Math 313: Analysis I

Fall 2024


Time and Location: MWF 12:00-12:50, Taft 219

Credit hours: 3

Instructor:

Michael Greenblatt
Office: 528 SEO
e-mail: greenbla@uic.edu

Office hours: MW 1-1:50 in SEO 528.

Topics:

This course will describe the rigorous foundations for calculus and related matters. In the typical freshman calculus course, many methods are given intuitive justifications which do not necessarily lead to actual proofs. In fact, during the original development of calculus many things were believed that turned out not always to be true. In this course we start from the fundamentals, and we do not assume anything until it has been proved. Our goal will be to truly understand why calculus works, providing an understanding well beyond what is given in a standard calculus course. In addition, in the homework you will be given a number of exercises that will help in this understanding.

As the semester proceeds, we will cover a number of topics, including the construction of the real numbers and its fundamental properties such as completeness, sequences and series, limits, continuity, uniform continuity, monotonicity and inverse functions, differentiation, Taylor’s theorem, the construction of the Riemann integral and its fundamental properties, and sequences and series of functions. Other topics will be included if time permits.

Required Textbook: “Elementary Real Analysis” 2nd edition, by Ross.

Additional Reference: “Introduction to Real Analysis” by Bartle and Sherbert.

Prerequisites: You must have passed Math 215 with a grade of C or higher.

Homework:

There will be homeworks due at the end of the day each Thursday, and turned in on Gradescope. The homeworks will appear on Blackboard and you will have approximately 1 week to do each assignment. The first homework will be due on September 5 and there will be no assignments due the weeks of the midterms. The assignments will focus on the previous week's material. The homeworks will be weighted equally and your lowest homework score will be dropped. You are allowed to (and are encouraged to) work with other students on the homework, but you must write up your assignments in your own words. Please avoid the use of AI programs when doing the homework as they often make mistakes and even when correct do not represent the student's work.

Late Homework:

Late homework is normally not accepted except in special circumstances, and permission must be granted in advance.

Exams:

There will be two in-class midterms, tentatively scheduled for on October 4 and November 8, and an in-class final exam at the end of the semester. Make-up exams will be allowed only in case of (documented) emergency and must be arranged in advance.

Grading:

The homework will count for 1/3 of your grade, each midterm will count for 1/6 of your grade, and the final exam will count for 1/3 of your grade.

Optional Math 294 class:

There is a section of Math 294 (CRN 43623, T Th 10-10:50) to provide extra assistance on assignments and more. This course is entirely optional and is shared by the two Math 313 classes.

Attendance/Participation Policy:

While attendance will not be taken, it is strongly encouraged to attend class. Much material and other useful information not in the textbook will be discussed, and hints on the homework will be given. Class participation is encouraged.

Classroom Conduct Policy:

We aim to create respectful classroom environment that fosters learning, creativity, and critical thinking. Be sure to treat everyone in the class with courtesy and dignity, giving the instructor and your fellow students due respect. Avoid any disruptive or inappropriate behaviors, such as interrupting others, using offensive language, or using your phone during class. Feel free to contact the instructor about any issues or concerns related to classroom conduct.

Disability Policy:

If you face or anticipate disability-related barriers while at UIC, please connect with the Disability Resource Center (DRC) at drc.uic.edu, via email at drc@uic.edu, or call (312) 413-2183 to create a plan for reasonable accommodations. In order to receive accommodations, you will need to disclose the disability to the DRC, complete an interactive registration process with the DRC, and provide me with a Letter of Accommodation (LOA).