MAD 2104, Notes

Assignments

The assignments will not be collected but they indicate what the upcoming quiz will be on.
Quizzes

These might be multiple choice. For those that are not, keep this in mind: You must give some indication as to how you arrived at your answer. Writing 26 with no explanation is unacceptable, even if the answer happens to be 26.
Don't put arrows, or equality signs, between your sentences or equations. Use descriptive words, even if it's just the word "so". Don't put an equality sign between to quantities unless you think they are equal to each other.
Collections

We will start in Chapter 2, Collections. The author talks about two kinds of collections: lists and sets. Lists are ordered: there is a first entry, a second, and so on until you reach the end of the list. A convenient notation for a list is to write the entries (elements) in order, separated by commas, with the whole thing enclosed in parentheses. For example: (2,3,5,7) is a list of length four. So is (2,3,2,2). The list (7,5,3,2) is not the same as the list (2,3,5,7) even though they have the same entries.

A set is like a list except we don't care about order and, unlike a list, there is no notion of an element appearing in the set more than once. We write (finite) sets by writing the elements in some order, separated by commas, and enclosed in braces. For example {2,3,5,7} is a set of size (or cardinality) four. So is {7,7,3,5,2,5,2,2}. In fact these two sets are equal because they contain exactly the same elements. Note that while the lists (2,3,5,7) and (7,5,3,2) are different, the sets {2,3,5,7} and {7,5,3,2} are the same.
18 January

The symbol in Section 11 that looks like the letter v is the logical symbol for the word "or". Compare the definition of union and intersection at the beginning of this section, where he uses the words "or" and "and", to the proof of Theorem 11.3 where he uses the logical symbol instead of the word "or". The symbol for "and" is the symbol for "or" turned upside down. See page 28 in Section 6 (Boolean algebra) of Chapter 1. George Boole wrote a book on the laws of thought in the nineteenth century.