MAT 319: Foundations of Analysis

Fall 2024

Department of Mathematics
Stony Brook University

Course Description: A careful study of the theory underlying topics in one-variable calculus, with an emphasis on those topics arising in high school calculus. The real number system. Limits of functions and sequences. Differentiations, integration, and the fundamental theorem. Infinite series.

Textbook: Elementary Analysis: The Theory of Calculus, by Kenneth Ross in collaboration with Jorge Lopez, 2nd Edition, Springer, 2013.

Prerequisite: C or higher in MAT 200 or MAT 250 or permission of instructor; C or higher in one of the following: MAT 203, 205, 211, 307, AMS 261, or A- or higher in MAT 127, 132, 142, or AMS 161.

Instructor: Marcus Khuri, Math Tower 3-122. Click here for office hours. Email: marcus.khuri@stonybrook.edu

Course Assistants: Aritra Chatterjee, Math Tower S-240A. Click here for office hours. Email: aritra.chatterjee@stonybrook.edu

Alessandro Pilastro, Math Tower S-240A. Click here for office hours. Email: alessandro.pilastro@stonybrook.edu

Owen Mireles Briones, Math Tower 3-117. Click here for office hours. Email: Owen.MirelesBriones@stonybrook.edu

Class schedule: TR 12:30-1:50pm, Earth and Space 001

Recitations: MW 11:00-11:55am, R01 in Physics P117, R02 in Lgt Engr Lab 152, R03 in Frey Hall 224

Homework: Homework is a fundamental part of this course, and you will have to work hard on the assigned problems in order to succeed. Assignments will be posted on the course website at the beginning of each week, and will be due on Wednesday of the following week at the end of your recitation for that day. Homework must be turned in to your course assistant at Wednesday's recitation. Late homework will not be accepted. Homework will account for 20% of the total grade. In order to receive full credit for any problem you must show all of your work, and you must provide full justification for your answers.

Homework 1 (Due 9/4) - 1.5, 2.3, 3.4, 3.6, 4.11, 4.12, 5.1, 5.2;

Homework 2 (Due 9/11) - Click here to view the assignment;

Homework 3 (Due 9/18) - 10.1, 10.2, 10.7, 10.10, 11.2, 11.3, 11.5, 11.8;

Homework 4 (Due 9/25) - 12.1, 12.3, 12.6, 12.8, 14.6, 14.7, 14.9, 14.14;

Homework 5 (Due 10/2) - 15.1, 15.3, 15.6a, 15.7a, 17.2, 17.4, 17.9c, 17.13a;

Midterm 1 solutions.

Homework 6 (Due 10/16) - 18.4, 18.5a, 18.7, 18.9; 19.1, 19.2b, 19.4a, 19.9abc;

Homework 7 (Due 10/23) - 20.1, 20.5, 20.11, 20.17, 20.18;

Homework 8 (Due 10/30) - 23.1c, 23.4, 23.5, 23.8, 24.2, 24.9, 24.13, 24.15;

Homework 9 (Due 11/6) - 25.2, 25.7, 25.10, 25.12, 26.2, 26.7, 26.8bc;

Homework 10 (Due 11/13) - 28.3a, 28.4, 28.8, 28.10, 29.2, 29.4, 29.5, 29.14;

Midterm 2 solutions.

Homework 11 (Due 12/4) - 30.2, 30.5, 30.6, 31.1, 31.4a, 31.11, 32.1, 32.2, 32.7;

Final exam solutions.

Exams: There will be two in-class midterms as well as a final. Each midterm will account for 22.5% of the total grade, while the final will account for 35% of the total grade. There will be no make-up exams. If you have a legitimate and well-documented reason for missing a midterm exam, your score on the final exam will be substituted instead. The midterm exams will be on Thursday, October 3 and November 14. The final exam will take place on Tuesday, December 17, 11:15am-1:45pm in our classroom: Earth and Space 001. By enrolling in this course, you are attesting to the fact that you will be available for the exams at these times.

Help: The Math Learning Center (MLC) is located in Math Tower S-235, and offers free help to any student requesting it. It also provides a locale for students wishing to form study groups. The MLC is open 10am-7pm Monday through Wednesday, 10am-6pm Thursday and 10am-2pm on Friday. A list of graduate students available for hire as private tutors is maintained by the Undergraduate Mathematics Office, Math Tower P-143.

 
Disability Support Services (DSS)
If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room 128, (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 Disability Support Services. For procedures and information go to the following website: http://www.stonybrook.edu/ehs/fire/disabilities

 
Academic Integrity
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. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/commcms/academic_integrity/index.html

 
Critical Incident Management
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 students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.