I have been asked for synthesis badges question solutions. I’m sorry that I’ve been slow to do this. Here they are: synthesis solutions.
Today there will be a proof quiz:
I will ask you to prove that something is or is not injective and/or surjective and/or bijective. This is of the style of Section 12.2. So read 12.2 and do exercises for Section 12.2 to prepare. It will be very similar, if not identical, to one of these or to examples 12.4 or 12.5. The methods are shown on pages 202 and 203.
Here’s the schedule for the last week of classes:
- Badges quiz — functions, relations and MODULAR ARITHMETIC (which we will cover in class Monday)
- In class, we’ll do functions and modular arithmetic
- Proof quiz, to make sure you haven’t forgotten how to prove things. I will give you a list of proofs it could be. UPDATE: I will ask you to prove that something is or is not injective and/or surjective and/or bijective. This is of the style of Section 12.2. So read 12.2 and do exercises for Section 12.2 to prepare. It will be very similar, if not identical, to one of these or to examples 12.4 or 12.5. The methods are shown on pages 202 and 203. I will do one in class Monday.
- In class, I’ll use what we know now to give an overview of some of the upper-year courses you can take, and what they are really about (so this will also serve as review)
- Badges quiz — counting, proofs, functions, relations, modular arithmetic
- I’ll continue with the “what’s out there in the world of math” theme of Wednesday, combining review with an overview of what else you can learn
Here’s what you should be doing this week:
- Check your badges progress on D2L, and make a list of the ones you still need. Come to office hour (as described here) to earn whichever ones you are struggling with, and prepare well for the in-class opportunities. You can do any badges except Synthesis I and II for which you will have two in-class opportunities this week.
- Reviewing the methods of proof and doing some example proofs on your own. Proofs will definitely be on the final exam.
- There is no group-work this week — use the extra time to review and study.
A little about the final:
- It will look a lot like badges and proofs quizzes stapled together in equal proportion — no surprises here
- It may also include a few more of the ‘synthesis’ type questions which involve putting it all together
- A warning: having earned a badge doesn’t mean you know how to do something on the final; time corrupts your abilities. In past, I’ve seen a much lower score on the final exam badges type questions than the badges score of the corresponding student. In retrospect, this isn’t surprising, but don’t be caught unaware. You need to keep your skills it up-to-date! Collect all your old badges quizzes and work through them — there are enough study questions there to keep you busy a long time.
Thanks for a fun student presentation day, including card tricks!
We will do FCQs today or Friday, depending on available time.
To do for class:
Please make sure you are up to Section 3, Composition of Functions, Problem 5 (on page 2), as a starting point for next class. Bring it back to class with you — the first thing you’ll do with your group in class is compare answers up to that point.
Happy Thanksgiving, all! Please enjoy family and friends, and recover your energy.
On the Monday we return, we will have a badges quiz on relations and functions.
Also, please bring back your most recent functions worksheet (from Wednesday before break).
Group presentation day.
If time permits, I may give a badges quiz on relations and functions.
NOTE: I’m afraid I have to cancel Wednesday’s office hour; please email to schedule another time if you’d like to come in.
To do for class:
- Please bring back your Monday functions worksheet to class (we’ll have extras).
- Please continue working and reading in Hammack, Sections 12.1 and 12.2. You are all set to do exercises from these, so have at it!
- Think about which missed sets/logic badges you’d like to prepare to earn in office hour and start work on those (see the previous post).
- Office Hour Monday will be at noon instead of 4:30 pm.
- The most recent badges quiz has been entered into D2L.
In-class Badges Quiz: Proofs, Counting, Relations, Functions I & II
Info about Sets/Logic Badges you may be missing:
- There will be no more sets/logic in-class quizzes.
- But you can earn a missing badge by doing the following. For the badge in question, write an exposition about the content (up to 1 page in length, typesetting not required). Imagine writing a study sheet for a student in the class: it should introduce the relevant information/definitions and give some examples. Then, bring this sheet to office hour where I’ll give you a five-minute oral exam to satisfy myself that you’ve learned that material. For example, I’ll ask you to do an example at the board.
- You can only do this office-hour badge thing one badge per day, so plan ahead.
To do for class:
- Read/reread Hammack Section 11.1-11.4. Do exercises from these sections. They are all excellent exercises, so plan to work through them all.
- Read Hammack, Section 12.1-12.2.
- Prepare for the badges quiz.
Today is a student presentation day. No quiz. If there’s time, we’ll take up the worksheet from Wednesday, available here.