1.2E: Exercises for Vectors in Space
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1) Consider a rectangular box with one of the vertices at the origin, as shown in the following figure. If point \(A(2,3,5)\) is the opposite vertex to the origin, then find
a. the coordinates of the other six vertices of the box and
b. the length of the diagonal of the box determined by the vertices \(O\) and \(A\).
- Answer
- a. \((2,0,5),(2,0,0),(2,3,0),(0,3,0),(0,3,5),(0,0,5)\) b. \(\sqrt{38}\)
2) Find the coordinates of point \(P\) and determine its distance to the origin.
For exercises 3-6, describe and graph the set of points that satisfies the given equation.
3) \((y−5)(z−6)=0\)
- Answer
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A union of two planes: \(y=5\) (a plane parallel to the \(xz\)-plane) and \(z=6\) (a plane parallel to the \(xy\)-plane)
4) \((z−2)(z−5)=0\)
5) \((y−1)^2+(z−1)^2=1\)
- Answer
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A cylinder of radius \(1\) centered on the line \(y=1,z=1\)
6) \((x−2)^2+(z−5)^2=4\)
7) Write the equation of the plane passing through point \((1,1,1)\) that is parallel to the \(xy\)-plane.
- Answer
- \(z=1\)
8) Write the equation of the plane passing through point \((1,−3,2)\) that is parallel to the \(xz\)-plane.
9) Find an equation of the plane passing through points \((1,−3,−2), (0,3,−2),\) and \((1,0,−2).\)
- Answer
- \(z=−2\)
10) Find an equation of the plane passing through points \((1,9,2), (1,3,6),\) and \((1,−7,8).\)
For exercises 11-14, find the equation of the sphere in standard form that satisfies the given conditions.
11) Center \(C(−1,7,4)\) and radius \(4\)
- Answer
- \((x+1)^2+(y−7)^2+(z−4)^2=16\)
12) Center \(C(−4,7,2)\) and radius \(6\)
13) Diameter \(PQ,\) where \(P(−1,5,7)\) and \(Q(−5,2,9)\)
- Answer
- \(x+3)^2+(y−3.5)^2+(z−8)^2=\dfrac{29}{4}\)
14) Diameter \(PQ,\) where \(P(−16,−3,9)\) and \(Q(−2,3,5)\)
For exercises 15 and 16, find the center and radius of the sphere with an equation in general form that is given.
15) \( x^2+y^2+z^2−4z+3=0\)
- Answer
- Center \(C(0,0,2)\) and radius \(1\)
16) \(x^2+y^2+z^2−6x+8y−10z+25=0\)
For exercises 17-20, express vector \( \vecd{PQ} \) with the initial point at \(P\) and the terminal point at \(Q\)
a. in component form and
b. by using standard unit vectors.
17) \(P(3,0,2)\) and \(Q(−1,−1,4)\)
- Answer
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\(a. \vecd{PQ}=⟨−4,−1,2⟩\)
\(b. \vecd{PQ}=−4\hat{\mathbf i}−\hat{\mathbf j}+2\hat{\mathbf k}\)
18) \(P(0,10,5)\) and \(Q(1,1,−3)\)
19) \(P(−2,5,−8)\) and \(M(1,−7,4)\), where \(M\) is the midpoint of the line segment \(\overline{PQ}\)
- Answer
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\(a. \vecd{PQ}=⟨6,−24,24⟩\)
\(b. \vecd{PQ}=6\hat{\mathbf i}−24\hat{\mathbf j}+24\hat{\mathbf k}\)
20) \(Q(0,7,−6)\) and \(M(−1,3,2)\), where \(M\) is the midpoint of the line segment \(\overline{PQ}\)
21) Find terminal point \(Q\) of vector \(\vecd{PQ}=⟨7,−1,3⟩\) with the initial point at \(P(−2,3,5).\)
- Answer
- \(Q(5,2,8)\)
22) Find initial point \(P\) of vector \(\vecd{PQ}=⟨−9,1,2⟩\) with the terminal point at \(Q(10,0,−1).\)
For exercises 23-26, use the given vectors \(\vecs a\) and \(\vecs b\) to find and express the vectors \(\vecs a+\vecs b, \,4\vecs a\) , and \(−5\vecs a+3\vecs b\) in component form.
23) \(\quad \vecs a=⟨−1,−2,4⟩,\quad \vecs b=⟨−5,6,−7⟩\)
- Answer
- \(\vecs a+\vecs b=⟨−6,4,−3⟩, 4\vecs a=⟨−4,−8,16⟩, −5\vecs a+3\vecs b=⟨−10,28,−41⟩\)
24) \(\quad \vecs a=⟨3,−2,4⟩,\quad \vecs b=⟨−5,6,−9⟩\)
25) \(\quad \vecs a=−\hat{\mathbf k},\quad \vecs b=−\hat{\mathbf i}\)
- Answer
- \(\vecs a+\vecs b=⟨−1,0,−1⟩, 4\vecs a=⟨0,0,−4⟩, −5\vecs a+3\vecs b=⟨−3,0,5⟩\)
26) \(\quad \vecs a=\hat{\mathbf i}+\hat{\mathbf j}+\hat{\mathbf k},\quad \vecs b=2\hat{\mathbf i}−3\hat{\mathbf j}+2\hat{\mathbf k}\)
For exercises 27-30, vectors \(\vecs u\) and \(\vecs v\) are given. Find the magnitudes of vectors \(\vecs u−\vecs v\) and \(−2\vecs u\) .
27) \(\quad \vecs u=2\hat{\mathbf i}+3\hat{\mathbf j}+4\hat{\mathbf k}, \quad \vecs v=−\hat{\mathbf i}+5\hat{\mathbf j}−\hat{\mathbf k}\)
- Answer
- \(\|\vecs u−\vecs v\|=\sqrt{38}, \quad \|−2\vecs u\|=2\sqrt{29}\)
28) \(\quad \vecs u=\hat{\mathbf i}+\hat{\mathbf j}, \quad \vecs v=\hat{\mathbf j}−\hat{\mathbf k}\)
29) \(\quad \vecs u=⟨2\cos t,−2\sin t,3⟩, \quad \vecs v=⟨0,0,3⟩,\quad\) where \(t\) is a real number.
- Answer
- \(\|\vecs u−\vecs v\|=2, \quad \|−2\vecs u\|=2\sqrt{13}\)
30) \(\quad \vecs u=⟨0,1,\sinh t⟩, \quad \vecs v=⟨1,1,0⟩,\quad\) where \(t\) is a real number.
For exercises 31-36, find the unit vector in the direction of the given vector \( \vecs a\) and express it using standard unit vectors.
31) \(\quad \vecs a=3\hat{\mathbf i}−4\hat{\mathbf j}\)
- Answer
- \(\frac{3}{5}\hat{\mathbf i}−\frac{4}{5}\hat{\mathbf j}\)
32) \(\quad \vecs a=⟨4,−3,6⟩\)
33) \(\quad \vecs a=\vecd{PQ}\), where \( P(−2,3,1)\) and \(Q(0,−4,4)\)
- Answer
- \(\frac{\sqrt{62}}{31}\hat{\mathbf i}−\frac{7\sqrt{62}}{62}\hat{\mathbf j}+\frac{3\sqrt{62}}{62}\hat{\mathbf k}\)
34) \(\quad \vecs a=\vecd{OP},\) where \(P(−1,−1,1)\)
35) \(\quad \vecs a=\vecs u−\vecs v+\vecs w,\) where \(\vecs u=\hat{\mathbf i}−\hat{\mathbf j}−\hat{\mathbf k},\quad \vecs v=2\hat{\mathbf i}−\hat{\mathbf j}+\hat{\mathbf k}, \quad\) and \(\vecs w=−\hat{\mathbf i}+\hat{\mathbf j}+3\hat{\mathbf k}\)
- Answer
- \(−\frac{\sqrt{6}}{3}\hat{\mathbf i}+\frac{\sqrt{6}}{6}\hat{\mathbf j}+\frac{\sqrt{6}}{6}\hat{\mathbf k}\)
36) \(\quad \vecs a=2\vecs u+\vecs v−\vecs w,\quad\) where \( \vecs u=\hat{\mathbf i}−\hat{\mathbf k}, \quad \vecs v=2\hat{\mathbf j} \quad\), and \( \vecs w=\hat{\mathbf i}−\hat{\mathbf j}\)
37) Determine whether \(\vecd{AB}\) and \(\vecd{PQ}\) are equivalent vectors, where \(A(1,1,1),\,B(3,3,3),\,P(1,4,5),\) and \(Q(3,6,7).\)
- Answer
- Equivalent vectors
38) Determine whether the vectors \(\vecd{AB}\) and \(\vecd{PQ}\) are equivalent, where \( A(1,4,1),\, B(−2,2,0),\, P(2,5,7),\) and \( Q(−3,2,1)\).
For exercises 39-42, find vector \( \vecs u\) with a magnitude that is given and satisfies the given conditions.
39) \(\quad \vecs v=⟨7,−1,3⟩, \, ‖\vecs u‖=10\), and \(\vecs u\) and \(\vecs v\) have the same direction
- Answer
- \(\vecs u=⟨\frac{70\sqrt{59}}{59},−\frac{10\sqrt{59}}{59},\frac{30\sqrt{59}}{59}⟩\)
40) \(\quad \vecs v=⟨2,4,1⟩,\, ‖\vecs u‖=15\), and \(\vecs u\) and \(\vecs v\) have the same direction
41) \(\quad \vecs v=⟨2\sin t,\, 2\cos t,1⟩, ‖\vecs u‖=2,\vecs u\) and \(\vecs v\) have opposite directions for any \(t\), where \(t\) is a real number
- Answer
- \(\vecs u=⟨−\frac{4\sqrt{5}}{5}\sin t,−\frac{4\sqrt{5}}{5}\cos t,−\frac{2\sqrt{5}}{5}⟩\)
42) \(\quad \vecs v=⟨3\sinh t,0,3⟩,\, ‖\vecs u‖=5\), and \(\vecs u\) and \(\vecs v\) have opposite directions for any \(t\), where \(t\) is a real number
43) Determine a vector of magnitude \(5\) in the direction of vector \(\vecd{AB}\), where \(A(2,1,5)\) and \(B(3,4,−7).\)
- Answer
- \(⟨\frac{5\sqrt{154}}{154},\frac{15\sqrt{154}}{154},−\frac{30\sqrt{154}}{77}⟩\)
44) Find a vector of magnitude \(2\) that points in the opposite direction than vector \(\vecd{AB}\), where \(A(−1,−1,1)\) and \(B(0,1,1).\) Express the answer in component form.
