MATH 554 - Math 703 I
Analysis I
Homework Assignments and Supplementary Materials
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Homework Assignments
(Each Problem is worth 10 pts.)
No. | Assignment Due | Page and No.'s | Solutions |
#1 |
Wednesday (1/21) |
In problems 1-2, assume F is a field:
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#2 |
Friday (1/30) |
Additional Graduate Student Problems: Page 30: 11 |
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#3 |
Friday (2/06) |
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#4 |
Friday (2/13) |
Click here to download the assignment. | ![]() |
#5 | Monday (2/23) | Click here to download the assignment.
Extra Credit (15 pts.)-- Prove the following about closure of sets:
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#6 | Friday (2/27) | Problem:
Suppose that S has the property that each sequence from S which
converges, must converge to a limit which belongs to S. Prove that
S is a closed set.
Extra Credit (10 pts.)-- Complete the proof of the following: Suppose in the real numbers the sequence {bn } converges to b and b is not zero. Prove that 1/bn converges to 1/b. |
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#7 | Friday (3/26) | You can download homework assignment #7 for Friday March 26, here. | ![]() |
#8 | Friday (4/9) | Problem:
Using properties of connectedness and the last theorem
proved in Monday's lecture (about continuity of inverse functions),
prove that for each natural number n:
Extra Credit (10 pts.)-- Fill in the details of the proof begun during Monday's lecture: Prove that a function is continuous if and only if the inverse image of a closed set is closed. Be sure to prove the set equality relating inverse images of the complements of sets. |
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