This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. The student will also take a look at ring factorization, general lattices, and vector spaces. Later this course presents more advanced topics, such as Galois theory - one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand. Upon successful completion of this course, students will be able to: Compute the sizes of finite groups when certain properties are known about those groups; Identify and manipulate solvable and nilpotent groups; Determine whether a polynomial ring is divisible or not and divide the polynomial (if it is divisible); Determine the basis of a vector space, change bases, and manipulate linear transformations; Define and use the Fundamental Theorem of Invertible Matrices; Use Galois theory to find general solutions of a polynomial over a field. (Mathematics 232)
This course is oriented toward US high school students. The course is divided into 10 units of study. The first five units build the foundation of concepts, vocabulary, knowledge, and skills for success in the remainder of the course. In the final five units, we will take the plunge into the domain of inferential statistics, where we make statistical decisions based on the data that we have collected.
This course introduces the history of the Age of Revolutions in the Atlantic World from 1776 to 1848. Running alongside and extending beyond these political revolutions is the First Industrial Revolution. The Atlantic World, dominated by European empires in 1776, was transformed through revolution into a series of independent states by 1848, experiencing profound changes through the development and consolidation of capitalism. Upon successful completion of this course, the student will be able to: think analytically about the history of the revolutionary age between 1776 and 1848; define what a revolution" means as well as describe what made 1776-1848 an "age of revolution"; define the concept of the Atlantic World and describe its importance in World History; explain the basic intellectual and technical movements associated with the Enlightenment and their relations to the revolutionary movements that follow; identify and describe the causes of the American Revolution; identify and describe the many stages of the French Revolution: the end of absolutist monarchy, the implementation of constitutional monarchy, and the rise of the Jacobin Republic; compare and contrast the Declaration of the Rights of Man and other major statements of the Revolutionary period and Enlightenment thinking; identify and describe the impact of the first successful slave rebellion in world history--the Haitian Revolution; compare and contrast the debate between Edmund Burke and Thomas Paine; analyze and interpret primary source documents that elucidate the causes and effects of the Age of Revolutions. This free course may be completed online at any time. (History 303)
This course will introduce the student to the history of the Atlantic slave trade from 1500 to 1900. The student will learn about the slave trade, its causes, and its effects on Africa, Europe, and the Americas. By the end of the course, the student will understand how the Atlantic slave trade began as a fledgling enterprise of the English, Portuguese, and Spanish in the 1500s and why, by the mid-eighteenth century, the trade dominated Atlantic societies and economies. Upon completion of this course, students will be able to: think analytically about the various meanings of 'slave' and 'slavery' during the age of the Atlantic slave trade; identify and describe the 'triangular trade' and define the Atlantic World; identify and describe the logic for enslavement of Africans by Europeans; identify and describe the African ethnic groups enslaved by Europeans and those captives' New World destinations; identify and describe the early slaving voyages of the Portuguese and Spanish. Students will also be able to describe how the Dutch and English later inserted themselves into the trade; identify and describe the expansion of the plantation complex in the New World in the 1600s and its impact on the Atlantic slave trade; identify and analyze the rise of European empires and the parallel expansion of the Atlantic slave trade; identify and analyze slavery within African societies. They will also be able to identify and describe the trans-Saharan slave trade and the Red Sea/Indian Ocean slave trade; identify and describe the nature of the African slave market and principal slaving ports in western Africa; analyze and describe New World slave societies and their impact on the Atlantic slave trade; identify and describe the 'Middle Passage' of the Atlantic slave trade; identify and describe the causes for the abolition of the Atlantic slave trade in the nineteenth century; analyze and interpret primary source documents that elucidate all aspects of the Atlantic slave trade. (History 311)
This course discusses how to use algebra for a variety of everyday tasks, such as calculate change without specifying how much money is to be spent on a purchase, analyzing relationships by graphing, and describing real-world situations in business, accounting, and science.