45) Consider the points \(A(2,α,0), \, B(0,1,β),\) and \(C(1,1,β)\), where \(α\) and \(β\) are negative real numbers. Find \(α\) and \(β\) such that \(\|\vecd{OA}−\vecd{OB}+\vecd{OC}\|=\|\vecd{OB}\|=4.\)
- Answer
- \(α=−\sqrt{7}, \,β=−\sqrt{15}\)
46) Consider points \(A(α,0,0),\,B(0,β,0),\) and \(C(α,β,β),\) where \(α\) and \(β\) are positive real numbers. Find \(α\) and \(β\) such that \(\|\overline{OA}+\overline{OB}\|=\sqrt{2}\) and \(\|\overline{OC}\|=\sqrt{3}\).
47) Let \(P(x,y,z)\) be a point situated at an equal distance from points \(A(1,−1,0)\) and \(B(−1,2,1)\). Show that point \(P\) lies on the plane of equation \(−2x+3y+z=2.\)
48) Let \(P(x,y,z)\) be a point situated at an equal distance from the origin and point \(A(4,1,2)\). Show that the coordinates of point P satisfy the equation \(8x+2y+4z=21.\)
49) The points \(A,B,\) and \(C\) are collinear (in this order) if the relation \({\|\vecd{AB}\|+\|\vecd{BC}\|=\|\vecd{AC}\|}\) is satisfied. Show that \(A(5,3,−1),\, B(−5,−3,1),\) and \(C(−15,−9,3)\) are collinear points.
50) Show that points \(A(1,0,1), \, B(0,1,1),\) and \(C(1,1,1)\) are not collinear.
51) [T] A force \(\vecs F\) of \(50 \,N\) acts on a particle in the direction of the vector \(\vecd{OP}\), where \(P(3,4,0).\)
a. Express the force as a vector in component form.
b. Find the angle between force \(\vecs F\) and the positive direction of the \(x\)-axis. Express the answer in degrees rounded to the nearest integer.
- Answer
- \(a. \vecs F=⟨30,40,0⟩; \quad b. 53°\)
52) [T] A force \(\vecs F\) of \(40\,N\) acts on a box in the direction of the vector \(\vecd{OP}\), where \(P(1,0,2).\)
a. Express the force as a vector by using standard unit vectors.
b. Find the angle between force \(\vecs F\) and the positive direction of the \(x\)-axis.
53) If \(\vecs F\) is a force that moves an object from point \(P_1(x_1,y_1,z_1)\) to another point \(P_2(x_2,y_2,z_2)\), then the displacement vector is defined as \( \vecs D=(x_2−x_1)\hat{\mathbf i}+(y_2−y_1)\hat{\mathbf j}+(z_2−z_1)\hat{\mathbf k}\). A metal container is lifted \(10\) m vertically by a constant force \(\vecs F\). Express the displacement vector \(\vecs D\) by using standard unit vectors.
- Answer
- \(\vecs D=10\hat{\mathbf k}\)
54) A box is pulled \(4\) yd horizontally in the \(x\)-direction by a constant force \( \vecs F\). Find the displacement vector in component form.
55) The sum of the forces acting on an object is called the resultant or net force. An object is said to be in static equilibrium if the resultant force of the forces that act on it is zero. Let \(\vecs F_1=⟨10,6,3⟩, \vecs F_2=⟨0,4,9⟩\), and \(\vecs F_3=⟨10,−3,−9⟩\) be three forces acting on a box. Find the force \(\vecs F_4\) acting on the box such that the box is in static equilibrium. Express the answer in component form.
- Answer
- \(\vecs F_4=⟨−20,−7,−3⟩\)
56) [T] Let \(\vecs F_k=⟨1,k,k^2⟩, k=1,...,n\) be \(n\) forces acting on a particle, with \(n≥2.\)
a. Find the net force \(\vecs F=\sum_{k=1}^n\vecs F_k.\) Express the answer using standard unit vectors.
b. Use a computer algebra system (CAS) to find \(n\) such that \(\|\vecs F\|<100.\)
57) The force of gravity \( \vecs F\) acting on an object is given by \( \vecs F=m\vecs g\), where \(m\) is the mass of the object (expressed in kilograms) and \(\vecs g\) is acceleration resulting from gravity, with \( \|\vecs g\|=9.8 \,N/kg.\) A 2-kg disco ball hangs by a chain from the ceiling of a room.
a. Find the force of gravity \(\vecs F\) acting on the disco ball and find its magnitude.
b. Find the force of tension \(\vecs T\) in the chain and its magnitude.
Express the answers using standard unit vectors.
- Answer
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\(a. \vecs F=−19.6\hat{\mathbf k}, \quad \|\vecs F\|=19.6 \,N\)
\(b. \vecs T=19.6\hat{\mathbf k}, \quad \|\vecs T\|=19.6 \,N\)
58) A 5-kg pendant chandelier is designed such that the alabaster bowl is held by four chains of equal length, as shown in the following figure.
a. Find the magnitude of the force of gravity acting on the chandelier.
b. Find the magnitudes of the forces of tension for each of the four chains (assume chains are essentially vertical).
59) [T] A 30-kg block of cement is suspended by three cables of equal length that are anchored at points \(P(−2,0,0), Q(1,\sqrt{3},0),\) and \(R(1,−\sqrt{3},0)\). The load is located at \(S(0,0,−2\sqrt{3})\), as shown in the following figure. Let \(\vecs F_1, \vecs F_2\), and \(\vecs F_3\) be the forces of tension resulting from the load in cables \(RS,QS,\) and \(PS,\) respectively.
a. Find the gravitational force \(\vecs F\) acting on the block of cement that counterbalances the sum \(\vecs F_1+\vecs F_2+\vecs F_3\) of the forces of tension in the cables.
b. Find forces \(\vecs F_1, \vecs F_2,\) and \( \vecs F_3\). Express the answer in component form.
- Answer
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a. \(\vecs F=−294\hat{\mathbf k}\) N;
b. \(\vecs F_1=⟨−\frac{49\sqrt{3}}{3},49,−98⟩, \vecs F_2=⟨−\frac{49\sqrt{3}}{3},−49,−98⟩\), and \(\vecs F_3=⟨\frac{98\sqrt{3}}{3},0,−98⟩\) (each component is expressed in newtons)
60) Two soccer players are practicing for an upcoming game. One of them runs 10 m from point A to point B. She then turns left at \(90°\) and runs 10 m until she reaches point C. Then she kicks the ball with a speed of 10 m/sec at an upward angle of \(45°\) to her teammate, who is located at point A. Write the velocity of the ball in component form.
61) Let \(\vecs r(t)=⟨x(t),\, y(t), \, z(t)⟩\) be the position vector of a particle at the time \(t∈[0,T]\), where \(x,y,\) and \(z\) are smooth functions on \([0,T]\). The instantaneous velocity of the particle at time \(t\) is defined by vector \(\vecs v(t)=⟨x'(t), \, y'(t), \, z'(t)⟩\), with components that are the derivatives with respect to \(t\), of the functions \(x, y\), and \(z\), respectively. The magnitude \(∥\vecs v(t)∥\) of the instantaneous velocity vector is called the speed of the particle at time \(t\). Vector \(\vecs a(t)=⟨x''(t), \, y''(t), \, z''(t)⟩\), with components that are the second derivatives with respect to \(t\), of the functions \(x,y,\) and \(z\), respectively, gives the acceleration of the particle at time \(t\). Consider \(\vecs r(t)=⟨\cos t,\, \sin t, \, 2t⟩\) the position vector of a particle at time \(t∈[0,30],\) where the components of \(\vecs r\) are expressed in centimeters and time is expressed in seconds.
a. Find the instantaneous velocity, speed, and acceleration of the particle after the first second. Round your answer to two decimal places.
b. Use a CAS to visualize the path of the particle—that is, the set of all points of coordinates \((\cos t,\sin t,2t),\) where \(t∈[0,30].\)
- Answer
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\(a. \vecs v(1)=⟨−0.84,0.54,2⟩\) (each component is expressed in centimeters per second); \(∥\vecs v(1)∥=2.24\) (expressed in centimeters per second); \(\vecs a(1)=⟨−0.54,−0.84,0⟩\) (each component expressed in centimeters per second squared);
\(b.\)
62) [T] Let \(\vecs r(t)=⟨t,2t^2,4t^2⟩\) be the position vector of a particle at time \(t\) (in seconds), where \(t∈[0,10]\) (here the components of \(\vecs r\) are expressed in centimeters).
a. Find the instantaneous velocity, speed, and acceleration of the particle after the first two seconds. Round your answer to two decimal places.
b. Use a CAS to visualize the path of the particle defined by the points \((t, \, 2t^2, \, 4t^2),\) where \(t∈[0, \, 60].\)
Contributors
Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org .


2.2: Paradigms, Theories, and How They Shape a Researcher’s Approach
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Learning Objectives
- Define paradigm, and describe the significance of paradigms.
- Identify and describe the four predominant paradigms found in the social sciences.
- Define theory.
- Describe the role that theory plays in sociological inquiry.
The terms paradigm and theory are often used interchangeably in social science, although social scientists do not always agree whether these are identical or distinct concepts. In this text, we will make a slight distinction between the two ideas because thinking about each concept as analytically distinct provides a useful framework for understanding the connections between research methods and social scientific ways of thinking.
Paradigms in Social Science
For our purposes, we’ll define paradigm as an analytic lens, a way of viewing the world and a framework from which to understand the human experience (Kuhn, 1962).See Kuhn’s seminal work for more on paradigms: Kuhn, T. (1962). The structure of scientific revolutions . Chicago, IL: University of Chicago Press. It can be difficult to fully grasp the idea of paradigmatic assumptions because we are very ingrained in our own, personal everyday way of thinking. For example, let’s look at people’s views on abortion. To some, abortion is a medical procedure that should be undertaken at the discretion of each individual woman who might experience an unwanted pregnancy. To others, abortion is murder and members of society should collectively have the right to decide when, if at all, abortion should be undertaken. Chances are, if you have an opinion about this topic you are pretty certain about the veracity of your perspective. Then again, the person who sits next to you in class may have a very different opinion and yet be equally confident about the truth of his or her perspective. Which of you is correct? You are each operating under a set of assumptions about the way the world does—or at least should—work. Perhaps your assumptions come from your particular political perspective, which helps shape your view on a variety of social issues, or perhaps your assumptions are based on what you learned from your parents or in church. In any case, there is a paradigm that shapes your stance on the issue.
In Chapter 1 we discussed the various ways that we know what we know. Paradigms are a way of framing what we know, what we can know, and how we can know it. In social science, there are several predominant paradigms, each with its own unique ontological and epistemological perspective. Let’s look at four of the most common social scientific paradigms that might guide you as you begin to think about conducting research.
