(Adapted from the Course Calendar) Some of the topics covered
in this course are: basic set theory, graphs and algebras, introduction
to logic and proofs, number structures, basic combinatorics,
and algorithms. This is a two semester course that also includes
one lab a week.
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Time |
Class: MWF 2:30-3:30 Lab: Th 8:30-9:30 |
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Place |
Class: RC 0005 Lab: RC 0005 |
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Instructor |
Adam Van Tuyl |
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Office: RB 2015 |
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Office Hours: Tues. 2:30-3:30 Wed. 10:00-11:00
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Text |
Discrete Mathematics and Its Applications, 5th Edition by K. Rosen
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Email |
avantuyl@sleet.lakeheadu.ca |
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Web Page |
flash.lakeheadu.ca/~avantuyl/courses/2003_fall_math1281.html
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Some links that you might find useful:
Any relevant news about the course will be posted in
this
section. Please check here for information about the course, homework
assignments, etc.
News last updated: April 20, 2004
Second Semester
- April 20, 2004 The final exams have been graded. You can
check out your exam mark, and your unofficial course mark here:
Also make sure to check your homework marks below. Have a good summer
and see you next year! --Adam
- The pre-exam marks have been calculated. You can check out your
mark here:
All the old homework assignments are now outside my office. If you
notice any problems with the grades, please let me know.
- April 2, 2004 There will be no offical class. However, I
will there to answer any questions you may have, and to pick up the
final homework assignment. Homework assignments will be available
starting Monday outside my office.
- March 31, 2004 Today we reviewed for the final. To help you
study, I also placed the solutions of last year's final on ERES.
- March 29, 2004 We finished Section 10.4 on Karnough maps.
You should be able to use Karnough maps to simplify functions in
two or three variables. As well, I handed out a review sheet for
the final exam (you can find a copy at the bottom of this page).
- March 26, 2004 We will talk briefly about topics from
Sections 10.1, 10.2, and 10.3. As well, the final homework assignment
will be given out.
- March 24, 2004 Today we started Chapter 10 on Boolean
Algebra.
- March 22, 2004 We finished Chapter 9 by looking at two
different algorithms for finding the minimal spanning tree.
- March 19, 2004 Spanning trees were introduced (Section 9.4),
and two methods for find spanning trees were described.
- March 17, 2004 Today we studied two uses for trees: a
binary search tree, and a decision tree.
- March 15, 2004 We looked at Section 9.1 on trees. I gave
the basic definitions and described some simple properties of trees.
- March 10, 2004 Today we will finish our look at Chapter 8
by looking at Section 8.8 on Graph Colouring. I also gave out a new
homework assignment since there is no class on Friday.
- March 8, 2004 We looked at Section 8.7 on planar graphs.
- March 5, 2004 Today we looked at Section 8.6 on Shortest
Path Problems. A new homework assignment was also given out -- please
note that it is due on Monday March 15, since I will be gone
next Friday.
- March 3, 2004 I finished Section 8.5. You should know what
an Euler circuit and path are, as well as Hamilton paths and circuits.
- March 1, 2004 I handed back the midterm. I also looked
at Section 8.5 on Euler circuites.
- Feb. 28, 2004 I have finished grading the exams. You will
get them back on Monday. I will also put the solutions on reserve today
(they should show up on Monday.)
- Feb. 27, 2004 We had the midterm. There is no homework for
next week.
- Feb. 25, 2004 We looked at Section 8.4 on connectedness.
- Feb. 23. 2004 We looked at Section 8.3 on paths and
circuits.
- Feb. 14, 2004 We finished looking at Section 8.2.
- Feb. 11, 2004 Today we started looking at Graph Theory
(Chapter 8). I also handed out the review sheet for the midterm. You
can find a copy at the bottom of this page.
- Feb. 9, 2004 Today, we did a review of Chapter 7. As
well, we looked at the Kevin Bacon Number, and it's relation
to relations. For more on the Kevin Bacon Number, check out
the Oracle of Bacon.
The Erdos Number, the mathematical equivalent of the Kevin
Bacon Number also has its own
website
- Feb. 6, 2004 We did the last section of Chapter 7
on partial orders. I also gave out a new homework assignment.
On Monday, I'll be doing a review, so please come with questions.
- Feb. 4, 2004 On Wednesday we looked at equivalence relations
(Section 7.5).
- Feb. 3, 2004 Brief note. In HWA 4, you only need to
do 32af in Section 7.1, not all the parts of 32.
- Feb. 2, 2004 We did Section 7.4 on the closure of relations.
