.3 | |

7 | 5.1, 5.2, review | Midterm Exam 2 |

8 | 5.3, 5.4, 6.1 | |

9 | 6.1, 6.2, 6.3 | No class Monday |

10 | 6.4, review | |

11 | Final Exam; No classes |

# Homework Resources

Remember that I expect your homework to follow these guidelines, taken from the course syllabus:

- Your name, assignment number, and due date are at the top of the front page.
- Multiple pages are stapled together.
- Pages are not torn from a spiral notebook (or at least cut off the "scruff").
- You have neat and complete solutions to all problems. In particular, it is expected that your solutions are written up with care. I suggest either keeping a rough draft of your homework during the week in order to write up and submit a "final draft," or typing your homework with LaTeX.
- Problems are organized in an easy-to-understand fashion and proper spacing between problems is given.

For homework help, you should come to my office hours and/or send me an email.

HW No. |
Problems | Due Date |
---|---|---|

0 | Available Here DUE IN OFFICE HOURS | April 7 |

1 | 1.1 #1, 2, 5, 6, 9; 1.2 #1, 2, 7, 8, 9; 2.1 #5, 6, 9, 12 |
April 12 |

2 | 2.2 #1,2,6,9,11; 2.3 #1,2,4,5,6 |
April 19 |

3 | 2.4 #2, 4, 5, 9, 14; 3.1 #2, 3, 8, 11, 19 |
April 26 |

4 | 3.2 #4, 7, 15, 19; 3.3 #3, 13, 16, 20 | May 3 |

5 | 3.4 #4, 5, 11, 13; 3.5 #3, 5, 12, 21 |
May 10 |

6 | 4.1 #1, 2, 8; 4.2 #1, 3, 10 |
May 17 |

7 | 4.3 #7, 12; 5.1 #5a-c, 6, 8a-e, 10; 5.2 #9, 12, 17 |
May 24 |

8 | 5.3 #2, 10a, 11e, 12; 5.4 #3, 5, 8; 6.1 #6 |
May 31 |

9 | 6.2 #5, 8, 9; 6.3 #6, 9, 13, 17 |
June 7 |

# Worksheets and Solutions

Week 1 (Solutions) Corrections: #1(e) is not a statement.

Week 2 (Solutions) Corrections: #2 should say "cross out any row that can't occur," not "...any column..."

Week 3 (Solutions)

Week 4 (Solutions)

Week 5 (Solutions)

Week 6 (Solutions) Corrections: There's a small typo in #3, but the proof is essentially correct.

Week 7 (Solutions)

Week 8 (Solutions)

Week 9 (Solutions)

Week 10 (Solutions)

# LaTeX Resources

Here is a sample homework document that you can edit and use on Overleaf. This is great if you don't want to worry about downloading a program onto your computer, but there are some disadvantages to using the browser-based system. The example given here was modified from this one.

I encourage you to download a TeX distribution, which you can do here. The distribution comes with some programs to allow you to open, edit, and compile .tex files on your computer. My favorite TeX compiler is called Texmaker and you can download it for free. In particular, a program with syntax highlighting will save you a lot of frustration.

Here is the .tex file for the sample homework document. Please do not feel as though you need to use this template! I encourage you to explore other styles and packages.

When you run into problems with TeX, you can almost always do a Google search for help (or stop by my office hours). Here is a list of symbols in LaTeX; note that you may need to use different packages than the ones you are currently using, e.g. amsmath. If you cannot find the symbol you need in that list, or don't want to look through a list, you can always try to detexify it. The algorithm isn't perfect but often does the trick!

If you want to get fancier, I suggest looking at my friend Dan Raies' page.

# Exam Resources

### Midterm 1

Midterm 1 will take place in class on Friday, April 28. The exam will cover sections 1.1-3.1. You will not be allowed to use any notes or electronic devices on the exam.

I have written a practice exam (Solutions), which is similar in length and difficulty to the real exam. Do not expect that Midterm 1 will look exactly like the practice exam! I promise that it will not. I suggest that you look at the practice exam only after you have completed many of the review problems. You should attempt to take it in a quite place and give yourself 50 minutes. I will post the solutions the evening prior to the exam.

Here is a list of review problems I suggest looking at (from the book). There will also be a review worksheet given next week.

- 1.1 #2, 3, 8
- 1.2 #4, 8, 10
- 2.1 #7, 11
- 2.2 #3, 6, 7, 8, 13
- 2.3 #5, 6
- 2.4 #3, 8, 9, 10
- 3.1 #1, 2, 4, 7, 12

### Midterm 2

Midterm 2 will take place in class on Friday, May 19. The exam will cover sections 3.2-4.2. You will not be allowed to use any notes or electronic devices on the exam.

Here is a review guide for Midterm 2. It contains many things with which you should be familiar with in order to succeed on the exam.

I have written a practice exam (Solutions), which is similar in length and difficulty to the real exam. Do not expect that Midterm 2 will look exactly like the practice exam! I promise that it will not. I suggest that you look at the practice exam only after you have completed many of the review problems. You should attempt to take it in a quite place and give yourself 50 minutes. I will post the solutions the afternoon prior to the exam.

Here is a list of review problems I suggest looking at (from the book). There will also be a review worksheet given next week. Note that 3.6 is a review secion; we did not cover it in class and there is no material from that section that will be covered on the exam. However, there are review problems from that section that I suggest taking a look at.

- 3.2 #1, 2, 3, 5, 6, 10, 11
- 3.3 #2, 4, 6, 9, 11, 12
- 3.4 #2, 6, 7, 10
- 3.5 #2, 4, 10, 13, 14, 16-18
- 3.6 #3, 6, 7, 10
- 4.1 #3, 7, 10, 12, 14
- 4.2 #7, 11, 13, 16

### Final Exam

The final will take place on Tuesday, June 13 from 10:15-12:15 in our usual classroom. It will cover matrial from sections 1.1-6.3. For sections 1.1-4.2, you should focus on studying the homework problems and worksheets corresponding to those sections. You should also take a look at the proof techniques listed in the Midterm 2 review guide (see above) and make sure you are familiar with them; you should also know the choose-an-element method. For the newer stuff, also consider the homework and worksheet problems. Additionally, here are some review problems that I would suggest looking at, taken from the most recent sections.

- 5.1 #9
- 5.2 #1, 4, 8, 11
- 5.3 #4b, 8b
- 5.4 #4, 6
- 6.1 #7
- 6.2 #3, 7, 10
- 6.3 #2, 5, 12, 16

I will expect you to be able to state the definitions of each of the following words/phrases.

- Ch 5: subset, intersection of two sets, union of two ssets, set difference, complement of a set
- Ch 6: injective function, surjective function

Here is the practice final (Solutions). Note that I will also have office hours on Monday, June 12th, from 9-10:30 and 1-3pm.