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MAT 371. Advanced Calculus Fall 2013. Line number 72082 Abbreviated syllabus For full details, a day-to-day schedule including assignments, handouts, old tests etc., consult the class’ home-page which is maintained online at http://math.la.asu.edu/~kawski/classes/mat371/13fall/mat371.html The class does NOT maintain a BLACKBOARD page Logistics Line number: Time and places Text: Instructor: Contact info: 72082 MW 2:00-3:15 in PSA 107 Introduction to Analysis" by E.~Gaughan. Matthias Kawski [email protected] (preferred) e-mail: Goldwater Center room 354 office: office hours: M 2:10-3:00, W 3:10-3:50, Th 1:10-2:00, and by appointment office phone: (480) 965 3376 home phone: (480) 893 0107 (for emergencies) Content, goals and objectives The General Catalog lists the following required contents: MAT 371 Advanced Calculus I. Course description: Real numbers, completeness, sequences/series, continuity, uniform theorems, derivative, Riemann integral, pointwise/uniform convergence, Taylor's theorem. Credit is allowed for only MAT 371 or 370 toward a mathematics degree. Prerequisites: MAT 272 (or MAT 267) and MAT 300 (or 243) with a C or better The class has multiple objectives and outcomes: Students shall develop a solid understanding of the rigorous foundations of calculus and basic topics of analysis, preparing for advanced coursework in analysis, as well as providing all students (especially future secondary teachers) with the depth of background essential for teaching calculus. Students will learn to (partial listing only): work from precise definitions involving real numbers, convergence, continuity, compactness, derivatives, and Riemann integrals, precisely state theorems related to these topics, and apply them, reproduce outlines of the proofs of major theorems, and identify the key steps in these create proofs of, or counterexamples for statements in the context of calculus of real-valued functions of a single real variable, develop intuition about the correctness of statements and proofs and identify mistakes, communicate proofs and other arguments in both written and verbal form, especially, learn to be skeptical of arguments presented in class, and communicate why "not happy" with a presented argument. General expectations and policies All students are expected to present their work on the board in class. Volunteer early! -- don't wait until the end of the course when the material gets ever more demanding. This class is first of all about writing concise arguments -- "proofs". Expect to do a lot of REWRITING. All homework and exams are expected to use grammatically meaningful sentences and to use proper punctuation. (Lists of symbols and equations without explanations of their logical relationships using words are generally unacceptable.) Expect to work a minimum of three hours for each credit hour (Board of Regents policy 2-224), possibly substantially more if your MAT 300 background is weak. Collaboration for homework and class preparation is highly encouraged and expected for typical inclass assignments! Unless announced otherwise, the default rule is that written homework be handed in by teams of three or four students. Each set has to bear the signatures of all team members. The signature of each student is understood to certify that this student has contributed to all results and completely understands the submitted work in its entirety. Each student should be prepared to present the work submitted by the team in class (else, the entire team may lose credit for the work). Students are NOT expected to type-set their work, but it must be professional in appearance. A critical component of the class is that students create their own proofs. The default policy is that students may collaborate with each other, use help from the instructor and consult our textbook. All sources (WWW, other books, friends, ...) must be properly acknowledged in writing. If considered necessary, stricter (or more detailed) policies will be announced in class and posted on this WWW-site. Attendance: A substantial part of the course grade will be based on contributions made in class. Moreover, the classes, recitations, and exams may involve material that is not found in the textbook in a similar form, but which may be asked for on the examinations. Thus make every effort to attend and participate in every class. Unless otherwise agreed upon, there will be two one-hour in class tests and one two-hour final exam. These are taken individually. If judged suitable, there may also be almost daily "pop-quizzes". Late homework will not be accepted. Make-up exams will only be allowed in extreme cases with proper documentation. University rules and deadlines for withdrawals and grades of incomplete will be strictly enforced. Highest standards of academic integrity are expected from all participants in the class. For many parts of the course, teamwork and use of modern technology are strongly encouraged - always indicate clearly the intellectual ownership, what exactly your personal contribution is. Technology is evolving -- and so are standards of its use. Never hesitate to ask if in doubt about what are proper procedures. Special needs: Qualified students with special needs who will require accommodations (e.g., religious observances, disabilities, or ASU sanctioned activity such as athletes travel, disabilities) shall inform the instructor as soon as possible (no later than the end of the second week of classes). Verification of eligibility from the Disability Resource Center (DRC) is required prior to receiving disability accommodations. Disability information is confidential. Daily routine Students are expected to prepare for each class by reading the upcoming section in the textbook, starting to work exercises, and prepare in writing a list of questions regarding the new material. Do NOT expect that everything from the textbook will be copied to the black-board. A substantial part of every class may be devoted to student presentations of their proofs -- questioning by the class, and suggestions for improvements. If judged suitable, every class may start with a very short quiz: Typically, the first part will address a question related to homework on previous topics, the second part will be a check of the preparation of the new material (e.g. a simple vocabulary test). Grading policies Unless otherwise agreed upon, the semester grade will be composed of 30 % Homework, and in-class participation (and possibly mini-quizzes), 30 % final examination (two hours, in-class)and constructive criticism of the presented work. especially, black-board presentations, 40 % in-class tests A weighted average of 90% and above is guaranteed to earn an A-, 80% and above is guaranteed to earn a B-, 65% and above is guaranteed to earn a C, 55% and above is guaranteed to earn a D. For a tentative schedule, topics covered, and homework assignments follow the “Tentative calendar, homework and due dates”- link from the class www-page. First homework assignments: Rework the diagnostic test. Prepare sections 0.1-0.4 (due M 8/26) and ch. 0: 3, 6, 10, 17, 18, 21 due F 8/30.