MATH 1600
March 12, 2013 HOMEWORK
Professor R. Rand
1. As stated in the lecture, Herodotus supposedly wrote that the 4-sided pyramid at Giza was constructed so that the area of each lateral face was equal to the area of a square that had one side as long
Worksheet 1
Math 1600
Spring 2011
This set of questions invites you to explore the model for monocular vision Euclid set forth in Optics. The model is based on the following seven assumptions about "the appearance of things": 1. Let it be assumed that lin
Fibonacci Homework (due 02/15/11)
1. Use the first formula to show (Fn+1)/(Fn) < G (Fn+1)/(Fn) > G if n is odd if n is even
2. If you use a 6 decimal place approximation to 5 , what is the smallest value of n when the second formula for Fn gives the wrong
Math 160 Homework - Diophantine Equations Due February 22, 2011 1) Find infinitely many nonprimitive Pythagorean triplets (a, b, c) where c = b + 2. You'll need c2 - b2 to be a perfect square. For which numbers b can you arrange this? 2) Show there is no
Math 1600, Homework February 22, 2011
1. Suppose that you have a framework in the line at distinct points p1 , p2 , p3 , p4 , on the line where p1 > 0, p3 > 0, and p2 < 0, p4 < 0, where there a bars from p1 to p2 to p3 to p4 to p1 . Show that any any othe
MATH 1600
March 3, 2010 HOMEWORK
Professor R. Rand
1. As stated in the lecture, Herodotus supposedly wrote that the 4-sided pyramid at Giza was constructed so that the area of each lateral face was equal to the area of a square that had one side as long a
Math 1600 - Big numbers homework
1. Explain why, at a gathering of any six people, some three of them are either mutual acquaintances or complete strangers. Show that this need not be the case at a gathering of five people. 2. Show that it takes 2n - 1 st
Homework for RSA Encryption April 7, 2011 1. Encrypt the plaintext BOMB using the affine cipher (9x + 2) mod 26. 2. The ciphertext UCR was encrypted using the affine cipher (9x + 2) mod 26. Find the plaintext. 3. The following ciphertext was encrypted by
Math 1600 HW 11
1. Which of the following pairs of events are independent? If they are not independent, decide whether P (A|B) is bigger or smaller than P (A), and by about how much; and the same for P (B|A) compared with P (B). (a) Flip two fair coins, a
Math 1600 - Solving Systems of Polynomial Equations Homework
Handed out April 21, 2010 Problem 1. Let f (x, y, z) and g(x, y, z) be polynomials in three variables. Recall that V (f, g) = cfw_(a, b, c) | f (a, b, c) = g(a, b, c) = 0. 1. Explain in your own
Math 1600 Homework 4/28/11 1. Solve the initial-value problem
y = 1, y(0) =(0) = ex + 0, y 1.
2. Solve for the tip deflection, y(1), of a "diving board" under uniform load:
d4y = 1, 0 < x < 1, y (0)= y(0)= y(1)= y(1)= 0. dx 4
3. As shown in class, the sha
Math 1600 (01/29/13)
"On Shortest Paths & Optimal Choices" by A. Vladimirsky
Homework (due on Thursday, 01/31/13)
Problem 1.
Learn about Snell's law (on internet or from textbooks) & re-derive it using the following example: Suppose the speed of motion is
Math 1600 Homework for February 5, 2013 class 1) Let a population as function of time be denoted P (t). Suppose P (0) = 100000 and the rate of growth of the population is equal to 20% of the current population. Use the method of class to find P (10) by in
Worksheet 1
Math 1600
Spring 2013
This set of questions invites you to explore the model for monocular vision Euclid set forth in Optics. The model is based on the following seven assumptions about "the appearance of things": 1. Let it be assumed that lin
Homework 1: due Feb. 1st
Of course these aren't going to make sense until after the talk. 1. Play the "find the highest root game" on the graph D_n. Describe all the roots you can meet along the way; there should be n(2n-1) of them. 2. Make a new kind of