MA361 Midterm Study Guide

The midterm examination will be held Thursday, October 29th.

The exam will consist of three sections:

Obviously due to time limitations the latter set of proofs will have to be relatively short ones.

The terms will be taken from the following list:

TermText Reference
one-to-oneDefinition 1.29
onto
bijection
bounded aboveDefinition 1.10
supremum
bounded belowDefinition 1.19
infimum
bounded
R,N,Z,QSection 1.2 p.7
image of a set under fDefinition 1.33
inverse image of a set under f
finite setDefinition 1.38
countable set
at most countable set
uncountable set
convergent sequenceDefinition 2.1
subsequenceDefinition 2.5
bounded (above/below) sequence Definition 2.7
divergent sequenceDefinition 2.14
increasing sequenceDefinition 2.18
decreasing sequence
monotone sequence
Cauchy sequenceDefinition 2.27
limsupDefinition 2.32
liminf
function limit (2-sided)Definition 3.1
left hand function limitDefinition 3.12
right hand function limit
function limits involving infinityDefinition 3.15
continuityDefinition 3.19
uniform continuityDefinition 3.35

The theorems (on the matching section) will be taken from the following list:

TermText Reference
fundamental theorem of absolute valuesTheorem 1.6
approximation property for supremaTheorem 1.14
completeness axiomPostulate 3 p.18
Archimedean principleTheorem 1.16
reflection principleTheorem 1.20
monotone propertyTheorem 1.21
well-ordering principleTheorem 1.22
DeMorgan's lawsTheorem 1.36
at most countable characterizationLemma 1.40
Bolzano-Weierstrass theoremTheorem 2.26
comparison theorem (functions)Definition 3.10
sequential characterization of continuityTheorem 3.21
preservation of Cauchy sequencesLemma 3.38