# MATH 3333 - Intermediate Analysis

****This is a course guideline. Students should contact instructor for the updated information on current course syllabus, textbooks, and course content****

**Prerequisite**: MATH 2415 and MATH 3325.

**Course Description**: A rigorous treatment of single variable calculus: topological properties of the real numbers, limits, continuity, differentiation, Riemann integration, the fundamental theorems of calculus, sequences and series

**Note: This course is required for Math majors.*

**Text**: “Analysis with an Introduction to Proof”, 5th Edition, by Steven R. Lay, Prentice-Hall, 2004. **ISBN:** 9780321747471

**Description**: MATH 3333 is the first rigorous theorem/proof-type course in analysis at the University of Houston. Its role is to prepare students for advanced mathematics, especially for all math courses in analysis numbered 3334 and higher. The goal of the course is to teach students mathematical reasoning and the construction of proofs in the environment of R^{1}. Topics covered include the topology of R^{1}, convergence and limits, and the proofs of well-known calculus theorems such as the Mean Value Theorem, the Intermediate Value Theorem, the Inverse Function Theorem in R^{1}, and the Fundamental Theorem of Calculus. Some instructors may require students to write homework solutions at the board that will be critiqued by their classmates and/or the instructor.

**Suggested Syllabus**

Chapter 3: “The Real Numbers” (Natural numbers and induction, ordered fields, the Completeness Axiom, topology of the real numbers, compact sets—omit Metric Spaces)

Chapter 4: “Sequences” (Convergence, limit theorems, monotone sequences and Cauchy sequences, subsequences)

Chapter 5: “Limits and Continuity” (Limits of functions, continuous functions, properties of continuous functions—cover uniform continuity in the context of Chapter 7 and omit continuity in Metric Spaces)

Chapter 6: “Differentiation” (The derivative, the Mean Value Theorem; include l’Hopital’s Rule and Taylor’s Theorem as time permits)

Chapter 7: (as time permits) “Integration” (The Riemann integral, properties of the Riemann integral. The Fundamental Theorem of the Calculus)

**Suggested Homework Problems**

Assignment #1: 10.5,10.7,10.13,10.16 (b)

Assignment #2: 11.3 (a) - (c), 12.1(a) -( c), 12.3 (e) (g) (i) 12.6

Assignment #3: 13.2 (a ) (b), 13.3 ( a)- (c ) ,13.4 (a)- (c) , 13.5 (a )- ( c) ,13.7

Assignment #4: 13.13, 14.4,16.2,16.4(c ) - (e)

Assignment #5: 17.5 (b),(f),(I),17.6 (a),(b),17.7.17.14

Assignment #6 18.3 (a) (d),18.4 (a)-(c),

Assignment #7: 19.2 (a)-(c),19.4,20.4

Assignment #8: 21.3,21.5,21.6.22.4,22.6

Assignment #9: 25.1,25.6,25.7(a),(c),26.5 (a),(d),(j),26.15

Assignment #10: 27.5,28.4,29.3,29.10,30.4,30.10

**Grading**: Please consult your instructor's syllabus regarding any and all grading guidelines.

**Justin Dart Jr. Center Accommodations:**

**Academic Adjustments/Auxiliary Aids**: The University of Houston System complies with Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, pertaining to the provision of reasonable academic adjustments/auxiliary aids for students who have a disability. In accordance with Section 504 and ADA guidelines, University of Houston strives to provide reasonable academic adjustments/auxiliary aids to students who request and require them. If you believe that you have a disability requiring an academic adjustments/auxiliary aid, please visit Justin Dart Jr. Student Accessibility Center website at https://www.uh.edu/accessibility/ for more information.

**UH CAPS**

Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach (CAPS) by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus.