# Math 2090N Winter 2003 Course Information

## Announcements:

• Unofficial grades are now available. They are posted by last 5 digits of student number. To view, click here.

• The exam list for the exam is available. Click for pdf version.
• (Mar 31) Quiz 4 papers will be returned tomorrow in class. Here is some information to help you assess your relative performance.
```Quiz scores:

0.0    0.5    2.0    2.5    3.0    3.5    4.0    4.0    4.0    5.0    6.0
6.0    6.5    7.0    7.5    8.0    8.0    8.0    8.0    8.5    8.5    8.5
8.5    9.0    9.0    9.0    9.0    9.5    9.5    9.5    9.5    9.5    9.5
9.5   10.0   10.0   10.5   10.5   11.0   11.0   11.5   12.0   12.0   12.0
12.0   12.5   13.0   13.5   13.5   14.5   14.5   15.0   15.5   15.5   16.0
16.0   16.0   16.5   17.5   19.0   19.5   20.0   20.0

Descriptive statistics:

N     MEAN   MEDIAN   TRMEAN    STDEV   SEMEAN
63   10.167    9.500   10.149    4.731    0.596

MIN      MAX       Q1       Q3
0.000   20.000    8.000   13.500

Graphical representation:

.
:
.         ::: :     :         .
..   ... .: .  :.. .::: :::: .:.. : :. ::.  .  . .:
+---------+---------+---------+---------+---------+-------
0.0       4.0       8.0      12.0      16.0      20.0
```
• (Mar 22) Review for Quiz 4 should include problems 1 - 15 from the Chapter 14 list. One quiz question will involve Mathematical Induction.

• (Mar 17) Quiz 3 papers will be returned tomorrow in class. Here is some information to help you assess your relative performance.
``` Quiz 3 grades in ascending order:

0.0    1.0    2.0    2.0    2.0    2.0    3.0    3.0    4.0    4.0    4.0
4.0    4.0    5.0    6.0    6.0    6.0    6.0    6.0    6.0    7.0    7.0
7.0    7.0    7.0    7.5    8.0    8.0    8.0    8.0    8.0    8.0    8.5
8.5    8.5    9.0    9.0    9.0    9.0    9.0    9.0    9.5   10.0   10.5
10.5   11.0   11.0   11.5   11.5   12.0   12.0   12.0   12.5   12.5   12.5
13.0   13.0   13.0   13.0   13.0   13.0   13.5   14.0   14.5   15.0   15.0
15.0   15.0   15.0   17.0   17.5   19.0   19.0

N     MEAN   MEDIAN   TRMEAN    STDEV   SEMEAN
73    9.212    9.000    9.154    4.428    0.518

MIN      MAX       Q1       Q3
0.000   19.000    6.000   12.750

.     :  .  :  :          :     .
:    :     :  :  :. :       . .:     :
.  .  :  : :  .  :  :. :: :. .:: :: :: ... :     ..   :
+---------+---------+---------+---------+---------+-------
0.0       3.5       7.0      10.5      14.0      17.5

```
• (Mar 3) Thursday's quiz will cover the introductory material from Chaper 14. You should understand how to do problems 1, 3, 4, 5, 6 from the Chapter 14 list. Note that there is a simpler solution to problem 1 using 14 RP (Extended).

• (Mar 2) A proof of an extension of 14 RP is available in (postscript) and in (pdf).

• (Feb 24) The midterms will be returned tomorrow in class. Here is some information to help you assess your relative performance.
``` Midterm grades in ascending order.

10    14    16    17    21    22    23    24    26    27    28    29    30
31    34    35    35    36    37    37    38    40    41    42    43    43
44    44    44    44    49    51    51    52    52    54    55    56    56
57    57    57    58    58    58    59    60    60    60    61    61    62
62    63    63    64    64    65    65    66    66    66    67    67    68
69    70    70    71    71    72    73    74    74    75    75    77    77
77    78    78    79    79    80    80    82    82    83    88    89    90
95

N     MEAN   MEDIAN   TRMEAN    STDEV   SEMEAN
92    56.01    59.50    56.46    19.93     2.08

MIN      MAX       Q1       Q3
10.00    95.00    41.25    71.00

:        :    .
.    :    :   :: : :. : . .:
.  ... .:..:.: .::..::   .: :::::::::.:.::::::.  .:  .
-----+---------+---------+---------+---------+---------+-
16        32        48        64        80        96
```
• (Feb 12) The Mathematical Induction question on tomorrow's midterm will be on the same level as the examples done in Tuesday's lecture.

• (Feb 10) I have booked an additional room for the midterm on Thursday.
If your family name starts with A - G go to FAC 312 (directions below)
If your family name starts with H - Z go to the classroom, Curtis C.
YOU MUST GO TO THE INDICATED ROOM.

FAC is the Fine Arts Centre which is across from the Student Union. Enter at the Burton Auditorium. You will see a lounge area on the right. Once you enter the lounge area you will be facing the Art Gallery. Take the stairs to the right of the gallery entrance to the 3rd floor. Once on the 3rd floor take the doors to the right. Room 312 is near the end of the hall on your right.

• (Feb 5) I will return the quizzes in class tomorrow. Here is some information which will help you assess your relative performance.
```Quiz 2 grades:

0     0     0     0     0     1     1     2     2     2     3     3     3
3     3     3     4     4     4     5     5     5     5     5     6     6
6     6     7     7     7     7     7     7     7     8     8     8     8
8     8     8     9     9     9     9     9    10    10    10    10    10
10    10    11    11    11    11    11    11    11    11    11    11    12
12    12    13    13    13    13    13    13    14    14    14    14    15
15    15    15    15    15    15    15    16    16    16    17    18    18
19    20    20    20    20

Descriptive statistics for Quiz 2 grades:

N     MEAN   MEDIAN   TRMEAN    STDEV   SEMEAN
96    9.448   10.000    9.395    5.249    0.536

MIN      MAX       Q1       Q3
0.000   20.000    5.250   13.000

:
.  .    . :         :
.      :    .    :  : .  : :    :    :
:    . :  . :  : :  : :  : :  . :  : :  .         :
: :  : :  : :  : :  : :  : :  : :  : :  : .  : .  :
+---------+---------+---------+---------+---------+-------C2
0.0       4.0       8.0      12.0      16.0      20.0
```
• (Jan 26) I have been asked to provide some study guidance for Thursday's quiz. You should be able to use everything on the Chapter 11 list other than (11.12) and (11.23). You should understand how to do problems 1, 2, 3, 4, 5, 10a, 11 from the Chapter 11 exercise list.

• (Jan 19) Quiz performance was extremely poor. The grading scheme for the course has been changed so that the quiz grade is calculated using the best 3 of the 4 quiz grades.

The first problem required a syntactic proof. Please review the posted solutions.
Proofs based on |- 5>0 = true received only part credit.

```Quiz grades in ascending order

0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    1.0
1.0    1.0    1.0    1.0    1.0    1.0    1.0    1.5    2.0    2.0    2.0
2.0    2.0    2.0    2.0    2.0    2.5    3.0    3.0    3.0    3.0    3.0
3.0    3.0    3.0    4.0    4.0    4.0    4.0    4.0    4.0    4.5    4.5
4.5    4.5    4.5    5.0    5.0    5.0    5.0    5.0    5.0    5.5    6.0
6.0    6.0    6.0    6.0    6.0    6.0    6.5    6.5    7.0    7.0    7.0
7.0    7.0    7.0    7.0    8.0    8.0    8.0    8.0    8.5    9.0    9.0
10.0   10.0   10.0   10.0   10.0   10.0   10.0   10.0   10.0   10.5   11.0
11.0   11.0   11.0   11.0   11.0   12.0   12.0   12.0   12.0   12.0   12.0
12.5   13.0   13.0   13.0   13.5   15.0   18.0   19.0   20.0

Descriptive statistics

N     MEAN   MEDIAN   TRMEAN    STDEV   SEMEAN
108    6.222    5.750    5.985    4.578    0.440

MIN      MAX       Q1       Q3
0.000   20.000    2.125   10.000

:                        .
: :  : :       . .       :
: :  : :  :.:  : :       : :  :
: :  : :  :::  : :  :    : :  : .
: : .:.:  ::: .:::  :.:  :.:  :.: .  .       . .  .
+---------+---------+---------+---------+---------+-------C2
0.0       4.0       8.0      12.0      16.0      20.0
```
• You can follow these links to check out the quizzes and tests from last term's 2090
• Quiz 1: September 26, 2002
• Quiz 2: October 31, 2002
• Midterm Test: October 17, 2002    Solutions in postscript or pdf are available.
• Midterm Test: November 21, 2002    Solutions in postscript or pdf are available.
• Lecturer: Eli Brettler
Office: South 508 Ross
Telephone: 736-5250 Extension 66321
E-mail: brettler@mathstat.yorku.ca
WWW: http://www.math.yorku.ca/Who/Faculty/Brettler/
Normal Office hours: M W noon - 1:00 p.m. and by appointment.

