This unit introduces you to the language of mathematics. If you think of writing mathematics as learning a new language, and think back to the time when you learned French, Spanish, German or English (or other languages, if your high school was lucky enough to offer them), you will remember how slow it was initially to express yourself in that new language!
We will learn the structure of the language of mathematics through logic. Many times, mathematics and English will agree, but sometimes they will differ, and those instances will require extra care.
This unit is meant for you to work through independently, and then attend one of the discussion sessions hosted by your professor or the class learning assistant. Completing this content will count as one homework assignment on which you received full credit.
Before watching any videos about logic, or reading from the textbook, begin with the first video introducing standard notation for sets of numbers. If you have covered this in class already, you may skip this video.
This worksheet is a guided reading to several sections of the textbook. Please do the reading and try the suggested problems on the sheet. The sections in the text are discussed in the videos below as well. For help with these problems, write to your professor, come to office hours, attend a session with a learning assistant or join a discussion session about these problems. You do not have to turn in these problems, but you would be expected to complete similar problems on a quiz or exam.
Please watch these videos after you have completed the readings and problems on the Logical Reasoning worksheet linked above.
This worksheet accompanies the above two videos. After watching each one, complete the relevant parts of the worksheet. Solutions are linked here.
This video contains two additional examples of how to determine the truth value of, and then justify, doubly quantified statements. Watching this video is optional.
This worksheet contains examples of doubly quantified statements; you should decide whether they are true or false and justify your response. Solutions are linked here.