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CSU Northridge - AE - 11859
Page 1 of 42The Crisis DeepensMAIN IDEATurmoil over slavery led to acts of violence.WHY IT MATTERS NOWViolence can make compromise more difficult.TERMS & NAMESHarriet Beecher Stowe Uncle Toms Cabin Fugitive Slave Act popular sovereignty K
CSU Northridge - AE - 11859
Page 1 of 84The California Gold RushMAIN IDEAGold was found in California, and thousands rushed to that territory. California quickly became a state.WHY IT MATTERS NOWThe gold rush made California grow rapidly and helped bring about Californ
CSU Northridge - AE - 11859
Page 1 of 64Beginnings of Slavery in the AmericasMAIN IDEASlavery in the Americas began in order to provide cheap labor for the colonies.WHY IT MATTERS NOWThe effects of slavery, including racism, helped shape attitudes and social conditions
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia Fernndez.May 9-16A real number x between 0 and 1 is chosen uniformly at ran dom. If x is written as a decimal in base 10, what is the probability that its rst non-zero digit is equa
CSU Northridge - SF - 70713
Problem of the Week 12, Fall 2008Determine the expected value of the area of a triangle whose vertices are chosen uniformly and independently at random on a circumference of radius 1.3 Solution by organizers. The expected value is 2 . To prove this
CSU Northridge - SF - 70713
Problem of the Week 1, Fall 2008Find an integer number such that the number formed by its rst three digits is a multiple of 3; the number formed by its second, third, and fourth digits is a multiple of 4; the number formed by its third, fourth, and
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia Fernndez.April 18-25We dene a recursive sequence of points in the plane as follows: The initial point has coordinates (x0 , y0 ) and all other points are obtained from their precedi
CSU Northridge - SF - 70713
Problem of the Week #4Proposed by Bill Watkins.March 29-April 5, 2004Guillermo goes to the bank to cash a check. The teller inadvertently switches the cents and the dollars on the check and gives the corresponding amount to Guillermo. After buyi
CSU Northridge - SF - 70713
Problem of the Week.Proposed by Bernardo brego and Silvia Fernndez.May 3-10In an election, two candidates, Carlos and Luis, have in a ballot box 10 and 5 votes respectively. If ballots are randomly drawn and tallied one at a time, what is the pr
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia Fernndez.September 20-27Today, September 20, 2004, is my birthday and I noticed a curious fact: My fathers age (in whole years) is exactly twice mine (also in whole years). I wonder
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia Fernndez.February 21-28has a solution with a and b positive integers. Justify your answer.Find the smallest positive integer k for which the equation a a2 k + b b2 k = 2005
CSU Northridge - SF - 70713
Problem of the Week 11, Fall 2008Determine all the positive integers that are equal to the square of their number of positive divisors. Solution by organizers. Clearly n = 1 and n = 9 work. We prove that these are the only possibilities. Assume n >
CSU Northridge - SF - 70713
Problem of the Week 6, Fall 2008There is a fortune-teller at the annual village fair. Nine fortune-tellers out of ten are always right; the other ones are always wrong. Nobody at the fair knows which sort of fortune-teller is there this year. Anothe
CSU Northridge - SF - 70713
Problem of the Week 1, Spring 2006Solution by Lucas Lembrick (edited). 945 is an odd abundant number. Note that 945 = 33 57, so all divisors of 945 excluding 945 are: 1, 5, 7, 57, 3, 35, 37, 357, 32 , 32 5, 32 7, 32 57, 33 , 33 5, 33 7. The sum of t
CSU Northridge - SF - 70713
Problem of the Week.Proposed by Bernardo brego and Silvia Fernndez.April 12-19Let P (x) = x4 +ax3 bx2 +cx+1 be a polynomial with real coecients. Prove that if |a + c| < b2 then P has four dierent real roots (that is, there are four dierent real
CSU Northridge - SF - 70713
Department of MathematicsFind the maximum value of bc ca ab + + a b c b c a + + bc ca ab over all triples of non-zero real numbers a < b < c such that a + b + c = 0. Solution by George Craciun. Let E = E(a, b, c) be the required expression. The
CSU Northridge - SF - 70713
Problem of the Week 11, Fall 2005Solution by the organizers. This solution does not require the concept of curvature. We rst nd the largest circle that touches the parabola at (0, 0). The center of such disk must be located at (0, r) where r is the
CSU Northridge - SF - 70713
Problem of the Week 7, Fall 2008Let n > 0 be a natural number. Determine all n-degree polynomials P (x) with n positive real roots such that P (x) = xn + an1 xn1 + an2 xn2 + . . . + a2 x2 + a1 x + 1 and a1 = an1 = n 10. Solution by organizers. We s
