**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 8/30 | 1. The language of mathematics | Exercises 1.1-1.4 |

Wed 9/1 | 2. Implications | Exercises 2.1-2.5 |

Mon 9/6 | No class | Labor Day |

Wed 9/8 | No class | Rosh Ha Shanah |

Mon 9/13 | 3. Proofs | Exercises 3.2-3.4,4.2,4.3,4.7 |

Wed 9/15 | 4. Proof by contradiction | HW due: p.53, problems 1,2,3,5; Drop deadline |

Mon 9/20 | 5. The induction principle | Exercises 5.1-5.7 |

Wed 9/22 | 5. Induction (continued) | HW due: p.54, problems 4,6,7,9,10,11 |

Mon 9/27 | 6. The language of set theory | Exercises 6.3-6.6,7.1,7.3-7.7,7.9 |

Wed 9/29 | 7. Quantifiers | HW due: pp.54-57, problems 12,13,14,16,18,21,22*,25,26* |

Mon 10/4 | 8. Functions | Exercises 8.1-8.5, 9.1-9.5 |

Wed 10/6 | 9. Injections, surjections and bijections | HW due: pp. 115-117, problems 1,3,4,8,12,13,14,15 |

Mon 10/11 | Review of chapters 1-9 | |

Wed 10/13 | Midterm I: Practice 1,
Practice
2, Practice
3. | Covers chapters 1-9. Solutions |

Mon 10/18 | Geometry 1-2. Introduction | Exercise in Eccles 9 |

Wed 10/20 | Geometry 3-4. Axioms | HW due: Eccles; p.117, problems 16,18; Geometry 2.4,2.5,2.6 |

Mon 10/25 | Geometry 5. Triangles | |

Wed 10/27 | Geometry 5. (continued) | HW due: Geometry 3.1, 3.2, 3.3, 3.12, 3.14, 4.3, 4.5, 4.8 |

Mon 11/1 | Geometry 6. Parallels | "W" Drop deadline is 10/29 |

Wed 11/3 | Geometry 7. Similarity and Pythagoras | HW 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 11/10 | 10. Counting | Exercises 10.2,10.3,10.4,11.2,11.4,11.5,11.6 |

Mon 11/15 | 11. Properties of finite sets | HW due:
p.182, problems 1,3,4 |

Wed 11/17 | 12. Counting functions and subsets | Exercises 12.1-12.7, 13.1,13.2 |

Mon 11/22 | 13. Number systems | HW due:
p.183, problems 5,6,10,11,14 |

Wed 11/24 | No class | Stony Brook Friday |

Mon 11/29 | 19. Modular arithmetic | Exercises 19.1,19.2,19.3.19.5,21.1,21.2,21.3 |

Wed 12/1 | 20. Linear congruences | HW due: p.184, problems 16,17,23; p. 271, problems 1,2,4,7 |

Mon 12/6 | 21.
Congruence classes | Exercises 21.4,21.6,22.1,22.2,22.3 |

Wed 12/8 | 22. Partitions and equivalence relations | HW due: p.272, problems 9,13,16,18,19 |

12/18-12/20 | Special office hours: 12/18 12-2; 12/19 10-12; 12/20 12-2 | |

Mon 12/20 | Final 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 http://www.ehs.sunysb.edu 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
http://www.stonybrook.edu/uaa/academicjudiciary/.

**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.