Advanced Calculus I
MAA 4226/5306 Spring 2019
200 LOV
MWF 9:05--9:55 am

Prof. Alec N. Kercheval
contact me
202B Love Building; 644-8701 (office); 644-2202 (front desk)
Note: See the course Canvas page for handouts and other materials.
office hours MWF 10-11 am; 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 expected that students will be able to spend significant time each week thinking about and doing mathematics.
  • Required textbook: Charles C. Pugh, Real Mathematical Analysis, 2nd Editon, Springer, 2015.
  • Optional additional reading: Walter Rudin, Principles of Mathematical Analysis, 3rd edition, McGraw-Hill, 1976.

This course develops an understanding of the concepts and methods underlying calculus, emphasizing careful argument and proof. 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 mathematical study. The focus will be on developing the ability to solve conceptual problems rather than on computation, and on understanding why and how calculus works.

Topics in the first semester will include a review of set theory and logic, cardinality of sets, metric space topology, and differentiation and Riemann integration in one real variable, corresponding to Chapters 1-3 of the text.

Faithful and on-time attendance is closely linked to success in this class. Graded in-class activities will take place periodically. Students are responsible for any material or announcements covered in class even if absent. Courtesy dictates that students arrive to class on time, and inform the instructor if they need to leave early for any reason.
Homework will be assigned regularly to be handed in and discussed in class. In-class problems may be assigned without notice, and short quizzes may be given with prior notice. Students should be prepared to explain their homework solutions in front of the class at the chalkboard. Your collected homework solutions should be assembled and submitted for final review at the time of the final exam.
There will be three in-class exams. Two 50 minute exams will cover approximately each of the first two chapters, on dates to be announced. A final exam will cover chapter 3 and also include questions on the earlier sections. The final exam is scheduled for University designated final exam day, Wednesday, May 1, 2019, 12:30 - 2:30 pm.
The course grade will be computed as follows: homework 10% (including in-class presentations), Quizzes and in-class activities 10%, each of the first two exams 25%, and the final exam 30%. Attendance and class participation will be used to resolve borderline grades.
An unexcused missed exam receives a zero. Those with prior permission or sufficient documentation will substitute an oral exam.

Academic Honor Policy: The FSU 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. Students are responsible for reading the Academic Honor Policy and for living up to their pledge to ''. . . be honest and truthful and . . . strive for personal and institutional integrity'' at FSU. (The FSU Academic Honor Policy is 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 quizzes must reflect only your own work unassisted by others.

Audio, video, or photographic recording of class activity is not permitted except by express permission of the instructor.

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.

For more information about services available to FSU students with disabilities, contact: SDRC, 874 Traditions Way, 108 Student Services Building, FSU, Tallahassee, FL 32306-4167, (850) 644-9566 (voice), (850) 644-8504 (TDD),,

FSU's 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.