# Mathemapundit

Being a weblog devoted to a variety of topics. Including Mathematics. And Mathematical Finance. Sometimes with homework.

## Monday, December 20, 2010

### 21-370: Final Statistics

Here are the final Statistics for the semester. You can see grade cutoffs for each exam and for cumulative averages. It also shows grade distrubutions for each of the exams.

### 21-260: Final Statistics

Here are the final Statistics for the semester. You can see grade cutoffs for each exam and for cumulative averages. It also shows grade distrubutions for each of the exams.

## Tuesday, October 19, 2010

### 21-370: Stock price for HW#9

As I announced in class, the initial stock price for the third homework problem is S0=8. I've updated the assignment to reflect this.

UPDATE: I've also made a correction to problem 1. Xn+1(H)=gn(Xn) and Xn+1(T)=hn(Xn).

## Sunday, October 17, 2010

### 21-370: Homework - Wek #9

The reading and homework assignments for Week #9 have been posted. The reading is from a set of notes written by Profs. Hrusa and Kramkov. I've posted a pdf file of the notes. The homework assignment is also a downloadable pdf. Since I've posted this late this week, I'll give you until Friday to complete the assignment this week. You can follow the links from the Schedule page.

## Monday, September 27, 2010

### 21-260: Week #6

The reading and homework assignments for Week #6 have been posted. You can follow the link from the schedule page.

## Friday, September 17, 2010

### 21-370: Week #5

The reading and homework assignment for Week #5 have been posted.

## Friday, September 10, 2010

### 21-260: Week #4

The reading and homework assignments for Week #4 have been posted. Follow the link from the Schedule page.

### 21-370: Homework - Week#4

The reading and homework assignments for Week #4 have been posted. You can follow the link from the Schedule page.

## Tuesday, September 7, 2010

### 21-260: Pay No Attention to the Hint for Problem 2.1.23b

The WileyPLUS "Hint" for this problem is incorrect. The "transition from one type of behavior to another" is this: for some initial conditions, the solutions increase without bound as t approaches infinity; for other initial conditions, the solutions decrease without bound. You want to find the initial condition y(0)=a_0 that identifies the solution that separates these two types of behavior. The solution doesn't involve finding derivatives and setting them equal to zero.

## Monday, August 30, 2010

### 21-260: Dfield and Wiley Support

First, the dfield applet I used in class today is available from this site.

Second, you can contact WileyPLUS customer support to submit a question or use their live chat feature. This should help you get the help you need in a more timely fashion.

## Friday, August 27, 2010

### 21-260: Week #2

The reading and homework assignments for Week #2 have been posted. You can follow the link from the Schedule page.

## Thursday, August 26, 2010

### 21-370: Week #2

The reading assignment for Week #1 and the reading and homework assignments for Week #2 are now posted. You can follow the links from the Schedule page.

### 21-370: The Textbook is Available

I've heard reports that the textbook, Stochastic Calculus for Finance I: The Binomial Asset Pricing Model by Steven E. Shreve, is now in stock at the bookstore.

## Tuesday, August 24, 2010

### Nature By Numbers

Boing Boing highlights this
Dreamlike animation illustrating Fibonacci sequence, Golden Ratio, and more
.

### The Duality of Money - Walter Schachermayer

Noted mathematician Walter Schachermayer will give this year's Nash Lecture, titled "The Duality of Money." According to Schachermayer, the dual relationship between goods and their prices is a classical idea in economics. In his lecture, he will discuss current research on duality in modern and complex financial markets. Schachermayer is best known for combining functional analysis and stochastic analysis in the field of financial mathematics. He, with fellow mathematician Freddy Delbaen, proved the Fundamental Theorem of Asset Pricing in its general form. This theorem, first conjectured by economists in the 1970s, explains the relationship between the absence of arbitrage in financial markets and the existence of a probability measure that can be used to price derivative securities. Later, Schachermayer and Carnegie Mellon Professor Dmitry Kramkov established the definitive methodology for using duality to solve the problem of optimal investment in incomplete markets.

The talk will be at 4:30pm on Tuesday, September 7, in the Rashid Auditorium in the Hillman Center.

## Friday, August 20, 2010

### 21-260: Fall 2010

Welcome to 21-260 for the Fall 2010 semester. I'll use this blog as a means to distribute information and notifications for the class. More information can be found on the 21-260 Website. This site has information about lectures, recitations, schedules and more. There is also a Blackboard site for the course. I'll mainly use Blackboard to post grades and distribute solutions. You will also be using the WileyPLUS site to complete some required assignments.

## Tuesday, May 18, 2010

### 21-241: Final Wrap-Up

Well, we have reached the end of the semester. I've turned in the final grades, and you can all see your final exam grades on Blackboard. I think I've got the Blackboard "Cumulative Average" computing everything correctly (I use a separate spreadsheet to calculate and assign grades). (A few students have discussed issues with some of their homework assignments this semester. I believe I've resolved those issues, but have not changed the Blackboard grades to reflect that.)

The grade cutoffs for the final exam were:

A cutoff - 80
B cutoff - 70
C cutoff - 60
D cutoff - 40

and the grade cutoffs for cumulative averages were:

A cutoff - 82.37
B cutoff - 69.47
C cutoff - 56.58
D cutoff - 40.26

I enjoyed working with you all this semester, and I hope you have a great summer.

## Thursday, May 6, 2010

### 21-241: More solutions

I've posted the solutions to the review problems from section 6.3 on the Blackboard site - on the Assignments page with the other solutions.

I will be available in my office tomorrow (Friday) between 11:30 and 1:00 to field any last minute questions, are return any homework that anyone would like to pick up.

## Tuesday, May 4, 2010

### 21-241: Solutions

I've posted some more solutions on the Blackboard site. Solutions to Exam #2, the makeup for Exam #2 and for HW#15 are now available from the Assignments section of the Blackboard site.

## Monday, May 3, 2010

I've heard from a few of you asking how to interpret your "Cumulative Average" from the Blackboard gradebook. As you are likely aware, the grade cutoffs for your final averages will depend on the grade cutoffs for each assignment. I average these cutoffs (the same way I compute your averages) to get the cutoffs for final averages.

To interpret your "cumulative average" you should use the following cutoffs, based on the mid-terms and homework to date.

A cutoff - 83.21
B cutoff - 69.29
C cutoff - 55.36
D cutoff - 40.36

The final cutoffs will depend on the grade cutoffs for the final exam. The final cutoffs may be above or below these cutoffs, but probably not by too much.

## Saturday, May 1, 2010

### 21-241: Final Exam

I've posted the review page for the final exam. The final will be Friday, May 7 at 5:30pm in UC McConomy.

I'll make solutions available for the review problems from sections 5.6 and 6.3, as these topics were not covered on a regular homework assignment.

## Friday, April 30, 2010

I returned Exam #2 during class today. As you know, there was a relatively large number of students who took an alternate exam. The average grades on the two exams were significantly different (though the standard deviations were roughly the same). In order to treat all students as fairly as possible, I've scaled up the grades on the alternate exam. If you took the (pink) exam on Friday morning, the grade recorded on Blackboard will be 18 points above the grade on your exam.

I've also created a column on the Blackboard gradebook called Cumulative Average. This is your average so far in the course (including the 5% of your graded given by the higher of your two mid-term grades).

## Monday, April 26, 2010

### 21-241: Office Hours on 4/27

My office hours on Tuesday, April 27 will be from 1:30-3:15pm, rather than the usual 2-4.

## Thursday, April 22, 2010

### 21-241: Week #15

The reading and homework assignment for Week #15 have been posted.

## Wednesday, April 21, 2010

### Allan Metzler Speaks

Allan Meltzer, University Professor of Political Economy at the Tepper School of Business, will talk about some of the lessons about Federal Reserve policy from his 2 volume study of Federal Reserve history. He will use the lessons to discuss reasons for the credit and economic crisis and to discuss reform proposals now under discussion in the Congress.

The talk is on Thursday, April 22 at 4:30 PM in PH 100.

## Friday, April 16, 2010

### 21-241: Exam #2

Many of you have mentioned a conflict with a Physics exam at 8:00 next Wednesday. Others of you may have three exam on Wednesday, April 21. For those of you with these legitimate concerns, there will be a makeup exam on Friday, April 23. This exam will also be at 7:30am and will be in DH A310.

The Wednesday Exam will be in DH 2315, rather than DH 2210 as originally announced.

## Thursday, April 15, 2010

### 21-241: Exam #2 Review...

...has been posted.

## Thursday, April 8, 2010

### 21-241: Week #13

The reading and homework assignments for Week #13 have been posted. You can follow the link from the Schedule page.

## Wednesday, April 7, 2010

### 21-241: Homework Solutions

I've posted solutions the the recent homeworks on the Blackboard site. Solutions are now available for everything through HW#11.

## Tuesday, April 6, 2010

### XKCD

...is sometimes funny. And sometimes it is just way cool.

## Thursday, April 1, 2010

### 21-241: Week #12

The reqading and homework assignments for Week #12 have been posted. You can follow the link from the Schedule page.

## Tuesday, March 30, 2010

### XKCD

...joins the Tautology Club.

## Thursday, March 25, 2010

### 21-241: Week #11

The reading and homework assignments for Week #11 have been posted. You can follow the link from the Schedule page.

## Tuesday, March 23, 2010

### XKCD

...explores the limits of logical deduction.

## Friday, March 19, 2010

### 21-241 Week #10

The reading and homework assignment for Week #10 has been posted. There are two "homemade" problems and five from the text.

