# Lessons on Rings, Modules, and Multiplicities by D. G. Northcott

By D. G. Northcott

This quantity offers a transparent and self-contained advent to big leads to the idea of earrings and modules. Assuming purely the mathematical heritage supplied by means of an ordinary undergraduate curriculum, the speculation is derived by means of relatively direct and straightforward tools. it will likely be important to either undergraduates and study scholars specialising in algebra. In his ordinary lucid variety the writer introduces the reader to complex issues in a way which makes them either fascinating and straightforward to assimilate. because the textual content offers very complete factors, a few well-ordered routines are incorporated on the finish of every bankruptcy. those lead directly to additional major effects and provides the reader a chance to plot his personal arguments and to check his figuring out of the topic.

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**Sample text**

Although choral response might make kids feel good, it really masks what individual students are really thinking and what it is they understand. Just because they could come up with answers to my questions doesn’t mean that they really understand or that they have any idea how to apply it. I am now left wondering what they really learned from this experience. Reflecting at the End of the School Year 32. In early June, at the end-of-the-year retreat, my colleagues and I were asked to make a 10-minute presentation regarding the aspects of our teaching that we thought had changed most over the year.

If you currently are teaching mathematics, you might want to proceed to the “Connecting to Your Own Practice” section in which you are encouraged to relate the analysis of the ideas and issues raised in “The Case of Catherine Evans and David Young” to your own teaching practice. EXTENDING YOUR ANALYSIS OF THE CASE The questions listed in this section are intended to help you focus on particular aspects of the case related to teacher decision-making and student thinking. If you are working in collaboration with one or more colleagues, the questions can serve as a stimulus for further discussion.

How many on the top and the bottom? Angela: 10. Me: How many on the ends? Angela: 2. Me: How many all together? Angela: 22. Me: Let’s do another one. Listen to what she’s saying and see if you can do it also. Angela, in train 12, how many will there be on the top and bottom? Angela: 12. Me: And then how many will there be on the ends? Angela: 2. Me: How many will there be all together? Angela: 26. Me: Tamika, what’s she doing? Tamika: She’s taking the train number on the top and bottom and adding two.