SyllabusIn this course we'll study the foundations of Calculus of One Variable beginning with the real and complex numbers. We'll develop real and complex sequences, study series, explore the topology of metric spaces, and use these topological ideas to define and study continuous functions. With this foundation, we'll prove the basic theorems of differential and integral calculus in a rigorous fashion. This course is part of the preliminary examination sequence in Analysis. Students may opt to take either Real Analysis I or Complex Analysis I in the spring semester if they wish to take the Analysis preliminary examination in June 2019. This course divides into three parts: (1) Real and complex number systems, sequences, and series (2) Metric spaces, compactness, continuity, and continuous functions (3) Differential and integral calculus Our course text is Analysis: An Introduction by Richard Beals. We will be covering most of chapters 1-8 of this text. You can find errata for the text here. This course is also an introduction to the art of reading mathematical proofs with understanding and writing mathematical proofs with clarity. The suggested supplementary text, How to Think About Analysis by Lara Alcock, offers valuable suggestions and insights into understanding a "proof-oriented" mathematics course and explains in detail how to organize class notes and how to read and study mathematical proofs. Homework will be assigned weekly; please see the course schedule for due dates and plan ahead! All homework is taken from the text. "Homework #0" is a warm-up assignment which will not count toward your grade but will be graded, with comments, to help you understand the expectations for written work in the course. Also, students will be offered the chance to re-submit homeworks #1-#4 for full credit if their initial score is below 80%. We will have two in-class exams on Wednesday, October 3 and Wednesday, November 7. The final exam for this course will take place on Wednesday, December 12 at 1:00 PM in room CB 343. You can find a complete schedule for the course, including daily reading, homework due dates, and exam dates here.
Your course grade will be based on:
Letter grades for undergraduate students will be assigned as follows:
The "D" grade is not allowed for graduate students. Letter grades for graduate students will be assigned as follows.
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