SOLUTIONS: HOMEWORK 1.1 (MARCH 26-28, 2007)
Based on John Sternbergs solution.
1.1 Suppose an , bn > 1. Consider the statements (1) an bn and (2) ln an ln bn . Show
(a) that (1) does not imply (2), and
(b) if, in fact, an > 1 + for some xed positive then
Advanced Combinatorics Math-25905 Quiz Zero. March 26, 2007
Instructor: Lszl Babai
ao
Name:
Show all your work. Do not use book, notes, or scrap paper. Write
your answers in the space provided. (You may continue on the reverse.) Indicate the proof of your
Advanced Combinatorics Math-25905 Quiz One. March 29, 2007
Instructor: Lszl Babai
ao
Name:
Show all your work. Do not use book, notes, or scrap paper. Write
your answers in the space provided. (You may continue on the reverse.) Indicate the proof of your
Advanced Combinatorics Math-25905 Quiz Three. April 13, 2007
Instructor: Lszl Babai
ao
Name:
Show all your work. Do not use book, notes, or scrap paper. Write
your answers in the space provided. (You may continue on the reverse.)
Indicate the proof of you
Advanced Combinatorics Math-25905 Quiz Two. April 5, 2007
Instructor: Lszl Babai
ao
Name:
Show all your work. Do not use book, notes, or scrap paper. Write
your answers in the space provided. (You may continue on the reverse.) Indicate the proof of your s