This course will cover American political thought from the nation's founding through the 1960s, exploring the political theories that have shaped its governance. As there is no one philosopher or idea that represents the totality of American political thought, the student will survey the writings and speeches of those who have had the greatest impact over this period of time. Much of the study required in this course is based on the original texts and speeches of those who influenced political thought throughout American history. The student will learn and understand the impact that their views and actions have had on the modern American state. Upon successful completion of this course, students will be able to: describe the religious and political origins of the American political system; explain how Enlightenment thinkers, such as John Locke, Thomas Hobbes, and Jean-Jacques Rousseau, and Baron de Montesquieu, influenced the political philosophies of American founding fathers; analyze how the colonial American experience shaped many of the core values represented in American government and expressed in the Declaration of Independence and the U.S. Constitution; compare and contrast the differing opinions on the role of the government that the founders expressed; trace the development and evolution of the concepts of 'states rights' and 'federal (national) supremacy'; connect the observations of De Tocqueville in Democracy in America to the concepts of equality, individuality, and civic engagement in American political discourse; examine the evolution of race in the American political system (from slavery to the 2008 election of Barack Obama); discuss the changes in the political role of women in America from its colonial days to the present; connect the concept of 'American Exceptionalism' to the industrial revolution, capitalism, and imperialism; analyze the roots of reform in the Progressive Era and their impact on modern political discourse; explain major principles of American foreign relations over time; assess the purpose and impact of ĺÎĺĺĺŤAmerican war rhetoricĄ_ĺĺö over time; differentiate between 'liberal' and 'conservative' political beliefs in modern American government; illustrate how the political turmoil in the 1960s greatly shaped contemporary American political discourse; evaluate the current political discourse as represented in the 2008 and 2010 elections. (Political Science 301)
In this course, the student will study the emergence of the major civilizations of the ancient world, beginning with the Paleolithic Era (about 2.5 million years ago) and finishing with the end of the Middle Ages in fifteenth century A.D. The student will pay special attention to how societies evolved across this expanse of time - from fragmented and primitive agricultural communities to more advanced and consolidated civilizations. By the end of the course, the student will possess a thorough understanding of important overarching social, political, religious, and economic themes in the ancient world, ranging from the emergence of Confucian philosophy in Asia to the fall of imperial Rome. Upon successful completion of this course, the student will be able to: Identify and define the world's earliest civilizations, including the Neolithic Revolution, and describe how it shaped the development of these early civilizations; Identify, describe, and compare/contrast the first advanced civilizations in the world - Mesopotamia and Egypt; Identify and describe the emergence of the earliest civilizations in Asia: the Harappan and Aryan societies on the Indian subcontinent and the Shang and Zhou societies in China; Identify and describe the emergence of new philosophies - Daoism and Confucianism - during the Warring States period in China. Identify and describe the subsequent rise of the Qin and Han dynasties; Identify and describe the different periods that characterized ancient Greece - Archaic Greece (or the Greek Dark Ages), classical Greece, and the Hellenistic era; Identify and describe the characteristics of the Roman Kingdom, the Roman Republic, and Imperial Rome; Analyze the emergence of the Mauryan and Gupta empires during the 'classical age' in India; Identify and analyze the Buddhist and Vedic (Hindu) faiths; Identify and describe the rise of civilizations in the Americas, particularly in Meso and South America; Analyze and describe the rise of Islam in the Middle East; Identify and describe the emergence of the Arab caliphate, the Umayyad dynasty, and Abbasid dynasty; Identify and describe the rise and fall of the Byzantine Empire; Identify and analyze key facets of medieval society in Western EuropeĺÎĺĚ_ĺÜthe Catholic Church, feudalism, and the rise of technology and commerce; Analyze and interpret primary-source documents that elucidate the exchanges and advancements made in civilizations across time and space. (History 101)
This course is an exploration of visual art forms and their cultural connections for the student with little experience in the visual arts. It includes a brief study of art history and in depth studies of the elements, media, and methods used in creative processes and thought. Upon successful completion of this course, students will be able to: interpret examples of visual art using a five-step critical process that includes description, analysis, context, meaning, and judgment; identify and describe the elements and principles of art; use analytical skills to connect formal attributes of art with their meaning and expression; explain the role and effect of the visual arts in societies, history, and other world cultures; articulate the political, social, cultural, and aesthetic themes and issues that artists examine in their work; identify the processes and materials involved in art and architectural production; utilize information to locate, evaluate, and communicate information about visual art in its various forms. Note that this course is an alternative to the Saylor FoundationĺÎĺ_ĺĚĺ_s ARTH101A and has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. This free course may be completed online at any time. (Art History 101B)
This course is also intended to provide the student with a strong foundation for intermediate algebra and beyond. Upon successful completion of this course, you will be able to: simplify and solve linear equations and expressions including problems with absolute values and applications; solve linear inequalities; find equations of lines; and solve application problems; add, subtract, multiply, and divide various types of polynomials; factor polynomials, and simplify square roots; evaluate, simplify, multiply, divide, add, and subtract rational expressions, and solve basic applications of rational expressions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 001)
Introductory survey of quantitative methods (QM), or the application of statistics in the workplace. Examines techniques for gathering, analyzing, and interpreting data in any number of fieldsĺÎĺ from anthropology to hedge fund management.
