Daily Prep 4A -- MTH 350-01

--- tags: mth350, dailyprep --- # Daily Prep 4A -- MTH 350-01 ## Overview The concept of **prime numbers** has come up once or twice for us in the course, and now it's time to focus intently on this crucial set of integers and see what we can learn about them. In Module 4A, we will focus on getting a proper definition of "prime number" (for example, should 1 be considered a prime?) and then look carefully at the **Fundamental Theorem of Arithmetic** which allows us to factor any positive integer into a unique (sort of) product of prime numbers. ## Learning objectives **Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught. + State the definition of *prime* and *composite* numbers. + State and apply the *Fundamental Theorem of Arithmetic*. + State and apply *Euclid's Lemma* (both weak and strong forms) and Theorem 4.5. **Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class. + Explain line-by-line the existence portion of the proof of the Fundamental Theorem of Arithmetic. + Explain line-by-line the uniqueness portion of the proof of the Fundamental Theorem of Arithmetic. ## Resources for learning **Reading:** Read through Investigation 4, pages 45-50 (through the statement of the strong form of Euclid's Lemma) in the textbook. **Video:** None of these videos is required, but they are all interesting in their own way, and I hope you watch at least one of them because prime numbers are awesome. - Why are prime numbers important? https://www.youtube.com/watch?v=qQYeYyM1k9o - 1 and prime numbers (Numberphile) https://www.youtube.com/watch?v=IQofiPqhJ_s - Adam Spencer: Why I fell in love with monster prime numbers (TED talk) https://youtu.be/B4xOFsygwr4 - If you are really bored you can watch this guy recite prime numbers for 3 hours straight (no kidding): https://youtu.be/NHEaYbDWyQE **Other:** ## Exercises The exercises for this Daily Prep are found on the Google Form: https://docs.google.com/forms/d/e/1FAIpQLSdfPad_zwSxr2TTwuA2m2ohcHb9EIl2qOMEu1R3rD00yoeEYg/viewform ## Submission and grading To submit your work, simply submit the Google Form. You will receive a receipt via email to confirm your submission. (Look in your spam folders if you do not see the receipt.) A **Pass** mark is given if the Daily Prep is turned in before its deadline and if each item on the Daily Prep has a response that represents a good faith effort to be right. **Mistakes are not penalized**. A **No Pass** is given if an item is left blank (even accidentally), has an answer but it shows insufficient effort (including responses like "I don't know"), or if the Daily Prep is late.