Math 554 Homework Assignments

MATH 554 - Math 703 I
Analysis I

Homework Assignments and Supplementary Materials

To view an Acrobat PDF version of each Solution Set, click on the symbol .
(Free Acrobat reader can be found here.)
The icon indicates a PowerPoint file.

Homework Assignments
(Each Problem is worth 10 pts.)

No. Assignment Due Page and No.'s Solutions

#1
Aug. 30 (Thur.)
Assignment #1

#2
Sept. 6 (Thur.)
Assignment #2

#3
Sept. 13 (Thur.)
Prove that the product of a nonzero rational with an irrational is irrational.

Page 28: 8, 10, 20

#4
Sept. 18 (Tues.)
Page 35: 1 a),d), and (f) ; 9

Prove that

If 1 < a and 1 < b, then 1 < ab.

If 0 < a and n is a natural number, then 1 < (1+a)ⁿ.

If 0 < a and n is a natural number, then 1 + na < (1+a)ⁿ.

#5
Oct. 9 (Tues.)
Page 58-60: 6, 9 b), 11, 28; Page 66: 2
Extra Credit: Page 59: 17; Page 66: 3

#6
Oct. 18 (Thur.)

Prove each of the following:

Both IR and Æ are closed sets.
Arbitrary intersections of closed sets are closed.
Finite unions of closed sets are closed.
{0,1,[1/2],[1/3], ..., [1/n], ... } is a closed set.
In each problem justify your answer. The "space" in each case is IR.

Find the set of limit points for the set {1,1/2,1/3, ...}.

Determine the set of limit points for the set of rational numbers in the interval (0,1].

Determine the limit points for the set [-1,2) È {5/2} È [5,6].

#7
Nov. 6 (Tues.)
Assignment #7

#8
Nov. 13 (Tues.)
Assignment #8

#9
Nov. 20 (Tues.)
Assignment #9

This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated Aug. 28, 2001.
This page ©2000-2001, The Board of Trustees of the University of South Carolina.
URL: http://www.,math.sc.edu/~sharpley/math554

Return to Math 554 Home Page

No.	Assignment Due	Page and No.'s	Solutions
#1	Aug. 30 (Thur.)	Assignment #1
#2	Sept. 6 (Thur.)	Assignment #2
#3	Sept. 13 (Thur.)	Prove that the product of a nonzero rational with an irrational is irrational. Page 28: 8, 10, 20
#4	Sept. 18 (Tues.)	Page 35: 1 a),d), and (f) ; 9 Prove that If 1 < a and 1 < b, then 1 < ab. If 0 < a and n is a natural number, then 1 < (1+a)ⁿ. If 0 < a and n is a natural number, then 1 + na < (1+a)ⁿ.
#5	Oct. 9 (Tues.)	Page 58-60: 6, 9 b), 11, 28; Page 66: 2 Extra Credit: Page 59: 17; Page 66: 3
#6	Oct. 18 (Thur.)	Prove each of the following: Both IR and Æ are closed sets. Arbitrary intersections of closed sets are closed. Finite unions of closed sets are closed. {0,1,[1/2],[1/3], ..., [1/n], ... } is a closed set. In each problem justify your answer. The "space" in each case is IR. Find the set of limit points for the set {1,1/2,1/3, ...}. Determine the set of limit points for the set of rational numbers in the interval (0,1]. Determine the limit points for the set [-1,2) È {5/2} È [5,6].
#7	Nov. 6 (Tues.)	Assignment #7
#8	Nov. 13 (Tues.)	Assignment #8
#9	Nov. 20 (Tues.)	Assignment #9



This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated Aug. 28, 2001. This page ©2000-2001, The Board of Trustees of the University of South Carolina. URL: http://www.,math.sc.edu/~sharpley/math554