The scores in ascending order: 3 4 5 6 7 7 8 8 9 10 10 10 11 12 12 13 13 14 14 14 15 15 16 16 16 17 18 18 19 19 19 19 20 20 20 21 21 21 21 21 21 21 21 21 22 22 23 23 23 23 24 24 24 25 25 26 27 27 27 27 27 27 27 28 28 28 28 28 28 29 29 29 30 30 30 31 31 31 31 32 32 32 34 36 36 37 38 40 Basic descriptive statistics: N MEAN MEDIAN TRMEAN STDEV SEMEAN 88 21.648 21.500 21.700 8.578 0.914 MIN MAX Q1 Q3 3.000 40.000 15.250 28.000 Graphical representation: . : . : :: . . . : .: :. ::. .: . . .. .:: .: .: ::: :. :: ::: :: :. ::: :: : . : .. . -------+---------+---------+---------+---------+---------C2 7.0 14.0 21.0 28.0 35.0 42.0 MTB > nopaper

- (Nov 20) The midterm examination will be written in two rooms.
- If your family name starts with one of letters
**A - G**you must**write in Curtis M.** - If your family name starts with one of letters
**H - Z**you must**write in Curtis C.**

- If your family name starts with one of letters
- (Nov 14) The list provided for next Thursday's midterm will be
the exam list. Click for postscript or for pdf .

You will need all these theorems for the examination,**but not all of them for the midterm next Thursday**.**CLASSES OF RELATIONS will not be tested on the midterm**. - (Nov 7) I will return the quizzes in class today. Here is a brief
statistical summary of the quiz 2 results.
The scores in ascending order. 0.0 2.0 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 4.0 4.0 5.0 5.0 5.0 5.0 5.0 5.0 5.5 6.0 6.0 6.0 6.0 6.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 10.0 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 11.0 11.0 11.0 11.0 11.0 11.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 13.0 13.0 14.0 14.0 14.0 14.0 15.0 15.0 15.0 15.0 Statistical summary of scores. N MEAN MEDIAN TRMEAN STDEV SEMEAN C2 104 8.663 9.000 8.681 3.464 0.340 MIN MAX Q1 Q3 C2 0.000 15.000 6.000 11.000 Graphical representation of scores. . . : : : : : : : : . : . : . : : : : : : . : : : : : : : : : : : : : : : : : : . . : : :. : : : : : . : : : : : +---------+---------+---------+---------+---------+-------C2 0.0 3.0 6.0 9.0 12.0 15.0

- (Nov 1) I have placed the Test 1 papers in a box outside my
office door. A description of the class performance follows. Any
decision as to whether grades are to be scaled will be made by
Tuesday.
The scores in ascending order. 2.0 5.5 5.5 6.0 7.5 7.5 7.5 8.0 8.5 8.5 9.0 10.0 10.0 10.5 10.5 10.5 10.5 11.0 12.0 12.0 14.0 14.0 14.5 15.0 15.0 15.0 15.5 15.5 16.0 16.0 16.5 16.5 17.0 17.5 17.5 17.5 17.5 18.0 18.0 18.5 18.5 19.0 19.0 19.0 19.0 19.0 19.0 19.5 19.5 19.5 19.5 20.5 20.5 21.0 21.0 21.0 21.5 21.5 21.5 21.5 22.0 22.0 22.0 22.5 22.5 22.5 23.0 23.5 23.5 23.5 23.5 23.5 23.5 23.5 24.0 24.0 24.0 24.5 24.5 25.0 25.0 25.5 25.5 26.0 26.0 26.0 26.0 26.0 26.0 26.5 26.5 27.0 27.5 28.0 28.5 28.5 28.5 29.0 29.0 29.0 30.0 33.0 33.0 35.0 35.0 36.0 37.0 37.5 38.0 Basic descriptive statistics. N MEAN MEDIAN TRMEAN STDEV SEMEAN C2 109 20.362 21.000 20.298 7.669 0.735 MIN MAX Q1 Q3 C2 2.000 38.000 15.500 25.500 Visual representation of scores. : . : : : : : : : : : .:::: .:. : :: : . :. ::.::.: :::::::::::::.::::::.: . : :. .: +---------+---------+---------+---------+---------+-------C2 0.0 7.0 14.0 21.0 28.0 35.0

- (Oct 29) The quiz on Thursday will consist of one question on
Mathematical Induction. The problem itself will be about the size of
a set. The set will be defined using an inductive definition. It
will not involve change of variables.

The quiz will have two versions. We will write in the classroom, Curtis C, starting at about 10:50 a.m. - (Oct 15) The midterm examination will be written in two rooms.
- If your family name starts with one of letters
**A - L**you must**write in CSB B.** - If your family name starts with one of letters
**M - Z**you must**write in Curtis C.**

- If your family name starts with one of letters
- (Oct 10) Click for last summer's midterm (with solutions). This should give you some idea of what to expect in terms of coverage, level of difficulty, etc., on your test next week. Keep in mind that your test necessarily will be shorter.
- (Oct 2) I will return the quizzes in class tomorrow. Here is a brief statistical summary of the quiz 1
results:
These are the quiz scores in ascending order. 0.0 0.0 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.5 1.5 1.5 1.5 1.5 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.5 2.5 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.5 4.0 4.0 4.0 4.0 5.0 5.0 5.5 5.5 6.0 6.0 6.0 6.0 6.5 6.5 6.5 7.0 7.0 7.0 7.0 7.0 7.5 7.5 7.5 7.5 8.0 8.0 8.0 8.0 8.5 8.5 8.5 8.5 9.0 9.0 9.0 10.0 10.0 10.0 10.0 10.0 11.0 11.0 11.0 11.0 11.5 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.5 13.0 13.5 13.5 13.5 14.0 14.0 14.0 15.0 15.0 15.0 15.0 16.0 16.0 16.0 16.5 17.0 17.0 17.5 17.5 17.5 18.0 18.0 18.0 18.0 18.5 19.0 19.0 19.0 19.0 19.0 19.0 20.0 20.0 20.0 20.0 20.0 This describes the distribution of scores. N MEAN MEDIAN TRMEAN STDEV SEMEAN C2 122 9.102 8.250 8.986 6.136 0.555 MIN MAX Q1 Q3 C2 0.000 20.000 3.000 14.000 This gives a visual representation of the distribution of scores. . . . . : .: : . . : : . : :: : : :.: :::. : : : .. : . .: : : ::: :::: .: : :::: :::: : : .:.. :: : :.: ::.: : +---------+---------+---------+---------+---------+-------C2 0.0 4.0 8.0 12.0 16.0 20.0

- (Sep 18) Tutorial times and locations are Monday 12:30 - 1:30 in
N 501 Ross, Tuesday
12:30 -1:30 in N501 Ross, Thursday 12:30 - 1:30 in N 501.
**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:**MW 12:00 noon - 1:00 p.m. and by appointment.**Lectures:**TR 10:00 - 11:20 CLH C**Tutor:**T.B.A.

**Tutorials:**Monday 12:30 - 1:30 in N 501 Ross, Tuesday 12:30 -1:30 in N501 Ross, Thursday 12:30 - 1:30 in N 501 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 September 26, October 31 20% Midterm Tests October 17, November 21 40% Final Exam Examination Period 40% **Note:**The quizzes will be 30 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 November 8. It is extremely important to realistically assess your course performance prior to this date.

**Quiz and Midterm Solutions** - Quiz 1: September 26
- Solutions to Version 1 (blue) in (postscript) and (pdf).
- Solutions to Version 2 (white) in (postscript) and (pdf).

- Quiz 2: October 31
- Solutions to Version 1 (white) in (postscript) and (pdf).
- Solutions to Version 2 (pink) in (postscript) and (pdf).

- Midterm Test: October 17 Solutions in postscript or pdf are available.
- Midterm Test: November 21 Solutions in postscript or pdf are available.
**Resources:** - Professor Ganong's notes supplementing
the text's treatment of
*CON*textual substitution and the extended Leibniz rules.

Click for his*CON*textual substitution supplement and his Leibniz supplement - (*
*x, y*|*R*:*P*) supplement in (postscript) and (pdf). - Chapter 11 supplement in (html)
, (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).
- 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 Last modified: Thu Jan 2 12:57:30 EST 2003