Spring 2012 MAT 319: Foundations of Analysis | Spring 2012 MAT 320: Introduction to Analysis | |

Schedule | TuTh 10:00-11:20 Earth&Space 131 | TuTh 10:00-11:20 SB Union 237 (through 10/4: joint lectures in Earth&Space 131) |

Instructor | Samuel Grushevsky | Tony Phillips |

Office hours | Tu 11:30-1 Math 3-109, and Th 2:30-4 MLC | W 2-4 Math 3-113 |

During the joint lectures please attend the office hours of the professor lecturing | ||

Recitation | MW 11:00am-11:53am Harriman 112 | MW 11:00am-11:53am SB Union 237 |

TA | Joseph Adams | Jonathan Hales |

Office hours | MW 12-1 in MLC, W 1-2 in 2-104 | |

Description | A careful study of the theory underlying topics in one-variable calculus, with an emphasis on those topics arising in high school calculus. The real number system. Limits of functions and sequences. Differentiations, integration, and the fundamental theorem. Infinite series. | A careful study of the theory underlying calculus. The real number system. Basic properties of functions of one real variable. Differentiation, integration, and the inverse theorem. Infinite sequences of functions and uniform convergence. Infinite series. |

Overview | The purpose of this course is to build rigorous mathematical theory for the fundamental calculus concepts, sequences and limits, continuous functions, and derivatives. We will rely on our intuition from calculus, but (unlike calculus) the emphasis will be not on calculations but on detailed understanding of concepts and on proofs of mathematical statements. | An introductory course in analysis, required for math majors. It provides a closer and more rigorous look at material which most students encountered on an informal level during their first two semesters of Calculus. Students learn how to write proofs. Students (especially those thinking of going to graduate school) should take this as early as possible. |

Prerequisites | C or higher in MAT 200 or permission of instructor; C or higher in one of the following: MAT 203, 205, 211, 307, AMS 261, or A- or higher in MAT 127, 132, 142, or AMS 161 | |

Textbook | Kenneth Ross Elementary
Analysis: The Theory of Calculus | |

Homework | Weekly problem sets will be assigned, and collected in Wednesday recitation. 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. | |

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

** Syllabus/schedule (subject to change)**

__All joint lectures through 10/4 meet in Earth&Space 131.First recitation on Wed 8/29. During joint lectures through 10/4, students with last names starting A-M attend recitation in Harriman 112, students with last names N-Z attend recitation in SB Union 237__

Tue 8/28 | 1. | Joint class: Introduction, motivation: what are real numbers? (Grushevsky) | Read pages 1-15 | |

Thu 8/30 | 2. | Joint class: Properties of numbers; induction; concept of a field. (Grushevsky) | HW due 9/5: 1.3, 1.4, 1.5, 1.12, 2.1, 2.3, 3.1, 3.5, 3.6 | |

Tue 9/4 | No class: Labor
Day | |||

Thu 9/6 | 3. | Joint class: Completeness axiom for real numbers; Archimedean principle. (Phillips) | Read pages 19-25;HW due 9/12: parts ehlmno of: 4.1,4.2,4.3,4.4; and 4.8,4.10,4.11,4.12,4.15 | |

Tue 9/11 | 4. | Joint class: Infinity, unboundedness. Definition and examples of sequences. (Phillips) | Read pages 27-41 | |

Thu 9/13 | 5. | Joint class: Limit of a sequence. (Phillips) | HW due 9/19: 5.1, 5.2, 5.4, 7.2, 7.4, 7.5ab | |

Tue 9/18 | 6. | Joint class: Limit laws for sequences. (Grushevsky) | Read pages 43-53 | |

Thu 9/20 | 7. | Joint class: Divergence to infinity, more formal proofs. (Grushevsky) | HW due
9/26: 8.2ace, 8.4, 8.9, 8.10, 9.1, 9.4, 9.6, 9.9, 9.12, 9.13, 9.15 | |

Tue 9/25 | 8. | Joint class: Monotonic sequences, lim sup and lim inf. (Phillips) | Read pages 54-63 | |

Thu 9/27 | 9. | Joint class: Cauchy sequences, and decimal expansion. (Phillips) | No HW: prepare for the
midterm | |

Tue 10/2 | Joint Midterm I in Earth&Space 131. | |||

Thu 10/4 | 10. | Joint class: Subsequences; monotonic subsequences. (Grushevsky) | HW due 10/10: 10.1, 10.2, 10.4, 10.6, 10.10, 11.2, 11.3, 11.5, 11.7, 11.10 |

<\hline>

Tue 10/9 | 11. | Lim sup and lim inf | Read pages 75-77 |

Thu 10/11 | 12. | Review of sequences; series | HW due 10/17: 8.8,9.16,10.8,11.6,12.1,12.3,12.8,12.10 |

Tue 10/16 | 13. | Series | Read pages 90-98,103-104 |

Thu 10/18 | 14. | Alternating series; continuty | HW due 10/24: 14.2,14.5,14.7,14.10,14.12,14.14,15.1,15.6 |

Tue 10/23 | 15. | Continuity | Read pages 115-131 |

Thu 10/25 | 16. | Continuous functions | HW due 11/5 (date change):17.1,17.4,17.9,17.12,17.13,17.14, |

Tue 10/30 | No Class: hurricane Sandy | ||

Thu 11/1 | No Class: hurricane Sandy | ||

Tue 11/6 | 17. | Properties of continuous functions | |

Thu 11/8 | 18. | Continuity and limit | HW due 11/19 18.4,18.6,18.9,18.12,20.2,20.4,20.6,20.8 |

Tue 11/13 | Midterm II (another date change!) covers up to and including section 17 | ||

Thu 11/15 | 19. | Limits, derivative | Read pages 144-154,205-211 |

Tue 11/20 | 20. | Mean value theorem | Read pages 213-220 HW due 11/28: 28.2,28.4,28.6,28.8,28.14,28.15,29.1,29.7 |

Thu 11/22 | No class: Thanksgiving | ||

Tue 11/27 | 21. | L'Hospital's rule | Read pages 222-229 |

Thu 11/29 | 22. | Riemann integral | HW due 12/5: 29.11,29.14,29.16,29.18 |

Tue 12/4 | 23. | Properties of the integral | Read pages 243-266 |

Thu 12/6 | 24. | Fundamental theorem of calculus | |

Wed 12/12 10am-noon | Review Session in Math P-131: Joe | Practice Final | |

Thu 12/13 4pm-6pm | Review Session in Math P-131: Sam |

**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.