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Sets, Maps and Symmetry Groups Course Discussion List


Posted by Daniel Goroff on December 22, 1999 at 23:38:07:


The page below concerning Math 101 Plans was handed out in class last week. If you have already done group projects #1, #2, and #3, then just finish the practice final and you are, in principle, done since #3 counts double. (Participating in more than four group projects may help you in other ways, but only the best four you hand in will earn points.) In contrast to the material in Chapters 1 through 13 of the Notes, you are not expected to master every detail of the remaining projects and lectures. The purpose of these final activities is to consolidate the ideas and concepts you have learned by seeing how they get used in various contexts. Look for, think about, and work through chances to do that in this material since, if you want to be able to write proofs well in a few weeks on the final or in a few months in more advanced classes, it does not make sense just to stop now. And I hope that exposure to these ideas will interest many of you in taking other classes where you will be ready to study more of the details. As always, do not hesitate to e-mail, phone, or post messages to our web page if you have any questions.

Happy Holidays and Best Wishes for the New Year,




As it says in the syllabus, the final will count for the difference between a fixed target and the number of points you have accumulated during the term. In principle, this means that any points you miss during the term can be recovered on the final. In practice, it is best not to wait until the final! Make sure you keep up with the homework that has been assigned, especially the material about continuity since this is such a major theme. All regular homework should be handed in by class time on Tuesday, December 21.

As it also says in the syllabus, you should work on group projects and hand in at least four of them. The one about Sequences and Series is long enough and important enough to count double, that is, as two projects if you choose to hand it in. The next one expands on Rudin's definition of the exponential function. There will also be parts of group projects distributed during the class meetings that remain and time will be set aside during each of those classes to work together on them with lots of hints. All group projects should be handed in by Friday, January 7.

As it also says in the syllabus, there will be a second midterm. It is a take home, more of a practice final really, that I recommend you do in three hours as if it were a final. A copy will be available in class on Tuesday, December 21. Your answers should be handed in by class time on Tuesday, January 11. Some of the questions may relate to the basics of ideas discussed in the group projects and in the last few lectures.

Here is the plan for the class meetings that remain:

Thursday, December 16:
Lecture on the Algebra of Constructing the Complex Numbers and the Analysis of Constructing the Complex Exponential; Plus work on Group Project #3 and 4.

Tuesday, December 21:
Lecture on Solving for Roots or Fixed Points, Newton's Method, Fractals, and other Applications of the Contraction Mapping Theorem; Plus work on Group Project #4 and 5

Thursday, January 6:
Lecture on Groups, Symmetry, Why Exponentials Are So Important, and What We Mean by Geometry; Plus work on Group Projects #3, 4, and 5.

Tuesday, January 11:
Lecture on Proofs of the Fundamental Theorem of Algebra Using Compactness, Logarithms, and other Methods Related to the Course; Plus work on reviewing.

Thursday, January 13:
Review for the Final Examination.

Wednesday, January 18:
The Final Examination is scheduled for 2:15 in Sever 213.

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