Fall 2023  MAT 319: Foundations of Analysis NEW WEBSITE FOR MAT319 
MAT 320: Introduction to Analysis 

Lecture TuTh 12:20pm  Javits Lecture Center 110 
Library W4530 (through 10/4: joint lectures in Javits 110) 
Instructor (click name for office hours)  Dimitrios Ntalampekos  Raanan Schul 
Recitation MW 1111:53am 
R01@Library E4310, R02@ESS 131, R03@Frey 224 (obselete as of October 10)  Physics P113 
TA (click name of office hours) 
Spencer Cattalani, Dylan Galt, Daniil Glukhovskiy 
Daniil Glukhovskiy 
Recommendations on choosing MAT 319 vs MAT 320 will be made based upon your performance on the first midterm and homework to that date.  
Description  A careful study of the theory underlying topics in onevariable 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.  A careful study of the theory underlying calculus. The real number system. Basic properties of functions of one real variable. Differentiation, integration, and the inverse theorem. Infinite sequences of functions and uniform convergence. Infinite series. 
Overview  The purpose of this course is to build rigorous mathematical theory for the fundamental calculus concepts, sequences and limits, continuous functions, and derivatives. We will rely on our intuition from calculus, but (unlike calculus) the emphasis will be not on calculations but on detailed understanding of concepts and on proofs of mathematical statements.  An introductory course in analysis, it provides a closer and more rigorous look at material which most students encountered on an informal level during their first two semesters of Calculus. Students learn how to write proofs. Students (especially those thinking of going to graduate school) should take this as early as possible. 
Prerequisites 
C or higher in MAT 200 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. Math majors are required to take either MAT 319 or MAT 320  
Textbook  Bartle and Sherbert Introduction to Real Analysis, 4th edition  
Homework  Weekly problem sets will be assigned, and collected in the Wednesday recitation. The emphasis of the course is on writing proofs, so please
try to write legibly and explain your reasoning clearly and fully. You are encouraged to discuss the homework problems with others, but your writeup must be your own work.
Late homework will never be accepted, but under documented extenuating circumstances the grade may be dropped. Your lowest homework grade will be dropped at the end of the class.  
Grading  Homework: 20%, Midterm I: 20%, Midterm II: 20%, Final: 40%. 
Syllabus/schedule (subject to change)
Week  Chapter.section  Homework  Note 

1 (8/289/1) (Joint classes. Ntalampekos) 
1.1, 1.2, 1.3  (Due week 2) p. 10: 6, 15, 16, 22 p. 15: 1, 9, 16 p. 22: 3, 4, 12 

2 (9/49/8) (Joint classes. Ntalampekos) 
2.1, 2.2, 2.3  (Due week 3) p. 30: 7, 8, 26 p. 35: 2, 4, 17 p. 39: 4, 6, 11 
Monday is Labor Day 
3 (9/119/15) (Joint classes Ntalampekos) 
2.4, 2.5  (Due week 4) p. 44: 4, 7, 12, 13, 15 p. 52: 3, 5, 7, 9 

4 (9/189/22) (Joint classes. Schul) 
3.1, 3.2  (Due week 5) 3.1: 5ab, 6, 8, 9, 10, 12 3.2: 2, 5, 7 

5 (9/259/29) (Joint classes. Schul) 
3.3  (Due week SEVEN) 3.3: 1, 7, 9 (note that you may repeat elements) 

6 (10/210/6)  Tuesday is midterm 1. Thursday we will cover 3.4  Midterm I on Tuesday this week 
Week  Chapter.section  Homework  Note 

7 (10/910/13)  3.5, 3.6  (Due week 8) 3.4: 1, 4b, 10, 12, 19 3.5: 5, 8, 
Monday and Tuesday off. 
8 (10/1610/20)  3.7, 4.1  (Due week 9)) 3.6: 6, 9, 10 3.7:2, 5, 11, 12, 17ab 

9 (10/2310/27)  4.1, 4.2, 4.3  (Due week 10) 4.1: 8, 12c, 14, 15 4.2:5, 6, 7, 9 4.3:2, 4 

10 (10/3011/3)  5.1, 5.2, 5.3  (Due week 11) 5.1: 10, 12 (but think about (1, 3, 7, 11) 5.2: 10 (but think about 3, 5, 7) 

11 (11/611/10)  review + midterm  (Due week 12) 5.3: 2, 4, 11, 14, 18 
Midterm Thursday 
12 (11/1311/17)  5.4, 5.6 (in recitation), 6.1  (Due week 13, either in recitation or class b/c of Thanksgiving) 5.4: 2, 6, 10, 13 

13 (11/2011/24)  6.2  (Due Monday of week 15) 5.6: 6, 10, 12 6.1: 4, 14 6.2, 4, 8, 12, 14 
Thanksgiving (half week) 
14 (11/2712/1)  In recitation: 6.3, 6.4 In class: 7.1, 7.2 
(Due in class on Thursday of week 15) 7.1: 4, 8, 9, 15 7.2: 7, 8, 12, 13 7.3: 5, 9, 15, 20 

15 (12/412/8)  In recitation: 7.3, parts of 8.3, 8,4 In class: 8.1, 8.2, and chapter 9(briefly) 

Finals  Cumulative  Thurs. Dec. 21, 11:151:45 pm 
Disability Support Services: If you have a physical, psychological, medical, or learning disability that may affect your course work, please contact Disability Support Services (DSS) office: ECC (Educational Communications Center) Building, room 128, telephone (631) 6326748/TDD. DSS will determine with you what accommodations are necessary and appropriate. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated. All information and documentation of disability is confidential. Students requiring emergency evacuation are encouraged to discuss their needs with their professors and DSS. For procedures and information, go to the following web site http://www.ehs.sunysb.edu and search Fire safety and Evacuation and Disabilities.
Academic Integrity: Each student must pursue his or her 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 instance 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 at http://www.stonybrook.edu/uaa/academicjudiciary/.
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, and/or inhibits students' ability to learn.