The homeworks are modeling problems. As such, they rarely if ever have correct or incorrect answers. All that is asked is that you explore the topics assigned in teams of 2-3 students and write a reasoned answer in good technical English. All members of the team must read and edit the text of your solution before it is turned in. Aim for clear concise prose.
The homeworks can be turned in via BlackboardŐs Digital Dropbox feature (preferred) or emailed to firstname.lastname@example.org. I am hoping BlackboardŐs Discussion feature will also prove useful in enabling the discussions / revisions needed to work with the other members of your team.
Week 1: Read chapter 1 of BenderŐs book. Do problems 1, 2, 7, and 8 at the end of the chapter (pp. 12-14).
Due date September 10
Week 2: Read section 2.1 of BenderŐs book. Do problems 4, 5, and 6 at the end of the section (pp. 31-34).
Optional assignment: It is hoped that each of the final projects during the last third of the semester come from a real modeling problem related to a thesis/dissertation/research project by some member of the class. If you have such a problem and would like to work on it as part of your efforts for this class, please submit a few sentences describing your problem.
Due date September 17
Week 3: Read section 2.2 of BenderŐs book. Do problems 1, 2, and 3 at the end of the section (pp. 40-42).
Starting with this homework set, you may substitute a summary paragraph on the weekŐs computational science seminar or a paragraph written to one of the online threads for one of the problems (your choice).
Due date September 24
Week 4: Read sections 3.1 and 3.2 of BenderŐs book. Do problems 6, 7, and 8 at the end of the section (p. 57).
Due date October 1
Week 5: Read section 3.3 of BenderŐs book. Do problems 1, 3, and 4 at the end of the section (p. 63-4).
Due date October 8
Week 6: Midterm 1
Due date October 15
Week 7: Read section 4.1 of BenderŐs book. Do problems 1, 2, and 3a-e at the end of the section (p. 76-7).
Due date October 29
Week 8: Read section 4.2 of BenderŐs book. Do problems 2, 3a-b, and the following game theory problem:
GT1. Consider the following game intended to be a simplified model of bluffing in poker. It is played with a deck consisting of two cards: a high card and a low card. After an ante of $1 by each player, the first player (P1) is dealt one of the cards, each with equal probability. While P1 can look at the card immediately, P2 is not allowed to see the card until the end of the hand. The rules of the game are:
If P1 gets the high card he must bet $1 while if he gets the low card he can either bet $1 or he may fold, i.e. accept a loss of his $1 ante.
P2 can respond to a bet of $1 either by calling P1, and risking a total of $2, or by accepting a loss of his $1 ante. If P1 bet and P2 calls him then P1 wins or loses $2 according to whether he does or does not hold the high card.
Formulate "pure" strategies of each player and construct the payoff matrix. Note that this is a game with a chance move (the dealing of the card) and so a11 is the mean payoff to P1 if both players use their respective first strategies many times. What is the value of the game? What are the optimal mixed strategies of the two players?
Due date November 5
Week 9: Do problem 4a-d on page 99 and problem 5 on page 133 in BenderŐs book along with the following maximum entropy problem:
ME1. The distribution of energies in a physical system maximizes entropy. A cavity contains 1000 electrons whose total energy is 750 ev. If the energy of each electron is quantized to be either 0, 1, or 2 ev., how many electrons have energy 0? If the temperature is the reciprocal of the Lagrange multiplier corresponding to the energy constraint, what is the temperature of the system?
Due date November 12
Week 10: Midterm 2
Due date November 19