Math 825 Section 001, 1st Semester, '07-'08
Math 825, Mathematical Analysis I is offered by the
Department of Mathematics
of the University of Nebraska-Lincoln.
There is only one section, which meets 1:30-2:20 MWF in Oldfather 304
and is taught by
Allan Donsig.
Announcements
The policy
handout and
syllabus
are available, in pdf format.
closure argument.
Tests
Information about tests, and their solutions, will be posted here.
The first test will be from 3:30 to 5:30 pm on Tuesday, October 16 in Bessey 108.
The test covers Chapters 2, 3, and Sections 4.1, 4.2, and 4.3.
Here is an old test from
the last time I taught this class, along with the
solutions to it.
Note that we have covered part of Chapter 4, which is not on the old test, and that I
will not ask you for the proof of a theorem.
Assignments
Assignments will be posted here, in pdf format.
Solutions will be posted on blackboard, also in pdf format.
(I do not want to make solutions to textbook exercises publicly available.)
The TeX code for the assignments is posted
somewhere else.
Note that, in addition to the file for the assignment, helpfully
called assignNN.tex, you will also need the file
newtest.cls, which specifies the macros used in the assignment file.
Further, you'll need to be using LaTeX2e (almost certainly, you are)
and have access to the amsmath package (which I think is part of the
default distribution).
- Assignment 1
- Assignment 2
- Assignment 3
- Assignment 4
- Assignment 5
- Assignment 6
- Assignment 7
- Assignment 8
- Assignment 9
- Assignment 10
- Assignment 11
Quizzes
Here is a list of quiz questions. Since the answers are
clearly stated in the lectures and the textbook, I don't
give them here.
- 1 Define ``L is the limit of (a1,a_2a_3...)''
- 2 Define `A (contained in F) is bounded below', and b) State the Squeeze Theorem.
- 3 State the Least Upper Bound Principle and the Bolzano-Weierstrass Theorem.
- 4 State the Cauchy Criterion for Convergence of a Series.
- 5 State the Ratio Test.
- 6 State a) The Rearrangement Theorem, and b) The Schwarz Inequality.
- 7 Define a) The closure of a set A, a subset of Rn and
b) B, a subset of Rn, is an open set.
- 8 Define a) A, a subset of Rn, is compact, and
b) f from S to Rm, $S$ a subset of Rn, is continuous
at s in S.
- 9 State the sequential characterization of continuity.
- 10 State Fermat's Theorem.
- 11 Define U(f,P) for a bounded function f : [a,b] -> R and
a partition P={a=x0 < x1 < .... < xn = b} of [a,b],
including any symbols used in your definition.
Comments?