UPDATE: The homework assignment for Week #10 will be due on Wednesday, as usual, not Friday, like last week. The assignment page was incorrect, but it is fixed now.

## Tuesday, March 16, 2010

### XKCD

An interesting description of the Collatz Conjecture.

## Monday, March 8, 2010

### 21-241: Week #9

I didn't get the assignment for Week #9 posted until today, so rather than the normal Wednesday deadline, the assignment will be due on Friday, March 19, That will give you a little more time to work on it.

UPDATE: Problem 3.3.35 and 3.3.36 refer to "the same four points." They mean the points in problems 3.3.32 and 3.3.33, i.e. the points (t,b) in {(0,0), (1,8), (3,8), (4,20)}. Sorry for the confusion.

## Tuesday, March 2, 2010

### Pittsburgh Snowstorm

I just ran across this movie filmed after our big snowstorm in early February. It's got pretty good production values, and is entertaining, if you like that sort of thing.

## Monday, March 1, 2010

### 21-241: Final Exam

Our Final Exam will be given on Friday, May 7, from 5:30-8:30pm. Please make sure that your travel plans do not require you to leave campus before the end of the exam. No student will be permitted to take the final exam early.

### 21-241: Exam #1

I returned the exams in class today. The grade cutoffs for Exam #1 were as follows:

A: >80

B: 65-79

C: 50-64

D: 35-49

Here are a wide range of statistics for the course so far. Solutions to the exam are available in the Assignments section of the Blackboard site.

## Wednesday, February 24, 2010

### 21-241: Cumulative Average Comutation

15% Homework Average

50% Mid-term Exam Average

25% Final Exam

5% Higher of two Mid-term Exams

5% Higher of Mid-term Average and Final Exam

## Friday, February 12, 2010

### 21-241: Week #6

The reading and homework assignment for Week #6 have been posted. You can follow the link from the Schedule Page.

## Monday, February 8, 2010

### Out of Office on Tuesday

With the canceling of classes on Tuesday, February 9, I am also canceling my office hours that day. Maybe they can get things cleared up by Wednesday...

UPDATE: There will be no "recitation" this evening either.

## Sunday, February 7, 2010

### 21-241: Exam #1 Review Session

The review session for Exam #1 will be this evening, from 4:00 to 5:30 in PH 100. See you there.

## Friday, January 29, 2010

### 21-241: Homework #2 Solutions

The solutions to Homework #2 are now available on the Blackboard site.

## Thursday, January 28, 2010

### 21-241: Week #4

The reading and homework assignments for Week #4 have been posted. You can follow the link from the Schedule page.

## Wednesday, January 27, 2010

### 21-241: Homework #1 Solutions

The solutions to Homework #1 are now available on the Blackboard site.

## Thursday, January 21, 2010

### 21-241: Week #3

The reading and homework assignments for Week #3 have been posted. You can follow the link from the Schedule page.

## Friday, January 15, 2010

### 21-241: Week #2

The assignment for Week #2 has been posted. Note that the assignment is due on Wednesday, January 20.

## Thursday, January 14, 2010

### 21-241: Using Tecnology

I've been asked about the use of technology (graphing calculators, computer algebra systems) on your homework assignments. I don't place any restrictions on the use of these tools. As you use them, however, you need to bear in mind a few things:

1. The goal of the course (and homework assignments) is for you to learn techniques, not "get answers." If a question requires you to solve some system of equations, using Maple's 'solve' command will not get you any credit. You can, however, use commands that make Maple perform the various operations, just as if you were doing them on paper.

2. As you work on your assignments, bear in mind that you will not have access to a calculator on the exams. Don't come to rely too heavily on technological approaches.

3. At the same time, some homework problems may assume that you do have access to a calculator. If a problem requires you do divide 12.983 into 137.98372423, don't worry about how you would do that on the exams. Just get out your calculator and do it.

### 21-241: Office Hours

My office hours this semester will be on Tuesdays, from 2:00-4:00pm, in WEH 6214. Additionally, our TA, Timothy Naumovitz will hold several office hours: Mondays from 6:30-7:30 and Thursdays from 10:30-11:30, both in WEH 6215. He will also hold a "recitation-like" homework review session on Tuesday evenings, 9:00-10:00pm, in a room yet to be determined.

As announced in class, I'll be holding office hours on Thursday this week starting at 2:00. I said I'd be here until four, but I'll actually need to leave a little earlier than that - say 3:45.

## Monday, January 11, 2010

### 21-241: Welcome to Matrix Algebra

Welcome to 21-241 Matrix Algebra. Most information about the course can be found on the Course Website. There is also a Blackboard site for the course, which will be used mainly to record homework grades and provide solutions to exercises and exams.

The homework assignment for Week #1 is now available. It is due on Friday, either before or after class, or in your TA's mailbox before 3:20.