MAT 319 provides a closer, more rigorous look at the fundamental concepts of one-variable calculus. The main focus will be on the key notions of convergence and continuity; we will also study the properties and axioms describing real numbers and subsets of R. The course provides a good opportunity for students to learn how to read and write rigorous proofs. The course is writing intensive; all students will have the opportunity to complete the proof-oriented component of the Department of Mathematics upper division writing requirement.
TEXTBOOK: Introduction to Real Analysis, by R. Bartle and D. Sherbert, Third ed, Wiley.
MEETING TIMES. Lecture: TU and TH 11:20-12:40, SBUnion 231; Recitation MO and WE 9:35am-10:30am, SBUnion 237. First day of class: TU FEB 1; last TH MAY 12. Spring Recess April 18-24.
ETIQUETTE: Punctuality: no late arrivals, no early departures: they are disruptive. If, occasionally, you need to arrive late and/or leave early, let the instructor know beforehand. Silence: it is always a good rule and even more important for us since it is a big class; do show respect to other fellow students by not disturbing the class. NO CELL PHONES etc.. NO FOOD.
PREREQUISITES: C or higher in MAT 200 or permission of instructor; plus one of the following: MAT 203, 205, 211, AMS 261, or A- or higher in MAT 127, 132, 142 or AMS 161.
GRADE: Midterm I = 25%, Midterm II =25%, Final = 30%, Homework = 20%.
Maximum scores: Midterms I and II: 250pts each; each homework: 20pts (the best ten are used to grade); Final 300pts. Total maximum: 1000pts. The numerical grade will be converted to a final letter grade only AFTER the final test has been graded. However, after each midterm an approximate letter grade will be given to you.
To do well in this class we strongly encourage you to: read the section to be covered before class, do the homework, plan to work on reading and homework for 6-8hours a week, start preparing for tests well in advance.
SCHEDULE OF EXAMS. The sections to be covered will be announced well in advance. Bring your Stony Brook ID. No books, no notes, no calculators, no phones etc. Be sure to be available on these days and times:
Midterm I: THURSDAY MARCH 10 ( ATTENTION: THIS IS THE CORRECT NEW DATE!!!) (IN CLASS).
Covers sections: SUBJECT TO CHANGE 1.1, 1.2, 1.3, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 3.2. SUBJECT TO CHANGE
Link to old MAT 319 webpages. Click, scroll down to the MAT 319 section. There are tests posted in the S2007 and F2007 and F2008 sections. Keep in mind that in 2007 they covered a bit less material and that their test was 50minutes-long (ours is 80 minutes-long).
How to prepare for the test. The test consists of 6 problems. Some of them are made of several parts. You may be asked to prove a theorem among the following list (however, all other theorems etc. are to be used in the test): countability of Q etc, Cantor Theorem, 2.1.4, 2.1.9, triangle-type inequalities, Archimedean properties the existence of the square root of 2, the density theorems, characterization of intervals, nested interval property, uniqueness of limits, limit theorems for sum product and absolute value, Squeeze Theorem.
2008 Midterm I with solutions.
2011 Midterm I with solutions.
Appoximate curve (please remember that we curve only after ALL tests are taken; this is just an indication of how you are doing right now): A range: 190 and up; B range 150 and up; C range 110 and up. D range 90 and up. The highest score is 225. The average is 114.
Midterm II: THURSDAY APRIL 7 (IN CLASS)
Covers sections 3.3, 3.4, 3.5, 3.6, 3.7, 4.1 and 4.2.
How to prepare for the test. The test consists of 6 problems. Some of them are made of several parts. You may be asked to prove a theorem among the following list (however, all other theorems etc. are to be used in the test): Monotone Convergence Theorem 3.3.2, 3.4.2, Cauchy Convergence Criterion 3.5.5, 3.6.3, n-th Term Test 3.7.3, Uniqueness of Limit 4.1.5. In the proof, if you need to refer to a previous theorem, lemma etc, state separately the needed result (i.e. do not identify it with a number: e.g. the proof of Theorem 3.3.2 in the textbook starts by referring to Thm. 3.2.2, in that case, in the test, write something like: ``A convergent sequence is bounded (this was proved in class)."
