Gillaspy, Elizabeth A.

English

University of Montana

University of Montana ScholarWorks at University of Montana University of Montana Course Syllabi Open Educational Resources (OER) Fall 9-1-2020 M 381.R01: Advanced Calculus I Elizabeth A. Gillaspy University of Montana, Missoula, elizabeth.gillaspy@mso.umt.edu Follow this and additional works at: https://scholarworks.umt.edu/syllabi Let us know how access to this document benefits you. Recommended Citation Gillaspy, Elizabeth A., "M 381.R01: Advanced Calculus I" (2020). University of Montana Course Syllabi. 11377. https://scholarworks.umt.edu/syllabi/11377 This Syllabus is brought to you for free and open access by the Open Educational Resources (OER) at ScholarWorks at University of Montana. It has been accepted for inclusion in University of Montana Course Syllabi by an authorized administrator of ScholarWorks at University of Montana. For more information, please contact scholarworks@mso.umt.edu. 	 	 	 	 	 	 	                                                                                                                                                                                                                                                                                                                                                                                           M381 Advanced Calculus I – Fall 2020 Instructor information: Elizabeth GillaspyOffice: Math 012Email: elizabeth.gillaspy@mso.umt.eduOffice Phone: 243-4126Office hours: Monday 4:30 - 5:30; Wednesday 10 - 11; or by appointment.Although our class will meet over Zoom (Meeting ID: 923 9798 0993, Password: Analysis), I willhold in-person office hours. While the weather permits, I'll hold office hours on the patio to thesoutheast of the Math building (above Urey Lecture Hall). However, I may wait in my office,rather than outside, until students arrive for office hours. So if you don't see me on the patio,come downstairs to my office!Course description:Welcome to Advanced Calculus. At other universities, this class is sometimes called "RealAnalysis" and to be honest I think that's a better name.While many of the topics we'll study in M 381 are familiar from calculus (limits, continuity,derivatives, integrals) the approach we take in M 381 is really very different. This class is allabout applying your "but *why* is it true?" skills, that you've honed in M 307 and your otherproof-writing classes, to things like the limit laws and differentiation rules. Plus, we'll see a lot ofreally cool and counterintuitive examples, like the Cantor set (it is as big as the real line, but has length zero) and a function which is continuous on [0,1] but is not differentiable at any point in[0,1].The proofs in M 381 have a very different feel to them than the proofs in Number Theory orAbstract Algebra. Learning to think in this way is an important part of your mathematicaltraining, and it will also be extremely helpful if you want to take a class like Complex Analysis orIntroduction to Topology in the future. Plus, I think M 381 will be fun! I hope you do too.Learning Outcomes:Upon completion of this course, students will be able to:1.	*Understand and use the precise definition of a limit for both sequences and functions;2.	*Understand the proofs of the basic results from single variable calculus (e.g., limit laws,product rule, Fundamental Theorem of Calculus, etc.);3.	*Read and write basic proofs in analysis;4.	*Communicate mathematics orally and in writing.Required textbook: Abbott, "Understanding Analysis," second edition.Course Structure:There will be weekly written homework, due on Wednesdays.  We will also have two midterm exams and a final exam, all of which will be oral exams. The midterms are tentatively scheduledfor the week of September 14 and October 19. Our final exam is scheduled for Tuesday,November 24, 1:10 – 3:10 PM.On the homework, I encourage you to work together to figure out the solutions, but what youturn in should represent the understanding in your own brain.  For that reason, please use onlyyour own brain (and pencil/paper/LaTeX) to write up the homework solutions! Don’t write the                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     homework up while you’re in office hours or a group discussion – wait till later. Take notes onthe results of the discussion, by all means, but try to write the solution without consultingthose notes (or your textbook, or the internet, or a friend). If you get stuck, look at thenotes/textbook/etc for a hint – but try to use as few hints as possible. This way, you will build up the “mental muscles” that will enable you to succeed in this course, and in particular on theexams (where you won’t have notes/internet/friends helping you). You’ll turn in the homeworkby uploading a PDF to Moodle.Each week, (at most) one problem on the homework assignment will be starred (e.g. Chapter 6,problem 4*). These problems will usually be more challenging than the rest of the homework.The starred problem should be turned in on a separate page from the rest of the writtenhomework. I will grade these problems on a credit/no credit basis (but with comments so thatyou know what you need to fix). If you receive a score of no credit, you can resubmit theproblem the next week along with that week's homework assignment, and you can continue thisprocess until you receive credit. The primary point of these problems is to make sure thateveryone learns to write good proofs. The secondary point is to encourage you to solve problems which might require more than one week of thinking -- but not all of the starred problems will be that hard!Reading the textbook will be another regular component of the course. Learning how to learn from the textbook will serve you well in any future math or science courses (or if you have toconsult your old textbooks for a refresher!).  