This course is oriented toward US high school students. Its structure and materials are aligned to the US Common Core Standards. Foci include: derivatives, integrals, limits, approximation, and applications.
This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using NewtonĺÎĺ_ĺĚĺ_s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)
In this course, the student will explore campaigns and elections, learning their purpose and significance and observing the impact that they have on the American political system. The course will focus on the history and evolution of elections and voting laws in the United States, as well as what compels individuals to run for office and how campaigns are structured. Also, the course will teach the student the role that political parties, interest groups, voters, and the media play in elections. Lastly, the student will take a closer look at electoral outcomes and the impact that elections have on public policy after votes are counted, as well as what types of proposals could be implemented to improve our electoral system. Upon successful completion of this course, the student will be able to: explain the importance of elections, voting, democracy, and citizenship in the United States; describe the various types of elections that exist within the American political system; identify the legal and constitutional bases of campaigns and elections in the United States; explain the types of individuals that run for political office and why; analyze the influence of incumbency in elections; explain how candidates develop campaigns and financing; discuss the role of money in political campaigns; discuss the influence of political parties on campaigns and elections; describe the characteristics of the U.S. party system; explain the role of interest groups in influence campaigns and election outcomes; explain the various influences and motivations of the American voter; describe the factors associated with both nonvoter and voter disenfranchisement in contemporary elections; analyze and explain the critical role of the media in campaigns and elections; explain how election outcomes impact government actions and public policy; analyze both historical and contemporary election reforms. (POLSC333)
The purpose of this course is to trace the twin paths of capitalism and democracy through American history. This course is premised on the idea that capitalism and democracy are intertwined, though they have often conflicted with one another. It provides students with a brief introduction to the history of capitalism and democracy in Europe and then to explore how they evolved in North America between 1600 and the present. Upon successful completion of this course, students will be able to: define and identify the terms 'capitalism' and 'democracy' in a variety of different modern historical eras; identify and define the historical connections between capitalism and democracy and identify periods of tension between capitalism and democracy, explaining how they both strengthen and weaken one another; identify important events, personalities, and concepts related to American democracy and capitalism; identify and describe the emergence and development of both capitalism and democracy in the United States; identify and describe the different periods of American history as they relate to the concepts of capitalism and democracy. (History 312)
This course will introduce the student to the history of Latin and South America from the year in which European explorers first discovered and began to colonize the region to the early 19th century, when many Latin and South American colonies declared their independence from European rule. The student will learn about the major political, economic, and social changes that took place throughout Latin and South America during this 400-year period. By the end of the course, the student will understand how the interaction between native peoples and European settlers created diverse and complex colonial societies throughout Latin and South America, and why the colonies of the region eventually declared their independence from European political control. Upon successful completion of this course, student will be able to: Think critically about the history of Latin and South America from the pre-colonial period though the beginning of the 19th century; Compare and contrast the political, economic, and social practices of the peoples of Iberia, Africa, and the Americas in the pre-colonial period; Analyze the political, social, and military interactions between Iberian explorers and conquerors and the indigenous peoples of the Americas in the 15th and 16th centuries; Identify how Spanish colonists settled Latin and South America in the 16th century and analyze the role played by imperial and religious institutions in colonization efforts; Assess the role of European Mercantile policies in the formation of colonial economies and trade networks; Analyze the structure of Spanish and Portuguese colonial societies and assess the role of women, indigenous peoples, and Afro-Latinos in these societies; Students will be able to assess the status of Latin and South American colonies in the Spanish and Portuguese Empires of the 17th and 18th centuries and identity how European conflicts affected political and economic life in the colonies; Identify how the Napoleonic Wars of the early 19th century led to the rise of independence movements in the colonies of Latin and South America; Assess how political revolutions and wars for independence throughout Latin and South America ended European colonial control of the region, and compare and contrast the consequences of these revolutions for ethnic European and indigenous populations; Analyze and interpret primary source documents from the pre-colonial period though the beginning of the 19th century using historical research methods. (History 221)