2011 Midterm II with solutions.
Data for midterm II: Average : 136. Highest 250.
Appoximate curve (please remember that we curve only after ALL tests are taken; this is just an indication of how you are doing right now): A range: 210 and up; B range 170 and up; C range 130 and up. D range 110 and up.
Final: TUESDAY MAY 17, 2:15-4:45pm HUMANITIES 1003.
Sample final (discussed during review session will be posted here by TH).
Special office hours: Monday May 16, 10am-noon, MAT 5-108.
IMPORTANT: if you have missed a midterm and have not given me proper documentation, then your grade on the missed midterm is 0.
Note that the final's time is assigned by Registrar's. If you have a conflict with another class it probably means that the other class has placed the final in conflict with this class (please resolve this issue with the instructor in charge of the other class). As per university's regulations, I cannot change the date of the final.
Final covers All sections (see syllabus) EXCEPT 6.3 and 6.4 (there will be no questions on the test on 6.3 and 6.4).
How to prepare for the final. SUBJECT TO CHANGE The final consists of 10 problems. Some of them are made of several parts. You will be asked to prove a theorem among the following list (however, all other theorems etc. are to be used in the test): 5.2.6, 5.3.7, 5.4.3, 5.6.4, 6.1.5, 6.2.3. In the proof, if you need to refer to a previous theorem, lemma etc, state separately the needed result (i.e. do not identify it with a number: e.g. in 3.3.2 the proof starts by referring to Thm. 3.2.2, in that case write something like: ``A convergent sequence is bounded (this was proved in class)."
Important. You must bring your SUNY ID to the exams. There will be no make-ups for missed exams and homework. However, if you miss a midterm exam for an acceptable and documented reason, then the relevant mid-term will be `dropped' (ignored) in computing your course grade. A letter stating that you were seen by a doctor or other medical personnel is NOT an acceptable document, unless it states that it was reasonable/proper for you to seek medical attention and medically necessary for you to miss the exam (for privacy reasons this note/letter need not state anything beyond this). If you miss more than one midterm etc., we shall evaluate the circumstances. Incompletes will be granted only if documented circumstances beyond your control prevent you from taking the final exam.
Curve for final test: A>= 270; C>=180
Curve for final grade: A>= 880; A->=830; B+>=780; B>=725; B->=665; C+ >= 620; C>= 535; C- >=505; D+ >= 445; D>=400; F <400.
WEEK-BY-WEEK SYLLABUS. Subject to Change We shall (tentatively) cover Ch. 1-6.
Week of FEB 1 : 1.3, 2.1 (students are responsible for reviewing 1.1 and 1.2 on their own). Be sure to familiarize yourselves with 2.1.1 and 2.1.5 (i,ii,iii) BEFORE FEB 1's CLASS.
Week of Feb 08 : 2.2,2.3.
Week of Feb 15 : 2.4, could not start 2.5 will go a bit faster next week
Week of Feb 22 : 2.5, 3.1, 3.2.
Week of Mar 01 : 3.3, 3.4.
Week of Mar 08 : 3.5, TH Mar 10 TEST ( NOTE CORRECTED DATE! ).
Week of Mar 15 : 3.6, 3.7.
Week of Mar 22 : 4.1, 4.2.
Week of Mar 29 : 5.1, 5.2.
Week of Apr 05 : 5.3, TH April 7 TEST.
Week of Apr 12 : 5.4 (up to the end of p.140)
Week of APR 19 : SPRING BREAK.
Week of Apr 26 : 5.6, 6.1
Week of MAY 03 : (6.1 continued) 6.2 (Up to the bottom of page 171)
Week of May 10 : 6.3, 6.4 (No Newton's Method). TH May 12 LAST DAY OF CLASS.
HOMEWORK: Posted here every TH and due the following week on WE during recitation. Graded homework will be returned the following week on WE during recitation. If you miss the recitation, you may collect it during the grader's office hours (posted below). Questions about the grading of the homework should be directed to the recitation leader. NO EXCEPTIONS: late homework will not be accepted; the homework must be stapled WITH A METALLIC STAPLE. Unstapled homework will not be accepted/graded.
