This record should enable Enhanced Studies Program (ESP) students
to check how much material has been covered each week, and also
internal students who miss any lectures.
MARKS
for your Assignments 2, 4, 6, 8 and 10 (the best FOUR of which count 4% each
towards your total marks)
will be available here about a week after
the submission dates for these assignments.
Your Mid-semester Test will be in the lecture time, 12 noon on
Thursday 28 April 2005.
We also looked at three facts, not listed explicitly in the workbook:
Then Peter Jenkins took over the lectures and just started on Chapter 10, Relations.
Weekly Record of Lectures, MATH1061/7861, Semester 1, 2005
TUTORS are listed here
for the tutorial groups.
WEEK 1:
Tues 1 March
Welcome! Today we started with Logic, Chapter 1, after the
introductions and talk about assessment, rooms, tutorials, contact hours etc.
We did Exercises 1a,b on page 5 of the workbook, and dealt with
simple statements, and logical connectives
"not", "and" and "or".
If you missed this lecture, make sure you have a paper copy of the profile,
assignments, study guide, old tests and exams! Spares are available
outside my office, 67-653.
NOTE the lecture room changes for Wednesday and Thursday!
Wed 2 March
Today we completed Section 1.1 and just started on Section 1.2, about
"if p then q". Here is another example I used:
In Normal, Illinois, a city rule to aid snow clearing on the streets says that
if there is a snowfall of 2 or more inches, then cars can't be parked overnight
on the streets.
Let p denote "there is a snowfall of 2 or more inches"
and let q denote
"cars can't be parked overnight on the streets".
So the city rule says "if p then q".
The only time the rule is violated is when p is true
(so at least 2 inches of snow) and q is false (so a car IS parked on the street
overnight).
If it doesn't snow, the rule isn't violated!
No one cares whether cars are parked on streets or not.
So the truth table for "if p then q"
only has the value FALSE when p is true and q is false!
For all other values of p and q, the truth value of
"if p then q" is TRUE!
Thurs 3 March
Today we completed Section 1.2 and just started on Section 1.3.
See the extra reading for Section 1.3 near the BACK of the Workbook.
We deal very slightly differently with arguments.
We also just looked at Example 1(b), but we used a truth table, and showed
it's invalid because there is a value FALSE taken in one row.
However, next week we'll see examples where we work somewhat differently
to check whether an argument is invalid or valid.
After all, if there are 5 statement forms we don't want to have to make a truth
table with 32 rows!
WEEK 2:
Tues 8 March
Today we finished Chapter 1 (Section 1.3 briefly, and not Section 1.4).
And we started Chapter 2: looking at "for all" (an upside-down capital A)
and "there exists" (a backward capital E).
Wed 9 March
Today we finished the Workbook pages on Chapter 2, and just started on Chapter 3.
Make sure you READ the pages at the back of the Workbook (in the Reader part)
for Section 3.0.
Thurs 10 March
We covered Section 3.0 (see the Reader at the back of the Workbook)
and also Section 3.1. We did the exercises for Section 3.1 from the Workbook.
WEEK 3:
Tues 15 March
Read Sections 3.2 and 3.3 before this lecture if you want to get ahead!
Today we completed sections 3.2 and 3.3 in the Workbook.
Wed 16 March
Today we completed section 3.4 on mod and div, and started on section 3.5,
floor and ceiling functions.
Thurs 17 March
We completed Section 3.5 and did Sections 3.6 and 3.7.
WEEK 4:
Tues 22 March
Today we did the Euclidean Algorithm (Section 3.8 - and note the extra reading in
the back of the workbook!). We also covered Section 3.9
(1) Given any integer a, and a positive integer b, there
exist unique integers q and r such that
a = b.q + r where 0 <= r < b.
(That should say 0 is less than or equal to r etc., but I've no idea
how to type "less than or equal to" in html...only in LaTeX!)
(2) If a and b are positive integers with
b not equal to 0, and q and r
are non-negative integers such that
a = b.q + r,
then gcd(a,b) = gcd(b,r).