The first paradigm we’ll consider, called positivism , is probably the framework that comes to mind for many of you when you think of science. Positivism is guided by the principles of objectivity, knowability, and deductive logic. Deductive logic is discussed in more detail in the section that follows. Auguste Comte, whom you might recall from your introduction to sociology class as the person who coined the term sociology , argued that sociology should be a positivist science (Ritzer & Goodman, 2004).Ritzer, G., & Goodman, D. J. (2004). Classical sociological theory (4th ed.). New York, NY: McGraw-Hill. The positivist framework operates from the assumption that society can and should be studied empirically and scientifically. Positivism also calls for a value-free sociology , one in which researchers aim to abandon their biases and values in a quest for objective, empirical, and knowable truth.
Another predominant paradigm in sociology is social constructionism . Peter Berger and Thomas Luckman (1966)Berger, P. L., & Luckman, T. (1966). The social construction of reality: A treatise in the sociology of knowledge . New York, NY: Doubleday. are credited by many for having developed this perspective in sociology. While positivists seek “the truth,” the social constructionist framework posits that “truth” is a varying, socially constructed, and ever-changing notion. This is because we, according to this paradigm, create reality ourselves (as opposed to it simply existing and us working to discover it) through our interactions and our interpretations of those interactions. Key to the social constructionist perspective is the idea that social context and interaction frame our realities. Researchers operating within this framework take keen interest in how people come to socially agree, or disagree, about what is real and true. Consideration of how meanings of different hand gestures vary across different regions of the world aptly demonstrates that meanings are constructed socially and collectively. Think about what it means to you when you see a person raise his or her middle finger. We probably all know that person isn’t very happy (nor is the person to whom the finger is being directed). In some societies, it is another gesture, the thumbs up, that raises eyebrows. While the thumbs up may have a particular meaning in our culture, that meaning is not shared across cultures (Wong, 2007).For more about how the meanings of hand gestures vary by region, you might read the following blog entry: Wong, W. (2007). The top 10 hand gestures you’d better get right. Retrieved from http://www.languagetrainers.co.uk/bl...-hand-gestures
It would be a mistake to think of the social constructionist perspective as only individualistic. While individuals may construct their own realities, groups—from a small one such as a married couple to large ones such as nations—often agree on notions of what is true and what “is.” In other words, the meanings that we construct have power beyond the individual people who create them. Therefore, the ways that people work to change such meanings is of as much interest to social constructionists as how they were created in the first place.
A third paradigm is the critical paradigm . At its core, the critical paradigm is focused on power, inequality, and social change. Although some rather diverse perspectives are included here, the critical paradigm, in general, includes ideas developed by early social theorists, such as Max Horkheimer (Calhoun, Gerteis, Moody, Pfaff, & Virk),Calhoun, C., Gerteis, J., Moody, J., Pfaff, S., & Virk, I. (Eds.). (2007). Classical sociological theory (2nd ed.). Malden, MA: Blackwell. and later works developed by feminist scholars, such as Nancy Fraser (1989).Fraser, N. (1989). Unruly practices: Power, discourse, and gender in cotemporary social theory . Minneapolis, MN: University of Minnesota Press. Unlike the positivist paradigm, the critical paradigm posits that social science can never be truly objective or value-free. Further, this paradigm operates from the perspective that scientific investigation should be conducted with the express goal of social change in mind.
Finally, postmodernism is a paradigm that challenges almost every way of knowing that many social scientists take for granted (Best & Kellner, 1991).Best, S., & Kellner, D. (1991). Postmodern theory: Critical interrogations . New York, NY: Guilford. While positivists claim that there is an objective, knowable truth, postmodernists would say that there is not. While social constructionists may argue that truth is in the eye of the beholder (or in the eye of the group that agrees on it), postmodernists may claim that we can never really know such truth because, in the studying and reporting of others’ truths, the researcher stamps her or his own truth on the investigation. Finally, while the critical paradigm may argue that power, inequality, and change shape reality and truth, a postmodernist may in turn ask, whose power, whose inequality, whose change, whose reality, and whose truth? As you might imagine, the postmodernist paradigm poses quite a challenge for social scientific researchers. How does one study something that may or may not be real or that is only real in your current and unique experience of it? This fascinating question is worth pondering as you begin to think about conducting your own sociological research. Table 2.1 summarizes each of the paradigms discussed here.
| Paradigm | Emphasis | Assumption |
|---|---|---|
| Positivism | Objectivity, knowability, and deductive logic | Society can and should be studied empirically and scientifically. |
| Social constructionism | Truth as varying, socially constructed, and ever-changing | Reality is created collectively and that social context and interaction frame our realities. |
| Critical | Power, inequality, and social change | Social science can never be truly value-free and should be conducted with the express goal of social change in mind. |
| Postmodernism | Inherent problems with previous paradigms | Truth in any form may or may not be knowable. |
Sociological Theories
Much like paradigms, theories provide a way of looking at the world and of understanding human interaction. Like paradigms, theories can be sweeping in their coverage. Some sociological theories, for example, aim to explain the very existence and continuation of society as we know it. Unlike paradigms, however, theories might be narrower in focus, perhaps just aiming to understand one particular phenomenon, without attempting to tackle a broader level of explanation. In a nutshell, theory might be thought of as a way of explanation or as “an explanatory statement that fits the evidence” (Quammen, 2004).Quammen, D. (2004, November). Was Darwin wrong? National Geographic , pp. 2–35. At their core, theories can be used to provide explanations of any number or variety of phenomena. They help us answer the “why” questions we often have about the patterns we observe in social life. Theories also often help us answer our “how” questions. While paradigms may point us in a particular direction with respect to our “why” questions, theories more specifically map out the explanation, or the “how,” behind the “why.”
Introductory sociology textbooks typically teach students about “the big three” sociological theories—structural functionalism, conflict theory, and symbolic interactionism (Barkan, 2011; Henslin, 2010).The theory discussions in each of the following texts provide useful examples: [citation redacted per publisher request] ; Henslin, J. M. (2010). Sociology: A down to earth approach, core concepts (4th ed.). Boston, MA: Pearson. Most also mention at least a few additional theories or theorists (Sprague, 1997).See Sprague’s 1997 critique of social theory for a compelling and well-developed argument in favor of sociology reorganizing theory with the aim of increasing its relevance to social life today and bridging, rather than building, boundaries across diverse perspectives and disciplines: Sprague, J. (1997). Holy men and big guns: The can[n]on in social theory. Gender & Society, 11 , 88–107. As you probably recall from your introductory sociology course, structural functionalists focus on the interrelations between various parts of society and how each part works with the others to make society function in the way that it does. Conflict theorists are interested in questions of power and who wins and who loses based on the way that society is organized. Finally, symbolic interactionists focus on how meaning is created and negotiated though meaningful (i.e., symbolic) interactions. Just as researchers might examine the same topic from different levels of inquiry, so, too, could they investigate the same topic from different theoretical perspectives. In this case, even their research questions could be the same, but the way they make sense of whatever phenomenon it is they are investigating will be shaped in large part by the theoretical assumptions that lie behind their investigation.
| Paradigm | Focuses on | A study of sport might examine |
|---|---|---|
| Structural functionalism | Interrelations between parts of society; how parts work together | Positive, negative, intended, and unintended consequences of professional sport leagues |
| Conflict theory | Who wins and who loses based on the way that society is organized | Issues of power in sport such as differences in access to and participation in sport |
| Symbolic interactionism | How meaning is created and negotiated though interactions | How the rules of sport of are constructed, taught, and learned |
Within each area of specialization in sociology, there are many other theories that aim to explain more specific types of interactions. For example, within the sociological study of sexual harassment, different theories posit different explanations for why harassment occurs. One theory, first developed by criminologists, is called routine activities theory. It posits that sexual harassment is most likely to occur when a workplace lacks unified groups and when potentially vulnerable targets and motivated offenders are both present (DeCoster, Estes, & Mueller, 1999).DeCoster, S., Estes, S. B., & Mueller, C. W. (1999). Routine activities and sexual harassment in the workplace. Work and Occupations, 26 , 21–49. Other theories of sexual harassment, called relational theories, suggest that a person’s relationships, such as their marriages or friendships, are the key to understanding why and how workplace sexual harassment occurs and how people will respond to it when it does occur (Morgan, 1999).Morgan, P. A. (1999). Risking relationships: Understanding the litigation choices of sexually harassed women. The Law and Society Review, 33 , 201–226. Relational theories focus on the power that different social relationships provide (e.g., married people who have supportive partners at home might be more likely than those who lack support at home to report sexual harassment when it occurs).  These theories posit that the way our current gender system is organized, where those who are the most masculine have the most power, best explains why and how workplace sexual harassment occurs (MacKinnon, 1979).MacKinnon, C. 1979. Sexual harassment of working women: A case of sex discrimination . New Haven, CT: Yale University Press. As you might imagine, which theory a researcher applies to examine the topic of sexual harassment will shape the questions the researcher asks about harassment. It will also shape the explanations the researcher provides for why harassment occurs.
KEY TAKEAWAYS
- Paradigms shape our everyday view of the world.
- Sociologists use theory to help frame their research questions and to help them make sense of the answers to those questions.
- Some sociological theories are rather sweeping in their coverage and attempt to explain, broadly, how and why societies are organized in particular ways.
- Other sociological theories aim to explain more specific events or interactions.
EXERCISES
- Of the four paradigms described, which do you find most compelling? Why?
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Feeling confused about the social constructionism paradigm? Check out the 10-minute lecture that illustrates this framework online at:
www.youtube.com/v/GVVWmZAStn8
.
After watching this lecture, come up with a two- to four-sentence description of social constructionism that would make sense to someone who has no background in sociological theory.


9.1: Maxwell’s Equations in Differential Phasor Form
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In this section, we derive the phasor form of Maxwell’s Equations from the general time-varying form of these equations. Here we are interested exclusively in the differential (“point”) form of these equations. It is assumed that the reader is comfortable with phasor representation and its benefits; if not, a review of Section 1.5 is recommended before attempting this section.
Maxwell’s Equations in differential time-domain form are Gauss’ Law: \[\nabla\cdot{\bf D}=\rho_v \label{m0042_eGL} \] the Maxwell-Faraday Equation (MFE): \[\nabla\times{\bf E}=-\frac{\partial}{\partial t}{\bf B} \label{m0042_eMFE} \] Gauss’ Law for Magnetism (GSM): \[\nabla\cdot{\bf B}=0 \nonumber \] and Ampere’s Law: \[\nabla\times{\bf H}={\bf J} + \frac{\partial}{\partial t}{\bf D} \nonumber \]
We begin with Gauss’s Law (Equation \ref{m0042_eGL}). We define \(\widetilde{\bf D}\) and \(\widetilde{\rho}_v\) as phasor quantities through the usual relationship: \[{\bf D} = \mbox{Re} \left\{ \widetilde{\bf D} e^{j\omega t} \right\} \nonumber \] and \[\rho_v = \mbox{Re} \left\{ \widetilde{\rho}_v e^{j\omega t} \right\} \nonumber \]
Substituting these expressions into Equation \ref{m0042_eGL}: \[\nabla \cdot \left[ \mbox{Re} \left\{ \widetilde{\bf D} e^{j\omega t} \right\} \right] = \mbox{Re} \left\{ \widetilde{\rho}_v e^{j\omega t} \right\} \nonumber \] Divergence is a real-valued linear operator. Therefore, we may exchange the order of the “Re” and “\(\nabla\cdot\)” operations (this is “Claim 2” from Section 1.5): \[\mbox{Re} \left\{ \nabla \cdot \left[ \widetilde{\bf D} e^{j\omega t}\right] \right\} = \mbox{Re} \left\{ \widetilde{\rho}_v e^{j\omega t} \right\} \nonumber \]
Next, we note that the differentiation associated with the divergence operator is with respect to position and not with respect to time, so the order of operations may be further rearranged as follows: \[\mbox{Re} \left\{ \left[ \nabla \cdot \widetilde{\bf D} \right] e^{j\omega t} \right\} = \mbox{Re} \left\{ \widetilde{\rho}_v e^{j\omega t} \right\} \nonumber \] Finally, we note that the equality of the left and right sides of the above equation implies the equality of the associated phasors (this is “Claim 1” from Section 1.5); thus, \[\boxed{ \nabla \cdot \widetilde{\bf D} = \widetilde{\rho}_v } \label{m0042_e1} \] In other words, the differential form of Gauss’ Law for phasors is identical to the differential form of Gauss’ Law for physical time-domain quantities.
The same procedure applied to the MFE is only a little more complicated. First, we establish the phasor representations of the electric and magnetic fields: \[{\bf E} = \mbox{Re} \left\{ \widetilde{\bf E} e^{j\omega t} \right\} \nonumber \] \[{\bf B} = \mbox{Re} \left\{ \widetilde{\bf B} e^{j\omega t} \right\} \nonumber \]
After substitution into Equation \ref{m0042_eMFE}: \[\nabla \times \left[ \mbox{Re} \left\{ \widetilde{\bf E} e^{j\omega t} \right\} \right] = -\frac{\partial}{\partial t} \left[ \mbox{Re} \left\{ \widetilde{\bf B} e^{j\omega t} \right\} \right] \nonumber \] Both curl and time-differentiation are real-valued linear operations, so we are entitled to change the order of operations as follows: \[\mbox{Re} \left\{ \nabla \times \left[ \widetilde{\bf E} e^{j\omega t} \right] \right\} = -\mbox{Re} \left\{ \frac{\partial}{\partial t} \left[ \widetilde{\bf B} e^{j\omega t} \right] \right\} \nonumber \]
On the left, we note that the time dependence \(e^{j\omega t}\) can be pulled out of the argument of the curl operator, since it does not depend on position: \[\mbox{Re} \left\{ \left[ \nabla \times \widetilde{\bf E} \right] e^{j\omega t} \right\} = -\mbox{Re} \left\{ \frac{\partial}{\partial t} \left[ \widetilde{\bf B} e^{j\omega t} \right] \right\} \nonumber \] On the right, we note that \(\widetilde{\bf B}\) is constant with respect to time (because it is a phasor), so:
\begin{aligned}
\operatorname{Re}\left\{[\nabla \times \tilde{\mathbf{E}}] e^{j \omega t}\right\} &=-\operatorname{Re}\left\{\widetilde{\mathbf{B}} \frac{\partial}{\partial t} e^{j \omega t}\right\} \\
&=-\operatorname{Re}\left\{\widetilde{\mathbf{B}} j \omega e^{j \omega t}\right\} \\
&=\operatorname{Re}\left\{[-j \omega \widetilde{\mathbf{B}}] e^{j \omega t}\right\}
\end{aligned}
And so we have found: \[\boxed{ \nabla \times \widetilde{\bf E} = -j\omega\widetilde{\bf B} } \label{m0042_e2} \]
Let’s pause for a moment to consider the above result. In the general time-domain version of the MFE, we must take spatial derivatives of the electric field and time derivatives of the magnetic field. In the phasor version of the MFE, the time derivative operator has been replaced with multiplication by \(j\omega\). This is a tremendous simplification since the equations now involve differentiation over position only. Furthermore, no information is lost in this simplification – for a reminder of why that is, see the discussion of Fourier Analysis at the end of Section 1.5. Without this kind of simplification, much of what is now considered “basic” engineering electromagnetics would be intractable.
The procedure for conversion of the remaining two equations is very similar, yielding: \[\boxed{ \nabla \cdot \widetilde{\bf B} = 0 } \label{m0042_e3} \] \[\boxed{ \nabla \times \widetilde{\bf H} = \widetilde{\bf J} + j\omega\widetilde{\bf D} } \label{m0042_e4} \] The details are left as an exercise for the reader.
The differential form of Maxwell’s Equations (Equations \ref{m0042_e1}, \ref{m0042_e2}, \ref{m0042_e3}, and \ref{m0042_e4}) involve operations on the phasor representations of the physical quantities. These equations have the advantage that differentiation with respect to time is replaced by multiplication by \(j\omega\).


10.1: Prelude to Hypothesis Testing with Two Samples
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Learning Objectives
By the end of this chapter, the student should be able to:
- Classify hypothesis tests by type.
- Conduct and interpret hypothesis tests for two population means, population standard deviations known.
- Conduct and interpret hypothesis tests for two population means, population standard deviations unknown.
- Conduct and interpret hypothesis tests for two population proportions.
- Conduct and interpret hypothesis tests for matched or paired samples.
Studies often compare two groups. For example, researchers are interested in the effect aspirin has in preventing heart attacks. Over the last few years, newspapers and magazines have reported various aspirin studies involving two groups. Typically, one group is given aspirin and the other group is given a placebo. Then, the heart attack rate is studied over several years.
There are other situations that deal with the comparison of two groups. For example, studies compare various diet and exercise programs. Politicians compare the proportion of individuals from different income brackets who might vote for them. Students are interested in whether SAT or GRE preparatory courses really help raise their scores.
You have learned to conduct hypothesis tests on single means and single proportions. You will expand upon that in this chapter. You will compare two means or two proportions to each other. The general procedure is still the same, just expanded.
To compare two means or two proportions, you work with two groups. The groups are classified either as independent or matched pairs. Independent groups consist of two samples that are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population. Matched pairs consist of two samples that are dependent. The parameter tested using matched pairs is the population mean. The parameters tested using independent groups are either population means or population proportions.
This chapter relies on either a calculator or a computer to calculate the degrees of freedom, the test statistics, and p -values. TI-83+ and TI-84 instructions are included as well as the test statistic formulas. When using a TI-83+ or TI-84 calculator, we do not need to separate two population means, independent groups, or population variances unknown into large and small sample sizes. However, most statistical computer software has the ability to differentiate these tests.
This chapter deals with the following hypothesis tests:
Independent groups (samples are independent)
- Test of two population means.
- Test of two population proportions.
Matched or paired samples (samples are dependent)
- Test of the two population proportions by testing one population mean of differences.


14.3: Reading- Cultural Factors Shaping the Global Marketing Environment
The Immense Impact of Culture in Global Marketing
Culture refers to the influence of religious, family, educational, and social systems on people, how they live their lives, and the choices they make. Marketing always exists in an environment shaped by culture. Organizations that intend to market products in different countries must be sensitive to the cultural factors at work in their target markets. Even cultural differences between different countries–or between different regions in the same country–seem small, marketers who ignore them risk failure in implementing their programs.
Culture is complex, and fully appreciating its influence takes significant time, effort, and expertise. Various features of a culture can create an illusion of similarity, but marketers need to dig deeper to make sure they truly understand the people and environments in which they work. Even a common language does not guarantee similarity of interpretation. For example, in the U.S. we purchase “cans” of various grocery products, but the British purchase “tins.” In India, where English is one of a number of officially recognized languages, “matrimonial” is used as a noun in casual conversation, referring to personal ads in newspapers seeking marriage partners.
Several dimensions of culture that require particular attention from global marketers are listed below.
Language
As suggested above, the importance of language differences cannot be overemphasized, and there are nearly three thousand languages in the world. Language differences can be a challenge for marketers designing IMC campaigns, product labels, brand and product names, tag lines, and so on. Finding a single brand name that works universally in terms of pronunciation, meaning, and “ownability” is a monumental challenge. Of course, correct and grammatical use of language in marketing communication is essential for a product, brand, or company to be viewed as credible, trustworthy, and of high-quality.
Language gains complexity when a country has more than one officially recognized language. To illustrate, in Canada, national law requires that labels include both English and French. In India and China, more than two hundred different dialects are spoken. India has more than twenty officially recognized languages. Mainland China’s official spoken language is Standard Mandarin, and several autonomous regions have designated other additional official languages. Meanwhile in Hong Kong and Macau, Cantonese Chinese, English, and Portuguese are the official languages. Clearly language can become a very complicated issue for marketers very quickly!
Finally, marketers should be attuned to what they communicate when they choose which languages to use–or not use. In Eastern Europe, for example, the long history of Soviet occupation during the Cold War has left many inhabitants with a negative perception of the Russian language. Products that carry Russian labeling may suffer accordingly.
Customs and Taboos
All cultures have their own unique sets of customs and taboos. It is important for marketers to learn about these customs and taboos so that they will know what is acceptable and unacceptable for their marketing programs. For example, in Japan, the number four is considered unlucky, and products packages containing four items are avoided by many consumers. In Middle Eastern countries where Islamic law is strictly observed, images displaying the uncovered arms or legs of the female body are considered offensive. Meanwhile in Egypt, where many women wear the headscarf or hijab in public, an increasing number of younger women are in work and educational settings where gender segregation does not exist. Marketers struggle with whether to portray women with or without the hijab , knowing that they risk offending some of their target audience with either choice. Marketers should seek guidance from native experts familiar with local culture and customers. Marketing research can also help marketers understand and navigate these complex issues.
