Math 364 Spring 2005 Schedule


TuesdayThursday
  13 January

Syllabus
Introduction
18 January

Section 1.1
20 January

Quiz on Section 1.1
Section 1.2
25 January

Section 1.2, cont
Begin Section 1.3
27 January

Quiz on Section 1.2
Continue Section 1.3
1 February

Finish section 1.3
Section 1.4
3 February

Quiz on Section 1.3
Section 1.4
8 February

Section 1.5
10 February

Quiz on Section 1.4 and contrapositives
More on Section 1.5
Section 1.6
15 February

Review 		17 February

Exam 1

22 February

Exams returned
TFAE proofs
24 February

Section 1.7
1 March

Homework problems from Section 1.7
3 March

Quiz on Section 1.7
Section 2.1
8 March

Section 2.2
10 March

Quiz on Sections 2.1 and 2.2
Section 2.3
March 14 - March 17

No classes - Spring Break
22 March

Review of section 2.3
Section 2.4
24 March

Quiz on Section 2.3
Section 2.4, cont
29 March

Section 2.4, cont.
31 March

Quiz on Section 2.4
Section 2.5
5 April

Review for exam
7 April

Exam 2
12 April

Section 3.1
14 April

No class
19 April

Section 3.2
21 April

Quiz on Sections 3.1 and 3.2
Section 3.3
26 April

More on Sections 3.1 and 3.2
28 April

Quiz on Section 3.2, 3.3
Section 4.1
3 May

5 May

  12 May

Final Exam
11:00 am - 1:00 pm
in our normal classroom

January 13


Topics CoveredHomework
Syllabus
Introduction
The square root of 2 is irrational
There are an infinite number of primes
There are a countable number of rational numbers
Read Section 1.1

January 18


Topics CoveredHomework
Section 1.1
An introduction to logic, including
propositions
paradox
negation
conjunction
disjunction
truth tables
logically equivalent
Section 1.1, problems 1-4 and
Worksheet (1a-d, 2a-e, 3, 4) are
fair game for Thursday's quiz.

January 20


Topics CoveredHomework
Quiz on Section 1.1

Section 1.2
Conditional statements, including
truth tables
converse
inverse
contrapositive
the conditional as disjunction
negating conditional statements
Section 1.2

January 25


Topics CoveredHomework
Worksheet
Section 1.2
Conditional statements, including
Review of concepts from Thursday
biconditional statements and their truth tables

Section 1.3 Begin discussion of quantifiers
Existential and universal quantifiers
negating quantifiers
Section 1.2
Begin Section 1.3
Do the Lewis Carroll problem on today's worksheet
Negate the statements:
``Not all precious stones are beautiful''
and
``No one loves everyone''

January 27


Topics CoveredHomework
Quiz on Section 1.2

Section 1.3
Existential and universal quantifiers
negating quantifiers
examples of statements with two quantifiers
The Lewis Carroll problem on Tuesday's worksheet
Negate the statements:
``Not all precious stones are beautiful''
and
``No one loves everyone''
Section 1.3

February 1


Topics CoveredHomework
Section 1.3
There exists a unique!
Section 1.4
tautologies
format of proof
modus ponens
defn of even
defn of odd
propositions 1-3
Section 1.3
Thursday's quiz will cover section 1.3
Begin Section 1.4

February 3


Topics CoveredHomework
Section 1.4
modus ponens
defn of even
defn of odd
definition of divides
propositions 4-8
Section 1.4
Thursday's quiz will cover section 1.4 and 1.5

February 8


Topics CoveredHomework
Review materials for exam 1 handed out
Section 1.5
proof by contraposition
proof of biconditionals
proof by contradiction
propositions 9 - 14
Section 1.4
Section 1.5
Thursday's quiz will cover section 1.4 and 1.5 (contrapositive)

February 10


Topics CoveredHomework
Quiz on Sections 1.4 and beginning of 1.5
Section 1.6
existential proofs
proofs of non-existence
proofs involving universal quantifiers
Section 1.5
Section 1.6

February 15


Topics CoveredHomework
Review, including
quantifiers
some proofs from Section 1.6
Sections 1.1 - 1.6
Study for the exam!

February 22


Topics CoveredHomework
Exams returned
"The following are equivalent" proofs
 Complete the proof of the following:
Proposition 23:
Let m and n be integers. Then TFAE
1. m^2-n^2 is even
2. m-n is even
3. m^2+n^2 is even

Due Thursday, 2/24

February 24


Topics CoveredHomework
Section 1.7
lcm
gcd
Division algorithm
Euclidean algorithm
Section 1.7
Quiz Thursday on Section 1.7

March 1


Topics CoveredHomework
Section 1.7
Discussion of homework problems
 Section 1.7
Quiz Thursday on Section 1.7

March 3


Topics CoveredHomework
Quiz on Section 1.7
Section 2.1
Definition of set
elements of sets
set notation
subsets
proper subsets
universal set
number of subsets
 Section 2.1
Quiz Thursday on Sections 2.1 and 2.2

March 8


Topics CoveredHomework
Section 2.2
definition of complement
definition of union
definition of intersection
properties of union, intersection, etc
 Section 2.1
Section 2.2

Quiz Thursday on Sections 2.1 and 2.2

March 10


Topics CoveredHomework
Section 2.3
Families of sets
index
indexing set
unions of families of sets
intersections of families of sets
pairwise disjoint
nested
 Section 2.3

Quiz Thursday on Section 2.3

March 22


Topics CoveredHomework
Section 2.4
Peano's axioms
Properties of natural numbers
Inductive sets
 Section 2.3

Quiz Thursday on Section 2.3

March 24


Topics CoveredHomework
Quiz on Section 2.3
Section 2.4
Principle of Mathematical Induction
 Section 2.4

Quiz Thursday on Section 2.4

March 29


Topics CoveredHomework
Section 2.4
Generalized Principle of Mathematical Induction
 Section 2.4

Quiz Thursday on Section 2.4

March 31


Topics CoveredHomework
Section 2.5
Strong PMI
Well-ordering principle
Archimedean principle
 Section 2.5
Study for exam
Practice exam 2

April 5


Topics CoveredHomework
Review for Exam 2
 Study for exam
Practice exam 2

April 12


Topics CoveredHomework
Section 3.1
Cartesian product
Relation
Inverse Relation
Domain
Range
Composition of relations
 Section 3.1
No class Thursday, Apr 14

April 19


Topics CoveredHomework
Section 3.2
Symmetric relations
Reflexive relations
Transitive relations
Equivalence relations
Equivalence classes
modular arithmetic
 Section 3.1
Section 3.2
Thursday's quiz will cover Section 3.1

April 21


Topics CoveredHomework
Quiz on Section 3.1
Section 3.3
definition of Partition
equivalence relations give partitions
partitions give equivalence relations
Section 3.2
Section 3.3
Thursday's quiz will cover Sections 3.2 and 3.3

April 26


Topics CoveredHomework
More on Section 3.2 and Section 3.3
 Homework problems worked 		Section 3.2
Section 3.3
Thursday's quiz will cover Sections 3.2 and 3.3
Practice Final
Final exam is Thursday, 12 May from 11 am - 1 pm

April 28


Topics CoveredHomework
Section 4.1
definition of function
domain
range
codomain
image
pre-image
Section 4.1
Thursday's quiz will cover Sections 4.1 and 4.3
Practice Final
Final exam is Thursday, 12 May from 11 am - 1 pm


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