MAT 200: Logic, Language and Proof - Lecture 1

Instructor: Samuel Grushevsky
Office hours: Monday, Tuesday 1.30-2.30 in Math 3-109; Monday 2.30-3.30 in MLC or 3-109
Grader: Chirasree Chatterjee
Office hours: Tuesday 2.30-3.30 in S240A (the office within MLC), Thursday 3-4, Friday 12-1 in MLC

Schedule: MW 5:20pm - 6:40pm
Classroom: Chemistry 128

Overview: The goal of the course is to introduce the student to mathematical reasoning and proofs. This course serves as an introduction to rigorous mathematics used in upper-division mathematics courses, but the rigorous reasoning skills are also generally useful in life, whatever your pursuits.
We will first discuss logical language and operations, and methods of proof in general. We will then focus on sets and maps between them - the foundational objects of mathematics. Finally we will apply the rigorous language to systematically define and study some notions of number theory, elementary analysis, and Euclidean geometry.

Textbook: Peter J. Eccles: An Introduction to Mathematical Reasoning: numbers, sets and functions and Stony Brook's own Geometry Notes. Reading the assigned chapter of the textbook before lecture will greatly help you!

Homework: Weekly problem sets will be assigned and collected in class on Wednesdays. 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.

In addition to homework problems, exercises are given in the book, and some are recommended below. The solutions for the exercises do not need to be turned in with the homework. Please practice by trying to solve the exercises first and only then reading the solutions in the book (by reading the solution without first trying to do the exercise in your own way you are only cheating yourself).

Grading: Homework: 20%, Midterm I: 25%, Midterm II: 20%, Final: 35%.

Syllabus/schedule (subject to change)
Mon 8/301. The language of mathematics Exercises 1.1-1.4
Wed 9/12. Implications Exercises 2.1-2.5
Mon 9/6No class Labor Day
Wed 9/8No class Rosh Ha Shanah
Mon 9/133. Proofs Exercises 3.2-3.4,4.2,4.3,4.7
Wed 9/154. Proof by contradiction HW due: p.53, problems 1,2,3,5; Drop deadline
Mon 9/205. The induction principleExercises 5.1-5.7
Wed 9/225. Induction (continued)HW due: p.54, problems 4,6,7,9,10,11
Mon 9/276. The language of set theoryExercises 6.3-6.6,7.1,7.3-7.7,7.9
Wed 9/297. QuantifiersHW due: pp.54-57, problems 12,13,14,16,18,21,22*,25,26*
Mon 10/48. FunctionsExercises 8.1-8.5, 9.1-9.5
Wed 10/69. Injections, surjections and bijectionsHW due: pp. 115-117, problems 1,3,4,8,12,13,14,15
Mon 10/11Review of chapters 1-9
Wed 10/13 Midterm I: Practice 1, Practice 2, Practice 3.Covers chapters 1-9. Solutions
Mon 10/18Geometry 1-2. IntroductionExercise in Eccles 9
Wed 10/20Geometry 3-4. AxiomsHW due: Eccles; p.117, problems 16,18; Geometry 2.4,2.5,2.6
Mon 10/25Geometry 5. Triangles
Wed 10/27Geometry 5. (continued)HW due: Geometry 3.1, 3.2, 3.3, 3.12, 3.14, 4.3, 4.5, 4.8
Mon 11/1Geometry 6. Parallels"W" Drop deadline is 10/29
Wed 11/3Geometry 7. Similarity and PythagorasHW due: Geometry 5.2, 5.8, 5.9, 5.10, 6.2, 6.4, 6.5
Mon 11/8   Midterm II Practice problems Covers Geometry chapters 1-6. Solutions
Wed 11/1010. CountingExercises 10.2,10.3,10.4,11.2,11.4,11.5,11.6
Mon 11/1511. Properties of finite setsHW due: p.182, problems 1,3,4
Wed 11/1712. Counting functions and subsetsExercises 12.1-12.7, 13.1,13.2
Mon 11/2213. Number systemsHW due: p.183, problems 5,6,10,11,14
Wed 11/24No class Stony Brook Friday
Mon 11/2919. Modular arithmeticExercises 19.1,19.2,,21.1,21.2,21.3
Wed 12/120. Linear congruences HW due: p.184, problems 16,17,23; p. 271, problems 1,2,4,7
Mon 12/621. Congruence classesExercises 21.4,21.6,22.1,22.2,22.3
Wed 12/822. Partitions and equivalence relationsHW due: p.272, problems 9,13,16,18,19
12/18-12/20Special office hours: 12/18 12-2; 12/19 10-12; 12/20 12-2
Mon 12/20Final 2:15pm-4:45pm (in the regular classroom). Practice I and II.Covers everything, with emphasis on the last third

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) 632-6748/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 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

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.

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