In Math 254 you will learn the logic and set theory that underlies all of modern mathematics and computer science. You will also learn how to prove mathematical statements.
| Week | Dates | Chapter | Topic | Homework |
|---|---|---|---|---|
| 1 | 1/17 - 1/21 | 01 | Sets | HW01 |
| 2 | 1/24 - 1/28 | 02 | Logic | HW02 |
| 3 | 1/31 - 2/04 | 03 | Counting | HW03 |
| 4 | 2/07 - 2/11 | 04 | Direct Proof, Midterm 1 | HW04 |
| 5 | 2/14 - 2/18 | 05 | Contrapositive Proof | HW05 |
| 6 | 2/21 - 2/25 | 06 | Proof by Contradiction | HW06 |
| 7 | 2/28 - 3/04 | 07 | Proving Non-Conditional Statements | HW07 |
| 8 | 3/14 - 3/18 | 08 | Proofs Involving Sets | HW08 |
| 9 | 3/21 - 3/25 | 09 | Disproof | HW09 |
| 10 | 3/28 - 4/01 | 10 | Mathematical Induction | HW10 |
| 11 | 4/04 - 4/08 | 11 | Relations | HW11 |
| 12 | 4/11 - 4/15 | 12 | Functions | HW12 |
| 13 | 4/18 - 4/22 | 14 | Cardinality, Midterm 2 | |
| 14 | 4/25 - 4/29 | TBA |
Attendance in this class is expected, and you are responsible for any material that you miss. However, if you have a fever or are not feeling well, then please do not come to class that day. As long as you let me know the reason for your absence, I will do my best to help you stay caught up and make up any material that you missed. The key is to communicate with me when you aren’t able to attend class.
My office hours are shown above on my weekly schedule. I am also available by appointment. My office is Blake B-02, which is one of the Blake apartments. You can find it on this map. It looks like a student apartment, but I am using it as my office while the new science building is being built. During my regularly scheduled office hours the front door should be unlocked, so feel free to come in. I’ll be right upstairs. If you would prefer to schedule online office hours, let me know and I’ll be happy to set up a Zoom meeting.
The term grade will be based on the results of the examinations and homework.
| Component | Proportion |
|---|---|
| Homework | 50% |
| Midterm 1 | 15% |
| Midterm 2 | 15% |
| Final Exam | 20% |
There will be two in-class midterm exams and a cumulative final. The first midterm exam will cover sets, logic, and counting principles. The second midterm will focus on mathematical induction, relations, and functions. All of the exams emphasize definitions and concepts rather than proof writing.
There will be homework assignments due almost every week. The best thing you can do to succeed in this class is to make sure that you keep up with and understand all of the homework. Starting in week 4, most of the homework will involve writing proofs. This is a skill that takes a lot of practice to master, so be prepared to spend some time on these assignments. Here are some rules for writing proofs:
Start by writing the proposition that you are trying to prove. You can copy this part from the assignment. Make sure to clearly indicated that it is not part of the proof by adding the word Claim or Proposition at the beginning.
Next, on a separate line, indicate where the proof starts by writing: Proof.
Every step in the proof should be a complete sentence. It is okay to use mathematical symbols and shorthand, as long as those symbols make a complete sentence when you read them out loud.
Indicate where the proof ends by writing a small box symbol: \(\square\).
Short answer questions will be graded on a two point scale: 2 if correct, 1 if incorrect but you tried something, and 0 points if the solution is missing (or mostly missing). Proofs will be graded on a more detailed 4 point scale:
Late homework will not be accepted, but the lowest homework grade will be dropped from your average.
In compliance with the Hampden-Sydney College policy and equal access laws, I am available to discuss appropriate academic accommodations that may be recommended for students with disabilities. Requests for academic accommodations are to be made at the beginning of the semester (except for unusual circumstances) so that appropriate arrangements can be made. Students are required to contact the Office of Academic Success in order to verify their eligibility for appropriate accommodations.
If we need to switch to an online virtual course at any point during the semester, the basic outline and schedule of topics for the course will remain the same. I will provide asynchronous video guided notes and workshops to help learn the material. I will also divide the class into smaller groups and schedule Zoom meetings during our regular class time where we can go over the material in more detail. I may also incorporate a short oral examination as part of one or more of the midterm or final exams. If you know that you will have trouble with Zoom from home, please let me know.