Home Page for Math 1C03: Introduction to Mathematical Reasoning 2007-2008

Textbook:  1) How to prove it: A structured approach,  2nd edition, Daniel J. Velleman, Cambridge University Press.
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: Tuesdays 13:00-14:30, Thursdays 9:00-10:30

TA: Jonah Horowitz. Office hours: Tuesday 16:30-17:30 in the Math Help Centre

Course requirements, in brief (consult the  course information sheet  for more detailed information).
Homework: 25%  
Midterm: 20%
Presentation: 15%
Final: 40%


15 April 2008 Some mistakes in the file with term marks; I have taken it offline until it is fixed.

15 April 2008 Marks for all the assignments, midterm and presentation are given here: term marks. Recall that the homework counts 25%, the midterm counts 20%, the presentation counts 15% and the final exam (marked out of 60) counts 40%. Let me know by Wednesday, April 16 at the latest, if there are any mistakes in the marks.

7 April 2008 I incorrectly announced in class today that there was a homework for Wednesday. This is not the case; my apologies. Solutions to the last two homeworks are posted below.

7 April 2008 A copy of last year's final exam is posted here for you to look over. Solutions will not be posted; I will talk about this exam in class on Wednesday. Note that Part II will be identical on this year's exam.

21 March 2008 Solutions to assignments 8 and 9 are now posted. Homeworks until the end of term are posted. Please review the schedule of presentations, as it has been changed.

12 March 2008 Solutions to assignment 7 are now posted. The deadline for the assignment due March 19 is postponed to March 20.

6 March 2008 Homework for March 12 and 19 is now posted.

28 February 2008 Marks on the midterm, as well as all the assignments marks so far are posted here. Please check that all of your marks are recorded correctly. Midterms will be returned in class on Monday. The average mark on the midterm was 20/30.

26 February 2008 The schedule for presentations as it exists so far is given below. Please check, as the scheduled times are not identical to the requested times in the sign-up sheet. If you are currently planning to work by yourself, please consider joining up with a couple of other singles, as the schedule is very tight. There are still ten people on the classlist who do not have a presentation time. Please contact me if  you are one of those people! Also, if you do not yet have a topic listed, please tell me what book you will be reading.

19 February 2008 The midterm will be on Wednesday, February 27, in REF 102, 19:15-20:45. It will cover through to the end of Chapter 3 of "How to prove it".  The problems will be very similar to the homework. Indeed, one problem will be taken verbatim from the list of recommended problems. The best way to study for the midterm is to do as many problems as you can from the textbook.

19 February 2008 The preliminary schedule for student presentations is posted below the course calendar. I will bring a sign-up sheet to class on Monday, or you can email me before Monday to request a particular time.

5 February 2008 Homework problems for Feb 13 are now posted below.

5 February 2008 The reading list is now posted. You should choose a book, either from the list or elsewhere, and let me know what book you plan to read, and the group you are working with. Presentations will start the week after Reading Week, so you should start preparing!

29 January 2008 Notes for Dr Valeriote's talk are posted below. Jonah's office hours are posted above. I will be away on Thursday 31 Jan, but Jonah will teach the class. Office hours are cancelled that day.

27 January 2008 The second guest lecture on the Millenium Problems is this week. Please read the chapter on the Birch Swinnerton-Dyer conjecture before Wednesday.

20 January 2008 Problems for this week's homework are now posted. My apologies for the lateness.

20 January 2008 The first guest lecture on the Millenium Problems is this week. Please read the introduction and the chapter on P versus NP before Wednesday.

COURSE CALENDAR (subject to revision)

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

 Monday Homework
due Wednesday
 Wednesday Thursday Comments
Jan 7 - 11 Introduction
p.6: 2
Intro p6: 1, 3
sec 1.1 p13: 1, 2, 6
sec 1.1, 1.2
sec 1.3

Jan 14 - 18
sec 1.4, 1.5
sec 1.2 p24: 8
sec 1.3 p33: 8
sec 1.5 p53: 3
sec 1.2 p24: 5, 11, 16
sec 1.3 p33: 4, 5
sec 1.4 p42: 8, 9
sec 1.5 p53: 9, 10
sec 2.1
sec 2.2