Hmk 1, due week of Feb 8: 1.3: 6,7,9,11,12; 2.1: 6,9,15,19,21. Solutions HMK # 1.
Hmk 2, due week of Feb 15: 2.2: 3,7,9,12,14,15; 2.3: 4,5,8,11,12. Solutions HMK # 2.
( NOTE CORRECTED DATE FOR MIDTERM I: TH MARCH 10!!! )Hmk 3, due week of Feb 22: 2.4: 4,6,7,10,11,15,18; since I could not start 2.5 the hmk for 2.5 carries over to next week.
Hmk 4, due week of Mar 1 : 2.5: 3,6,9,11; 3.1: 6,13,16,17; 3.2: 8,15,18,21. Solutions HMK # 3. Solutions HMK #4. Solutions to HMK 3 amd 4 will be posted TH March 3. They contain solutions to few more problems.
Hmk 5, due week of Mar 15 (yes, March 15 so you can focus on the test) : 3.3: 4,5,6,10,11,12,13,15. 3.4: 4,6,7,8,9,14,15. Solutions HMK #5 3.3. Solutions HMK #5 3.4.
Hmk 6, due week of Mar 15: 3.5: 1,2a,3b,6,7,9,10,12. Solutions HMK #6.
Hmk 7, due week of Mar 22: 3.6: 4,5,6,7,8,9,10 ; 3.7: 2,4,5,6b,7,8,9,10. Solutions HMK #7.
Hmk 8, due week of Mar 29: 4.1: 1, 3, 8, 9, 11, 14; 4.2: 1, 14, 2, 3, 11, 12 : Solutions HMK #8.
Hmk 9, due week of APR 12 (due to test): 5.1: 1,3,5,10,15; 5.2: 1,3,6,7,12,13 : Solutions HMK #9.
Hmk 10, due week of APR 26 (NOTE THE CHANGE IN DATE): : 5.3: 1,4,6,12,13,15,17,19 : Solutions HMK #10.
Hmk 11, due week of APR 26: 5.4: 2,4,7,8,11,12,13,14 : Solutions HMK #11.
Hmk 12, due week of MAY 3: 5.6: 1,5,8,9,13,15, 6.1: 1,2,7,9,11 : Solutions HMK #12.
Hmk 13, due week of MAY 10: 6.1: 14,15,16,17, 6.2: 2,5,6,8,11,13 : Solutions HMK #13.
Hmk 14, neither collected, nor graded: 6.3: 2,4,6,8,10,12, 6.4: 2,4,5,6,8,10 : Solutions HMK #14.
CONTACTING THE STAFF (instructors and hmk graders. The best way is to approach us after the lectures/recitations or to see us during office hours. You may use e-mail, but it is less efficient. E-mail is not, however, a good way to ask math questions, as our typing abilities are very limited. After the course is over, if you have any questions about your final grade send a letter (not an e-mail) to your instructor, c/o Dept. Math, SUNY Stony Brook, Stony Brook N.Y. 11794-3651. You will receive a written reply. These matters will be dealt with in writing only; that way, we have a written record of what the student says, and what we reply.
STAFF:
Lecture: Mark de Cataldo; mde at math dot sunysb dot edu ; Office Hours: (Note the change, valid until further notice) TH 9:45-11:15am and 1-2:30pm, MAT TOWER 5-108
Recitation: Chaya Rosen; rosen at math dot sunysb dot edu ; Office Hours: MO 12-2pm MLC and TU 5:30-6:30 MAT TOWER 3-103.
SUPPORT RESOURCES : (*) The MATH LEARNING CENTER (MLC), located in MATHEMATICS BUILDING, FLOOR S, ROOM S-240A, (631) 632-9845, is a place where students can go for help and/or to form study groups. Check the link for more info. Their hours are: MTuW 10-9, Th 10-6, F 10-2. (**) The instructors have regular office hours.
SPECIAL NEEDS. If you have a physical, psychological, medical, or learning disability that may impact on your ability to carry out assigned course work, you are strongly urged to contact the staff in the Disabled Student Services (DSS) office: Room 133 in the Humanities Building; 632-6748v/TDD. The DSS office will review your concerns and determine, with you, what accommodations are necessary and appropriate. All information and documentation of disability is confidential. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated.