## MAT 200 LOGIC, LANGUAGE AND PROOF SPRING 2006

### Grades are posted. Info is below. Please note that there has been an error on our side in computing the grade of a student (ID number -----9916). As a result the posted grade is not correct and it will be changed from C to D+. The student can contact me for clarifications.

CLASS MEETS IN MAT TOWER P-131, 11:20-12:40 TU-TH

The basic aim of MAT 200 is to introduce the student to mathematical reasoning and proofs.

The course will begin with a discussion of logical language, operations, and rules, as well as their use in mathematical proofs. We will then examine how these ideas are used in the context of classical Euclidean geometry, with an emphasis on the interplay between geometric reasoning, language, and formal logic. Finally, we will spotlight the tools used in most modern mathematics: sets, and maps between them.

Textbook: Proof, Logic, and Conjecture: The Mathematician's Toolbox, by Robert S. Wolf, W.H. Freeman, 1998.

Geometry notes: Clik here.

Etiquette: Punctuality: no late arrivals, no early departures: they are disruptive. If, occasionally, you need to arrive late and/or leave early, let me 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:

• a grade of A- or higher in
• MAT 125, MAT 131, MAT 141, or AMS 151;
• or an average of B- or better in
• MAT 125/126/127, MAT 131/132, MAT 141/142, or AMS 151/152;
• or a grade of C or higher in both
• MAT 203, MAT 205 or AMS 261; and
• MAT 211 or AMS 210;
• or permission of the instructor.

Grade: Midterm I = 25%, Midterm II =25%, Final = 35%, Homework = 15%. Maximum scores: Midterms 1 and 2: 250pts each; each homework: 15pts (the best ten are used to grade); Final 350pts. 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.

SCHEDULE OF EXAMS. The sections to be covered will be announced well in advance. Be sure to be available on these days and times:

Midterm I: THURSDAY MARCH 2, IN CLASS. Covers sections 2 and 3. Sample test I with solutions. Midterm I with solutions.

Data for Test I: Average=161.5/250. Points: 1=(4x15)60; 2=40; 3=40; 4=30; 5=(30+20)50; 6=30. de Cataldo has graded 1,2,6. Basu: 3,4,5. Please direct questions to the grader of each problem only.

Appoximate curve: A > 237.5, A- >225, B+ > 212.5, B > 200, B- > 187.5, C+ > 175, C > 162.5, C- > 150, D+ > 137.5, D >= 112.5, F< 112.

Midterm II: THURSDAY APRIL 6, IN CLASS. Covers sections 4, 5.1, 5.2 and 6.1 and the definition of function on page 193 (of section 7.1) Examples of proofs. Sample test II with solutions. Midterm II with solutions.

Data for Test II: Average 131.6/260. Points: 1,2,3,4 = 4x40=160; 5,6 = 2x50=100. Total is 260, that is 10 more than the expected 250. That is because I wanted to give a little extra credit (10points). It is to your advantage. de Cataldo has graded 1,3,5; Basu:2,4,6. Please direct questions to the grader of each problem only.

#### FINAL: THURSDAY MAY 11, 11am-1:30pm; in class (MAT P-131).

Final covers: sections 2,3,4,5.1,5.2, 6.1, 7.1,7.2,7.3 and the geometry notes pages 1-12.

REVIEW: TU 5/9: 12-2pm, P-131.

de Cataldo's office hours for the final: TU 5/9: 2-4pm, 5-108.

S. Basu's office hours for the final: Monday 5/8: 4-6pm MLC (if closed than MAT TOWER 3-120, 4-5pm). Tu and Wed 4-5 pm, MAT TOWER 3-120

Average in the final test: 217.5/350. Final was curved to determine A and C grades for the final: A>=320. C >=220.

Average in the course: 596.92. Curve for final grade (out of 1000pts). F<=400; D<=450; D+<=550; C-<=600; C<=630; C+<=700; B-<=750, B<=790; B+<=850; A-<=880; A>880. We doubled the second midterm score if better than the first one (which was then dropped). If you scored A on the final, your final grade is A; if you scored C in the final, your final grade is at least C. Borderline cases were considered in conjunction with performance. There is a rather big divide between C and C- in the class final grades.

Contact Mr. Basu if you want to know your score on the final. Please do not ask him to give you all your scores. You should have them. The final cannot be returned for a whole semester (SUNY regulations). If you want to see it, please come to my office on WED May 16-17, 1-3pm (sorry: I had to cancel the TU office hours)

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.

Homework: It will be posted here every Thursday and it will be due the following week on Thursday in class. Graded homework will be returned in class; if you do not come to class on that day you may collect it during Mr Basu's office hours. Questions about the grading of the homework should be directed to Mr Basu. Only some of the problems will be graded, but which ones will not be announced in advance. Late homework will not be accepted. The homework must be stapled. No exceptions.

HMK 1, due TH FEB 2: 2.1: 1d,2b,3b,4b,6a,9a,10a; 2.2: 1,2,3,6c,6k,7,8,13.

HMK 2, due TH FEB 9: 2.3: 1,2,4,5(formal solutions), 8,9,10.

HMK 3, due TH FEB 16: 3.2: 1,3,5d,6a,7,8b; 3.3: 1,2,3,4,5f,7a,8,9c,10a.

HMK 4, due TH FEB 23: 3.4: 1,2,3,5,7,8,10,11.

HMK 5, due TU MAR 7: 4.2: 3,5c,12,14; 4.3: 1,5a,5d,17.

HMK 6, due TH MAR 9: 4.4:2,4,6,14,18,26,29.

HMK 7, due TH MAR 16: 4.5: 4,10,13,19; 5.1: 2,5,9.

HMK 8, due TH MAR 23: 5.2: 2(part g only),3f,4h,6c,7e;5.3:1de,4a,4b,17; 6.1:1abcd,2cdef.

HMK 9, due TH MAR 30: 6.1:3c,5,13,14a; 7.1: 1ai,2,6,7ab,8c; 7.2: 1,2,9,15,16

HMK 10, due TH 4/27. 7.3: 1,2,3a,4,9,10,14. From geometry notes: ex 2.2.

HMK 11, due TH 5/2. Geometry notes Exercises: 2.6, 3.1, 3.4, 3.5, 3.9, 3.14, 4.1, 4.2.

HMK 12, will not be collected nor graded. Solutions will be posted. Geometry notes: Exercises: 4.4, 4.5, 4.6, 4.7, 4.8, prove Theorem 4.3.

Solutions to HMKs 11 and 12. The proof of 4.3 is incomplete in the solution set. Proof was given in class. Proof is not required in the final.

Contacting the staff. The best way is to approach me after the lectures/recitations or to see me 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.

Instructor: Mark Andrea de Cataldo; mde at math dot sunysb dot edu ; Office Hours: MAT TOWER 5-108 (on TH I may be in P-148): TU and TH 2:30-4pm.

Teaching Assistant: Somnath Basu; basu at math dot sunysb dot edu ; Office Hours: MLC MO 4-6pm and MAT 3-120 WED 4-5pm.

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 instructor has 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.

• Mark Andrea de Cataldo's homepage.