Projects
days until the end of spring semester.days until Snakes on a Plane.
Boxes unpacked
Math article project
Finished mathematical core of article. Next: Write analytical core of article.
Dummit and Foote, Abstract Algebra
Finished section 1.6 (86 to go)
Silverman and Tate, Rational Points on Elliptic Curves
FInished 2.5 (31 to go)
Conway, Functions of One Complex Variable I
Finished section 7.5 (27 to go)
Munkres, Topology
Finished section 21 (60 to go)
Royden, Real Analysis
Finished section 2.4 (97 to go)
Nonfiction book project
Todo list uptodate
Fiction book project
1443 out of 100,000 projected words written.
Top 100 novels of all time
Reading Ulysses
IMDB top 250 films
Tengoku to jigoku next in queue.
Blogroll
This academic life
Academic CoachConfessions of a Community College Dean
Learning Curves
The Little Professor
My Hiding Place
New Kid on the Hallway
One Bright Star
Planned Obsolescence
Tall, Dark, and Mysterious
Math blogs
Ars MathematicaMathForge
MathPuzzle
Think Again
Archives

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Vito Prosciutto: Teaching community college math on the road to a PhD.
Tuesday, September 30, 2003
15:09Test review strategy triedit's a success
15:05Bilingual classroom
Sunday, September 28, 2003
10:33First week of observations over
I've given a list of classes that I'd like to see to the department head. I've decided that I want to see at least one section of every class that they offer from the most remedial level to AP calculus, so that means I won't do any longitudinal observations this week.
I've been laid up this weekend with a nasty cold, which is unfortunate since I'm behind in my homework already and I've got a big stack of midterms to grade for Tuesday.
Wednesday, September 24, 2003
19:55Another NCLB horror story
Monday, September 22, 2003
15:01Observation begins
Having been reading and talking about observations, I was looking at the classroom with fresh eyes, paying close attention to how the teacher approached the class. I think viewing a class as "a class from hell" altered how the teacher dealt with one of the remedial classes. I was also struck by how lecturedriven his class was. My style is much more of a questioning style. Or at least I hope it is. My plan is to videotape as much of my teaching as possible so I can reflect on what I do (and if I've got some good lessons, I can include copies of the tape with my portfolio).
Wednesday, September 17, 2003
12:19Do Not Learn Not Important
Well, it amused me.
11:07Getting ready for teaching on Saturdays
My syllabus is also heavily weighted away from graded homework assignments. The bulk of the grade will be determined by two tests and a journal (which will be, effectively, the students creating their own textbook). The journaling will provide the students to get used to the idea of writing about mathematics and help fulfill the goal of teaching writing across the curriculum.
Tuesday, September 16, 2003
12:36Cultural bias
The perimeter of a football field is 962 feet not including the endzones. How wide is the football field.A simple enough question, assuming that the reader knows that a football field is 100 yards long. The illustration accompanying the question almost provides that information, but the yard line markers are not identified with units, so there's no way for the reader to know that they are yard markers and not, say foot markers. Just one of those little cultural things that we can easily be blind to.
Sunday, September 14, 2003
16:43More on No Child Left Behind
If you're as outraged as I am about this, I suggest going here and making your views known to congress.
Friday, September 12, 2003
13:42Inside Secrets of Finding a Teaching Job
Thursday, September 11, 2003
10:16I'm a morning person now
The 9a class is beginning to distinguish themselves from the 8a class. The later class has more students asking questions than the earlier class, and glancing over the quizzes, I think that they did better on the quiz. I did make an error and covered one more section on the quiz than I should have, so I'll possibly add an adjustment to scores. I'm thinking taking the class average on the first three questions, then adding the difference between that and the average on the fourth question which went beyond the standard material. This will also compensate for some differences in what was discussed before the quiz began.
Wednesday, September 10, 2003
20:10Fall observation assignments are here
10:36My little mathematical breakthrough
For readers who may not have studied abstract algebra, let me back up and explain what these terms mean.
First, a group consists of a set and a binary operation (for example, the set of integers and the operation +) with the following requirements:
 There exists an identity (we'll call it e) such that e+a=a+e=a for all a in the set (note that I'm using + as my operation here).
 The associative law applies.
 For each a in the set there exists an element a^{1} such that a+a^{1}=a^{1}+a=e
Note that we do not require a commutative law, and there are plenty of groups which meet the above requirements but are not commutative (one of the most notable being the set of invertible 2x2 matrices with the operation being binary multiplication).
When we talk about the order of a group, it's the number of elements in the group. The order of the group defined by integers and addition is infinite. On the other hand, if we choose the set of complex numbers {1, 1, i, i} and the operation multiplication, the order of this group will be 4.
When we talk about the order of an element we mean the smallest positive integer k such that a^{k}=e. The order of the identity is always 1, and with addition and integers all non0 integers have infinite order (note that in this instance when we talk about a^{k}, we really mean ka.
For our second example, the order of 1 will be 2 ((1)^{2}=1), the order of i will be 4 (i^{4}=1), and the order of i will also be 4.
One of the easiest ways to verify that you have a group is to construct the multiplication table and if you can have each element of the set appear exactly once in each row and column, then you have a group. I played around with some ideas using the set of whole numbers for a while trying to make a^{2}=e for all elements and this morning I finally hit upon an arrangement which worked. Looking at patterns I realized that my binary operation was a bitwise binary exclusive or. For nonCS types reading this, the operation works by expressing the two nonnegative integers in binary. In each bit position, the result will be 1 if only one of the two integers has that bit position on, 0 otherwise. So, for example, 5$3 will have the bits 101 and 011 and will result in 110 or 6 as its result. For any number a 0$a=a and a$a=0.
In fact, we can extend this to an infinite number of groups by taking the breakdown of an integer in base n and having a$b being the sum of each digit position being taken mod n. This is actually the additive group of polynomials Z/nZ[x] but without the upper limit on the power of polynomials (although it seems to me that the upper limit of the exponents should be n1. In this instance, the order of each element will be no greater than n.
After coming up with this, I also realized that if we take the set of complex numbers with the property that x^{k}=1 for some integer k, we also have a finite order for every element in the group, although here it's not bounded.
I'm afraid this might not be as clear as I'd like it to be, but it should be possible for someone with some basic group theory to follow this argument at least in outline.
Tuesday, September 09, 2003
20:51My sin is pride
During the tutoring hour, one of my former students came in for help. She had failed during my semester teaching, but retaking the class over the summer she had made the breakthrough to being able to do algebra. She's in very good shape now from what I saw. So why the headline? Because there's a big part of me that is disappointed that she didn't make the breakthrough under my watch. I have to remember that not every accomplishment has to be by ME.
She's also a great exemplar of the student who may have difficulty with arithmetic but who can still do algebra. She couldn't do 208 without her calculator, but she could do algebraic manipulation with no difficulty.
Saturday, September 06, 2003
19:34My Saturday job
One of my goals will be to make sure that they're learning an adequate amount of information to be able to handle the university's flawed math placement test.
Speaking of which, it looks like many of my algebra II students are trying to get placed into more advanced math classes.
Thursday, September 04, 2003
14:33No Child Left Behind
Read more about this and sign a petition opposing it here
08:34Note to self
But overall, I was pretty happy with the results of the class. It looks like a few students are taking my advice and trying to move into higherlevel classes.