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saylor.org Academy  ●  Online
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. Such functions, beautiful on their own, are immediately useful in Physics, Engineering, and Signal Processing. 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. Simply put, you will be working with lines and sets and very specific functions on the complex plane—drawing pictures of them and teasing out all of their idiosyncrasies. You will again find yourself calculating line integrals, just as in multivariable calculus. However, the techniques you learn in this course will help you get past many of the seeming dead-ends you ran up against in calculus. Indeed, most of the definite integrals you will learn to evaluate in Unit 7 come directly from problems in physics and cannot be solved except through techniques from complex variables. We will begin by studying the minimal algebraically closed extension of real numbers: the complex numbers. The Fundamental Theorem of Algebra states that any non-constant polynomial with complex coefficients has a zero in the complex numbers. This makes life in the complex plane very interesting. We will also review a bit of the geometry of the complex plane and relevant topological concepts, such as connectedness. In Unit 2, we will study differential calculus in the complex domain. The concept of analytic or holomorphic function will be introduced as complex differentiability in an open subset of the complex numbers. The Cauchy-Riemann equations will establish a connection between analytic functions and differentiable functions depending on two real variables. In Unit 3, we will review power series, which will be the link between holomorphic and analytic functions. In Unit 4, we will introduce certain special functions, including exponentials and trigonometric and logarithmic functions. We will consider the Möbius Transformation in some detail. In Units 5, 6, and 7 we will study Cauchy Theory, as well as its most important applications, including the Residue Theorem. We will compute Laurent series, and we will use the Residue Theorem to evaluate certain integrals on the real line which cannot be dealt with through methods from real variables alone. Our final unit, Unit 8, will discuss harmonic functions of two real variables, which are functions with continuous second partial derivatives that satisfy the Laplace equation, conformal mappings, and the Open Mapping Theorem.
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saylor.org Academy  ●  Online
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. One reason that democracy and capitalism often conflict is because capitalism has the capacity for both enormous construction and enormous destruction; these contradictory impulses often appear in tandem. This course is structured to provide 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. Throughout the course, students will be exposed to primary and secondary readings as well as video and audio lectures that will explore the connections between America’s economic and political development This course assumes a basic working knowledge of U.S. history. A good resource for review is http://en.wikibooks.org/wiki/US_History. Also available in: PDF
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saylor.org Academy  ●  Online
A course in elementary number theory concerns itself primarily with simple, arithmetical manipulations of counting numbers: 1, 2, 3, and so forth. These numbers hold a great deal more secrets than one might imagine at first. Despite their apparent simplicity, some of the hardest, most difficult problems in mathematics arise from the study of the theory of numbers. Grade-schoolers can comprehend questions whose solutions evade centuries of investigation. Entirely new fields of mathematical study have grown from research into these questions made possible by number theory. One of the fundamental objects of study involves the prime numbers. Nearly every integer can be built by multiplying prime numbers, which means that we can solve a large number of problems simply by thinking about them in terms of prime numbers. Even when a number n is not prime, we can restrict our arithmetic to a set of numbers relatively prime to n and recover many properties of a prime number. A signal for this is related to another important tool of number theory, the greatest common divisor (gcd). The gcd allows us to solve linear Diophantine equations, which look like the linear equations you studied in precalculus, but restrict their solutions to integer values. Related to the study of linear Diophantine equations is a clockwork mathematics called congruence, where you can assert with a straight face that, for example, 1 + 1 = 0 and not be thrown out of the room. As the course draws to its finale, we combine prime numbers, relatively prime numbers, and congruence to explain how a deceptively simple problem – factoring an integer into two primes – is in fact so difficult that it can guarantee the security of internet communication, including the credit card number you type when you make an online purchase! Along the way, we take a few detours for the sake of sightseeing. We examine some problems that fascinated the ancient Greek cult of Pythagoreans – perhaps unto death! This segues nicely into classes of numbers that are obtained easily from the integers, but have some unsettling properties. A recurring theme will focus on how these other classes of numbers preserve the so-called ring properties of the integers. We look at different ways to represent numbers, including the technique of continued fractions, which enjoys some surprising properties. Neither last, nor least, we construct numbers that turn traditional notions of arithmetic on its head, requiring us to reconsider even the definition of our beloved primes! Some aspects of this course will be experimental: we introduce you to a computer algebra system, Sage, and encourage you to infer patterns and solutions by experimentation.