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia Fernndez.February 7-14A restaurant oers ve menus each priced a dierent whole amount of dollars between $10 and $19 inclusive. Last Friday there were 15 couples dining at the restaur
CSU Northridge - SF - 70713
Problem of the Week Chuck Goodman Dec 1 We need to randomly pick 3 points on the unit circle and nd the expected value of area of the resulting triangle is. This is a geometric probability problem. As is always the case in probability problems, the e
CSU Northridge - SF - 70713
Problem of the Week 3, Fall 2005Solution by the organizers. Consider a graph G with six vertices representing each of the six irrational numbers. We color each of the edges connecting every pair of vertices according to the following rule. If x, y a
CSU Northridge - SF - 70713
Problem of the Week 5, Fall 2005Solution by George Craciun (edited). Let x1 , x2 , x3 , x4 the roots of the equation x4 (3m + 2) x2 + m2 = 0. Then, in order for these roots to be in arithmetic progression we set x1 = a 3r, x2 = a r, x3 = a + r, x
CSU Northridge - SF - 70713
Problem of the Week #2Proposed by Bernardo brego and Silvia Fernndez.March 15-22, 2004Find with proof the exact value of the sum 1 2 3 n + 2 + 3 + . + n + . 1 2 2 2 2Note: If you are familiar with -notation, the sum above can be written as X
CSU Northridge - SF - 70713
Diophantine equations. A Diophantine equation is a linear equation with integer coecients requiring integer solutions. The Diophantine equation ax + by = c has an integer solution if and only if gcd (a, b) divides c. To nd one solution to the Diophan
CSU Northridge - SF - 70713
Problem of the Week.Proposed by Bernardo brego and Silvia Fernndez.April 26-May 3Prove that if nine points are chosen in the interior of a unit square, then three of them form a triangle with area at most 1/8. (Note: If three points are on the s
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia Fernndez.May 2-9The following is a well known fact: If a positive integer is not prime then it has a prime factor less than or equal its square root. Show that a positive integer ha
CSU Northridge - SF - 70713
Problem of the Week.Proposed by Bernardo brego and Silvia Fernndez. September 6-13Suppose A = Find a, b, c, d.a b c dis a matrix with a, b, c, d real numbers and A =36 2 7 1 .Note: A3 represents the matrix multiplication of A with
CSU Northridge - SF - 70713
Problem of the Week 9, Fall 2008Triangle ABC has AC = 9, AB = 12, and BC = 15. The points M and N are the midpoints of the segments AC and AB, respectively. A point L is constructed on segment BC, such that LC = 3. Segments BM and CN intersect at O,
CSU Northridge - SF - 70713
Rolling a ball to the nearest player Solution by Jason Hughes Problem Fifteen girls are standing on a field and each of them has a ball. All distances between girls are different. Each girl throws her ball to the girl standing closest to her. Show th
CSU Northridge - SF - 70713
Problem of the Week.Proposed by Bernardo brego and Silvia Fernndez.April 19-26Two players A and B alternate turns during a game as follows: Player A starts by calling a whole number between 1 and 10. Each turn a player calls a whole number large
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia FernndezNovember 7-14Fifteen girls are standing on a field and each of them has a ball. All distances between girls are different. Each girl throws her ball to the girl standing clo
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia FernndezOctober 2-9Zeus, Athena, and Poseidon visit Mount Olympus exactly once every day. They each arrive at a random time between 8:00 AM and 5:00 PM, and stay for 2 hours. If two
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia FernndezMarch 5-12Find all positive integers with two or more digits such that if we insert a 0 between the units and tens digits we get a multiple of the original number.This cont
CSU Northridge - SF - 70713
Problem of the Week 4, Fall 2006Solution by organizers. Let x be the time (in hours) between 8:00 am and the rst gods arrival, y be the time between the rst and second gods arrivals, and z be the time between the second and third gods arrivals. Then
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia FernndezSeptember 26- October 3Suppose you have two individually shuffled poker decks (52 cards in each), one on top of the other. For each card C in the top deck, count the number
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia Fernndez.February 28-March 7Deadline: March 7, 2005 before 9:00 PM. Look for the Problem of the Week every Monday in the Daily Sundial (Daily Spotlight section) or in our web site w
CSU Northridge - SF - 70713