This course will introduce the student to a comparative history of New World societies from 1400 to 1750. The student will learn about European exploration and colonization as well as the culture of native peoples of the Americas. By the end of the course, you will understand how the New World evolved from fledgling settlements into profitable European colonies and how New World societies were highly varied polities. Upon successful completion of this course, the student will be able to: analyze what constituted the 'New World' in the fifteenth century; identify and describe the major tribes/native civilizations of North America, Central America, South America, and the Caribbean at the time of European contact; identify and describe the effects of European colonization on native peoples; identify and describe the reasons for the European Age of Discovery in the New World; identify and describe early New World exploration and initial settlements by Portugal and Spain; identify and describe how and why the consolidation of powerful European states in the 1600s resulted in New World exploration, settlement, and commerce; compare and contrast New France, French Louisiana, the French West Indies, and French Guiana; compare and contrast British North America (New England, Middle and Lower Colonies), the British West Indies, and British Central and South America; compare and contrast New Spain, the Spanish Caribbean, and Spanish South America; analyze and describe Portuguese Brazil; identify and describe the African slave trade and will also be able to compare and contrast the enslavement of Africans in New World societies; identify and describe inter-European conflicts and European-Native Indian violence in the New World; analyze and interpret primary source documents that elucidate the causes and effects of exploration and colonization in the New World. (History 321)
This course is an introduction to complex analysis, or the theory of the analytic functions of a complex variable. Put differently, complex analysis is the theory of the differentiation and integration of functions that depend on one complex variable. Because of the algebraic properties of the complex numbers and the inherently geometric flavor of complex analysis, this course will feel quite different from Real Analysis, although many of the same concepts, such as open sets, metrics, and limits will reappear. Upon successful completion of this course, the student will be able to: manipulate complex numbers in various representations, define fundamental topological concepts in the context of the complex plane, and define and calculate limits and derivatives of functions of a complex variable; represent analytic functions as power series on their domains and verify that they are well-defined; define a branch of the complex logarithm; classify singularities and find Laurent series for meromorphic functions; state and prove fundamental results, including CauchyĺÎĺ_ĺĚĺ_s Theorem and CauchyĺÎĺ_ĺĚĺ_s Integral Formula, the Fundamental Theorem of Algebra, MoreraĺÎĺ_ĺĚĺ_s Theorem and LiouvilleĺÎĺ_ĺĚĺ_s Theorem; use them to prove related results; calculate contour integrals; calculate definite integrals on the real line using the Residue Theorem; define linear fractional transformations and prove their essential characteristics; find the image of a region under a conformal mapping; state, prove, and use the Open Mapping Theorem. This free course may be completed online at any time. (Mathematics 243)
This course focuses on linear ordinary differential equations (or ODEs) and will introduce several other subclasses and their respective properties. Despite centuries of study, numerical approximation is the only practical approach to the solution of complicated ODEs that has emerged; this course will introduce you to the fundamentals behind numerical solutions. Upon successful completion of this course, students will be able to: Identify ordinary differential equations and their respective orders; Explain and demonstrate how differential equations are used to model certain situations; Solve first order differential equations as well as initial value problems; Solve linear differential equations with constant coefficients; Use power series to find solutions of linear differential equations, Solve linear systems of differential equations with constant coefficients; Use the Laplace transform to solve initial value problems; Use select methods of numerical approximation to find solutions to differential equations. (Mathematics 221; See also: Mechanical Engineering 003)
This course introduces the history of the Middle East and Southwest Asia from the pre-Islamic period to the end of World War I. Upon successful completion of this course, the student will be able to: discuss the history of East Asia from the pre-Islamic period through the beginning of the 20th century; analyze the interactions between ancient civilizations of the Middle East and Southwest Asia in the pre-Islamic period; identify the origins of Islam, and assess the political and cultural impact of the Muslim faith on the peoples of the Middle East and the Mediterranean Basin; identify the origins of the Umayyad and Abbasid Empires, and assess how these dynasties reshaped political and economic life throughout the Middle East and Southwest Asia; describe and assess the social and cultural impact of Islam on the peoples of the Middle East and the Mediterranean Basin; identify external threats to the Muslim world during the Middle Ages, and analyze how Muslim leaders responded to these threats; identify the origins of the Ottoman Empire, and assess how the Ottomans established political and economic control over the Eastern Mediterranean and the Middle East; analyze the political, economic, and military interactions between the Ottoman Empire and the nations of Europe in the 18th and 19th centuries; explain how European imperialism destabilized the Middle East and Southwest Asia in the 19th and early 20th centuries and allowed European nations to establish political control over many Middle Eastern nations; analyze the political impact of World War I on the peoples and nations of the Middle East; analyze and interpret primary source documents from the pre-Islamic period through the beginning of the 20th century using historical research methods. This free course may be completed online at any time. (History 231)