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saylor.org Academy  ●  Online
What is strategy? When your friend tells you that his “strategy” in basketball is to win, he is not telling you a strategy at all. A strategy is a plan of action designed to achieve a goal—in the case of your friend, a more appropriately defined strategy for his basketball game would be: “I am going to apply defensive pressure and force the opposing team to make mistakes with the end goal of winning the game.” In this course, you will learn that you must first clearly define your goals before you develop strategies in order to achieve them. You will also learn that strategy in business is similar to strategy in sports, war, or politics; the parallels are so close that early business strategists studied military strategies in depth. The science of strategy development has developed beyond this by now, but the parallels still exist. Strategic Management involves two processes: first, the process of identifying specific goals for a firm and designing strategies to achieve those goals, and second, the process of implementing those strategies. It is easy to say that your goal is to increase sales by 50% in three years, but how do you go about achieving that goal? Are you going to lower prices, acquire a competitor, move into other businesses, or something else? Assuming you are going to lower prices, how are you going to do so and keep profits up? These are the sorts of questions that strategists must answer. This course is the capstone of the business major, because it incorporates elements from all of the core courses you should have already completed. Almost every topic should be familiar to you to some degree; however, Strategic Management ties them all together. This course begins with an introduction to the field and the definition of some important terms and concepts. You will then move on to identifying goals and formulating strategies before addressing implementation topics. This course will conclude with strategies for the 21st century. This course should be taken after all core courses have been completed and, ideally, near the end of your completion of the elective courses.
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saylor.org Academy  ●  Online
In common conversation, we often use the phrase “contemporary art” to refer to current artistic production—the art being produced today. However, in the art history field, the phrase denotes a specific period of art and artistic practice starting in the 1960s and continuing today. It is characterized by a break from the modernist artistic canon and a desire to move away from the dominant Western cultural model, looking for inspiration in everyday and popular culture. More specifically, many contemporary artworks reject traditional modernistic artistic media (such as painting or sculpture) in favor of a more collaborative, ephemeral, and multimedia approach that further blurs the boundaries between high and mass culture. In its subject matter, this art also tends to reflect a shift away from purely aesthetic issues to more socially oriented concerns. Finally, it is important to note that contemporary art should not be seen as a progression of different artistic styles but as series of different cultural, social, and political inquiries that occupied contemporary art practice over the course of the past 50 years or so. We will examine these important aesthetic and cultural changes within their historical and social context as we progress through this course. This course will survey contemporary art, starting with the 1960s and concluding in 2010. While the focus is on Western art and culture, we will also explore a selection of contemporary art and artistic practices around the globe, which have become increasingly influential in the definition of contemporary art today. Each of the units will examine a set of specific aesthetic and social issues and look at the different strategies contemporary artists proposed and used in their work. By the end of this course, you should be able to recognize and interpret most important aspects of contemporary art and contemporary visual culture while better understanding some of the cultural and social aspects of our daily life in today’s global world.
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saylor.org Academy  ●  Online
Heat transfer is the thermal energy in transit due to a spatial temperature difference. The topic of heat transfer has enormous applications in mechanical engineering, ranging from cooling of microelectronics to design of jet engines and operations of nuclear power plants. In this course, you will learn about what heat transfer is, what governs the rate of heat transfer, and why heat transfer is so important. You will also learn about the three major modes of heat transfer: conduction, convection, and radiation. Heat conduction is the transport of heat through a solid body, by vibrations of molecules or in the case of electrical conductors, by movement of electrons from one molecule to another. Heat convection is a process by which heat is transferred through a fluid by motion of fluid. Thermal radiation is the transport of energy between two bodies by electromagnetic waves. In addition to the three main modes of heat transfer, you will also learn about heat transfer during phase changes (boiling and condensation heat transfer).
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saylor.org Academy  ●  Online
Have you ever wondered what qualities billionaire Warren Buffet, visionary Steve Jobs, or upcoming Jeff Bezos of Amazon.com all have in common? After you finish studying business practices in this course, you may discover that you have some of the same qualities as other successful entrepreneurs. This course is designed as a survey course that will expose you to business terminology, concepts, and current business issues. The intent is to develop a viable business vocabulary, foster critical and analytical thinking, and refine your business decision-making skills. These skills will be acquired by the reading materials, exercises, and research assignments in this course that simulate the workplace today. By delving into the five units of this course, you will be able to fine tune your direction and choice of career in business. A major goal of your education is to help you become a citizen who can contribute and compete in an increasingly global environment. Elements of this course will focus on multicultural aspects of markets and business. Additional elements will ask you to look at other countries and evaluate the combination of business models and country characteristics.
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saylor.org Academy  ●  Online
This course will introduce you to the major concepts of and debates surrounding industrial and organizational psychology. Industrial and organizational psychology is the application of psychological research and theory to human interaction (both with other humans and with human factors, or machines and computers) in the workplace. The phrase “industrial and organizational psychology” (sometimes referred to as “I/O”) may be somewhat misleading, as the field deals less with actual organizations and/or industries and more with the people in these areas. As mentioned above, “I/O” is an applied psychological science, which means that it takes research findings and theories that may have originally been used to explain a general phenomenon of human behavior and applies them to human behavior in a specific setting (here, the workplace). Consider, for example, the fact that many jobs require applicants to take a personality test. Psychologists originally developed this test to detect and diagnose abnormal personalities; they are now frequently used to determine whether a given applicant will be a good “fit” for a position or the dynamic of a company’s staff. In this case, we are applying traditional psychology research to the workplace. Or consider the traditional job interview. Everything from the interaction between interviewer and interviewee to the nature of the Q&A can be examined from a psychological standpoint. While these quick examples pertain to only one area of human workplace interaction (the employee selection area), there are a number of additional areas that we will learn about in this course. We will begin by taking a look at how we evaluate jobs and candidates for jobs (employees) before exploring how we evaluate and motivate employees, noting what encourages versus discourages employee job commitment. We will then study leadership and group influences in the workplace and conclude with units on working conditions and humans factors. In addition, performance management and work teams will be discussed. Leadership interaction and the leadership theories are also covered. Note: Because this is an applied psychological science, you should have a strong background in theory and have taken an Introduction to Psychology course prior to taking this course.
