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# MATH 422 Syllabus

### Real Analysis I

Revised: September, 2014

### Course Description

Sequences of real numbers, continuous functions, and differentiation. Prerequisite: MATH 250 and MATH 255. Three Semester Hours.

### Prerequisites

Math250 and Math255.

### Student Learning Objectives

By the end of the course students will be able to:

• Use the definitions of convergence as they apply to sequences, series, and functions;
• Determine the continuity, differentiability, and integrability of functions defined on subsets of the real line;
• Produce rigorous proofs of results that arise in the context of real analysis; and
• Write proofs of theorems that meet rigorous standards based on content, precision, and style.

### Text

Gordon. Real Analysis, A First Course, Second Edition. Addison-Wesley, 2002.

### Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

### Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

### Course Outline

• Chapter 1: Real Numbers (6 days) Completeness; countable and uncountable sets; real valued functions
• Chapter 2: Sequences (10 days) Convergent monotone and Cauchy sequences; subsequences; Bolzano-Weierstrass
• Chapter 3: Limits and Continuity (14 days) Limit theorems; one-sided and infinite limits; continuous functions; intermediate and extreme values; uniform continuity; monotone functions
• Chapter 4: Differentiation (10 days) The definition and rules of differentiation; mean value and L'Hopital
• Chapter 5: Integration (5 days, if time allows) Riemann Integral; conditions for Riemann integrability

Times above include review and testing.