Home Page for Math 1C03: Introduction to Mathematical Reasoning 2006-2007



Textbook:  1) Sets, functions and logic: an introduction to abstract mathematics,  3rd edition, Keith Devlin, Chapman & Hall/CRC.
2) The Millenium Problems, Keith Devlin, Basic Books.

Course objective: The goals of this course are threefold. First, to learn the basic language and underlying logical tools of advanced mathematics. Second, to begin to get a glimpse of the character of advanced mathematics - the kind of questions one can ask, and the mathematics needed to answer them. Finally, to learn to communicate about mathematics.

Instructor: Dr. D. Haskell, HH316, ext.27244
Course meeting time: MWR 10:30 - 11:20
E-mail: haskell@math.mcmaster.ca
Office hours: Mondays 11:30-13:00, Wednesdays 13:00-14:30

Course requirements, in brief (consult the  course information sheet  for more detailed information).
Homework: 30%  
Midterm: 20%
Class participation: 5%
Presentation: 15%
Final: 30%

ANNOUNCEMENTS

4 April 2007: The precise wording for the two essay questions which will be on the final exam is as follows:
1) [20 points] Write a short description (1--2 pages) of one of the Millennium Problems. Your account of it should include the name and an approximate statement of the problem, some background explaining the terminology used in the statement, and some context on why the problem is important.

2) [10 points] Write a short description (1/2--1 page) of one of the student presentations. Your account should focus on the mathematics that was presented, not on the structure of the talk. Indicate clearly which presentation you are describing. You may not choose your own presentation, nor a presentation on the same book that you read.

The exam will also include more technical questions, similar to the midterm.

4 April 2007: Notes for the Millenium problem lectures are posted with the appropriate lecture on the course calendar below.

2 April 2007: Solutions to homework assignments 5 and 6 are posted below.

18 March 2007: Homework 6 is posted below.

9 March 2007: The presentation assessment form is posted here. We will discuss it in class on Monday.

5 March 2007: At popular request, solutions to the midterm practice problems are here.

1 March 2007: Solutions to the first four homework assignments are posted below.

25 February 2007: The midterm will be held in JHE A102 on Tuesday, 6 March 19:15-20:15. Students with a conflict at this time should let me know immediately. The exam will cover the kind of problems that you have been doing for homework up until now. Some sample problems can be found here.

15 February 2007: There will be two invited talks in the week after Reading Week. All the material for the homework due that Thursday has been covered in lectures already.

12 February 2007: As discussed in class today, a help session will be run every Tuesday 11:30-12:20 in BSB/B138 by George Dragomir. I have not had confirmation from George for this week, so I do not know for certain if he will be there tomorrow. If I am free, I will come along myself to answer questions.

11 February 2007: Here  Assignments 4 and 5 are now posted. The due dates have been changed to perserve two weeks between assignments. See the calendar below.

11 February 2007: DATE of MIDTERM 1 has been changed by one week and one day. It is now tentatively scheduled for the evening of Tuesday, March 6. Please let me know at once if this represents a conflict.

29 January 2007: Here is the reading list again. You should tell me before Friday, February 16 on what book you plan to present.

28 January 2007: Homework 3 is posted and the calendar has been updated.

24 January 2007: Problem 9 in section 3.1 is written somewhat ambiguously, though the ambiguity is hidden in the notation.  The problem should say: "prove that A is a subset of B" and not "prove that A is a proper subset of B".

16 January 2007: Due to the cancellation of class on Monday, 15 January, there is a slight modification to Homework assignment 2; the problem from section 3.3 has been moved to Homework 3.

8 January 2007: I made a mistake in class today: I said that the converse of an implication is the negation. This is not correct. The converse of
A implies B
is the implication in the other direction; that is,
B implies A.
Thus the converse of "if Karl plays then the team wins" is "if the team wins then Karl plays".
Notice that the truth value of the converse is NOT the same as the truth value of the orginal implication (nor of its negation).
Sorry about the mistake.

Assignment dates and midterm dates are still tentative. Actual test dates and assignment due dates will be announced in class and posted on this website at least one week in advance.

Homework due dates are tentative and subject to change.

Homework 1:  due Thursday January 11    SOLUTIONS
sec 2.1 p19: 1b, 2a,b,c,d
sec 2.2 p26: 2, 3, 4, 9a, 11, 13, 14, 15d,f
sec 2.3 p32: 1b, 2a, 3a,d, 4
sec 2.4 p39: 1b,f,j, 2b,d,i,j,k,o,p, 3b,f,j, 5, 6

Challenge problems (extra credit): 
sec 2.2: 20, 21, 22,
sec 2.3: 7
sec 2.4: 7

Homework 2: due Thursday January 25   SOLUTIONS
sec 2.5 p48: 1g,h,i, 2, 6, 7b, 8b
sec 2.6 p53: 1(iii),(vii), 6
sec 3.1 p60: 1, 2, 9
sec 3.2 p66: 8, 9, 10, 12, 13

Challenge problems:
sec 2.5: 4
sec 2.6: 3, 4
sec 3.1: 11
 
Homework 3: due Thursday February 8     SOLUTIONS
sec 3.3 p69: 1
sec 3.5 p74: 1
sec 3.6 p78: 3, 4, 5
sec 3.7 p80: 2, 6
sec 4.2 p92: 3, 6
sec 4.4 p98: 6, 7, 9

Challenge problems:
sec 3.8 p85: 1, 2
sec 4.4 p98: 14


Homework 4: due Thursday March 1        SOLUTIONS
sec 4.5 p102: 5, 9
sec 4.6 p107: 4, 5, 8, 9
sec 4.7 p111: 2, 5

Homework 5: due Thursday March 15      SOLUTIONS
 sec 5.2 p117: 5, 7, 13
sec 5.3 p120: 1c, 2b, 5a,e, 7
sec 5.5 p125: 4, 8, 10


Homework 6: due Thursday, March 29      SOLUTIONS
sec 5.6 p128: 1defg, 2b,c
sec 5.8 p133: 2, 3, 4
sec 5.9 p136: 2, 5

Challenge problems:
sec 5.6: 5
sec 5.9: 6

Planned course schedule (subject to revision):  

BE PREPARED:  Read the scheduled sections of the textbook before the class.


Dates
  Monday  Wednesday
  Thursday Homework
 Comments
Jan 1-5
 NO CLASS
 Introduction
 SFL: 2.1, 2.2
 sec 2.1 p19: 1b, 2a,b,c,d
sec 2.2 p26: 2, 3, 4, 9a, 11, 13, 14, 15d,f
Jan 8-12
 SFL; 2.3
 SFL: 2.4
SFL: 2.5
Homework due
 sec 2.3 p32: 1b, 2a, 3a,d, 4
sec 2.4 p39: 1b,f,j, 2b,d,i,j,k,o,p, 3b,f,j, 5, 6
Jan 15-18
 SFL: 2.6
snow day
 SFL: 3.1, 3.2
2.5 		SFL: 3.3, 3.4
2.6
sec 2.5 p48: 1g,h,i, 2, 6, 7b, 8b
sec 2.6 p53: 1(iii),(vii), 6
sec 3.1 p60: 1, 2, 9 		Read CH 6 of TMP in preparation for Dr Sharifi's talk.
Jan 22-26
 SFL: 3.5
2.6, 3.1
 Dr R. Sharifi: The Birch and Swinnerton-Dyer Conjecture
lecture notes
 SFL: 3.6, 3.7
3.1, 3.2
Homework due
 sec 3.2 p66: 8, 9, 10, 12, 13
 Read Ch 3 of TMP in preparation for Dr Haskell's talk
Jan 29 - Feb 2
 SFL: 4.1, 4.2, 4.3,
3.3, 3.4, 3.5
Dr D. Haskell:  The P vs NP problem
lecture notes
 SFL: 4.4
3.6, 3.7
sec 3.3 p69: 1
sec 3.5 p74: 1
sec 3.6 p78: 3, 4, 5
sec 3.7 p80: 2, 6
 Read Ch 7 of TMP in preparation for Dr Hambleton's talk
Feb 5-9
 SFL: 4.5
4.1, 4.2, 4.3, 4.4
 Dr I. Hambleton: The Hodge Conjecture
lecture notes
 SFL 4.6
4.5
Homework due 		sec 4.2 p92: 3, 6
sec 4.4 p98: 6, 7, 9 		Read Ch 1 of TMP in preparation for Dr Kolster's talk
Feb 12-16 SFL: 4.6, 4.7
 Dr M. Kolster: The Riemann Hypothesis
snow day
 SFL: 4.7 sec 4.5 p102: 5, 9
sec 4.6 p107: 4, 5, 8, 9
sec 4.7 p111: 2, 5 		Inform me BEFORE reading week of the book you plan to read for your presentation
Feb 19-23
 READING WEEK
 READING WEEK READING WEEK
Read Ch 4 of TMP in preparation for Dr Craig's talk
Feb 26 - Mar 2
 Dr M. Kolster: The Riemann Hypothesis
lecture notes
 Dr W. Craig: The Navier-Stokes Equations
lecture notes
 SFL: 5.1, 5.2
Homework due
 sec 5.2 p117: 5, 7, 13 Read Ch 2 of TMP in preparation for Dr Hurd's talk
Mar 5-9
 SFL: 5.3, 5.4
MIDTERM (Tuesday evening)
 Dr T. Hurd: Yang-Mills theory and the Mass Gap Hypothesis
lecture notes
 SFL: 5.5

 sec 5.3 p120: 1c, 2b, 5a,e, 7
sec 5.5 p125: 4, 8, 10 		Read Ch 5 of TMP in preparation for Dr Min-Oo's talk
Mar 12-16
 SFL: 5.5, 5.6
 Dr M. Min-Oo: The Poincare Conjecture
lecture notes
 SFL: 5.7
Homework due
By now, you should have finished reading your chosen book, and started planning your presentation.
Mar 19-23
 SFL: 5.8
 SFL: 5.9
 Student Lectures

Mar 26-30
 Student Lectures Student Lectures Student Lectures
Homework due

Apr 2-6
 Student Lectures Student Lectures Conclusions