MTH435
Introduction to Mathematical Analysis I

MW 3:00-4:45 PM
Lippitt Hall 201

Instructor    Araceli Bonifant
Office: Lippitt Hall 202 G
Phone: 874-4394
Email: bonifant@uri.edu

Office Hours:

Book: Introduction to Real Analysis by Robert G. Bartle and Donald R. Sherbert, 4th. Edition

Course Description. This course is an introduction to Real Analysis. In this course we will look more deeply at the concepts you learned in your Calculus classes. We will discuss how to prove many of the facts you have used in the past. You will learn precise definitions of notions, get a deeper understanding of concepts, and make your reasoning more rigorous. A very important component of this course is to expose you to proofs. The goal is for you to learn how to write proofs.

Prerequisites. MTH 215 and 243 and 307 or permission of instructor.

Tentative List of Topics:

• The Real Number System: Algebraic and order properties of ${\mathbb R}$, Absolute value, The completeness Property of ${\mathbb R}$, Applications of the supremum property. Intervals, Infinite sets.

• Sequences and Series: Sequences and their limits, Subsequences and the Bolzano-Weierstrass theorem, The Cauchy criterion.

• Limits: Limit theorems.

• Topology of Real Numbers: Open and close sets in ${\mathbb R}$, compact sets, metric spaces.

• Continouous Functions: Continuous functions, Uniform continuity, Monotone and Inverse functions.

• Differentiation: The mean value theorem, L'Hospital's rules, Taylor's theorem.

• Evaluation Policy:

• Homeworks and Quizzes             25%
• Exam I                                         20 %    Wednesday October 12
• Exam II                                         20 %    Wednesday November 16
• Final Exam                                   35 %    Wednesday December 14        3:00 pm - 6:00 pm
• Standards of behaviour: Students are responsible for being familiar with and adhering to the published "Community Standards of Behavior: University Policies and Regulations" which can be accessed in the University Student Handbook. If you must come in late, please do not disrupt the class. Please turn off all cell phones, pagers, or any electronic devices.

Special Accommodations: Any student with a documented disability is welcome to contact me as early in the semester as possible so that we may arrange reasonable accommodations. As part of this process, please be in touch with Disability Services for Students Office at 330 Memorial Union, 401-874-2098.