**Welcome to the class!
Class announcements and useful documents will appear here. New
material will be added at the top. Make it a habit to look here.**

**My
office is MB240A. I have M287 (Communication in Mathematics) 12-2 pm
T/Th and M406 (Number Theory) 10:30-11:45 am WF. I have logic seminar
on Tuesdays at 2 pm. My official office hours will be 10:30-11:45
T/Th and 3:15-4:45 T/W/Th/F effective immediately. Students should be
warned that afternoon department meetings or colloquium talks may
cause 3:15 office hours to be cancelled; I will provide notification
of this on my door, and will try to provide other notification online
when I can. I will very likely not be on campus on Mondays; on the
other four weekdays I will usually be on campus from 10:30 (or
possibly earlier) to 5. If I am in my office I will usually be
available to you.**

**Announcement:****
****During the last
two weeks of class Dr. Coskey will lead activities, as I need surgery
soon after April 25**^{th}**.
I will be assigning final grades in the class, but I will be doing
this from home later.**

**Unit 4 will officially
be due (a lab report in the style of Units 1 or 3, and you may tell
me in email where I should find relevant Sage files recording your
experiments) at the ****beginning****
****of class
Tuesday the 29**^{th}**.
I will evaluate these labs when I am computing your final grades
after I am out of the hospital. Dr. Coskey should not be spending
class time on Lab 4. I will be looking for evidence of activity
and quality of writeup more than completeness; there is plenty of
material in this lab, and a final version would contain even more,
and I know we have not spent that long on it. ****Be
sure to turn in your individual proofs for Question 1 along with your
lab reports. **

**Also be sure to bring your clickers this Thursday. I
shall try to do a brief intro to them so that Dr Coskey can start out
quickly with the lab he will do with you starting next week.**

**Here
is the text for Lab 4 (now complete). I am quite deliberately going
to release it bit by bit rather than all at once (there are places
where I want you to discover things which I will say openly later).
The text may be a bit longer by Tuesday (when you will be able to
start) or Thursday (when we will all start) but I won't show my whole
hand all at once. You can also look at my Lab 4 file on Sage; please
make your own copy rather than editing mine, of course. There is
quite a lot more in the Sage file than in the lab text!**

**You may notice that I
have cleaned up the files in the public Math 287 project. I have left
files there that I identify as belonging to particular people, but
please make a habit of keeping your working files in separate
projects shared with your group members (and me).**

**The
book seems to be out of print. Please order a copy of ***Laboratories
for Mathematical Experimentation, a bridge to higher mathematics***,
authors Cobb et. al. ISBN 0-387-94922-4 from Amazon or another used
book outlet online. The statement on the shelf at the bookstore that
the text is available as a free download is as far as I know
incorrect.**

**Please do get a clicker.
This was something the original instructor ordered for the class; he
no doubt had some ideas of how to use it: I have a general idea about
this and no doubt will develop specific ideas.**

**If you have a laptop
computer please bring it with you. I want to know whether people can
reliably connect to the university wireless in the room. It is not
necessary for everyone in the class to have a computer, but it is
advisable for the activities we have in mind to have a computer for
at least one student in each working group. I need to know what our
tech situation is right at the outset so that we can take any special
measures that are needed promptly.**

**It is a good idea to set
up your free Sage account (see links below) before the first session.**

**You should have a lab notebook dedicated to this class.**

**page 1 in the book. The
computer code in the book is ancient, to be replaced by code supplied
in my Sage project (which you can see that I have copied from Dr.
Coskey; correct attribution of sources is important!)**

**http://math.boisestate.edu/m287/lab-1-iteration-of-linear-functions/
on Dr Coskey's site**

**My code project in Sage
is at **

**You will need to make a
free Sage account to access this, and you should copy the code I
provide into your own Lab I Sage project.**

**We will start working on
this in class as soon as we can (hopefully on day 1). I am not
setting due dates until I see how the first day goes. More details of
what is expected as a final product to appear!**

**What you should be doing
is addressing the questions one by one in your lab group (somewhere
between two and four students). You need to write something down in
connection with each question. ****You should
have a place to write things down: that is, you should have a lab
notebook for this class.**** ****This
should be some English (complete sentences) supported by evidence
which you will describe (Sage computation of examples, a general
algebraic computation that ought to work in all cases, an actual
proof) for your answer to each question. This class is about
communication: you are investigating a mathematical problem and
communicating to me and/or your colleagues in your group and/or your
colleagues in the whole class both what your solution is and what
evidence you have for it. The process of investigation and reporting
of results is just as important or more important than the specific
content.**

**http://www.sagemath.org/
is the home of the online SAGE computer algebra system, which we will
be using as a resource.**

**https://www.writelatex.com/
is the home of an online LaTeX editor. We will be learning LaTeX in
this class, as this typesetting program is in effect the standard for
mathematical communication. There is also a LaTeX environment
integrated into SAGE.**

**The
manual of logical style This is a document about proof style
which I have been working on for many years and which exists in
multiple versions. It will need revisions for use in this course, I
am certain, which will be manifested here.**

** ****http://math.boisestate.edu/m287/****
****Dr. Coskey's
WordPress site for his past offering of Math 287. We will have our
own WordPress site soon. I like his syllabus and his rubric for Lab
Reports; take a look at these; I will have to make my own rubric for
lab reports in due course.**

**You may notice that I
have taken this straight from Dr. Coskey's class resources. I may
make revisions to this as I see how the class goes.**

**Most
of the actual investigation and experimentation will be done during
class time. For homework, you will be asked to document the results
of your experiments in the form of a lab report. Make sure that
you ***keep
a notebook*** ****for
your classroom experiments so you can still reference them when you
go home to write up your report!**

Lab reports consist of at least three sections, outlined below. In the Introduction, the textbook describes one possible layout for your write-ups. You may follow their advice, or alternatively, mine here:

*Section
1*: Begin by writing an introduction explaining the topic of the
module. Assume that your audience is somebody who is familiar with
mathematical language, but not necessarily with this particular
topic. Be sure to include motivation for studying this topic, either
from the text or from your own thoughts. Write careful definitions
for any of the fundamental concepts used in the module (again,
remember your audience). Finally, preview some of the questions you
will be addressing in the upcoming sections.

*Section
2*: In this section, describe the technical results of your
investigations. Results come in three types: examples and
counterexamples, conjectures supported by experimental evidence, and
theorems supported by formal proof. Provide context for each of your
results, giving thought to the order in which you give them and the
transitions between them. Try to state each result as a mathematical
statement using language which is as precise as possible. Sometimes,
you have more results than you have space to write up, and in that
case choose the most important ones. Be sure to include at least one
formal proof in this section.

*Section
3*:
In the last section, summarize the state of your progress on this
line of research from a very high level. Always include material for
further research—it is impossible to answer *everything* in
one go! What were the questions you were unable to answer, and why
are they important to you? Did you make any further conjectures that
you are currently unable to support with solid evidence or proof?

Your labs will be assessed on the following four criteria:

*Exposition*:
The quality and effectiveness of your writing, not including proofs.
Includes introduction and motivation, presentation of results, style,
structure, and clarity throughout.

*Proofs*:
The quality and clarity of your technical mathematical writing, that
is, the statements of results and definitions and the proofs of
results.

*Depth*:
The strength and completeness of your experimental and theoretical
results, scientifically speaking.

*Synthesis*:
How well you conveyed understanding of the results and goals of the
lab as a whole. This can be done in many ways, including: summarizing
results, motivating and asking questions, making conjectures, and
drawing connections between the results, evidence, and conjectures.

**We are currently working
on Unit 2 on logic and proof. I would like any proof write-ups from
the first couple of days turned in by Tuesday the 25**^{th}**.
I will have the ones that I have in hand from the 18**^{th}**
****reviewed and back
to you on the 25**^{th}**
****(I was distracted
with getting the computer lab ready).**

**Here
is the promised summary of what is required. I expect in-class work
on this unit to be finished by Thursday March 6, though I may accept
computer submissions longer than that. This isnt a guarantee, of
course: it depends on how things go.**

**Here is the Python
source code pythonmarcel.py
for the theorem prover. I may make improvements: I will advise you if
you should download a new version. (As of 2/25/2014, you should
download the new version – it has much better display, spaces
added for readability and no dots! 2/27/2014 there is a minor
improvement to the display)**

**I have reorganized the
actual Lab 2 file in the shared Sage project so that it looks like a
tutorial more or less following what we did in class, and added some
helpful notes. The actual assigned work is preserved in comments at
the front. Notice that there are also some writing exercises. I will
do at least one more extensive demonstration proof.**

**We are not in a hurry;
we may spend a couple of days working with the software giving you
time to get friendly with it, and there will be more discussion of
format for proofs in English:**

**The
manual of logical style This is a document about proof style
which I have been working on for many years and which exists in
multiple versions. It will need revisions for use in this course, I
am certain, which will be manifested here.**

**here
is the document with the axioms for the inclass proof writing
exercises.**

**Currently, we are in the
middle of Lab 3. By request from the class, I have moved the due date
for Lab 3 to end of class on Tuesday April 8**^{th}**.
The report on Lab 3 should be of the same general kind as the report
on Lab 1: I am especially interested in statistics and graphs giving
summaries of your numerical experiments, in this lab.**

**I have not made a formal
requirement that you turn in a draft, but if you do turn in a draft
of your project materials before the end of the day Thursday the 3**^{rd}**,
I will review it and get comments back to you before the weekend.**

**There is an additional
proof question which you may work on (easier than question 5 I would
say): show that if you take two steps of the Euclidean algorithm the
remainder you get will be reduced by a factor of more than 2 (will be
cut in half and then some). This fact tells you something about why
the algorithm is fast (and perhaps about what kind of function of N
the number of steps to compute the gcd of two numbers less than N
will be). Here are the
notes on this.**

**I believe that everyone
understands how to retune Euclid1 to return the gcd value instead of
the number of steps: I do point out that you could actually make
separate copies of the functions Euclid1 to Euclid3 for each kind of
output, as one student at least has done. **

**I'll have more general
guidance about the lab to offer at the beginning of the period on
Thursday the third. Here are some notes
of guidance for working on your Lab 3 report.**