- Jan. 30, 2004 We looked at representation of relations
using zero-one matrices. Homework assignment 4 as also been posted to
the web.
- Jan. 28, 2004 We finished Section 7.1, and we took a quick
look at the material of Section 7.2.
- Jan. 26, 2004 We began our look at relations (Section 7.1).
We will finish this section on Wednesday. I also handed back
assignments 1 and 2.
- Jan. 23, 2004 We went back to Chapter 2 to look at Section
2.7 on matrices. Next class we will look at Chapter 7. A new
homework assignment has been given out.
- Jan. 21, 2004 We covered the last two sections
of Chapter 6. These sections discussed the principle of
inclusion-exclusion. On Friday we will look at Section 2.7 on
zero-one matrices.
- Jan. 19, 2004 We finished our look at generating functions
(Section 6.4). You should know how to do problems like those mentioned
in class, and in the homework assignment. On Wednesday we will finish
Chapter 6.
- Jan. 14. 2004 In Wednesday's class I will start Section 6.4.
Please note that I will be out of town on Thursday and Friday, so
there will be no lab nor class on Friday. Also, your current homework
will be due on Monday, Jan 19. I will also give out this week's
assignment.
- Jan. 12, 2004 We finished looking at Section 6.2. After
today's lecture, you should know how to solve linear homogeneous
recurrence relations of degree 1 and 2.
- Jan. 9, 2004 Today we started our look at Section 6.2. We
will finish our look at this section on Monday. The first homework
assignment has also been posted below.
- Jan. 7, 2004 In Wednesday's class I continued our discussion
of recurrence relations by looking at Section 6.1 in more detail.
- Jan. 5, 2004 The first day of second semester. I will
hand back the Christmas Midterms. We will also start our discussion
of Section 6.1.
First Semester
- Dec. 15, 2003 The first semester grades are now finished.
To see them, use the link below:
Math 1281 Grades (First
Semester)
If you see any errors, please let me know. Have a good break, and
see you in the new year! - Adam
- Nov. 24, 2003 On Monday, we continued our investigation
of Probability Theory.
- Nov. 22, 2003 Start Studying! The information sheet
on the Christmas Exam is now ready
(This will also be handed
out in class.)
- Nov. 21, 2003 We looked at more advanced features of
probability. This material comes from Section 5.2. We will
finish Section 5.2 on Monday. I also gave out a new homework
assignment.
- Nov. 19, 2003 We started our discussion of Discrete
Probability (Chapter 5). I covered all of the material of Section 5.1.
- Nov. 17, 2003 I finished Section 4.5, and discussed part
of Section 4.6 on ordering permutations.
- Nov. 14, 2003 Picking up from Wednesday's class, we continue to look at
Section 4.5 on generalized permuations and combinations. A new
homework assignment was also given out.
- Nov. 12, 2003 We began our look of Section 4.5 on
generalized permutations and combinations.
- Nov. 10, 2003 On Monday we looked at binomial coeffecients
in more detal. This material is Section 4.4.
- Nov. 7, 2003 We continued our look at counting techniques
by looking at Section 4.3 on permutations and combinations.
- Nov. 5, 2003 We looked at Section 4.2, and discussed
the Pigeonhole Principle.
- Nov. 3, 2003 I started on Chapter 4 by looking at Section
4.1.
- Oct. 31, 2003 We covered the material of Section 3.4 and
3.5 on recursive functions, sets, and algorithms. A new homework
assignmet was also given out.
- Oct. 29, 2003 I handed back the midterms (the solutions are
posted on ERES -- see below). I also continued with Section 3.3 on
induction.
- Oct. 27. 2003 We began our discussion of Section 3.3
on Induction. We will continue looking at induction in Wednesday's
class. As well, the midterm will be handed back. There is no homework
assignment due this week.
- Oct. 24, 2003 Midterm 1 was held.
- Oct. 22, 2003 We looked at Section 3.2 on sequences and
summations. Click here to check out the
On-Line Encyclopedia of Integer Sequences
- Oct. 20, 2003 We began our introduction of Chapter 3 by
covering the material of Section 3.1. I described the process by which
proofs are made. I also described some open conjectures.
- Oct. 17, 2003 I introduced the Euclidean Algorithm, and
showed how one can solve linear congruences. I also gave a hand out
describing the midterm. You can download a copy from below.
- Oct. 15, 2003 There was no class on Monday because of the
holiday. In Wednesdays class I finished our look at Section 2.4 on
modular arithmetic.
