Math 138AWinter 2010R. SchultzGENERAL REMARKSThe course text is Elementary Differential Geometry (Second Edition), by B. O’Neill (Academic Press,1997, ISBN: 0–125–26745–2). This course will essentially cover the first five chapters with a few omissionsand additions at various points. Online lecture notes give a more accurate description of the course contents(see below for more information on these).Contact information. My office is Surge 221, and it is around the corner from the Department’sadministrative front desk (Surge 202). Normally I am available in my office between 10:30 and 11:30 onFridays, and at other times by appointment. My telephone number is 951-827-6459 (as usual, suppressthe area code from inside the 951 region, and also replace the 827 by a 2 if calling from an extension atUCR). Another highly recommended option is electronic mail; my full address is [email protected] of electronic mail is often easier than trying to play telephone tag. IMPORTANT: The default filtersfor electronic mail on the Department network are not very restrictive and sometimes there is an enormousamount of garbage in my electronic mailbox. Therefore I strongly recommend that you include somethinglike Math 138A in the subject heading so that your message does not get inadvertently deleted without beingread. Also, since the authors of junk messages often use only capital letters in their subject headings, thisshould be avoided as well.Grading policy: There will be an in-class midterm examinations, which will count 27 per cent of thecourse grade, a final examination that will count for 45 per cent, a take-home examination which will countfor 10 per cent and three quizzes in the discussion sections which will each count for 6 per cent.Tentatively the midterm examinations is scheduled for Wednesday, February 3, and the final examinationis scheduled for Tuesday, March 16. The due date for the take-home assignment is scheduled for Friday,February 26; the exam will be posted between one and two weeks before the due date. and part in-class(with a later starting time!). Quizzes are scheduled for January 16, February 16 and March 3 (all Tuesdays).No books, notes or calculators are allowed for examinations or quizzes. You should always bring yourUCR identification card to examinations and quizzes (there might be identification checks). Most questionswill be problems from the assignment sheets, examples from the text or lectures or discussion classes, orstraightforward modifications of these (usually slightly different numbers or functions).Course handouts and notes: All printed handouts for the course will be available on the WorldWide Web from the following site:http://www.math.ucr.edu/∼res/math138AThe contents of this directory include a copy of this handout (aabInformation.pdf), the course outline, thehomework assignments, and various files containing supplementary material. All files except a few ordinarytext files are available as pdf files. These can be opened, downloaded, read or printed with the free Acrobatreaders that are currently available or easily downloadable for most PC’s (including both Macintosh andUnix based systems — there are also such readers for some smart cell phones, Blackberries and similarpocket-sized devices, but I do not have complete information on availability).There are also directories containing background material from some fairly closely related courses in thedirectoryhttp://math.ucr.edu/∼resSpecifically, the subdirectories math10A, math10B and math132 contain background material which is partic-ularly relevant to this course.IMPORTANT. (1) Please contact me immediately if you have problems viewing or printing out anyof these files.(2) These files are only intended for classroom purposes and are not meant for widespread publiccirculation. In some cases further distribution may be a violation of copyright laws or the terms of use formaterial in the files.Discussion sessions: In addition to the three meetings with the primary instructor each week, thereis a discussion sections which is scheduled for one hour each week; the instructor is Mr. E. Burkard. Furtherinformation will be made available at discussion section meetings.General expectations. Students are expected to attend all classes, both lectures and discussions,but this will not be enforced except in the case of examination dates. However, missing class can seriouslyaffect one’s course grade. It is important to keep up with the course and finish homework assignments ina timely manner. Preparing for the lectures by reading the book before class is strongly encouraged, asare taking notes and asking questions during class if you do not understand something or if something inthe class seems incorrect – even if everyone else seems to understand what is going on (if there is not timeto answer some questions during class, arrangements can be made to do so afterwards). It is essential toattempt the homework problems before going to discussion. Solving many problems is the best way tosolidify your understanding of mathematics and to prepare for examinations. If you find you can’t dosomething ask for help.Students are responsible for understanding how to do all the exercises listed in the course homeworkfile; for the most difficult ones, only a passive understanding of the solutions is necessary, but for exercisesthat are easy or just moderately difficult the ability to explain the solutions clearly, or to do this for a slightvariation of the problem, is something that is certain to be appear on exams. Some solutions (or sketches)and hints will be posted.Student questions during primary class sessions are encouraged. Please do not hesitate to ask questions,especially if you do not understand something or if something in the lecture seems wrong — even if everyoneelse seems to understand. Questions on homework or review are generally best answered at the beginningof class and should be asked at that time. In general such questions are encouraged, but in some cases itmight be necessary to limit such question periods or to post the answers online after class.The primary instructor and teaching assistant will attempt to answer electronic messages regarding thecourse in a reasonably timely manner, especially during regular working hours, and in some instances one orthe other may respond outside of such hours. Complete answers to more complicated questions may requireadditional