Values
The role of values in society is to dictate what is acceptable or unacceptable. Values are part of the societal fabric of a culture, and they can also be expressed individually, arising from the influence of family, education, moral, and religious beliefs. Values are also learned through experiences. Not surprisingly, values can influence consumer perceptions and purchasing behavior. For example, consumers in some countries, such as the United States, tend to be individualistic and make many purchasing decisions based on their own personal preferences. In other countries, such as Japan, the well-being of the group is more highly valued, and buying decisions are more influenced by the well-being of the group, such as the family. Based on these differences in values, it is not surprising that ads featuring individuals tend to do better in countries where individualism is an important value, and ads featuring groups do better in countries where the group’s well-being is a higher value.
Time and Punctuality
Different cultures have different sensitivities around time and punctuality. In some countries, being slightly late to a meeting is acceptable, whereas in other countries it is very insulting. For cultures that highly value punctuality, being on time is a sign of good planning, organization, and respect. In cultures where precise punctuality is less important, there is often a greater emphasis on relationships. The fact that a meeting happens is more important than when it happens.
While there are cultural stereotypes about time management (such as the laid-back “island time” many residents of island nations refer to), the best rule of thumb in business is to be punctual and meet deadlines as promised. You will not insult people by following this rule. Also, it is wise not to apply popular stereotypes to individual people for whom the cultural stereotype may or may not be true. You should let a person’s behavior speak for itself, and always treat others with the same level of courtesy you would expect from them.
Business Norms
Business norms vary from one country to the next and may present challenges to foreigners not used to operating according to the particular norms of the host country. In business meetings in Japan, for example, it is expected that the most senior person representing an organization will lead the discussion, and more junior-level colleagues may not speak at all. The role of alcohol in business meetings varies widely by culture: in Middle Eastern cultures where alcohol is forbidden, it may be insulting to serve or even offer an alcoholic beverage. In China, many rounds of toasts are customary as part of formal dinner meetings.
Likewise, business norms around greetings and physical contact also vary. American-style handshakes have become accepted as a business norm in many cultures, but this custom is not universal. In Japan and some other Asian cultures, a respectful bow is the traditional business greeting, although the handshake is becoming more common. In Islamic cultures, contact between men and women is a sensitive issue, even in business settings. In those regions and cultures, it is best to shake hands with a woman only if she extends her hand first. Similarly, Western women may avoid causing embarrassment by shaking hands only if a hand is extended to her. In India, the namaste (a slight bow with hands brought together on the chest) remains a respectful, if traditional business greeting particularly when interacting with women and older people.
Always seek guidance from a trusted colleague or friend who has experience in the local customs and can offer coaching on proper etiquette.
Religious Beliefs and Celebrations
As discussed earlier in this module, religious beliefs and practice can strongly influence what consumers buy (or don’t buy), when they shop, and how they conduct business. It is important for marketers to understand the influence of religion on consumer culture in the markets where they operate, so that their marketing activities can be appropriately sensitive. Failing to respect religious beliefs or cultures can seriously undermine the reputation of a company or brand. At the same time, marketers who are attuned to the impact of religion on local culture can find great advantage in aligning marketing messages and promotional opportunities to religious practice.
For example, all the major world religions observe holidays that include feasting and gift giving. These festival seasons tend to be prime shopping seasons as well, such as the Christmas season in Western cultures, or Ramadan in Muslim cultures. Religious beliefs lead to sensitivities about certain products: in the Hindu religion, cows are considered sacred and people refrain from eating beef. Observant Jews and Muslims consider pork unclean, and they consume only kosher or halal meats, respectively. Many religions eschew alcohol: for example, devout Sikhs, Muslims, Mormons, Buddhists, and Southern Baptists all refrain from drinking.
Religious beliefs may cause sensitivities around revealing images or sexually suggestive material. Religious beliefs associated with the symbolism of different colors may create either preferences for or rejection of certain products and marketing materials. The link between religious practice and gender roles may affect which members of the family influence which types of buying decisions. It is important, however, for marketers not to oversimplify how decision making happens in these settings. Even if a woman, for example, is not the primary buyer, she may exercise strong influence of many consumer decisions.
Here, as in other areas of cultural impact, is it crucial for marketers to educate themselves about the people and cultures they are targeting for marketing and business in order to use cultural knowledge to advantage.
Contributors and Attributions
- Revision and adaptiona. Provided by : Lumen Learning. License : CC BY-SA: Attribution-ShareAlike
- The Global Marketing Environment. Provided by : Lumen Learning. Located at : courses.candelalearning.com/principlesmktg1x2kscope/chapter/13-2-the-global-marketing-environment/. License : CC BY-SA: Attribution-ShareAlike
- Matthew G. Authored by : Matthew G. Located at : https://www.flickr.com/photos/streetmatt/13926933406/ . License : CC BY: Attribution
- Fixing my hijab. Authored by : rana ossama. Located at : https://www.flickr.com/photos/ranoush/2113881040/ . License : CC BY-SA: Attribution-ShareAlike
- Too Cool, Surmi Tribe. Authored by : Rod Waddington. Located at : https://www.flickr.com/photos/rod_waddington/10659035426/ . License : CC BY-SA: Attribution-ShareAlike
- President Obama Offers Namaste Greeting in India. Provided by : The White House President Barak Obama. Located at : https://obamawhitehouse.archives.gov/photos-and-video/photo/2015/01/president-obama-offers-namaste-greeting-india . License : Public Domain: No Known Copyright


24.2: Structure and Properties of Amines
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- Steven Farmer, Dietmar Kennepohl, Layne Morsch, & William Reusch
- University of Illinois Springfield
Objectives
After completing this section, you should be able to
- describe the geometry and bonding of simple amines.
- explain why most chiral amines cannot be resolved into their two enantiomers.
Key Terms
Make certain that you can define, and use in context, the key term below.
Study Notes
Molecular models may help you to understand pyramidal inversion.
Bonding, Shape, and Hybridization of Amines
The nitrogen atom in most amines is sp 3 hybridized. Three of the sp 3 hybrid orbitals form sigma bonds with the fourth orbital carrying the lone pair electrons. Single-bonded nitrogen is trigonal pyramidal in shape, with the non-bonding lone electron pair pointing to the unoccupied corner of a tetrahedron. Due to crowding by the lone pair electrons, the C-N-C bond angle between alkyl substituents on an amine is roughly 108 o which is slightly less than the 109.5 o bond angle for a perfect tetrahedral geometry.
The C-N bonds (147 pm) of non-conjugated amines is shorter than C-C bond (154 pm) in alkanes, and longer than the C-O bond (143 pm) present in alcohols. This difference in bond length is expected given that the relative atom sizes are C > O > N.
Chirality of Amines
Due to their tetrahedral configuration, amines with three different substituents are chiral. The R and S enantiomeric forms of a chiral amine cannot be resolved due to their rapid interconversion by a process called pyramidal or nitrogen inversion. During the inversion, the sp 3 hybridized amine momentarily rehybridizes to a sp 2 hybridized, trigonal planar, transition state where the lone pair electrons occupy a p orbital. The nitrogen then returns to a tetrahedral sp 3 hybridization causing the lone pair electrons to return to a sp 3 orbital on the opposite side of the nitrogen. During this process substituents invert to form the enantiomer. The thermodynamic barrier for this inversion (~25 kJ/mol) is low enough to allow rapid inversion at room temperature, leading to a mixture of interconverting R and S configurations. At room temperature a nitrogen atom exists as a racemic mixture of R and S configurations at equilibrium.
Quarternary amines lack lone pair electrons and therefore do not undergo pyramidal inversions. Quarternary amines with four different substituents are chiral and are readily resolved into separate enantiomers.
Boiling Point and Water Solubility
Methyl, dimethyl, trimethyl, and ethyl amines are gases under standard conditions. Most common alkyl amines are liquids, and high molecular weight amines are, quite naturally, solids at standard temperatures.
It is instructive to compare the boiling points and water solubility of amines with those of corresponding alcohols and ethers. The dominant factor here is hydrogen bonding, and the first table below documents the powerful intermolecular attraction that results from -O-H --- O- hydrogen bonding in alcohols (light blue columns). Corresponding -N-H --- N- hydrogen bonding is weaker, as the lower boiling points of similarly sized amines demonstrate. Alkanes provide reference compounds in which hydrogen bonding is not possible, and the increase in boiling point for equivalent 1º-amines is roughly half the increase observed for equivalent alcohols.
A Representation of the Hydrogen Bonding in Methyamine
| Compound | CH 3 CH 3 | CH 3 OH | CH 3 NH 2 | CH 3 CH 2 CH 3 | CH 3 CH 2 OH | CH 3 CH 2 NH 2 |
|---|---|---|---|---|---|---|
| Mol.Wt. | 30 | 32 | 31 | 44 | 46 | 45 |
|
Boiling
Point ºC |
-88.6º | 65º | -6.0º | -42º | 78.5º | 16.6º |
The second table illustrates differences associated with isomeric 1º, 2º & 3º-amines, as well as the influence of chain branching. Since 1º-amines have two hydrogens available for hydrogen bonding, we expect them to have higher boiling points than isomeric 2º-amines, which in turn should boil higher than isomeric 3º-amines (no hydrogen bonding). Indeed, 3º-amines have boiling points similar to equivalent sized ethers; and in all but the smallest compounds, corresponding ethers, 3º-amines and alkanes have similar boiling points. In the examples shown here, it is further demonstrated that chain branching reduces boiling points by 10 to 15 ºC.
| Compound | CH 3 (CH 2 ) 2 CH 3 | CH 3 (CH 2 ) 2 OH | CH 3 (CH 2 ) 2 NH 2 | CH 3 CH 2 NHCH 3 | (CH 3 ) 3 CH | (CH 3 ) 2 CHOH | (CH 3 ) 2 CHNH 2 | (CH 3 ) 3 N |
|---|---|---|---|---|---|---|---|---|
| Mol.Wt. | 58 | 60 | 59 | 59 | 58 | 60 | 59 | 59 |
|
Boiling
Point ºC |
-0.5º | 97º | 48º | 37º | -12º | 82º | 34º | 3º |
Most aliphatic amines display some solubility in water, reflecting their ability to form hydrogen bonds. Solubility decreases proportionally with the increase in the number of carbon atoms in the molecule – especially when the carbon atom number is greater than six. Aliphatic amines also display significant solubility in organic solvents, especially in polar organic solvents.
The water solubility of 1º and 2º-amines is similar to that of comparable alcohols. As expected, the water solubility of 3º-amines and ethers is also similar. The basicity of amines allows them to be dissolved in dilute mineral acid solutions, and this property facilitates their separation from neutral compounds such as alcohols and hydrocarbons by partitioning between the phases of non-miscible solvents.
