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Math 250: Foundations of Mathematics

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Course Materials:

Syllabus
[uploaded 01.05.16]
Textbook
[uploaded 01.05.16]
Daily Prep Guidelines
[uploaded 01.05.16]
Proof Portfolio Guidelines
[uploaded 01.05.16]
LaTeX Template
[uploaded 01.05.16]
Course Outline
[uploaded 01.11.16]

Course Log:

Week 1
[01.06.16]

Welcome to the math 250 course page! This website will be a resource for you as we move through the course. I’ll be using it as a place to post important course updates and materials, as well as a place to remind you about due dates. Check back often!

I’ll say more about the proof portfolio as we move through the semester, but sometime before Thursday 01.14, go to overleaf.com and set up an account. We’ll take some time in class on 01.14 to work through the basics of LaTeX (pronounced like “Lah-Tech,” not like the stuff doctor gloves are made out of).

Week 2
[01.12.16] - Daily Prep
[01.14.16] - Daily Prep

On Friday you will have your first proof portfolio draft due, you can choose one of the problems in Problem Group A. Your draft should be submitted to me via email, by sending me the link to your overleaf page, no later than 5 pm tomorrow 01.15. Please remember to use the following subject line in your email: Math 250 Problem A2 Draft 1 (of course replace A2 with whichever problem you choose). You can see the sample draft at the end of the proof portfolio guidelines if you’re not sure what your submission should look like.

Here is a link to a helpful LaTeX guide, thanks to Natalie for sharing that!

Week 3
[01.19.16] - Daily Prep
[01.21.16] - Daily Prep

Great job with the proof writing on the board today; we’re going to try and do more of that as the semester progresses. We didn’t make it to sections 2.3 and 2.4 today, so there will be no daily prep on Tuesday 01.26 (although it might be a good idea to review sections 2.3 and 2.4 before class that day). Because of this delay, I may move the first exam back to the week of 02.08-02.12, but I’ll keep you informed about that.

Remember that now every Tuesday and Friday, until the end of time, we have a proof portfolio draft due.

Week 4
[01.26.16] - No Daily Prep
[01.28.16] - Daily Prep

For Friday you can start working on problems from Problem Group B. Please check the revised course schedule above, I’ve moved our first exam back to make sure we get through chapter 3 before the exam. You can anticipate that it will cover everything up though section 3.5 in the textbook. Remember, that means you should be doing the exercises from the book, since the exam questions will come directly from these problems. There are lots of them, so don’t wait until the last minute, and as always, please come and visit me if you want to go over any of the exercises.

A note about proof portfolios: I will grade two drafts each week. If you’ve missed a draft, you can still make those up by submitting a draft on a non-due date (we’ll have those on the weeks of exams). However, I will only every grade two each week, so don’t build up too much of a backlog.

Week 5
[02.02.16] - Daily Prep
[02.04.16] - Daily Prep

Here is a formal proof of the irrationality of the square root of 2, as we discussed at the end of class today. For Thursday, please take a look at the prime divisor theorem, and consider how this proof might be extended to prove that other square roots are irrational.

For Tuesday 02.09, please come to class prepared to write the proof of Activity 3 in the 3.4 packet on the board. Recall, you will have portfolio drafts due Tuesday and Friday this week.

Week 6
[02.09.16] - Daily Prep
[02.11.16] - Daily Prep

Reminder, you still have a portfolio draft due this week on 02.12, but since next week is exam week (and I won’t be here) you won’t have any portfolio drafts due. Regular drafts will resume the following week. Dr. Flemming will be in class on 02.18 to work with you on some more induction problems.

Week 7
[02.16.16] - Exam 1
[02.18.16] - Daily Prep

Next week we’ll be back on schedule for proof portfolios and daily preps. Please remember, for Tuesday 02.23 you should be prepared to post at least one proof from activity 1, 2, or 3 from 4.2 on the board at the start of class.

Week 8
[02.23.16] - Daily Prep
[02.25.16] - Daily Prep

Here are the proofs from class today, 02.23. For next time, please come prepared to present the proof of activity 4 from 4.3.






Spring Break
Week 9
[03.08.16] - Daily Prep
[03.10.16] - Daily Prep

As promised, here are links to the sample set proof using the choose and element method, and the sample TFAE proof. We are back to the regular portfolio due dates this week, and in case you are ready for more problems, here is problem group C.

Week 10
[03.15.16] - No Daily Prep
[03.17.16] - Exam 2

Since we have an exam on Thursday 03.17 you don’t need to submit a proof portfolio on Friday 03.18. After today’s proof, your next proof will be due on Tuesday 03.22.

Week 11
[03.22.16] - Daily Prep
[03.24.16] - Easter Break (No Class)
Week 12
[03.29.16] - No Daily Prep
[03.31.16] - Daily Prep

Here is the pdf of the formal proof of bijectivity that we discussed in class today. Also, as promised here is a list of suggested homework problems for chapters 6 and 7. The final exam will be made up of questions from this list.

Week 13
[04.05.16] - Daily Prep
[04.07.16] - Daily Prep

The last day to submit a draft for your proof portfolio is Friday 04.15, until then I will still grade two proofs each week. Remember, the final printed out version of your final portfolio is to be handed in on the last day of class, Thursday 04.21. Check the proof portfolio guidelines handout above for all of the necessary details.

Week 14
[04.12.16] - Daily Prep
[04.14.16] - Daily Prep
Week 15
[04.19.16] - Daily Prep
[04.21.16] - Daily Prep
Final Exam
[04.27.16] - 1:30-3:30 pm