- Oct. 10, 2003 We will start our look at integers by looking
at Section 2.4. The new homework is below.
- Oct. 7, 2003 Today we looked at the efficiency of
algorithms. We showed how to measure time complexity using the language
of big-O notation.
- Oct. 5, 2003 We looked at the growth of functions. You
only need to know how to use the big-O notation. (The material
from pages 138-142 can be skipped).
- Oct. 3, 2003 Today we started our look at Chapter 2, by
looking at Section 2.1. The new homework assignment was also given out.
- Oct. 1, 2003 In Wednesday's class I finished the rest of
the material on functions in Section 1.8. You should now know the
difference between onto and one-to-one functions, as well as know what
a bijection and and a inverse function is.
- Sept. 29, 2003 Today in class we covered section 1.7 on
set operations and set identities. You should know how to use
a membership table to prove the equality of two sets. We also
started on section 1.8, on functions, which we will finish on Wednesday.
- Sept. 26, 2003 In Friday's class, I introduced the concepts of
sets. You should know how to make the power set of a set, and the
cartesian product of sets. The new homework assignment was given out,
and the first was returned.
- Sept. 25, 2003 In Wednesday's class we finished looking at
Section 1.5, where we looked at different methods for proving
theorems.
- Sept. 22, 2003 In Monday's class we took our second look
at Section 1.5. You should know the rules of inference dealing with
quantifiers.
- Sept. 19, 2003 In Friday's class, we will start covering
the material of Section 1.5 (we will spend 3 lectures on this material.)
After today's class, you should know the rules of inference.
The new homework was also given out (see below).
- Sept. 17, 2003 On Wednesday, we covered the material of
Section 1.4 on nested quantifiers.
- Sept. 15, 2003 In Monday, we covered Section 1.3. Know
what a proposition function is, plus know what the two quantifiers are.
- Sept. 12, 2003 In Friday's class, we will finish Section 1.1
and also do Section 1.2. Know all the logical operators, as well as how
to construct truth tables, and be able to decide if two compound
propositions are equivalent. The new homework assignment has also been
posted. Please note: since the new textbooks are not in yet, your
first assignment will be due on Monday, Sept. 22.
- Sept. 11, 2003 In Wednesday's class, we looked at Section 1.1.
You should know what all the logical operators are, and you should know
their truth tables. The lab was cancelled for Thursday.
- Sept. 9, 2003 On Monday, we had the first class. There
was
no lecture -- I simply introduced the course.
- August 12, 2003 Webpages created -- less than one month
until classes begin.
Homework Assignments and Solutions |
Note. If
you wish to hand in an assignment early, please put it under my
door.
Thanks! A.
Second Semester
- Assignment 1 (Due: Jan 16) (Now changed to Jan. 19 since I will be
out of town)
- Section 6.1 -- 2ac, 4ac, 6ac, 8ac, 24, 36
- Section 6.2 -- 2aceg, 4a
- Assignment 2 (Due: Jan 23)
- Section 6.2 -- 4defg, 8
- Section 6.4 -- 4bcde, 6abc, 8ac, 12d, 22, 24a
- Assignment 3 (Due: Jan 30)
- Section 6.5 -- 4, 6, 20
- Section 6.6 -- 2, 4, 8, 10
- Section 2.7 -- 2a, 4c, 15, 28, 30, 31
- Assignment 4 (Due: Feb. 6)
- Section 7.1 -- 4abd, 6af, 22, 24ab, 28, 30, 31, 32af, 54
- Section 7.2 -- 2, 14, 26
- Section 7.3 -- 2, 4, 8, 12, 14abcd
- Assignment 5 (Due: Feb. 13)
- Section 7.4 -- 2, 19ab, 20a, 26b, 19a
- Section 7.5 -- 2ae, 8, 18, 26, 32abcd, 34d, 42ab
- Section 7.6 -- 2, 8, 10ab
- Assignment 6 (Due: March 15 -- Please note the date)
