Advanced Calculus I
MAA 4226/5306 Spring 2014
102 LOV
MWF 10:10 -- 11 am

Prof. Alec N. Kercheval
113 Love Building; 644-8701 (office); 644-2202 (front desk)
office hours MWF 11-11:25, M 2-3, R 4:30 - 5:30, or by appointment
Prerequisites: Successful completion of MAC 2313 Calculus III and MAS 3105 Linear Algebra, or equivalent, and prior experience with mathematical proofs, such as MGF 3301 or a 4000-level proof-based mathematics course. It is also expected that students have significant time available each week for thinking about and doing mathematics. MAA 4226/5306 is open to both undergraduate and graduate students.
Walter Rudin, Principles of Mathematical Analysis, 3rd edition, McGraw-Hill, 1976, plus occasional handouts posted on the Blackboard course site.
This course develops the calculus of real and complex valued functions in depth, with an emphasis on understanding the underlying principles of the subject. We will emphasize careful argument and proof of our results. This is the first semester of a 2-semester sequence in the foundations of analysis that every undergraduate should know in preparation for graduate-level coursework. Topics include the real number system as a complete ordered field, metric space topology, sequences and series, and continuity of functions, covered in Chapters 1-4. The second semester will cover differentiation, integration, uniform convergence, and special functions. Students should be prepared to spend concentrated time working on hard problems throughout the semester, and presenting solutions in class.
Faithful and on-time attendance is closely linked to success in this class. An absent student is responsible for any material or announcements covered in class. Courtesy dictates that students arrive on time to class. Let me know in advance if you need to leave early.
Homework will be assigned regularly to be handed in, and discussed in class. There may be some short homework-based quizzes that will be announced in advance. Students should be prepared to present their homework solutions on the board in class.
There will be a one-hour midterm on a date to be announced, and a comprehensive final exam on the University-designated final exam day, Thursday, May 1, 10:00am -- noon.
Your course grade will be a weighted average of homework (including class presentations) and quizzes (30%), the midterm (30%), and the final exam (40%). Borderline grades will be resolved positively by good class participation and negatively by inconsistent attendance.
No written makeups are given. An unexcused missed exam receives a zero. Those with prior permission or sufficient documentation will substitute an oral exam.

Academic Honor Policy: The Florida State University Academic Honor Policy outlines the University's expectations for the integrity of students' academic work, the procedures for resolving alleged violations of those expectations, and the rights and responsibilities of students and faculty members throughout the process. Students are responsible for reading the Academic Honor Policy and for living up to their pledge to ''. . . be honest and truthful and . . . [to] strive for personal and institutional integrity at Florida State University.'' (Florida State University Academic Honor Policy, found at

In this class, you are permitted to work together with classmates on homework problems, but you must turn in only work written by yourself. All exams and any other assignments must reflect only your own work unassisted by others.

University Attendance Policy: Excused absences include documented illness, deaths in the family and other documented crises, call to active military duty or jury duty, religious holy days, and official University activities. These absences will be accommodated in a way that does not arbitrarily penalize students who have a valid excuse. Consideration will also be given to students whose dependent children experience serious illness.

Americans With Disabilities Act: Students with disabilities needing academic accommodation should: (1) register with and provide documentation to the Student Disability Resource Center (SDRC) and (2) bring a letter to the instructor indicating the need for accommodation and what type. This should be done during the first week of class. This syllabus and other class materials are available in alternative format upon request.

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Syllabus Change Policy: ''Except for changes that substantially affect implementation of the evaluation (grading) statement, this syllabus is a guide for the course and is subject to change with advance notice.''