STUDENT SYLLABUS
FOR
MATH 3333, INTERMEDIATE ANALYSIS
PREREQUISITE: MATH 2433
TEXT: “Analysis with an Introduction to Proof”, fourth Edition, by Steven R. Lay, Prentice-Hall, 2001.
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
.
Topics covered include the topology of , 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 , 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