- Section 8.3 -- 6, 8, 12, 16, 34, 42, 48, 54ab
- Section 8.4 -- 2, 6, 10, 18ab, 23, 24, 25, 26
- Section 8.5 -- 2, 4, 8, 10, 26ab, 30, 32, 36
- Section 8.6 -- 2, 6, 26
- Assignment 7 -- (Due: March 19)
- Section 8.7 -- 4, 6, 8, 12, 14, 16, 20, 24, 26
- Section 8.8 -- 2, 4, 6, 10, 13, 15, 16, 22cd
- Assignment 8 -- (Due: March 26)
- Section 9.1 -- 2, 4, 6, 16, 18, 20, 40, 44
- Section 9.2 -- 2, 5, 6
- Section 9.4 -- 4, 6, 10, 14, 16 (apply to 14 only), 20
- Assignment 9 -- (Due: April 2)
- Section 9.5 -- 2, 4, 6, 8, 12, 14
- Section 10.1 -- 2, 4ad, 18, 22, 26
- Section 10.2 -- 4
- Section 10.3 -- 2, 4, 6ad
First Semester
- Assignment 1 (Due: Sept. 22)
- Section 1.1 - 8cdef, 10def, 12de, 13fg, 16abc, 22ab, 24ef, 28ef, 34ab
- Section 1.2 - 8cd, 14, 26, 30, 34
- Assignment 2 (Due: Sept. 26)
- Section 1.3 - 8a-d, 10abcde, 16abcd, 22abc, 30ad
- Section 1.4 - 4de, 6cdef, 12abgh, 28abcdef, 32ab
- Section 1.5 - 2, 4, 8af
- Assignment 3 (Due: Oct. 3)
- Section 1.5 - 10ad, 12, 16, 20
- Section 1.6 - 4, 6, 8, 14, 15, 24ab
- Assignment 4 (Due: Oct. 10)
- Section 1.7 - 4, 10, 12e, 14e, 22, 24, 28
- Section 1.8 - 8abcd, 10, 16, 22, 28
- Section 2.1 - (read 125-127 on sorting) 4, 11, 16, 34, 52
- Assignment 5 (Due: Oct 17)
- Section 2.2 - 2abd, 10, 14ce
- Section 2.3 - 2, 7a, 8
- Section 2.4 - 6, 8abcd, 10abcd, 18ab, 25, 28abcd, 30 (apply to 28
abcd)
- Assignment 6 (Due: Nov 7)
- Section 3.2 - 4ac, 6ad, 10abe, 15ac, 18ac
- Section 3.3 - 1, 2, 10, 14
- Section 3.4 - 2ad, 4bc, 8ac, 24ab
- Section 3.5 - 2, 4
- Assignment 7 (Due: Nov 14)
- Section 4.1 - 4, 8, 12, 24, 26, 28, 30
- Section 4.2 - 6, 14, 18
- Section 4.3 - 5abc, 6abc, 12abc, 26, 28
- Assignment 8 (Due: Nov 21)
- Section 4.4 - 6, 8, 12, 22b 28b
- Section 4.5 - 4, 10, 20
- Assignment 9 (Due: Nov 28)
- Section 4.5 - 30, 36, 40
- Section 4.6 - 2, 4
- Section 5.1 - 6, 8, 13, 16, 20, 24, 36
- Section 5.2 - 6, 24, 26
The solutions are now avaliable on-line. To see them, see the
ERES
web page (e-Reserve web page) from the library.
The final grade is made up of three components.
- Homework (10%) A homework assignment will be given out
every Friday. It will be due the following Friday at the end of
class. There will be 9 homework assignments per semester.
The homework assignment with the lowest grade will not be counted.
Note: Homework must always be stapled together.
Also, it must be legible enough so that it be read. Failure to do
this will result in 5 points deducted from the assignment.
Homework will have 5 points deducted for every day
(the weekend is counted as one day) that it is late.
Homework can be handed in early by either giving it to me
or by placing it under my office door.
- Tests (2 Midterms, 15% each)
There will be two midterms. The dates of the midterms
are (provisionally):
- October 24, 2002 - Midterm 1
- Feb. 27, 2003 - Midterm 2
- Exams (Mid-year exam 20%, Final Exam 40%)
There will a mid-year exam in December that will be cumulative, and
a final exam in April, that will also be cumulative. The exact dates
will be given later.
- Sept. 8, 2003 - First semester classes begin
- Oct. 13, 2003 - Thanksgiving (no classes)
- Dec. 1, 2003 - First semester classes end
- Jan 5, 2004 - Second semester classes begin
- Feb. 9, 2004 - Last date for course withdrawal without academic
penalty
- Feb. 16-20, 2004 - Reading Week (no classes)
- April 2, 2004 - Second semester classes end
Any course handouts will also be posted to the web.
They will be posted as PDF documents, so make sure you
have Adobe Acroreader installed.
Adam Van Tuyl
URL:
http://flash.lakeheadu.ca/~avantuyl/coures/2003_fall_math1281.html
avantuyl@sleet.lakeheadu.ca