| Fall 2023 | MAT 319: Foundations of Analysis NEW WEBSITE FOR MAT319 |
MAT 320: Introduction to Analysis |
|---|---|---|
| Lecture TuTh 1-2:20pm | 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 11-11:53am |
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 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. | 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 write-up 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 (8/28-9/1) (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 (9/4-9/8) (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 (9/11-9/15) (Joint classes Ntalampekos) |
2.4, 2.5 | (Due week 4) p. 44: 4, 7, 12, 13, 15 p. 52: 3, 5, 7, 9 |
|
| 4 (9/18-9/22) (Joint classes. Schul) |
3.1, 3.2 | (Due week 5) 3.1: 5ab, 6, 8, 9, 10, 12 3.2: 2, 5, 7 |
|
| 5 (9/25-9/29) (Joint classes. Schul) |
3.3 | (Due week SEVEN) 3.3: 1, 7, 9 (note that you may repeat elements) |
|
| 6 (10/2-10/6) | Tuesday is midterm 1. Thursday we will cover 3.4 | Midterm I on Tuesday this week |
| Week | Chapter.section | Homework | Note |
|---|---|---|---|
| 7 (10/9-10/13) | 3.5, 3.6 | (Due week 8) 3.4: 1, 4b, 10, 12, 19 3.5: 5, 8, |
Monday and Tuesday off. |
| 8 (10/16-10/20) | 3.7, 4.1 | (Due week 9)) 3.6: 6, 9, 10 3.7:2, 5, 11, 12, 17ab |
|
| 9 (10/23-10/27) | 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 (10/30-11/3) | 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 (11/6-11/10) | review + midterm | (Due week 12) 5.3: 2, 4, 11, 14, 18 |
Midterm Thursday |
| 12 (11/13-11/17) | 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 (11/20-11/24) | 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 (11/27-12/1) | 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 (12/4-12/8) | In recitation: 7.3, parts of 8.3, 8,4 In class: 8.1, 8.2, and chapter 9(briefly) |
(never due) 8.1: 4, 14, 19, 23 8.2: 1, 3, 4, 8 |
|
| Finals | Cumulative | Thurs. Dec. 21, 11:15-1:45 pm |
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