!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN" "http://www.w3.org/TR/REC-html40/strict.dtd"> Math 104 Fall 2006

HOMEWORK

• Homework (due Thursday 27 January)
• page 25Do 4.1,4.2,4.3 and 4.4 for (b)(j)(l)(n) and (t) of 4.1.
• page 26:4.8,4.12,4.14,4.15 and 4.16.

• Homework (due Tuesday 1 February)
• 1) Show that in a complete ordered field every element is the sup of the set of rationals less than it. (this you have actually already done in the first homework, no need to do it again if you got it last time)
• 2) Show that in a complete ordered field a non-zero element is positive iff it is a square.
• 3) If F and G are complete ordered fields and f and g are nonzero maps from F to G satisfying f(x+y)=f(x)+f(y) (same for g) and f(xy)=f(x)f(y) (same for g), then f and g are equal bijections.
• 8.1(b),8.3,8.7(a)(c),8.10

• Last office hours

I will hold a review in the usual lecture room(I hope) on Tuesday 3 May 12:30-2. Then office hours the same day 2-3 and 4-5. Then I'll be in my office on the day of the exam, Thursday 12 May, from 10am to 11:45 am.

• Homework due Tuesday 8 February

Proof of the result in class about the equivalence of completeness of an ordered field and a property of monotone sequences.

• Equivalence relations and partitions.

Construction of the reals from the rationals.

Schroeder-Bernstein, Prof Woodin's proof.

A student's unofficial lecture notes.

Homework due Thursday 17 February

Homework due Thursday 24 February

Cardinality.

Definition of the Cantor set.

Homework due Thursday 3 March

Homework due Thursday 10 March

Homework due Thursday 17 March

Homework BY POPULAR DEMAND due only Thursday 7 april

Homework consisting of sample T/F questions for midterm. Not to be handed in.

Homework due Thursday 21 april (typo corrected in q.7)

Homework due Thursday 28 april

Last Homework not due.

A students homework solutions. (Unofficial.)

The set of scores in the midterm.

The set of scores in the makeup midterm.

Midterm solutions.

Makeup Midterm solutions.

Metric space concepts.

Compact iff sequentially compact.

Professor Morrison's notes.

My 104 final from last time.

Midterm instructions.