Naturally Occurring Amines
A large and widespread class of naturally occurring amines is known as alkaloids. The structures of the plant alkaloids are extraordinarily complex, yet they are related to the simple amines in being weak nitrogen bases. In fact, the first investigator to isolate an alkaloid in pure form was F. W. A. Sertürner who, in 1816, described morphine as basic, salt-forming, and ammonia-like. He used the term "organic alkali" from which is derived the name alkaloid. Alkaloids include compounds that may be classified as antimicrobial (quinine), as analgesics (morphine, codeine), as hallucinogens (mescaline, LSD), and as topical anesthetics (cocaine).
Certain amines and ammonium compounds play key roles in the function of the central nervous system as neurotransmitters and the balance of amines in the brain is critical for normal brain functioning. The amines acetylcholine chloride, adrenalin, and serotonin play important roles in nerve function in the human body.
Most amines have “interesting” odors. The simple ones smell very much like ammonia.  The stench of rotting meat is due in part to two diamines: putrescine and cadaverine. They are made during the decarboxylation of the amino acids, ornithine and lysine, by bacteria.


6.1: Introduction to Non-Brownian Motion
Detailed studies of contemporary evolution have revealed a rich variety of processes that influence how traits evolve through time. Consider the famous studies of Darwin’s finches, Geospiza , in the Galapagos islands carried out by Peter and Rosemary Grant, among others (e.g. Grant and Grant 2011) . These studies have documented the action of natural selection on traits from one generation to the next. One can see very clearly how changes in climate – especially the amount of rainfall – affect the availability of different types of seeds (Grant and Grant 2002) . These changing resources in turn affect which individuals survive within the population. When natural selection acts on traits that can be inherited from parents to offspring, those traits evolve.
One can obtain a dataset of morphological traits, including measurements of body and beak size and shape, along with a phylogenetic tree for several species of Darwin’s finches. Imagine that you have the goal of analyzing the tempo and mode of morphological evolution across these species of finch. We can start by fitting a Brownian motion model to these data. However, a Brownian model (which, as we learned in Chapter 3, corresponds to a few simple scenarios of trait evolution) hardly seems realistic for a group of finches known to be under strong and predictable directional selection.
Brownian motion is very commonly used in comparative biology: in fact, a large number of comparative methods that researchers use for continuous traits assumes that traits evolve under a Brownian motion model. The scope of other models beyond Brownian motion that we can use to model continuous trait data on trees is somewhat limited. However, more and more methods are being developed that break free of this limitation, moving the field beyond Brownian motion. In this chapter I will discuss these approaches and what they can tell us about evolution. I will also describe how moving beyond Brownian motion can point the way forward for statistical comparative methods.
In this chapter, I will consider four ways that comparative methods can move beyond simple Brownian motion models: by transforming the variance-covariance matrix describing trait covariation among species, by incorporating variation in rates of evolution, by accounting for evolutionary constraints, and by modeling adaptive radiation and ecological opportunity. It should be apparent that the models listed here do not span the complete range of possibilities, and so my list is not meant to be comprehensive. Instead, I hope that readers will view these as examples, and that future researchers will add to this list and enrich the set of models that we can fit to comparative data.


2.7: Discussion- The Wanderer
Source reading : “The Wanderer”
Discussion Prompt
Answer all parts of all questions.
- This poem, like “The Dream of the Rood,” has more than one speaker, and to understand this poem it is necessary to figure out who is speaking when. This poem has three speakers in all. Briefly explain the main point each one is making (the section by the Wanderer is long, so rather than summarizing the whole thing, just identify its overall idea). To identify the starting and stopping points you can use line numbers or a combination of line numbers and a quotation.
- The second speaker (the Wanderer) says, “I know it truly, / that it is in men / a noble custom, / that one should keep secure / his spirit-chest (mind) / guard his treasure chamber (thoughts) / think as he wishes” (12–16). If one should keep his thoughts to himself, what’s the point of writing this poem in the first place?
- You have listened to a recording of the original Old English of the poem. In this recording you could hear the rhythm of the poem and the alliteration of it, and both are representative of the style of Old English poetry. Did listening to the recording help you to better understand the poem even though you did not understand the words themselves?
- Consider the Anglo-Saxon readings from this week and last week. If you had to pick your favorite of the three we read, which one would it be? Why?
Discussion Board Instructions
Answer each question, unless otherwise specified. Number your answers (do not copy the prompt into your answers.) Answers need not be of equal length, but all answers must be well developed. The word count total (250+) refers to all answers added together.
In the first sentence or two of your first answer identify the name of the work and full name of the author (if applicable).
Include at least one quotation from the work in your overall response. Use line number(s) to identify the location of your citation. No works cited page is needed.
Grading Rubric
| Levels of Achievement | |||||
|---|---|---|---|---|---|
| Criteria | Excellent | Good | Adequate | Inadequate | Unacceptable |
| Response: Content Length and Development | 22 Points | 19 Points | 16 Points | 11 Points | 0 Points |
| Meets or exceeds the minimum length requirement. Demonstrates insight and understanding of the text(s) in an excellent, thorough, detailed, clear, and well developed response to the entire prompt. Response is comprised primarily of the student’s own answer(s), but is supported by at least one well chosen quotation. | Meets the minimum length requirement. Demonstrates understanding of the text(s) in a good, clear, well developed response to the entire prompt. Response is comprised primarily of the student’s own answer(s), but is supported by at least one well chosen quotation. | Meets or nearly meets the minimum length requirement. Demonstrates a basic understanding of the text(s) in a developed response to the prompt. Includes an adequate amount of the student’s own answer(s), but may incorporate too much summary, paraphrase, or quotations or lack a quotation for support. | Meets or falls 15%+ short of the minimum length requirement. Inadequately responds to the prompt with answer(s) that are substantively incorrect, superficial, underdeveloped, and/or reliant mostly on summary, paraphrase, or quotations. | Unacceptable development: Fails to meet at least 50% of the length requirement. | |
| Response: Source Identification and Citation | 4 points | 3.5 points | 3 Points | 2 Points | 0 Points |
| Clearly identifies by title and full name of author the name(s) of work(s) to be discussed. Cites material from source(s) as instructed in the assignment. | Identifies the work(s) and author(s). Cites material from source(s) as instructed in the assignment. | Identifies the work(s) or author(s). Cites adequately. | Inadequately identifies source(s) and author(s) and/or inadequately cites source(s). | Lacks identification and citation of source(s). | |
| Response: Grammar and Mechanics | 4 Points | 3.5 Points | 3 Points | 2 Points | 0 Points |
| Response is free or nearly free of errors in grammar (including but not limited to use of full sentences and appropriate word choice) and mechanics (including but not limited to spelling and punctuation). | Response demonstrates occasional errors in grammar or mechanics that do not affect overall clarity. | Demonstrates errors in grammar or mechanics that occasionally affect meaning. | Inadequately meets standards for grammar and mechanics. Clarity is frequently affected. | Unacceptable level of errors in grammar or mechanics. Clarity is greatly affected. | |
| Comment 1: Engagement and Content | 7 Points | 6 Points | 5 Points | 3.5 Points | 0 Points |
| Demonstrates thorough engagement in a comment that is detailed, well crafted, and reflective. | Demonstrates effective engagement in a comment that is effectively crafted and reflective. | Demonstrates an adequate engagement in a comment that addresses at least one point of an answer to the other student’s response. | Demonstrates inadequate engagement in a comment that only superficially or tangentially addresses the content of the other student’s response. | Unacceptable development: Fails to meet at least 50% of the minimum length requirement. | |
| Comment 1: Grammar and Mechanics and Length Requirement | 3 Points | 2.5 Points | 2 Points | 1.5 Points | 0 Points |
| Contains few if any grammar or mechanics issues. Meets or exceeds the minimum length requirement. | Contains few if any grammar or mechanics issues. Meets the length requirement. | Contains grammar and/or mechanics issues that occasionally affect clarity. Meets or falls within 10% of the minimum length requirement. | Inadequately meets standards for grammar and mechanics. Clarity is frequently affected. Meets or falls 15%+ short of the minimum length requirement. | Unacceptable level of errors in grammar or mechanics that greatly affect clarity. (No credit for this element if fails to meet at least 50% of the minimum length requirement.) | |
| Comment 2: Engagement and Content | 7 Points | 6 Points | 5 Points | 3.5 Points | 0 Points |
| Demonstrates thorough engagement with the content of the other student’s response in a comment that is detailed, well crafted, and reflective. | Demonstrates effective engagement in a comment that is effectively crafted and reflective. | Demonstrates an adequate engagement in a comment that engages with at least one point of content in the other student’s response. | Demonstrates inadequate engagement in a comment that only superficially or tangentially addresses the content of the other student’s response. | Unacceptable development: Fails to meet at least 50% of the length requirement. | |
| Comment 2: Grammar and Mechanics and Length Requirement. | 3 Points | 2.5 Points | 2 Points | 1.5 Points | 0 Points |
| Contains few if any grammar or mechanics issues. Meets or exceeds the minimum length requirement. | Contains a few grammar and/or mechanics issues, but these do not affect overall clarity. Meets the minimum length requirement. | Contains grammar and/or mechanics issues that occasionally affect clarity. Meets or falls within 10% of the minimum length requirement. | Inadequately meets standards for grammar and mechanics. Clarity is frequently affected. Meets or falls 15%+ short of the minimum length requirement. | Unacceptable level of errors in grammar or mechanics that greatly affect clarity. (No credit for this element if comment fails to meet at least 50% of the minimum length requirement.) |
- Survey of English Literature I. Authored by : Wendy Howard Gray. Provided by : Reynolds Community College. Located at : http://www.reynolds.edu/ . License : CC BY: Attribution


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Speaker
: Zeke
Evaluator
: Zelda
CRITERIA TO CONSIDER:
Introduction
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– I don’t believe you had a real attention getter. In fact, I think you began with a purpose statement, “Today I’m going to talk about…” The text says avoid such starts! Starting with the purpose statement doesn’t really pull me into your speech. You’ve had so many experiences with troubled kids, you could have started with a story—one that connects with us.
+ I really liked the way you followed the speech recipe. When I listened to you, I could follow you easily, especially when you made your transitions clear. You made me think you really wanted us to understand your message.
1 2 3 4
5
What was the central idea of this speech?
I’m not 100% sure, but I think the C.I. was “Alternative schools have several unique benefits over traditional schools.”
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1.2: Open Licensing and Creative Commons Primer
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This resource is a condensed adaptation of the Open Educational Resources: OER 101 Tutorials for Designers (CC-BY) authored by Linda Neff, Coconino Community College and Sandra Cerreta, Arizona Western Community College, most recently updated 3/15/22, and has been made available from the Canvas Commons.
