MATH 203: HOMEWORK 1
DUE BY 5PM ON FRIDAY, JANUARY 25
1) Donald Trump throws a party at his home at which you are invited.
To jazz up things, he decides to give out some presents to his guests.
The three presents are a brand new Mercedes, an iPod touch, a
MATH 203: HOMEWORK 11
DUE BY 5PM ON TUESDAY, APRIL 16
1)
(a) Prove that the additive group of Gaussian integers given by
m + n 1 for m, n Z is isomorphic to the multiplicative
group of rational fractions of the form 2n 3m for m, n Z.
(b) Show that both gr
MATH 203: HOMEWORK 10
DUE BY 5PM ON FRIDAY, APRIL 5
1) Determine which of the following are groups and justify your answer.
(a) All complex numbers of absolute value 1 under multiplication;
(b) All complex numbers z of absolute value 1 under the operation
MATH 203: HOMEWORK 9
DUE BY 5PM ON FRIDAY, MARCH 29
1) Finish Denis Guedjs The Parrots Theorem (chapters 20 to 26).
Write at least a page (hand-written is OK) but no more than two
pages with your reaction to those ve chapters and any questions or
observat
MATH 203: HOMEWORK 8
DUE BY 5PM ON FRIDAY, MARCH 22
1) Read chapters 16 to 20 of Denis Guedjs The Parrots Theorem.
Write at least a page (hand-written is OK) but no more than two
pages with your reaction to those ve chapters and any questions or
observati
MATH 203: HOMEWORK 7
DUE BY 5PM ON FRIDAY, MARCH 15
1) Read chapters 11 to 15 of Denis Guedjs The Parrots Theorem.
Write at least a page (hand-written is OK) but no more than two
pages with your reaction to those ve chapters and any questions or
observati
MATH 203: HOMEWORK 6
DUE BY 5PM ON FRIDAY, MARCH 1
1) Read chapters 6 through 10 of Denis Guedjs The Parrots Theorem.
Write at least a page (hand-written is OK) but no more than two pages
with your reaction to those ve chapters and any questions or observ
MATH 203: HOMEWORK 5
DUE BY 5PM ON FRIDAY, FEBRUARY 22
1) Read the rst ve chapters of Denis Guedjs The Parrots Theorem.
Write at least a page (hand-written is OK) but no more than two pages
with your reaction to those ve chapters and any questions or obse
MATH 203: HOMEWORK 4
DUE BY 5PM ON FRIDAY, FEBRUARY 15
1) Translate the following into symbolic notation:
(a) There are at least two objects such that P (x).
(b) There are at least three objects such that P (x).
(c) There are at least n objects such that
MATH 203: HOMEWORK 3
DUE BY 5PM ON FRIDAY, FEBRUARY 8
1) Determine whether each of the following statements is a grammatically correct symbolic statement. As usual, P , Q, and R are propositional variables, and x, y and z are mathematical variables. For e
MATH 203: HOMEWORK 2
DUE BY 5PM ON FRIDAY, FEBRUARY 1
1) An Aristotelian syllogism is a very famous classical inference rule.
Look it up online, and then write a paragraph or two describing it. Be
sure to provide some examples as well.
2) Replace each of
MATH 203: HOMEWORK 12
DUE BY 5PM ON WEDNESDAY, APRIL 24
1) (a) Let G be the group of transformations x ax + b of R into R,
where a = 0, a, b R, and let S be the group of all such transformations
satisfying a = 1. Describe the right and left cosets of S in