Solution by Humberto Raya. Suppose that you have two shuffled poker decks with one on top of the other. Each deck will have 52 cards. Note that the value of the number of cards that are within a card C in the top deck and the same card C in the botto
CSU Northridge - SF - 70713
Problem of the Week.Proposed by Bernardo brego and Silvia Fernndez.September 13-2030 ants are located at random on top of a narrow wooden stick measuring 12 inches long. Each ant starts walking, either left-bound or right-bound, at a speed of 2
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia FernndezNovember 20-27A hundred and one dwarves are seating around a table. There is exactly one dwarf per integer height between 700 and 800 millimeters. For each consecutive pair
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia FernndezNovember 27-December 4A mathematics teacher wants her two intelligent students B and S to derive the exact value of a 2-digit natural number by revealing the number of posit
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia Fernndez.October 25-November 15=3+2Consider the standard 28-domino set. Circular chains of dominoes can be formed 2=2+0 according to the next rule: domino a b can be placed right
CSU Northridge - SF - 70713
Problem of the Week.Proposed by Bernardo brego and Silvia Fernndez.April 19-26Two players A and B alternate turns during a game as follows: Player A starts by calling a whole number between 1 and 10. Each turn a player calls a whole number large
CSU Northridge - SF - 70713
Problem of the Week #3Proposed by Bernardo brego and Silvia Fernndez.March 22-29, 2004Let ABC be an arbitrary triangle. Let D and E be points on AC and BC respectively such that DE is parallel to AB. Let M be the intersection of BD and AE. Let F
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia Fernndez.February 7-14A restaurant oers ve menus each priced a dierent whole amount of dollars between $10 and $19 inclusive. Last Friday there were 15 couples dining at the restaur
CSU Northridge - SF - 70713
Department of MathematicsProposed by Bernardo brego and Silvia Fernndez.September 20-27Today, September 20, 2004, is my birthday and I noticed a curious fact: My fathers age (in whole years) is exactly twice mine (also in whole years). I wonder
CSU Northridge - SF - 70713
Problem of the Week 9, Fall 2005Additional questions. Given any two relatively prime positive integers a and b, 1. Find the largest n that cannot be written as the sum of numbers each equal to a or b. If a = 119, b = 18 then according to the Problem
CSU Northridge - SF - 70713
Problem of the Week 7, Spring 2006Solution by Andrew Jones. We want to maximize a1 a2 . an , where the constraint is that a1 + a2 + . + an = 20 and n is a positive integer. 1. First notice that all ai are equal (i (1, 2, .n), since the greatest
CSU Northridge - VCBIO - 001
COMPARISON OF MALE AND FEMALE FEEDBACK SYSTEMS BETWEEN BRAIN, PITUITARY AND GONADSMALEFEMALEHYPOTHALAMUS HYPOTHALAMUSHYPOTHALAMRELEASING FACTORS TURN OFF PITUITARY FSH + TURN OFF TESTIS INTERSTIT IAL CELLS OVARY CORPUS LUTEUM LH + OFF + + TU
CSU Northridge - SD - 51881
The relationship between regional and local species diversity in marine benthic communities: A global perspectiveJon D. Witman*, Ron J. Etter, and Franz Smith*Ecology and Evolutionary Biology Department, Brown University, Providence, RI 02912; Biol
CSU Northridge - BZ - 51361
Key Concept 8: Understand and Identify the Differences Between Civil and Criminal Liability1 Criminal Law - Crimes are public wrongs prohibited by a state or the federal government. Criminal law is comprised of principles and rules that protect all o
CSU Northridge - MSE - 18470
CSU Northridge - MSE - 608
CSU Northridge - MSE - 18470
CSU Northridge - MSE - 608
CSU Northridge - MSE - 18470
CSU Northridge - MSE - 608
CSU Northridge - VCMGT - 0
CSU Northridge - RDC - 536
Sensors and Actuators A 130131 (2006) 609615Fabrication of pyramid shaped three-dimensional 8 8 electrodes for articial retinaKyo-in Koo a,c,d,e,f,g , Hum Chung b,c,d,g , Youngsuk Yu b,c,g , Jongmo Seo b,c,d,g , Jaehong Park a,c,d,e,f,g , Jung-Mi
CSU Northridge - RDC - 73720
Sensors and Actuators A 130131 (2006) 609615Fabrication of pyramid shaped three-dimensional 8 8 electrodes for articial retinaKyo-in Koo a,c,d,e,f,g , Hum Chung b,c,d,g , Youngsuk Yu b,c,g , Jongmo Seo b,c,d,g , Jaehong Park a,c,d,e,f,g , Jung-Mi
CSU Northridge - RDC - 73720
ARTICLE IN PRESSUltramicroscopy 108 (2008) 1297 1301Contents lists available at ScienceDirectUltramicroscopyjournal homepage: www.elsevier.com/locate/ultramicPhotolithographic process for the patterning of quantum dotsYoung Joo Na, Sang Joon
CSU Northridge - RDC - 536
J Mater Sci: Mater Med (2008) 19:34893495 DOI 10.1007/s10856-008-3527-xFabrication of porous titanium scaffold materials by a fugitive ller methodT. F. Hong Z. X. Guo R. YangReceived: 16 January 2008 / Accepted: 25 June 2008 / Published online