Lectures: TR 10:00 - 11:20 CLH C

Tutors: Joy Abramson (M, T) and Tamar Grains (W, R)
Tutorials:

Monday, 12:30 - 1:30 in N501 Ross
Tuesday, 2:30 - 3:30 in N501 Ross
Wednesday, 10:30 - 11:30 in N501 Ross (tentative location)
Thursday, 1:30-2:30 in N501 Ross
Text: Gries and Schneider, A Logical Approach to Discrete Math.

Syllabus: The core consists of Chapters 8 (review), 9 (review), 11, 12, 14.

Homework: Homework will be assigned but will not be collected for grading. Problems will be assigned from the text as well as from the following problem lists.

• 1090 review problems in (postscript)  and  (pdf). Solutions are available in (postscript) and (pdf).

• Chapter 11 problems in (postscript)  and  (pdf). Solutions to the are available in (postscript) and (pdf).

• Chapter 12 problems in (postscript)  and  (pdf). Solutions to are now available in (postscript) and (pdf).

• Chapter 14 problems in (postscript)  and  (pdf). Solutions are available in (postscript) and (pdf).

To view and print pdf you need the free Acrobat reader.

## Evaluation:

 Quizzes January 16, January 30, March 6, March 25 25% (best 3 of 4) Midterm Test February 13 30% Final Exam Examination Period 45%

Note: The quizzes will be approximately 20 minutes in length, the midterm 75 minutes in length, and the exam 180 minutes in length.

Note: There will be no makeups for missed tests or quizzes. If you miss a test and provide a certificate indicating clearly that you were unable to write the test or quiz for reasons beyond your personal control, a grade will be assigned based on final exam performance. Otherwise, the mark for the missed work will be 0.

The last date to drop the course without academic penalty is March 7. It is extremely important to realistically assess your course performance prior to this date.

## Quiz and Midterm Solutions:

• Quiz 1: January 16
Solutions for the WHITE VERSION in postscript and pdf.
Solutions for the BLUE VERSION in postscript and pdf.
• Quiz 2: January 30
Solutions for the WHITE VERSION in postscript and pdf.
Solutions for the BLUE VERSION in postscript and pdf.
• Midterm: February 13
Solutions in postscript and pdf are available.
• Quiz 3: March 6
Solutions for the WHITE VERSION in postscript and pdf.
Solutions for the BLUE VERSION in postscript and pdf.
• Quiz 4: March 25
Solutions for the WHITE VERSION in postscript and pdf.
Solutions for the BLUE VERSION in postscript and pdf.

Resources:

• Professor Ganong's notes supplementing the text's treatment of CONtextual substitution and the extended Leibniz rules.   Click for his CONtextual substitution supplement and his Leibniz supplement

• (* x, y | R : P ) supplement in (postscript)  and   (pdf).

• Chapter 11 supplement in (postscript)  and   (pdf).

• Chapter 11 reference list (which will be used for tests and the exam) in (html) ,   (postscript) and (pdf).

• For some alternative solutions to a Problem of Dow, see Three Variations on a Theme of Dow in (postscript) or (pdf). A fourth variation, provided in a correspondance by David Gries, is available in (pdf).

• Powerset supplement in (html) ,   (postscript)  and   (pdf).

• Chapter 14 supplement in (html) ,   (postscript)  and   (pdf).

• An extension of 14 RP with application to #(S x T) is available in (postscript) and in (pdf).

• Chapter 14 reference list (which will be used for tests and the exam) in (html) ,   (postscript) and (pdf).

• The Chapter 11, 12, 14 list for the exam can be viewed in (postscript) or (pdf).

Elias Brettler