MAT 360  Introduction to Analysis  Fall 2026 TΘ   12:30-1:50 Until 9/24: Humanities 1003  Starting 9/29: Math Tower P-131

Prof. Claude LeBrun.
Office hours:
TΘ 2:00 -- 3:30,
Math Tower 3-108.
TA: Ceyhun Elmacioglu
Math Tower 2-115.

This course is taught in coordination with MAT 319, and all students should initially enroll in that course.

After the first midterm, some students will then be invited to move to MAT 320.

This course offers a careful study of the theoretical foundations of calculus. Topics will include:

• the real number system;
• basic properties of functions of one real variable;
• differentiation;
• integration;
• the inverse function theorem;
• infinite sequences of functions;
• uniform convergence;
• infinite series;
• metric spaces; and
• compactness.

Textbook:
Elementary Analysis: The Theory of Calculus
by Keneth A. Ross,
Springer Verlag,
Second edition, 2013.

Prerequistes. In order to register in MAT 319 or 320, you must first fulfill one of the following prerequisites:

• C or higher in MAT 200 or MAT 250; or
• C or higher in MAT 203, 205, 211, 307, or AMS 261; or
• A- or higher in MAT 127, 132, 142, or AMS 161; or
• (very unusually) permission of the instructor.

There will be two mid-term exams and a final.

Each midterm will determine 25% of your grade, with the final examine determining 35% of your grade.
The remaining 15% of your grade will be determined by your homework and quiz scores, from your recitation.

The first midterm exam will take place in class on Thursday, September 24.

Homework. Most Tuesdays, starting September 1, you will be expected to turn in a homework assignment in your recitation. After you turn in this assignment, there will then be a quiz. However, only students who have turned in their homework will be permitted to take the quiz. It will not be possible to turn in your homework late, and no make-up quizzes will be given. However, students who miss a recitation because of a verified illness or have another acceptable excuse will be able to arrange to have their homework and quiz scores "dropped" for the relevant recitation.

The homework in this course will teach you how to think like a mathematician, and especially will teach you how to write correct mathematical proofs. You will only be able to master the material by doing your homework --- and this of course means, by doing it yourself. For this reason, we will therefore require that all your homework solutions be hand-written. You are not allowed to copy someone else's solutions, and you are not allowed to use AI to do your homework. Violators of these rules, if caught, would automatically fail the course, and would be referred to the academic judiciary, where they would face truly dire consequences. Please don't go there! It really isn't worth it!

The Professor may be reached by e-mail at claude@math.sunysb.edu. This is the best method for making appointments outside normal office hours.

Student Accessibility Support Center (SASC) Statement: If you have a physical, psychological, medical or learning disability that may impact your course work, please contact the Student Accessibility Support Center (SASC), Stony Brook Union Suite 107, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.

Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the staff at the Student Accessibility Support Center (SASC). For procedures and information, please visit the SASC website.

Academic Integrity Statement: Each student must pursue their academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website.

Critical Incident Management Statement: Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits other students' ability to learn.