I was asked to provide a syllabus so here it is::
Math 260. Introduction to analysis.
Exisence and uniqueness of the real numbers. Sequences. Metric spaces.Open and closed sets. Continuity, Compactness and connectedness. Cantor sets.
Differentiability. Mean value theorem. Taylor's formula. Convergence of series and series of functions. Stone-Weierstrass theorem. Darboux sums and
Riemann integrability.
I will hold regular office hours, tentatively Monday 2-3 Wednesday 3-4 Friday 2-3 and by appointment.
The appointment should be made right before or after the lectures. These office
hours must be used appropriately. They are not for me to do the homework for
you or to repeat the lecture for you. Let us say that you may ask me a question
but only if you have already thought about it for at least half an hour
beforehand. Often you will find that simply by making yourself phrase the question correctly you will be able to answer it wihout help.
## First MIDTERM will be on Friday September 26

## HOMEWORK

first homework, due Monday 25 August

selected solutions to first homework, due Monday 25 August

second homework, due Monday 1 September

Main ideas of selected solutions to second homework

third homework, due Monday 8 September

## First MIDTERM will be on Friday September 26

fourth homework, due Monday 15 September

CONSTRUCTION OF THE REALS FROM THE RATIONALS

fifth homework, due Monday 22 September

WHAT THE FIRST MIDTERM MIGHT LOOK LIKE

sixth homework, due Monday 29 September updated version!!!!

seventh homework, due Monday 6 October

Notes on compactness, Heine Borel and sequential compactness

eighth homework, due Monday 13 October

Schroeder Bernstein dynamical systems proof

homework 9 due Monday 20 October

## Second MIDTERM will be on Friday November 7

Definition of the Cantor set

Uniform continuity, pointwise and uniform convergence, examples

## In an uncharacteristic bout of magnanimity I am not assigning any
homework due Monday 27 October

homework 9 due Monday 3 November

assignments for writing up selected homework exercises

## The second midterm, on Friday (7 November) will cover the course material
up to and including last Friday(31 October).

homework 11 due Monday 10 November

Students' solution of problem describing all open subsets of the reals

Students' solution of problem on rearrangements of sequences

homework 12 due Monday 17 November

homework 13 due Monday 1 December

A link from Win containing a dialogue about why the reals are necessary

Students' solution of problem on definitions of connectedness

Students' solution of problem on automorphisms of the reals.

homework 14 not due

metric space concepts

A nice discussion of the Cantor set found by Sunny (much more info than required in the course)

Final from a previous time I taught essentially the same course

Students' solution of problem on expressing reals in binary, page1.

Students' solution of problem on expressing reals in binary, page2.