Plus, reading the book gives you a model for how towrite mathematics that will complement what I demonstrate in class, and which I hope you willincorporate into your homework assignments.To that end, I will usually ask you to read a section of the textbook before class, and post acomment in the relevant Discussion forum in Moodle by 12 noon, one hour before class. I don'texpect you to be able to understand everything in the textbook at the beginning of the semester-- this is the role of the Discussion forums, for you to tell me what you didn't understand from thetextbook and what you want to focus on in class that day. However, I do expect you to putserious effort into the reading assignments, so that your ability to learn math from the textbookwill improve over the course of the semester. We will spend time in class discussing strategiesfor reading a math textbook; one aspect of this is to budget 10 minutes per page for thereading assignments.Your comments in the Discussion forums will be graded on a scale of 0 to 2, based on how wellyou convince me that you have read the section and thought about it, and I will drop your lowest5 scores.For example:•	* You will receive a 0 if you don't post any comment.•	* A comment like “Everything makes sense, I have no questions'' will earn a score of 0.(Even if everything makes sense, I'm sure you can find something more specific to say!How does this section connect with other sections? What did you think was interesting?Was there any part of the section that didn't make sense at first? What was it thateventually made that part make sense?)•	* If your comment asks a question that indicates to me that you only skimmed thetextbook, you will earn a score of 1. For example: ``What is the set S in Example 1.2.7?''(This is explained on page 10 of the textbook.)•	* A comment such as ``I don’t understand why Q doesn’t satisfy the axiom ofcompleteness. We know Q is a subset of R, and R satisfies it, so why doesn’t Q?'' willearn a score of 2. This question demonstrates that its author read the section andthought about what s/he read.                                                                                                                                                                                                                                                                                                                                                                      You are welcome to consult other textbooks for the reading assignments, if you prefer. Tofacilitate this, in each Moodle discussion forum, I will describe the topic of the reading so that you can find the appropriate material in another textbook.If you do consult other textbooks, please be careful to either use the notation from the course textbook on homework assignments and when posting in the Discussion forums, or to define thenotation you use.Course 	guidelines	a nd 	policies:	 Classroom and Course-related Behavior  University policy requires that all of us in the classroom treat each other with respect, andrefrain from behavior that will disrupt the educational process. Please refrain from using anyelectronics during class that are not directly related to what we are doing.I encourage you to ask questions at any time, and I will ask lots of questions of the class.  Tomake sure that I haven’t lost the majority of the class, I may call on people randomly to answermy questions. Saying “I don’t know” is a perfectly acceptable answer! You are almost certainlynot the only one who’s confused, so this is a signal for me to try another explanation, or give some more details.If you would prefer to be called by a different name, or gender pronoun, than is listed on the course roster, please let me know. Digital Access  Digital devices (like laptops and cell phones) are becoming increasingly important to success incollege. In this course, you may need digital devices to access readings, complete and submitwritten assignments, complete online quizzes, verify your attendance, take in-class polls,coordinate with other students regarding group projects, complete and submit group projects. Irecognize that some students are unable to afford the cost of purchasing digital devices and thatother students rely on older, more problem-prone devices that frequently break down or becomeunusable. I also recognize that those technology problems can be a significant source of stressfor students. Given those challenges, please contact me if you experience a technology-relatedproblem that interferes with your work in this course. I am more than happy to help you inaccessing support.Student Conduct Code  All students need to be familiar with the Student Conduct Code. You can find it athttp://www.umt.edu/student-affairs/dean-of-students/default.php or by searching in the “A to ZIndex” on the UM home page. In particular, discrimination and harassment are not tolerated at the University of Montana. If you feel that you have been subjected to discriminatory orharassing behavior, please contact the Office of Equal Opportunity and Affirmative Action at243-5710 or http://www.umt.edu/policies/browse/personnel/discrimination-harassment-sexual-misconduct-stalking-and-retaliation for help in addressing the situation. You can also report thediscrimination or harassment to me or to another faculty member you trust.Academic Honesty All students must practice academic honesty. Academic misconduct is subject to an academicpenalty by the course instructor and/or a disciplinary sanction by the University.Disability modifications  The University of Montana assures equal access to instruction through collaboration between students with disabilities, instructors, and Disability Services for Students. If you think you mayhave a disability adversely affecting your academic performance, and you have not alreadyregistered with Disability Services, please contact Disability Services in Lommasson Center 154                                                                                Item Percentage     Discussion posts (Reading reactions) 5%  Written Homework 40%  Starred Problems 10%  Midterm Exams (total) 25%   Cumulative final exam 20%  or call 406.243.2243. I will work with you and Disability Services to provide an appropriate modification.Due Dates and Late WorkUnless stated otherwise, all assignments are due at the beginning of class on the day on whichthey are due. Late work will receive no credit. However, to give everyone a buffer for busyweeks, the Homework category will be graded out of 85 points, although there will be 100possible points to earn (10 points for each of 10 assignments).Except in exceptional circumstances, exams must be taken at their scheduled time. If you knowyou have a conflict with an exam, please contact me early to see what arrangements can be made.Grading policy 

M 381.R01: Advanced Calculus I

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M 381.R01: Advanced Calculus I

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