---
# System prepended metadata

title: Daily Prep 12A -- MTH 350-01
tags: [mth350, ' dailyprep']

---

---
tags: mth350, dailyprep
---

# Daily Prep 12A -- MTH 350-01

## Overview 

In our final module in this course, we will take up the question of how to tell if two rings are "essentially the same" --- i.e. the rings have superficial differences but all the "essential" structural properties between the two are the same. We'll say that two such rings are **isomorphic** and develop a way of proving two rings are isomorphic using functions. 

## 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. 

+ (*Review*) Determine if a function between two sets is injective, surjective, or bijective. 
+ State what it means for a function between two rings to *preserve an operation*. 

**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. 

+ State the definition of an *isomorphism* between two rings and what it means for two rings to be *isomorphic* to each other; use the definition to decide whether a specific function between two specific rings is an isomorphism and whether two specific rings are isomorphic.
+ State the steps necessary to prove that a two rings are isomorphic and that a function between two rings is an isomorphism; also state what it means to say that two rings are *not* isomorphic. 

## Resources for learning

**Reading:** Read Investigation 10 starting with the Preview Activity and continuing up to, but not including Activity 10.6.


## Exercises 

The exercises for this Daily Prep are found on the Google Form: 

https://docs.google.com/forms/d/e/1FAIpQLScpAowj-S2k4dDYOdUceNaLWsiRhVc-8vJSzugHz_SGxF6aFw/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.