MATH 1242 PRACTICE FOR TEST #2.
This practice sheet covers sections 6.3-6.6 and 7.1-7.5 (old book sections 5.7-5.10 and
6.1-6.3 and 6.5). The problems on this sheet are intended to help you study for
Math 521 - Advanced Calculus I (Metcalfe)
Spring 2015
January 29, 2015
Quiz 1 Solutions
1. [10 points] Suppose that A, B R are nonempty and bounded above. Show that A B is
bounded above and that
sup(A
Math 521 - Advanced Calculus I
Instructor: J. Metcalfe
Due: February 3, 2015
Assignment 5
1. [10 points] If f and f g are one-to-one, does it follow that g is one-to-one? Justify your
answer.
2. [10 p
Math 521 - Advanced Calculus I
Instructor: J. Metcalfe
Due: February 5, 2015
Assignment 6
1. [10 points] A complex number z is said to be algebraic if there are integers a0 , . . . , an , not all
zero
Math 521 - Advanced Calculus I
Instructor: J. Metcalfe
Due: February 26, 2015
Assignment 10
1. [10 points] Let E be the set of all limit points of a set E. Prove that E is closed. Do E and
E always ha
Math 521 - Advanced Calculus I
Instructor: J. Metcalfe
Due: February 19, 2015
Assignment 9
1. [10 points] Show that if (xn ) is unbounded, then there exists a subsequence (xnk ) such that
lim(1/xnk )
Math 521 - Advanced Calculus I
Instructor: J. Metcalfe
Due: February 10, 2015
Assignment 7
1. [10 points] Verify, using the denition of convergence of a sequence, that the following sequences
converge
Math 521 - Advanced Calculus I
Instructor: J. Metcalfe
Due: January 15, 2015
Assignment 1
1. [10 points] Prove that n3 + (n + 1)3 + (n + 2)3 is divisible by 9 for all n N.
2. [10 points] Use the trian
Math 521 - Advanced Calculus I
Instructor: J. Metcalfe
Due: February 12, 2015
Assignment 8
1. [10 points] Suppose that cfw_xn is a convergent sequence and cfw_yn is such that for any > 0
there exist
Math 521 - Advanced Calculus I
Instructor: J. Metcalfe
Due: January 22, 2015
Assignment 3
1. [10 points] If sup A < sup B, then show that there exists an element b B that is an upper
bound for A.
2. [
Math 521 - Advanced Calculus I
Instructor: J. Metcalfe
Due: January 20, 2015
Assignment 2
These statements are implicitly claiming that the quantities in the conclusion exist. Be sure to
fully justify
Math 521 - Advanced Calculus I
Instructor: J. Metcalfe
Due: January 27, 2015
Assignment 4
1. [10 points] Suppose that S is a nonempty set of real numbers that is bounded. Prove that
inf S sup S.
2. [1
Math 521 - Advanced Calculus I (Metcalfe)
Fall 2012
September 28, 2012
Exam 1
Please show all of your work, and justify your answers completely.
Only one attempt at a solution will be graded per probl
Math 521 - Advanced Calculus I (Metcalfe)
Fall 2012
September 28, 2012
Exam 1
Please show all of your work, and justify your answers completely.
Only one attempt at a solution will be graded per probl
Math 521 - Advanced Calculus I (Metcalfe)
Spring 2015
January 29, 2015
Quiz 1
Please show all of your work, and justify your answers completely.
Only one attempt at a solution will be graded per probl
HOMEWORK 2 FOR MATH 521, FALL 2013
DUE MONDAY, 9 SEPTEMBER AT THE BEGINNING OF
LECTURE.
Do the following exercises from Abbott: 1.3.5, 1.3.7, 1.3.8, 1.4.4, 1.4.5.
1
HOMEWORK 5 FOR MATH 521, FALL 2013
DUE MONDAY, 30 SEPTEMBER AT THE BEGINNING OF
LECTURE.
Do the following exercises from Abbott: 2.3.3, 2.3.4, 2.3.7, 2.3.11, 2.3.12
1
HOMEWORK 6 FOR MATH 521, FALL 2013
DUE MONDAY, 7 OCTOBER AT THE BEGINNING OF
LECTURE.
Do the following exercises from Abbott: 2.4.2, 2.4.5, 2.5.1, 2.5.3, 2.5.6
1
HOMEWORK 4 FOR MATH 521, FALL 2013
DUE MONDAY, 23 SEPTEMBER AT THE BEGINNING OF
LECTURE.
Do the following exercises from Abbott: 2.2.1, 2.2.4, 2.2.6, 2.3.2, 2.3.5
Additional exercise(s) to turn in:
HW
HOMEWORK 11 FOR MATH 521, FALL 2013
DUE WEDNESDAY, 4 SEPTEMBER AT THE BEGINNING OF
LECTURE.
Do the following exercises from Abbott: 1.2.1, 1.2.2, 1.2.4, 1.2.5, 1.2.9.
Additional exercise(s):
HW1.1:
Le
HOMEWORK 3 FOR MATH 521, FALL 2013
DUE MONDAY, 16 SEPTEMBER AT THE BEGINNING OF
LECTURE.
Do the following exercises from Abbott: 1.4.7, 1.4.9, 1.4.12, 1.5.9(a,b)
Additional exercise(s) to turn in:
HW3
HOMEWORK 7 FOR MATH 521, FALL 2013
DUE WEDNESDAY, 23 OCTOBER AT THE BEGINNING OF
LECTURE.
Do the following exercises from Abbott: 2.6.1, 2.6.2, 2.6.4, 2.7.3, 2.7.4, 2.7.5,
2.7.9
1
HOMEWORK 9 FOR MATH 521, FALL 2013
DUE MONDAY, 4 NOVEMBER AT THE BEGINNING OF
LECTURE.
Do the following exercises from Abbott: 3.3.4, 3.3.5, 3.3.8, 4.2.1, 4.2.2 Additional
exercise(s) to turn in:
In c
QUIZ 1
PRINTED Name:
(1) Let inf denote the greatest lower bound of a set of reals. Prove the following statement: Let A R be bounded
below, and let s R be a lower bound. Then s = inf(A) if and only i
HOMEWORK 8 FOR MATH 521, FALL 2013
DUE MONDAY, 28 OCTOBER AT THE BEGINNING OF
LECTURE.
Do the following exercises from Abbott: 3.2.3, 3.2.5, 3.2.7, 3.2.9 Additional
exercise(s) to turn in:
HW8.1:
Writ
SYLLABUS FOR MATH 521-002, FALL 2013
1. Course Information
Instructor: Hans Christianson
Time and day: MWF, 12:00 - 12:50 pm.
Location: Phillips 385
Oce hours: Wednesday 2-3 pm and Friday 1-2 pm, or b