Instructor: Dr. D. Haskell, HH316, ext.27244
Course meeting time: MWR 10:30  11:20
Email: haskell@math.mcmaster.ca
Office hours: Tuesdays 13:0014:30, Thursdays 9:0010:30
TA: Jonah Horowitz. Office hours: Tuesday 16:3017:30 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%
ANNOUNCEMENTS
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 signup
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, 19:1520:45. 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 signup 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 SwinnertonDyer 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)
Dates 
Monday  Homework
due Wednesday 
Recommended Problems 
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 solutions 
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 solutions 
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 notes 
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 solutions 
sec 3.1
p93: 1, 9, 11, 13 
Guest Lecture Birch SwinnertonDyer Dr. R. Sharifi 
sec 3.2 

Feb 4  8 
sec 3.2 
sec 3.2 p106: 7, 12 solutions 
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 solutions 
sec 3.2
p121: 5, 6, 12, 19, 22, 24 sec 3.3 p133: 9, 12, 17, 22, 26 
Guest Lecture NavierStokes Dr. W. Craig 
sec 3.5, 3.6 

Feb 18  22 
READING WEEK 
READING WEEK 
READING WEEK  
Feb 25  29 
review 
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 19:1520:45 
Mar 2  7 
sec 4.3  sec 3.5 p143: 12 sec 4.2 p179: 9 solutions 
sec 4.1 p170: 3, 12 sec 4.2 p179: 1, 2, 7 
sec 4.6 
sec 4.6  
Mar 1014 
Student presentations  sec 4.3 p188: 19 sec 4.6 223: 14 solutions 
sec 4.3 p188: 12, 13, 14 sec 4.6 p223: 2, 6, 13, 
Guest Lecture Poincare Conjecture Dr. M. MinOo 
Student presentations  
Mar 17 21 
Guest Lecture Mass Gap Hypothesis Dr. T. Hurd 
sec 5.1 p234: 11 due Thursday solutions 
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 solutions 
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 solutions 
sec 6.1 p265: 3, 5, 13 sec 6.4 p296:3, 16, 17 
Student presentations  Student presentations  
Apr 7  11 
Student presentations  Conclusions 
Student presentation schedule (tentative)
When 
Who 
What 
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 