Math 74 – Homework Assignments.
Adam Booth.
Spring 2008.
1
Due 2/1.
From the book do: (1.1) 3, 4, 6, (1.2) 2, 4, 6, 8, 10, 12, 15, (1.3) 2, 4, 6, 8.
Also: Find two substantially diﬀerent proofs of Pythagorus’ theorem and present them
(acknowledging your sources). Each of these will probably use some other theorems from
High School Geometry; you should state these clearly, but need not prove them.
2
Due 2/8.
From the book do: (1.4) 2, 6, 7, 9, 14, (1.5) 3, 5, 7(b), (2.1) 2, 3, 5, 6, 8
Also: Read the handout
1
on axioms for the real numbers and use it to prove the
following facts directly from the axioms:
1. If
ab
=
ac
and
a
6
= 0, then
b
=
c
;
2. If
ab
= 0 then
a
= 0 or
b
= 0.
[There are ways of proving both these things which are ‘structurally’
2
very simple
and should remind you of proving algebraic or trigonometric identities, or doing the logic
proofs using the laws from last week. This style of proof is, in a way, the bread and butter
– we’ll add more sophisticated structures to it as we go through this course.]
3
Due 2/15.
From the book do: (2.2) 2, 3, 7, 9, 10 (2.3) 2, 3, 5, 6, 10, 14.
No reading assignment this week, to give you time to start preparing for the midterm.
4
Due 2/23.
From the book do: (3.1) 2, 3, 7, 8, 12, 15.
Also: Referring to p. 84 of M. E. Munroe,
Introduction to Measure and Integration
,
Reading, MA: Addison-Wesley (1953), answer the following questions.
1