You can find the slides from today’s lecture here:
If you did not get 6 out of 6 on problem 3 from the exam please redo it and turn in a properly written proof.
Here is the problem:
Let , and be sets. Prove that
Note that you must reason about arbitrary sets — you cannot prove this “by example”. Likewise if you use a truth table then you need to explain why it is relevant and make sure it is a truth table for statements. It makes no sense to say that is true or false if is a set.
The worksheets from past recitations are available here:
In class on Wednesday I mentioned the following book
It is a short, well written presentation of SOME of the topics we are considering in this course. I highly recommend it if you feel like you need some extra reading material.
A few years ago I wrote up some notes on logic and set theory for my analysis course. Those notes develop the topics we have discussed so far in a somewhat more formal fashion. They may be useful to you or they may not be. Use them if they are useful!
If you are interested in delving much deeper into the mathematical theory of logic and mathematical argument, I recommend the text
It is not a book to help you with this course! Instead it is something for you to look at it in case you are interested in seeing where all this can go.
In tomorrows lecture we look the idea of a set and how to combine sets through unions, intersections and other operations. Don’t forget to turn in your first assignment: Exercise 3.2(ii) (p. 33).
Recall that homework for the course is due at EVERY lecture. Your second assignment — Exercises 1.10 (p. 6), 1.33 (p. 11) and 1.34 (i-ii) (p. 12) — is due on Friday.
To succeed in this (or any other) math course, you MUST do the homework and attend recitations to work on the practice material. It is part of your grade, of course, but more importantly it is an indespensible step in the process of learning the subject. If for some reason you must miss a lecture please, let me know beforehand and make arrangements to get the homework to me. To give you a little flexibility, I have decided to drop ONE quiz for each student in case you need to miss ONE recitation meeting for some reason. Please let Alex and I know beforehand. There are only twelve recitation meetings, not counting the two exams, so please do not miss more than one! (Students missing more than one recitation will be dealt with on a case by case basis.)
Please note that the course schedule (which you may find at the above link) has reading assignments. Stay up to date with this! In partcular, note that Chapter 2 was on your reading assignment for Monday although we will not discuss it in lecture or recitation. Please read it, however! You will find the suggestions on how to read mathematics helpful.
In the previous post, I discussed the importance of mathematical writing. Here are some general guidelines that you should stick when writing up your homework in this course:
- Adhere to standard rules of grammar and punctuation.
- Be neat. You do not need to type your homework. But write neatly and clearly. Turn in the problems in the assigned order and one problem to a page.
- Figure out what you want to write before you write it. Write a rough draft or an outline and then write up the assignment.
- Break each proof into paragraphs each of which has a limited number of ideas (preferably just one idea, though that is not always possible).
- Do not start a sentence with a symbol.
- Define non-standard symbols before you use them.
- Use words to explain an idea or a computation if doing so is clearer or easier than using symbols.
- And remember equal means equal!
This course will most likely be very different from math courses you have taken previously. Chances are your mathematics education up to now has focused on computation. Continue reading