# 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 2433 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

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Details of this policy, and the corresponding responsibilities of the student are outlined in The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09) document under [STEP 4: Student Submission (5.4.1 & 5.4.2), Page 6]. For more information please visit the Center for Students with Disabilities Student Resources page.

Additionally, if a student is requesting a (CSD approved) testing accommodation, then the student will also complete a Request for Individualized Testing Accommodations (RITA) paper form to arrange for tests to be administered at the CSD office. CSD suggests that the student meet with their instructor during office hours and/or make an appointment to complete the RITA form to ensure confidentiality.

*Note: RITA forms must be completed at least 48 hours in advance of the original test date. Please consult your counselor ahead of time to ensure that your tests are scheduled in a timely manner. Please keep in mind that if you run over the agreed upon time limit for your exam, you will be penalized in proportion to the amount of extra time taken.

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