Introduction to OER
Overview
Open educational resources are somewhat different from open learning, in that they are primarily content, while open learning includes both content and educational services, such as specially designed online materials, in-built learner support and assessment.
Open educational resources cover a wide range of online formats, including online textbooks, video recorded lectures, YouTube clips, web-based textual materials designed for independent study, animations and simulations, digital diagrams and graphics, and even assessment materials such as tests with automated answers. OER can also include slides or lecture notes.
This video explains what Open Educational Resources (OER) are and provides an overview of Creative Commons licensing, which we will describe in this primer.
Attribution: “What is an open license and how does it work?” by The Council of Chief State School Officers is licensed CC BY 4.
Definition
Open educational resources (OER) are openly-licensed, freely available educational materials that can be modified and redistributed by users. They can include any type of educational resource, from syllabi to full courses.
The most comprehensive definition of OER available today is provided by the Hewlett Foundation:
Open Educational Resources are teaching, learning and research materials in any medium – digital or otherwise – that reside in the public domain or have been released under an open license that permits no-cost access, use, adaptation and redistribution by others with no or limited restrictions.
Most library subscriptions cannot be altered, remixed, or redistributed; therefore, these materials cannot be considered “open.” Although some materials are free to access for a library’s users, that does not mean that they are free to access for everyone (including the library). Similarly, while some open access resources are made available under a copyright license that enables modification, this is not always the case.
Benefits
As Figure 1 shows, the price of college textbooks has risen greatly over the past 35 years, outpacing all other consumer goods in the Consumer Price Index by a great margin.
According to the 2 018 Student Textbook and Course Materials Survey: Executive Summary, Download 2018 Student Textbook and Course Materials Survey: Executive Summary, the cost of textbooks has a profound impact on college students, many of whom must wait to purchase their course materials until well into the term or choose not to purchase them at all.
The problem of food and housing insecurity among college students compounded with the additional rising cost of textbooks can make the difference between a student persisting in college or dropping out.
Additionally, students have access to OER from day one. No more waiting in long bookstore lines or for their financial aid to come through in order to purchase expensive textbooks!
- Cost savings for students - One of the first aspects of OER to be praised by the general public was the cost savings that they could bring to students. The price of college textbooks has risen greatly over the past 35 years, outpacing all other consumer goods in the Consumer Price Index by a great margin (Data source: Bureau of Labor Statistics ).
- Access to quality materials for students - Open materials can be accessed before, during and after your course, without costs and without having to be affiliated with the university.
- Access to quality materials for faculty - Using high quality materials that align more closely to your student learning outcomes allows for customization, selection, the ability to easily update or create a second edition, and tailor ancillary materials.
- Network and collaborate with peers - Professors can access materials that have been peer-reviewed by experts in your field, create materials with colleagues, and even have students work to co-create certain materials.
Challenges
- Subject availability
- Format and material type availability
- Time and support availability
Considerations
- How will an OER improve your course?
- How will you tailor the OER to your target (and possibly secondary) audience(s)?
- Does the OER you need already exist?
- How will you share and update your OER?
- How can you learn the necessary expertise to develop your OER?
- What kind of copyright/open license will you want to use?
Copyright and Open Licensing
As you begin to explore OER for use in your classroom, it is important that you understand your rights over the works you create and what it means to give those rights away.
Most copyrighted works are under full, “all rights reserved” copyright. This means that they cannot be reused in any way without permission from the work’s rights holder (usually the creator). One way you can get permission to use someone else’s work is through a license, a statement or contract that allows you to perform, display, reproduce, or adapt a copyrighted work in the circumstances specified within the license.
Copyright Law
U.S. copyright law protects an author’s rights over their original creative works (e.g., research articles, books and manuscripts, artwork, video and audio recordings, musical compositions, architectural designs, video games, and unpublished creative works) ( U.S. Copyright Law ). As soon as something is “fixed in a tangible medium of expression,” it is automatically protected by copyright. A resource is considered fixed when:
“its embodiment …by or under the authority of the author, is sufficiently permanent or stable to permit it to be perceived, reproduced, or otherwise communicated for a period of more than transitory duration” ( U.S. Copyright Law ).
In other words, an idea for a book you want to write is not protected by copyright, but the first draft of your manuscript is. Copyright protection ensures that the creator of a work has complete control over how their work is reproduced, distributed, performed, displayed, and adapted ( U.S. Copyright Law ).
You do not need to register your resource with the U.S. Copyright Office for this to come into effect; it is automatic.
Public Domain
Works that are no longer protected by copyright are considered part of the public domain. Items in the public domain can be reused freely for any purpose by anyone, without giving attribution to the author or creator. [4]
Public domain works in the U.S. include works whose creator died 70 years prior, works published before 1924, or works dedicated to the public domain by their rights holder. The Creative Commons organization created a legal tool called CC 0 to help creators dedicate their work to the public domain by releasing all rights to it.
Fair Use
If an OER is available under a copyright license that restricts certain (re)uses, you can make a fair use assessment for reproducing or adapting that work. However, having explicit permission is preferable. We do not recommend using fully copyrighted works in OER projects without written permission from the work’s rights holder.
Open Licenses
All OER are made available under some type of open license, a set of authorized permissions from the rights holder of a work for any and all users. The most popular of open licenses are Creative Commons (CC) licenses. While we will focus on CC licenses, note that other open licenses exist, such as the GNU Free Documentation License, a fully open license for any type of resource, and the Free Art License, a fully open option for creative works.
One of the tenets of OER laid out early on in the open education movement was the idea of the 5 Rs introduced by David Wiley. See chart below.
- Retain = the right to make, own, and control copies of the content.
- Reuse = the right to use the content in a wide range of ways
- Revise = the right to adapt, adjust, modify, or alter the content itself
- Remix = the right to combine the original or revised content with other open content to create something new
- Redistribute = the right to share copies of the original content, your revisions, or your remixes with others
Background of OERs
Creative Commons
Creative Commons (CC) is a global nonprofit organization that enables the sharing and reuse of creativity and knowledge through the provision of free legal tools. Creative Commons (CC) licenses allow you to explain, in plain language, how your creative works can be reused. These licenses act as explicit, standing permissions for all users allowing others to reuse, adapt, and re-publish content with few or no restrictions. See more: History of Creative Commons.pdf
The Four Components of Creative Commons Licenses
These elements can be mixed and matched to create a total of six Creative Commons licenses :
The 5 Rs of Open Content
To help decide which license is best for your resource, explore the CC Chooser: License Chooser .
Before you choose a license, keep in mind that an OER should be able to exercise all the 5 Rs of open content. Note that the CC BY-ND and CC BY-NC-ND licenses do not allow revising or remixing content, two of the most significant freedoms of OER for many instructors.
Creative Commons has an online Marking Guide that demonstrates how to mark your CC license on different types of media. Making your license obvious on whatever item you are sharing is an important part of the dissemination process for OER. It must be clear, visible, and provide links to the license/work.
Attribution: “Wileys 5Rs and Creative Commons Licensing” is by Krysta McNutt, CC-BY 4.0 . To view the full version, visit the Google Drawing.
Types of Creative Commons Licenses
To help decide which license is best for your resource, explore the CC Chooser: License Chooser .
Before you choose a license, keep in mind that an OER should be able to exercise all the 5 Rs of open content. Note that the CC BY-ND and CC BY-NC-ND licenses do not allow revising or remixing content, two of the most significant freedoms of OER for many instructors.
There are six types of Creative Commons licenses that allow differing levels of openness.
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This license lets others distribute, remix, tweak, and build upon your work, even commercially, as long as they credit you for the original creation. This is the most accommodating of licenses offered. Recommended for maximum dissemination and use of licensed materials. |
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This license lets others remix, tweak, and build upon your work even for commercial purposes, as long as they credit you and license their new creations under the identical terms. This license is often compared to “copyleft” free and open source software licenses. All new works based on yours will carry the same license, so any derivatives will also allow commercial use. This is the license used by Wikipedia, and it is also recommended for materials that would benefit from incorporating content from Wikipedia and similarly licensed projects. |
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This license allows for redistribution, commercial and non-commercial, as long as it is passed along unchanged and in whole, with credit to you. This license is not an OER. |
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This license lets others remix, tweak, and build upon your work non-commercially, and although their new works must also acknowledge you and be non-commercial, they don’t have to license their derivative works on the same terms. |
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This license lets others remix, tweak, and build upon your work non-commercially, as long as they credit you and license their new creations under the identical terms. |
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This license is the most restrictive of the six main licenses, only allowing others to download your works and share them with others as long as they credit you, but they can’t change them in any way or use them commercially. This license is not an OER. |
Descriptions adapted from Licenses - Creative Commons - (CC BY 4.0)
NOTE: A remix that includes OER content with a variety of CC licenses will need to include those licenses on the parts, but to share the whole collection it must carry the most restrictive CC license of the collection.
If you wish to offer your own materials as open educational resources, it is a relatively simple process to choose a license and apply it to any piece of work (see Creative Commons Choose a License ).


12.3: The Presidential Election Process
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Learning Objectives
By the end of this section, you will be able to:
- Describe changes over time in the way the president and vice president are selected
- Identify the stages in the modern presidential selection process
- Assess the advantages and disadvantages of the Electoral College
The process of electing a president every four years has evolved over time. This evolution has resulted from attempts to correct the cumbersome procedures first offered by the framers of the Constitution and as a result of political parties’ rising power to act as gatekeepers to the presidency. Over the last several decades, the manner by which parties have chosen candidates has trended away from congressional caucuses and conventions and towards a drawn-out series of state contests, called primaries and caucuses, which begin in the winter prior to the November general election.
Selecting the Candidate: The Party Process
In the decades that followed, party organizations, party leaders, and workers met in national conventions to choose their nominees, sometimes after long struggles that took place over multiple ballots. In this way, the political parties kept a tight control on the selection of a candidate. In the early twentieth century, however, some states began to hold primaries , elections in which candidates vied for the support of state delegations to the party’s nominating convention. Over the course of the century, the primaries gradually became a far more important part of the process, though the party leadership still controlled the route to nomination through the convention system. This has changed in recent decades, and now a majority of the delegates are chosen through primary elections, and the party conventions themselves are little more than a widely publicized rubber-stamping event.
