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)
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VCCS's "Pathways" Course provides faculty with an introduction to the laws that influence the use, re-use, and distribution of content they may want to use in a course. Activities include finding openly licensed content for use in a class and publishing openly licensed works created by faculty. At the end of the course, students will have openly licensed content that will be ready for use in a course.
There are many layers when thinking about Open and Open Textbooks. In this first week of the workshop, we'll begin by peeling those layers back, starting with what Open actually means in the context of education. We'll then move on to looking at what an Open Textbook is. We've provided you with some resources to check out, and we ask that you post in the forum to talk to other participants about your experiences with openness.
The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.
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 asks students to consider the ways in which social theorists, institutional reformers, and political revolutionaries in the 17th through 19th centuries seized upon insights developed in the natural sciences and mathematics to change themselves and the society in which they lived. Students study trials, art, literature and music to understand developments in Europe and its colonies in these two centuries. Covers works by Newton, Locke, Voltaire, Rousseau, Marx, and Darwin.
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.
Prepare yourself to take an Algebra course with the Algebra2go䋢 prealgebra resources page. Whether you are attending Saddleback College's prealgebra class (math 351), taking a prealgebra class at another school, or need to refresh your math skills for a business or science class, Professor Perez and his favorite student Charlie have the tools that can help you. We have five primary types of study materials: class notes, video worksheets, video lectures, practice problems, and practice quizzes. For some topics we have some additional tools to assist you.
Part of the course for community college students featuring Professor Perez and his student Charlie, teaching about decimal concepts and operations.
This course is for community college students featuring Professor Perez and his student Charlie. This lesson demonstrates subtraction, including when the answer is negative, on the number line.
This is part of the course for community college students featuring Professor Perez and his student Charlie, teaching how to make conversions between different kinds of units.
This is a set of videos and "homework sets" for learning about ratios, proportions and percentages.
This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.
This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.
This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry.
In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and possible further topics at the discretion of the instructor.
This course focuses on the Great Depression and World War II and how they led to a major reordering of American politics and society. We will examine how ordinary people experienced these crises and how those experiences changed their outlook on politics and the world around them.