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Math 104: Introduction to Real AnalysisUC Berkeley, Summer 2006, Section 002-201Instructor: Patrick Barrowemail [email protected] 842 Evanshours 3:00 - class, Mon - Thurs.I am generally free during the afterno ons and will gladly sched-ule additional times as needed.Textbook: Elementary Analysis: The Theory of Calculus, by Kenneth A.RossSchedule: Monday - Thursday, 4:10 - 6:00, 75 Evans. We plan to doan hour of formal lecture per day, followed by a ten minutebreak, with the remainder left for problem solving and opendiscussion, and possibly more lecture.The course runs June 26 - August 17, except for July 4, whichfalls on a Tuesday. We will have three in class exams, eachfor the full 110 minutes, on July 13, August 3, and August 17(all Thursdays, also they are equally weighted). There are 8weeks total, and you will have 12 homeworks due. The firstis due on Thursday, June 29, and each subsequent homework isdue Tuesday/ Thursday, promptly at the start of class. Thereare no homeworks due on exam days. Because of the uniquenature of the summer schedule, we have to adopt a strict “nolate” policy with everything. If you have conflicts with any ofthe above dates, you simply cannot take this course.Grading: To compute your raw grade, I will average your cumulativehomework score with your 3 exam scores, so each will count25%. If your raw grade is greater than or equal to 80% thenyou are assured an A- or better, 60% a B-, 40% a C-, and 20%a D-. In the end I can revise this curve if the scores are lowerthan expected; this simply represents a minimum guarantee onmy part. After each exam I will give precise statistics, and Igenerally promise to be fair.1This is a “proof course.” That means answers are to be composed asif you are communicating a fully justified solution to a mathematicalcolleague. Undoubtedly this description is vague at the moment, buta major theme of this course will be learning exactly what it meansto communicate rigorous mathematics. As we progress I hope tomake this aspe ct of things as clear as possible. “Is this a proof?” isa great question for you to be asking at this stage.The above numbers may s eem low. This is because we plan to adoptthe grading philosophy of heavily penalizing incorrect reasoning.Arguments with logical gaps or false claims get no credit.That being said, generous partial credit will be awarded for progresstowards a full solution. If you have figured some things out, but arestuck at a specific point, then say so in your answer. Think of it asa response to a query. If you cannot fully respond, then you are alsoexpected to acknowledge that. Try to prove a specific case, work outan example, or conjecture that a particular theorem may be relevant.Whatever you do, DO NOT write something that is downright false.To know when you have a partial solution, and to identify preciselythe parts you are missing, are invaluable mathematical skills. Noone will solve every part of every problem.You are encouraged to work together to solve homework problems.Of course, the actual written solution must be your own composi-tion. The problems will come directly from the textbook. In fact,you may consider the table of contents a conceptual syllabus for theclass, with one section roughly corresponding to one lecture. Thismakes it easier for you, minimizes my errors, and gives us both acommon reference. For each exam I will give specific sections forwhich you will be responsible. When in doubt, you can study thebook.However, I strongly encourage you to seek other analysis texts, orinternet sources like Wikipedia or Mathworld (watch for mistakes!),as a study aid/ problem solving tool. You should be able to learnindependently from a resource, to an extent. I aim to provide agood mix of examples, both from the book and elsewhere.Finally, every time I make a mistake, it is actually on purpose,because I am testing


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Berkeley MATH 104 - Syllabus

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