# Synthesis Solutions

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.

# Wednesday, December 7th

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.

# Monday, December 5th

Here’s the schedule for the last week of classes:

• Monday:
• Badges quiz — functions, relations and MODULAR ARITHMETIC (which we will cover in class Monday)
• In class, we’ll do functions and modular arithmetic
• Wednesday:
• 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)
• Friday:
• 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.