Daily Prep 1.1 -- MTH 225

--- tags: mth225, dailyprep --- # Daily Prep 1.1 -- MTH 225 ## Overview Our first lesson in the course goes to the very foundations mathematics --- numbers, and how we write them. In this lesson, you'll learn about **base 10** or **decimal** representation of integers; representing integers in **base 2 (binary)**, **base 8 (octal)**, and **base 16 (hexadecimal)** form; and how to convert from one representation to another. ## 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. - Explain the meaning of "place value" in base 10 representation as well as in bases 2, 8 and 16. - Convert an integer in base 2, base 8 and base 16 to base 10. **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. - Convert an integer from base 10 to base 2, base 8, and base 16 using the base conversion algorithm. - Convert an integer in base 2 to base 8 and base 16 (without converting to base 10 first). - Make mathematical conjectures about different base representations of special numbers and explain why those conjectures may be true. ## Resources for learning **Video:** Watch these from [the MTH 225 playlist](https://vimeo.com/showcase/8667148) (total running time 28:09): <div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/575905500?badge=0&autopause=0&player_id=0&app_id=58479" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 1.1: Base 10 and Base 2 representation of integers"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script> <div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/575939514?badge=0&autopause=0&player_id=0&app_id=58479" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 1.2: Base 8 and Base 16 representation of integers"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script> <div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/578187581?badge=0&autopause=0&player_id=0&app_id=58479" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 1.3: Base 10 conversion algorithm"></iframe></div><script src="https://player.vimeo.com/api/player.js"></script> You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below. ## Exercises Once you have watched the videos above, go to this form and complete all the non-optional items on it: https://docs.google.com/forms/d/e/1FAIpQLSfLOVt5TFNh4_NFLiAIk97s3VVWv3w-1FVhYXcbPX7qIEWjpg/viewform There are optional items at the end you can use to send questions or comments. ## Submission and grading **Submitting your work:** Your work is submitted when you submit the Google Form. You should receive an email receipt indicating that the work was submitted successfully. **How this is graded:** The pre-class portion of the Daily Prep is graded either 0 points or 1 point, on the basis of completeness and effort. Wrong answers are not penalized. Earning a "1" requires that you: - Turn the work in before its deadline; - Leave no item blank or skipped, even accidentally; and - Give a good-faith effort at a correct answer on every non-optional item. More information can be found in the [Specifications for Satisfactory Work in MTH 225](/Cy6P0rGZQzuOM3NwZ3ZuMw) document. When you arrive for the class meeting, you'll be put into a group of 2-3 to complete a quiz over this material, which will be graded on a 0/1 scale on the basis of correctness.