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, Lgt Engr Lab 154; Recitation WE and FR 10:40-11:35, Lgt Engr Lab 154.
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 CELLULAR PHONES. 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: TUESDAY MARCH 04 (IN CLASS).
Covers sections: 1.1, 1.2, 1.3, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 3.2.
Link to old MAT 319 webpages. Click, scroll down to the MAT 319 section. There are tests posted in the S2007 and F2007 sections. Keep in mind that 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, Bernoulli and arithmetic-geometric mean inequalities, triangle-type inequalities, Archimedean Property, the existence of the square root of 2, the density theorems, characterization of intervals, nested interval property, uncountability of R, uniqueness of limits, Squeeze Theorem.
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: 180 and up; B range 145 and up; C range 90 and up. D range 80 and up. The highest score is 205. The average is 101.
Midterm II: THURSDAY APRIL 10 (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. 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)."
Midterm II , Solutions.
Data for midterm II: Average : 165. Highest 240. Lowest 100.
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 150 and up. D range 120 and up.
Final: TUESDAY MAY 20, 11:00AM-1:30PM
IMPORTANT: if you have missed a midterm and have not given me proper documentation, then your grade on the missed midterm is 0. Some of you contacted me after the midterms, but did not produce any documentation. If I do not receive this documentation by TH May 8 in class, then the grade for the missed midterm will be zero.
Please 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).
Location: IN CLASS (Lt Eng 154)
Final covers All sections (see syllabus).
How to prepare for the final. 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)."
Office hours J. Walsh will be available to show the test by appointment next week on Tu+Wed May 27 and 28. Solutions will be posted only later in the summer.
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>= 280. C>=170. Only A and C are relevant.
Curve for final grade: A>= 900. A- >= 800. B+ >= 750. B >= 700. B- >= 660. C+ >= 620. C >= 580. C- >= 530. D>= 450. F < 450.
WEEK-BY-WEEK SYLLABUS. We shall (tentatively) cover Ch. 1-6.
Week of Jan 29 : 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 JAN 31's CLASS.
Week of Feb 05 : 2.2,2.3.
Week of Feb 12 : 2.4, 2.5.
Week of Feb 19 : 3.1, 3.2.
Week of Feb 26 : 3.3, 3.4.
Week of Mar 04 : Mar 04 TEST (covers up to 3.2 included), 3.5.
Week of Mar 11 : 3.6, 3.7.
Week of Mar 18 : SPRING BREAK.
Week of Mar 25 : 4.1, 4.2.
Week of Apr 01 : 5.1, 5.2.
Week of Apr 08 : 5.3, TH April 10 TEST.
Week of Apr 15 : 5.4 (up to the end of p.140)
Week of Apr 22 : 5.6, 6.1
Week of Apr 29 : (6.1 continued) 6.2 (No Darboux Theorem)
Week of May 06 : 6.3, 6.4 (No Newton's Method).
HOMEWORK: Posted here every mid-week 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.
Hmk 1, due week of Feb 5: 1.3: 6,7,9,11,12; 2.1: 6,9,15,19,21. Solutions HMK # 1.
Hmk 2, due week of Feb 12: 2.2: 3,7,9,12,14,15; 2.3: 4,5,8,11,12. Solutions HMK # 2.
Hmk 3, due week of Feb 19: 2.4: 4,6,7,10,11,15,18; 2.5: 1,3,6,9,10,11. Solutions HMK # 3.
Hmk 4, due week of Feb 26: 3.1: 4,6,8,13,15,16,17; 3.2: 4,6,8,13,15,17,18,20,21. Solutions HMK # 4.
Hmk 5, due on FRIDAY MARCH 7 (DUE TO TEST):3.3: 4,5,6,10,11,12,13,15. Solutions HMK # 5.
Hmk 6, due week of Mar 11 :3.4: 4,6,7,8,9,14,15; 3.5: 1, 2a,3b, 6,7,9,10,12. Solutions HMK # 6.
Hmk 7, due week of Mar 25: 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 Apr 2: 4.1: 1, 3, 8, 9, 11, 14; 4.2: 1, 14, 2, 3, 11, 12. Solutions HMK # 8.
Hmk 9 , due on FRIDAY Apr 19 (DUE TO THE TEST): 5.1 : 1,3,5,10,15 ; 5.2: 1,3,6,7,12,13 . Solutions HMK # 9.
Hmk 10, due on FRIDAY APRIL 19: 5.3: 1,4,6,12,13,15,17,19. Solutions HMK # 10.
Hmk 11, due on FRIDAY APRIL 26: 5.4: 2,4,7,8,11,12,13,14. Solutions HMK # 11.
Hmk 12, due on April 30: 5.6: 1,5,8,9,13,15; 6.1: 1,2,7,9,11. Solutions HMK # 12.
Hmk 13, LAST COLLECTED HMK, Yeah!, due on May 6: 6.1: 14,15,16,17; 6.2: 2,5,6,8,11,13. Solutions HMK # 13.
Hmk 14, This is for practice only: it will not be collected : 6.3: even #s; 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.
Lecture: Mark de Cataldo; mde at math dot sunysb dot edu ; Office Hours: TU 1-4pm, MAT TOWER 5-108
Recitation: Joseph Walsh ; jwalsh at math dot sunysb dot edu ; Office Hours: MO 1-2pm, TU 4-5pm (MAT TOWER 2-105), AND FR 1-2 (in the MLC).
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.