The rise of the presidential primary and caucus system as the main means by which presidential candidates are selected has had a number of anticipated and unanticipated consequences. For one, the campaign season has grown longer and more costly. In 1960, John F. Kennedy declared his intention to run for the presidency just eleven months before the general election. Compare this to Hillary Clinton, who announced her intention to run nearly two years before the 2008 general election. Today’s long campaign seasons are seasoned with a seemingly ever-increasing number of debates among contenders for the nomination. In 2016, when the number of candidates for the Republican nomination became large and unwieldy, two debates among them were held, in which only those candidates polling greater support were allowed in the more important prime-time debate. The runners-up spoke in the other debate. In 2020, it was the Democratic party that had a large field that required staggered debates, before the field narrowed and ultimately led to the nomination of former vice president Joe Biden, who would go on to choose fellow campaigner Kamala Harris as his running mate.
Finally, the process of going straight to the people through primaries and caucuses has created some opportunities for party outsiders to rise. Neither Ronald Reagan nor Bill Clinton was especially popular with the party leadership of the Republicans or the Democrats (respectively) at the outset. The outsider phenomenon has been most clearly demonstrated, however, in the 2016 presidential nominating process, as those distrusted by the party establishment, such as Senator Ted Cruz and Donald Trump, who never before held political office, raced ahead of party favorites like Jeb Bush early in the primary process (Figure 12.6).
The rise of the primary system during the Progressive Era came at the cost of party regulars’ control of the process of candidate selection. Some party primaries even allow registered independents or members of the opposite party to vote. Even so, the process tends to attract the party faithful at the expense of independent voters, who often hold the key to victory in the fall contest. Thus, candidates who want to succeed in the primary contests seek to align themselves with committed partisans, who are often at the ideological extreme. Those who survive the primaries in this way have to moderate their image as they enter the general election if they hope to succeed among the rest of the party adherents and the uncommitted.
Primaries offer tests of candidates’ popular appeal, while state caucuses testify to their ability to mobilize and organize grassroots support among committed followers. Primaries also reward candidates in different ways, with some giving the winner all the state’s convention delegates, while others distribute delegates proportionately according to the distribution of voter support. Finally, the order in which the primary elections and caucus selections are held shape the overall race. 20 Currently, the Iowa caucuses and the New Hampshire primary occur first. These early contests tend to shrink the field as candidates who perform poorly leave the race. At other times in the campaign process, some states will maximize their impact on the race by holding their primaries on the same day that other states do. The media has dubbed these critical groupings “Super Tuesdays,” “Super Saturdays,” and so on. They tend to occur later in the nominating process as parties try to force the voters to coalesce around a single nominee.
The rise of the primary has also displaced the convention itself as the place where party regulars choose their standard bearer. Once true contests in which party leaders fought it out to elect a candidate, by the 1970s, party conventions more often than not simply served to rubber-stamp the choice of the primaries. By the 1980s, the convention drama was gone, replaced by a long, televised commercial designed to extol the party’s greatness (Figure 12.7). Without the drama and uncertainty, major news outlets have steadily curtailed their coverage of the conventions, convinced that few people are interested. The 2016 elections seem to support the idea that the primary process produces a nominee rather than party insiders. Outsiders Donald Trump on the Republican side and Senator Bernie Sanders on the Democratic side had much success despite significant concerns about them from party elites. Whether this pattern could be reversed in the case of a closely contested selection process remains to be seen.
Electing the President: The General Election
The Twelfth Amendment, ratified in 1804, provided for the separate election of president and vice president as well as setting out ways to choose a winner if no one received a majority of the electoral votes. Only once since the passage of the Twelfth Amendment, during the election of 1824, has the House selected the president under these rules, and only once, in 1836, has the Senate chosen the vice president. In several elections, such as in 1876 and 1888, a candidate who received less than a majority of the popular vote has claimed the presidency, including cases when the losing candidate secured a majority of the popular vote. A recent case was the 2000 election, in which Democratic nominee Al Gore won the popular vote, while Republican nominee George W. Bush won the Electoral College vote and hence the presidency. The 2016 election brought another such irregularity as Donald Trump comfortably won the Electoral College by narrowly winning the popular vote in several states, while Hillary Clinton collected nearly 2.9 million more votes nationwide.
Not everyone is satisfied with how the Electoral College fundamentally shapes the election, especially in cases such as those noted above, when a candidate with a minority of the popular vote claims victory over a candidate who drew more popular support. Yet movements for electoral reform, including proposals for a straightforward nationwide direct election by popular vote, have gained little traction.
Supporters of the current system defend it as a manifestation of federalism, arguing that it also guards against the chaos inherent in a multiparty environment by encouraging the current two-party system. They point out that under a system of direct election, candidates would focus their efforts on more populous regions and ignore others. 22 Critics, on the other hand, charge that the current system negates the one-person, one-vote basis of U.S. elections, subverts majority rule, works against political participation in states deemed safe for one party, and might lead to chaos should an elector desert a candidate, thus thwarting the popular will. Despite all this, the system remains in place. It appears that many people are more comfortable with the problems of a flawed system than with the uncertainty of change. 23
Get Connected!
Electoral College Reform
Following the 2000 presidential election, when then-governor George W. Bush won by a single electoral vote and with over half a million fewer individual votes than his challenger, astonished voters called for Electoral College reform. Years later, however, nothing of any significance had been done. The absence of reform in the wake of such a problematic election is a testament to the staying power of the Electoral College. The 2016 election results were even more disparate. While in 2000, Al Gore won a narrow victory in the popular vote with Bush prevailing by one vote in the Electoral College, in 2016, Clinton won the popular vote by a margin of almost 3 million votes, while Trump won the Electoral College comfortably. In 2020, the results aligned, with Joe Biden winning the popular vote and Electoral College by comfortable margins, although several battleground states were very close.
Those who insist that the Electoral College should be reformed argue that its potential benefits pale in comparison to the way the Electoral College depresses voter turnout and fails to represent the popular will. In addition to favoring small states, since individual votes there count more than in larger states due to the mathematics involved in the distribution of electors, the Electoral College results in a significant number of “safe” states that receive no real electioneering, such that nearly 75 percent of the country is ignored in the general election.
One potential solution to the problems with the Electoral College is to scrap it all together and replace it with the popular vote. The popular vote would be the aggregated totals of the votes in the fifty states and District of Columbia, as certified by the head election official of each state. A second solution often mentioned is to make the Electoral College proportional. That is, as each state assigns it electoral votes, it would do so based on the popular vote percentage in their state, rather with the winner-take-all approach almost all the states use today.
A third alternative for Electoral College reform has been proposed by an organization called National Popular Vote. The National Popular Vote movement is an interstate compact between multiple states that sign onto the compact. Once a combination of states constituting 270 Electoral College votes supports the movement, each state entering the compact pledges all of its Electoral College votes to the national popular vote winner. This reform does not technically change the Electoral College structure, but it results in a mandated process that makes the Electoral College reflect the popular vote. Thus far, fifteen states and the District of Columbia with a total of 196 electoral votes among them have signed onto the compact.
In what ways does the current Electoral College system protect the representative power of small states and less densely populated regions? Why might it be important to preserve these protections?
Follow-up activity: View the National Popular Vote website to learn more about their position. Consider reaching out to them to learn more, offer your support, or even to argue against their proposal.
Link to Learning
See how the Electoral College and the idea of swing states fundamentally shapes elections by experimenting with the interactive Electoral College map at 270 to Win.
The general election usually features a series of debates between the presidential contenders as well as a debate among vice presidential candidates. Because the stakes are high, quite a bit of money and resources are expended on all sides. Attempts to rein in the mounting costs of modern general-election campaigns have proven ineffective. Nor has public funding helped to solve the problem. Indeed, starting with Barack Obama’s 2008 decision to forfeit public funding so as to skirt the spending limitations imposed, candidates now regularly opt to raise more money rather than to take public funding. 24 In addition, political action committees (PACs), supposedly focused on issues rather than specific candidates, seek to influence the outcome of the race by supporting or opposing a candidate according to the PAC’s own interests. But after all the spending and debating is done, those who have not already voted by other means set out on the first Tuesday following the first Monday in November to cast their votes. Several weeks later, the electoral votes are counted and the president is formally elected (Figure 12.8).


15.10: Antisocial Behaviors, Violence, and Child Abuse
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Antisocial Behaviors
According to the American Academy of Psychiatry (2018),
Most kids will act up or become disruptive or defiant sometimes. Disruptive and conduct disorders, however, involve much more severe and longer-lasting behaviors than typical, short-lived episodes. Disruptive, impulse-control and conduct disorders refer to a group of disorders that include oppositional defiant disorder, conduct disorder, intermittent explosive disorder, kleptomania and pyromania. These disorders can cause people to behave angrily or aggressively toward people or property. They may have difficulty controlling their emotions and behavior and may break rules or laws. An estimated 6 percent of children are affected by oppositional defiant disorder or conduct disorder. 68
Oppositional Defiant Disorder (ODD): There is a recurrent pattern of negative, defiant, disobedient, and hostile behavior toward authority figures. It is important to remember that this is toward authority figures and not their peers. This occurs outside of normal developmental levels and leads to impairment in functioning (Lack, 2010). 69
Conduct Disorder (CD): Children with Conduct Disorder (CD) show acts of aggression towards others and animals. Children with conduct disorder (CD) usually show little to no compassion or concern for others or their feelings. Also, concern for the well-being of others is at a minimum. Children also perceive the actions and intentions of others as more harmful and threatening than they actually are and respond with what they feel is reasonable and justified aggression. They may lack feelings of guilt or remorse. Since these individuals learn that expressing guilt or remorse may help in avoiding or lessening punishment, it may be difficult to evaluate when their guilt or remorse is genuine. Individuals will also try and place blame on others for the wrong doings that they had committed.
Children with conduct disorders (CD) tend to have lower levels of self-esteem. Children diagnosed with conduct disorders (CD) are typically characterized as being easily irritable and often reckless, as well as having many temper tantrums despite their projected “tough” image portrayed to society. Conduct Disorder (CD) often accompanies early onset of sexual behavior, drinking, smoking, use of illegal drugs, and reckless acts. Illegal drug use may increase the risk of the disorder persisting. The disorder may lead to school suspension or expulsion, problems at work, legal difficulties, STD’s, unplanned pregnancy, and injury from fights or accidents. Suicidal ideation and attempts occur at a higher rate than expected. 71
Contributors and Attributions
68. What Are Disruptive, Impulse-Control and Conduct Disorders? (n.d.). Retrieved from https://www.psychiatry.org/patients-families/disruptive-impulse-control-and-conduct-disorders/what-are-disruptive-impulse-control-and-conduct-disorders .
69. Abnormal Psychology – Child Psychology references Abnormal Psychology: An e-text! by Caleb Lack, which is licensed under CC BY-NC-SA 4.0
71. Abnormal Psychology – Child Psychology references Abnormal Psychology: An e-text! by Caleb Lack, which is licensed under CC BY-NC-SA 4.0