Journals (ongoing, final version December 7): This will be your record of the
problems that you work on in class and your progress on them. You should obtain
a bound notebook that you plan to hand in at the end of the term (because I will
be unable to evaluate ongoing assignments). You should divide this notebook into
sections where you write about the problems that you are assigned and work on
for this class. Your journal will be evaluated at the end of the course and
I will ask you to hand it in on December 7. The journal should: (1) show that you
made progress and solved all or most of the problems you were assigned (2)
demonstrate how you arrived at your solutions by the examples you did and ideas
that you pursued, (3) list resources (including fellow students) you consulted
(4) at the end of the problem, provide a summary which explains the answer to the
question to someone that does not know what the problem is about
(5) your entries should consist of writing which is clear and grammatically correct
(6) explains the most general statement you can make about the question (e.g. if the question is
to explain something about an 8x8 grid, don't just tell
me what the answer is for an 8x8 case, I want to know what happens for an nxn
checkerboard for any positive integer n)
(7) a complete solution should go beyond simply copying what we did in class since I will expect
you to do work on these problems at home and extend beyond what we did together.
Assignments (ongoing, roughly every other week): These will consist of a
small set of problems that I will give you in relation to the topic under discussion.
Usually these few questions will develop after our discussions and will require
you to learn some mathematics and hopefully the assignments will make it easier to see
the relationship between the applications of mathematics and our topic.
Projects (topic title and description due Oct 5 (15%), written versions due Nov 2 (revised due
date Nov 9) (40%
script, 20% math questions/exercises),
final audio version due Nov 23 (revised due date Nov 30 (25%)): This component will consist of an oral and
written report that will be submitted either alone or in pairs. I would prefer if you
work with someone on this project, you will find that it will be easier to learn
new technology of making a podcast with two heads rather than one.
The written component of this assignment is a script of an explanation of
a topic (of your choice) and its connection with mathematics. This should be
accompanied by mathematics exercises that ideally ties math concepts to the topic
of your report (one or two exercises should be fine). I am looking for
you to pick something from everyday life, something that you wouldn't normally
associate with mathematics. I would like you to try to understand your topic
well enough to explain how mathematics is related.
To make this project out of the ordinary, I want it to be submitted
as a podcast and the written component will be the script.
Discussions in class will be similar to the type of projects that I
would like you to explore.
Important Links:
York University Important dates,
Mathematical Moments from the AMS
(ideas for your projects),
Mike's web page.
Other material:
(Sept 14, 2010) Pictures from class :
pic1,
pic2,
pic3,
pic4,
pic5,
pic6,
pic7,
pic8.
(Sept 14, 2010) Videos:
video 1 - queen starting point for discussion,
video 2 - computer generated 3d graphics.
(Sept 21, 2010)
The Binary System,
Wikipedia:
entry on binary or base 2,
Wikipedia:
XOR,
AND,
OR,
NOT,
IMPL.
(Sept 21, 2010)
Assignment #1 - due Oct 5
(Sept 24, 2010)
Problem #2 for your journals that I told you
about Sept 20. We will discuss this Sept 27 class.
(Sept 28, 2010) A copy of the
syllabus that I handed out last week.
(Sept 28, 2010)
My podcast on digital images when you
watch this look for the images which are embedded in it (without a display screen you will only
hear the audio). Here is
the script. Here is my
proposal,
however this one was written after the fact.
(Sept 28, 2010)
Problem #3 - think about this one for Oct 5 class
(Oct 6, 2010)
The audio clip from BBC radio that I played last night. This
is a single episode of a radio program by the author
Simon Singh about the number 7.
He also did
14 other episodes that are all very interesting.
(Oct 6, 2010) The
second assignment that I gave you about modular arithmetic and card shuffling.
Next time I will try and show you what they have to do with each other.
(Oct 6, 2010) Examples of Modular Arithmetic:
Reference 1 (wikibooks: High School Mathematics Extensions/Primes/Modular Arithmetic),
Reference 2 (BetterExplained),
Reference 3 (University of Regina),
Reference 4 (Rutgers),
Refence 5 (Tutor Vista).
(Oct 25, 2010)
The podcast on shuffling
and
the script (see 'announcements' for my
comments about this)
(Oct 25, 2010)
Problem #4 for discussion in class on Oct 26.
(Oct 26, 2010)
Problem #5 for discussion in class on Nov 2.
(Oct 26, 2010)
Assignment #3 - due Nov 16 - (assuming that we have time
to finish Nov 2)
(Nov 7, 2010)
The podcast on cryptography
and
the script.
(Nov 9, 2010)
The podcast on International Banking Account Numbers
and
the script.
(Nov 9, 2010)
Assignment #4 - due Nov 23
(Nov 9, 2010)
Problem #6 - for discussion in class Nov 16.
(Nov 22, 2010)
Problem #7 - for discussion in class Nov 23. 'Square Take Away' from Mason. Too
many things to do so we didn't get to this Nov 23. Will do Nov 30.
(Dec 5, 2010)
Assignment 5 - do problem #1&2 for Dec 7, we will work in groups on the rest.
(Dec 7, 2010)
The recorded experiment from last week - I sped
up the recording a bit so that it doesn't sound like it is in slow motion. It didn't turn out
as good as I would like since the claps seem to drown out the other sounds in the recording.
another experiment with pasted sounds.
(Carmen Plank and Nicole Lee) a podcast on
the mathematics of origami and an application to medicine
Finding Math
in the Folds in MP3
script
exercises
solutions.
(Mary Michael, Sharla Niroopan & Jocelyn Santos) podcast on a facial detection algorithm
podcast in MPEG 4
script and exercises
solutions to exericses.
(Stephanie Colangelo and Sara Russo) podcast on digital and analog hearing aids
podcast MPEG 4
script
exercises
solutions
(Maria Demude) podcast on mathematics and art
podcast MP3
script
exercises
solutions
solutions pt 2
(Sarah Tang and Caroline Wadid) podcast on kidney transplants
video on YouTube
script
exericses
(Mark Fernandez, Kimberly, Vhenus) podcast on digital sound
podcast in MP3
script
exercises
solutions
(Nikole Daws) podcast on Shazam
podcast on YouTube
script
exercises
(Julia Warner, Fatemah Dhirani, Katrina Booth) podcast on digital sound
podcast wav
script and exercises
solutions
(Arthur Frustaci) podcast "Taking the Luck out of Chance, and replacing it with - Math!!"
podcast mp3
script and exercises
solutions
(Dimitrios Kalfopoulos) podcast on computers use of boolean logic
podcast mov
script and exercises
(Jamila Husbands) podcast on music
podcast mp3
script
exercises
solutions
Announcements:
(Sept 14, 2010) The textbook for this course "Thinking Mathematically" currently has a new edition.
If you have a older edition of this textbook it should suffice, however if you find large
differences between editions you may need to let
me know so that I can provide you with missing information.
(Sept 14, 2010) I have some inside sources on Mathematics education events. Here
are two:
Fields
Mathematics Education Forum, next event is
Saturday, September 25, 2010, 10AM - 2PM
Fields Institute, 222 College Street, Toronto.
2010
Mathematics Conference for Elementary Teachers at York
University Wednesday, October 13, 2010
(Sept 24, 2010) Posting from the department: The
following information about detailed online resources covering the
basics of algebra and trigonometry might prove of some use to those
students who are struggling as a result of deficiencies
in their high school backgrounds.
(1) There is a quite extensive set of algebra tutorials, covering
a wide range of topics, maintained by West Texas A&M University.
The URL for the main page of this resource is
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra
though a quicker way to get to this page is via the link on the Bethune
College Math Help page,
http://www.yorku.ca/bethune/math
(2) There is also a detailed online course in Trig basics, which starts
right from the beginning, the URL for the main page of the course being
http://www.yorku.ca/bethune/math/trig.html
(as you can guess from this URL, the Bethune Math Help page has
a link which takes you to the Trig course main page).
Other potentially useful information is also listed on the Bethune
Math Help web page, and further online resources will be added there
as they become available.
(Sept 24, 2010) Katrina Booth is a student in our class and is having a family emergency
and was unable to make it to Tuesday's class.
She would like someone to send her the lecture notes from Tuesday's class if possible. Her
email is katrina_booth@hotmail.com.
(Sept 27, 2010) Don't forget that on October 5 I want your title and a brief outline about your
project that will be due later this term. The title and outline is worth 15% of the total
grade for the project. I have placed a few more details in the description above about
what I expect on this project and now you have a completed example that you can (roughly)
follow as a guide.
You will want to find a partner and
discuss with him/her about the topic you want to cover. Although it does not need to
contain specific details, the connection with mathematics should be clearer than:
"I will look at the algebra/trigometry/calculus related to my subject."
Your outline should make clear how you plan on connecting mathematics with your topic.
I am placing on the web page my first podcast as an example of what I am looking for.
FYI, I included images in my podcast
(a) because it was very easy to do with Garage Band and
(b) because the subject of my podcast was very visual. This
is not a necessary component and might even be very difficult to do if you don't
have access to "Garage Band" on a Mac.