Jan 21 - 25
sec 2.3
sec 2.1 p63: 8
sec 2.2 p72: 10
sec 2.3 p81: 6
sec 2.1 p63: 3, 5, 7
sec 2.2 p72: 9
sec 2.3 p81: 1, 4, 11
Guest Lecture
P vs NP
Dr. M. Valeriote
sec 3.1
Question 15 from sec 2.3 explains
Russell's Paradox; an issue that helped
to make rigorous the foundations of set theory. Challenge: work through this problem to understand the paradox.
Jan 28 - Feb 1
sec 3.1
sec 3.1 p93: 15, 16
sec 3.1 p93: 1, 9, 11, 13
Guest Lecture
Birch Swinnerton-Dyer
Dr. R. Sharifi
sec 3.2

Feb 4 - 8
sec 3.2
sec 3.2 p106: 7, 12
sec 3.2 p106: 1, 3, 5, 8
Guest Lecture
Hodge Conjecture
Dr. I. Hambleton
sec 3.3

Feb 11 - 15
sec 3.4
sec 3.3 p121: 18
sec 3.4 p133: 10, 11
sec 3.2 p121: 5, 6, 12, 19, 22, 24
sec 3.3 p133: 9, 12, 17, 22, 26
Guest Lecture
Dr. W. Craig
sec 3.5, 3.6

Feb 18 - 22

Feb 25 - 29
no homework - midterm
sec 3.5 p143: 8, 11, 26, 30
sec 3.6 p153: 1, 3, 5
Guest Lecture
Riemann Hypothesis
Dr M. Agarwal
sec 4.1, 4.2
Midterm 27 Feb
Mar 2 - 7
sec 4.3 sec 3.5 p143: 12
sec 4.2 p179: 9
sec 4.1 p170: 3, 12
sec 4.2 p179: 1, 2, 7
sec 4.6
sec 4.6
Mar 10-14
Student presentations sec 4.3 p188: 19
sec 4.6 223: 14
sec 4.3 p188: 12, 13, 14
sec 4.6 p223: 2, 6, 13,
Guest Lecture
Poincare Conjecture
Dr. M. Min-Oo
Student presentations
Mar 17 -21
Guest Lecture
Mass Gap Hypothesis
Dr. T. Hurd
sec 5.1 p234: 11
due Thursday
sec 5.1 p235: 12, 16
sec 5.1, 5.2, 5.3 Student presentations
Mar 24 - 28
sec 5.3
sec 6.1
sec 5.2 p243: 9, 15
sec 5.3 p252: 6
sec 5.2 p 243:6, 7, 11, 16
sec 5.3 p255: 12, 13
sec 6.2
Student presentations
Mar 31 - Apr 4
sec 6.4
sec 6.1 p265: 6, 12
sec 6.4 p296: 4
sec 6.1 p265: 3, 5, 13
sec 6.4 p296:3, 16, 17
Student presentations Student presentations
Apr 7 - 11
Student presentations


 Student presentation schedule (tentative)

10 March
Richard Kohar
Mike Heenan
Mahmoud Sharkawi
Clarence Prince, Melissa Cortina

Does God Play Dice?
Chaos: Making a new science
Prime Obsession
From Zero to Infinity

13 March
Andy Lovric, Riyaad Dinath, Srinithi Raghavan
Laura Chiarelli, Stephanie Dore and Meggie MacDougall
Maria Campanella, Danielle Nellich, Rochelle Quinn
From Zero to Infinity
The Math Gene
Chance and Chaos
20 March
WeiLiang Huang, LuYi Wang, Long Zheng, Mei Wang
Kam Lau, Yat Lau
Chelsia Baral, Moyeed Hussain
From Zero to Infinity
Four Colors Suffice
On the nature of space and time
27 March
Chelsia Baral, Moyeed Hussain
Daniela Margani, Allison Watson, Natalie Manzarpour,  Malorie Bell
Eamon Kavanagh, Olivia Sacco, Alyssa Burns

On the nature of space and time
Prime Obsession
Chance and Chaos

2 April
Allison MacDonald
Alex Petersen, Nathan Krueger, Liu Yang,  Wei Deng
Anthony Sinclair, Brad Han, Kelvin Wong, Shawn Harris
Sebastian Barinas
A brief history of time
Music of the Primes
A brief history of time
Four Colors Suffice
3 April
Nicholas Policelli
Sarah Seeley, Tim Hurley
Daryl Abbs, Matt Lappin
David Scarff
Axiom of choice
A brief history of time
Letters to a young mathematician
Evolutionary Dynamics
7 April
Daina Collet, Matthew Coles, Ryan Cuddy, Caitlin Daly
Tony Ho Ting Kan, Thanh Lemai, Dai Sun, Zhao To
Stephanie Chau, Suyeon Hwang, Ken Tam, Nicolas Mikhaili

Does God Play Dice?
The Nature of Space and Time
From Zero to Infinity
9 April
Minyoung Oh