(3) If r is a positive integer, then
gcd(r,0) = r.
Wed 23 March
Today we briefly dealt with 3.10 (see the reader at the back of the workbook)
and also Section 4.1, on sequences and sigma notation.
Then we just started Mathematical Induction (section 4.2).
Thurs 24 March
Mathematical Induction today; lots of nice examples!
Assignment 2 due in TODAY before 5pm, to box on level 4 in bldg 67.
EASTER BREAK: mid-semester break week
WEEK 5:
Tues 5 April
Today we revised induction and looked at so-called strong induction
and the well ordering principle for the integers.
Wed 6 April
Today we'll look at example 3 in the Workbook (p.83)
and then start on Chapter 5, Set Theory.
Yes, we did exactly that!
Thurs 7 April
Today we completed Section 5.1 and did most of Section 5.2 in the Workbook.
Don't worry about the names "Inclusion of Intersection" etc. But you should be
aware of these facts and be able to verify them by using truth tables for
the equivalent predicates.
WEEK 6:
Tues 12 April
Today we completed Section 5.3 (an important section!) and just started
on Chapter 11, Graph Theory.
Wed 13 April
Today we did more of Chapter 11, including complete graphs and bipartite graphs.
Thurs 14 April
Edition 3 has a typo in the graph on page 676.
The edge joining I and K should be removed!
(Vertices I and K each just have degree 2 - and in the room plan you cannot go
directly from room I to room K; you have to go via E (or via H and E).
Thanks to Vicky C (ESP student) for finding this!
Today (after a TEDI survey!) we continued with graph theory:
degrees of vertices, walks, paths, circuits.
The result that the sum of the degrees in a graph is equal to twice the number of edges is an important one!
Assignment 4 due in
TODAY before 5pm, to box on level 4 in bldg 67.
WEEK 7:
Tues 19 April
More graph theory, including Euler walks today!
We did the Euler walks section from 11.2,
but only one exercise is related to Hamilton circuits; example 2 on page 113 of the
workbook.
We also did Section 11.3 in the Workbook.
Wed 20 April
Today we completed the Graph Theory part of the Workbook, and did one extra example:
Can you draw a simple graph on 5 vertices with degrees
(a)
4, 2, 2, 1, 1
(b)
4, 3, 2, 1, 1
(c)
5, 4, 3, 2, 2
Answers: (a) yes - we drew one but I've no idea how to do this in html which I type
in as raw text!!! (Draw 5 vertices roughly in a circle; if you label them
a,b,c,d,e, then join a to all other vertices, making its degree 5;
then pick any two of the degree 1 vertices and join them, bringing their degrees up to 2.)
(b) No - degree sum is odd, yet it's supposed to be 2 times the number of edges, i.e. even.
Indeed, in ANY graph, the number of vertices of odd degree must be even!
(c) No; in a SIMPLE graph on 5 vertices, the maximum degree possible is 4.
Thurs 21 April
Today Section 10.1 was completed. Also the terms reflexive,
symmetric and transitive were defined - see the beginning of Section 10.2
REMEMBER next Tuesday is a MONDAY timetable!
WEEK 8:
Tues 26 April
Wed 27 April
Today we continued with section 10.2 (Reflexivity, Symmetry, and Transitivity)
and worked through examples 1-5.
Remember your mid-semester test TOMORROW! Please be punctual;
we'll start the test at 12 noon sharp. It is based only on Chapters 1-5,
and is very similar to last year's one - solutions to which are now
online linked from the math1061 home page.
Thurs 28 April
Mid-Semester TEST in lecture time.
Finally, make sure you can:
* prove things about divisibility and gcd etc
* do induction proofs
* draw Cayley tables and use them to help determine whether something is a group
* state whether a given relation is reflexive, antisymmetric etc and be able
to give explanations
* do the practice exam and assignment questions!
Thurs 2 June
Assignment 10 due in TODAY before 5pm, to box on level 4 in bldg 67.