(Sept 27, 2010) Finish the first assignment for Oct 19 (remember that we don't have class
the week of Oct 12) instead of Oct 5 as originally assigned. I will explain the third problem
next time. I will also give you another assignment next week.
(Oct 6, 2010) In case you might be interested in some upcoming conferences for
math educators. The Toronto Educators Association for Mathematics
(TEAMS) is holding a mini-conference Thursday, October 28 4-8pm. (
poster).
Also, the
Grand Valley Mathematics Association
is holding a Fall conference Thursday, November 4, 2010
(Please register by Thursday, October 14) 3:45 - 8:45 p.m in Waterloo.
(Oct 25, 2010) Here is the podcast that I presented on Tuesday night. Remember, this one is
a little more technical than I really liked and really required that you do the
second assignment in advanced to really understand. Even then, I think it was difficult to
follow the calculations. Live and learn.
The podcast on shuffling and the
corresponding
script.
(Oct 25, 2010) The topics that you submitted were mostly good (with a few exceptions
where we clarified those with individuals about those), but there were a few main
issues that I had with the submissions. The first was that you should keep in mind that
you are reporting on the use of mathematics in art, science or elsewhere. This is a
report and I want you to make connections it with a few mathematical exercises. Start to
give thought to what sort of exercises you are going to give. Some of the ones that you
described sound really hard. I want to move the due date for the script back a week.
Nov 2 is just a little
too soon because I want to give you some indication about what I will be marking
for on your scripts in class on Oct 26 and I didn't give them back until Oct 19.
The script and exercises are due Nov 9 and the podcast is due Nov 30.
I have increased the list of "advice" tips in the instructions for the podcast above.
(Oct 25, 2010) The web page did not get changed online until today! Sorry about that. I
had all of these new announcements and files to
add and I just had them changed on my local copy of the webpage. I added a lot of
discussion on the podcast. Make sure you read it and we can discuss it in class
tomorrow.
(Oct 25, 2010) Here is a really good example of what I WISH my podcasts sounded like.
This is a
3 minute story on NPR that is an interview with a scientist that found a formula
for how fast an animal must shake in order to dry off.
(Oct 26, 2010) I will try to tie together all the ideas that we discussed associated
with the thrid assignment next week. I kind of showed you how to do the problems, but
I am fully aware the "why" was a bit opaque in some of these problems. What you should
realize is that every transformation that I did on letters (e.g. add 14 (mod 26), multiply
by 5 (mod 26), multiply by 11 and add 20 (mod 26)) there was a transformation that
reversed the process (e.g. subtract 14 (mod 26), multiply by 21 (mod 26), multiply by 19
and add 10 (mod 26)).
(Nov 7, 2010) For those of you who weren't in class, I moved the due date for the
3rd assignment back a week because we didn't have time to cover the last problem on either
part of the assignment. FYI, the homework is not self-explanatory.
(Nov 9, 2010) I made some changes to my scripts and added some references (not much, but
it is where I got my information). I will recommend the book where I got some of
the information on cryptography. It is by Steven Levy called
Crypto: How the Code Rebels Beat the Government Saving Privacy in the Digital Age
and he tells a really good story.
(Nov 22, 2010) I made the announcement in class last week. It is not necessary to do ALL
of Homework #4 for class this week. Just question number (1). We will do the other
questions in class.
(Nov 29-30, 2010) To hand in your podcast you will need to send me your .mp3 (or other
file format, but I think that mp3 is the preferred way ... so far I've gotten .m4a, .mp3 and .wav
files). One way to do this is by
email. Another way is by giving me a USB drive that I can plug into my computer and
copy the files in class on Tuesday. Make sure that you also send me an electronic
version of your script, exercises and solutions to those exercises (I would like the solutions
in a separate file). I've gotten some podcast submission already and it turned out great!
I will be posting it shortly so have a listen.
(Dec 1, 2010) Your journals are due next week. Follow the instructions above and you will do fine.
If you have any questions on those instructions please email me.
(Dec 1, 2010) Please do question 1 (the survey for the course) and question 2 (find SID (mod 5) + 2
and SID (mod 3) + 7) for next week. We will get in groups to work on these problems.
I have only one other subject for the agenda next week so I am hoping that it is a
light evening.
(Dec 1, 2010) I got bombarded with emails to hand in your podcasts and I am having a hard
time knowing for sure if I haven't missed a file or two. If one of the files
that you sent me does not show up on the webpage please email me and let me know.