OverviewForemost, this is a 300-level mathematics course. Rather than attempting to give a comprehensive survey of the history of mathematics, we will focus on the development of three main topics: Cantor's surprising results on infinite sets, the long journey towards a proof of Fermat's Last Theorem, and the search for a general formula to solve fifth degree polynomials (similar to the quadratic formula for second degree polynomials). Our primary sources for each of these topics are English translations of the original papers written on these topics. I'm really looking forward to the semester.EvaluationYour final grade will be determined by
HomeworkA major emphasis in this course is that you learn how to write rigorous and precise mathematical arguments. This can be a challenging endeavor and may require several iterations, but the process will not only aid your mathematical development but can also great improve your clarity of thought in other disciplines and areas as well.With this emphasis, your homework should be precise, comprehensible, completely justified, and written in complete sentences. Most of the homework problems will be worth 5 points, and the possible grades will be 5, 4, or No Grade. A few of the problems may be worth 10 points, and the possible grades will be 10, 9, 8, or No Grade. After I have returned the homework, I will allow you one opportunity to rewrite any problem that you have made a serious effort to complete. However, you must turn in your rewrite, along with your original paper, within one week of when I return the homework to the class. An important aspect of your mathematical development is that you learn to discuss mathematics with others and collaborate on problems. The homework assignments will alternate between Individual assignments and Group assignments. On the group homework assignments, you will work in groups of two and turn in one paper. It is extremely important that both of you understand every solution that your group produces. On each assignment, one student will be designated as the primary author who writes-up the solutions, and the role of primary author must alternate between the members of the group. You may discuss the Individual assignments with other students, but each person must turn in a separate paper that represents his/her own work. ExamsYou will have at least five days to complete each Takehome Exam and at least one week to complete the Takehome Final. I would strongly suggest that you begin early on these to leave time to ask me questions about the exam.Inclass PresentationsYou will give two major group presentations during the semester, each approximately 20 minutes long. The first will be on one of the chapters from Journey Through Genius, and the other will cover a topic referenced during the semester that we have not covered in depth.I have extremely high expectations for the quality of these presentations. Reading AssignmentsI will put a copy of each reading assignment on the Math 104 homepage. Each assignment will contain a specific reading assignment and will have two or three questions that you should be able to answer after you have read the section.See the Guidelines for Submitting Reading Assignments and Suggestions for Reading a Math Book for more information. A Few Notes on Your Homework and ExamsHere are a few guidelines for the presentation of your written work. If you do not follow these, I reserve the right to return your homework ungraded!
Grading of Group AssignmentsEach group assignment will receive a single grade, and the group will determine how the points are allocated to each member. For example, if a group of three receives an 85 on a presentation, then the group will have 3x85=255 points to distribute among them. I will be available to mediate this process, if necessary.Few Other SuggestionsOne idea that I believe will help you with the historical perspective of the course is to keep your own timeline of the mathematicians and their writings that we read. I would also suggest that you keep your own glossary of terms defined in the text and where they are defined.Hudson River Undergraduate Mathematics ConferenceThe HRUMC will be held on April 28 at Skidmore College. I would strongly encourage all of you to attend, and you should also consider giving a talk. This is a really nice day to be involved with mathematics with other undergraduates. A good time will be had by all.If you do give a presentation, you will receive an extra 5% on your final grade. Each talk is attended by anywhere from 10 to 50 people, most of whom are other mathematics students from around New England. Before you submit an abstract to give a talk, we will need to discuss your topic and make sure that it is at the appropriate level. I have very high expectations for the quality of these talks so you should expect to devote significant effort to your presentation. I will, of course, work with each of you on your talk. Class AttendanceAlthough class attendance is not a specified percentage of your grade, I will keep a class roll to help me determine borderline grades at the end of the semester. If you do miss class, you are responsible for the material that was covered.Getting HelpPlease come see me during my office hours! If you have a conflict and cannot make my office hours, please call or email me and we can set up an appointment for another time.
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