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saylor.org Academy  ●  Online
If you pick up almost any newspaper looking for information about Africa, you will likely encounter stories about the HIV/AIDS epidemic in Malawi, riots in Tunisia, famine in Ethiopia, or environmental disaster in the Niger Delta—problems that journalists often link to dysfunctional government. Based on such accounts, you might consider Africa to be a pretty bleak place! However, these events highlight only one side of politics in Sub-Saharan Africa. While some African countries face great struggles, others offer great hope. This course provides an overview of African politics in historical context, synthesizing material from traditional comparative politics and area studies courses that examine democratization, economic development, and identity politics. This course also examines Africa’s position in a broader international framework by addressing conflict, political economy, and the processes of state division and integration. Seven units organize this course. We have organized the beginning of this course (Units 1 and 2) historically with Unit 1 focusing on colonization. Unit 2 reviews political development patterns in the post-colonial age, including the upheavals that led to an epidemic of weak and failed states. Subsequent units take a more focused look at various dimensions of African society, politics, economics, and international relations. The course concludes with an exploration of continent-wide challenges and the potential for an “African Renaissance.”
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saylor.org Academy  ●  Online
This course is designed to equip you with the basic academic, professional, and personal skills you will need to be successful in college. You are probably already familiar with some of the skills and topics that will be covered here; other concepts may be brand-new to you. For example, perhaps you have already learned some effective test-taking strategies that work well for you, but you have never heard of the concept of learning styles. Or, you may be familiar with your learning style, but you want to improve your listening skills and learn how to adapt your learning style to a new academic environment. Each student will have a different skill set when he or she starts this course. The point of this course is to give you—a new college student or a person considering a college education—a purposeful, thorough overview of the many tools and skills needed for undergraduate success, as well as to help you understand how you can improve each of these skills over time. Keep in mind that the terms skills, tools, and resources can refer to academic, social, psychological, and emotional skills and techniques as well as physical objects such as books and supplies. You may be tempted to consider some of the broad learning outcomes that are outlined in this course as unimportant for your immediate success in college. For example, you may wonder whether it is really worth your time to think about your long-term career goals or your exercise habits at the very beginning of your college experience. However, having a sense of purpose that motivates you and a lifestyle that supports your ability to focus on your academic goals are the basic building blocks of success in college and beyond. The first unit of this course will help you determine your goals for your college education. In other words, you will have the opportunity to thoughtfully answer the question, why am I pursuing an undergraduate degree? Knowing the answer to this question will help you stay motivated when you encounter challenges during your college experience. In units 2 and 3 of this course, you will learn how to manage your personal space and time in order to maximize your ability to learn, and in units 4 through 8 of this course, you will explore the learning process itself and the different skills and tools you can use to improve your academic performance. Unit 9 focuses on tests and test-taking, a subject that can cause great anxiety for many students, and units 10 and 11 provide you with general strategies for effectively communicating with college instructors as well as managing stress, anxiety, and other factors that affect your academic goals and overall health during college. Being a college student can present unique and new challenges to your health, and staying healthy, both physically and mentally, are crucial components of your success. Unit 12 of this course addresses the importance of your social life to your college success, and Unit 13, the final unit of this course, equips you with some tools to help prepare you for a career after college. By the end of this course, you will have gained a comprehensive overview of the skills, tools, and resources you will need for a successful, healthy, and happy college experience. You will understand how to apply the concepts discussed in this course to your individual academic and personal goals, and to practice the skills you have learned by testing them in specific college courses that you plan to take or are already taking. Finally, you will possess a strong starting point for applying your newfound skills to your job search and your career beyond college.
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saylor.org Academy  ●  Online
Welcome to PRDV103: Interviewing Skills. This course is the third in a series of four courses included in the Job Search Skills Program that also includes Job Search Skills, Resume Writing, and Professional Etiquette. The Interviewing Skills course is intended to help you showcase your personality, strengths, interests, and abilities to potential employers. At this stage of your career exploration, you will have researched and targeted appropriate jobs and have marketed yourself to these employers with an attention-getting resume. If you have not already done so and feel you would benefit from more information about how to conduct a successful job search, or how to formulate a resume that gets you that interview, please explore the other exciting courses in this track.
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saylor.org Academy  ●  Online
What makes a novel “Gothic”? Scholars have debated this question for decades: some consider “the Gothic” a literary time period, spanning from the 1760s to 1820; others view it as a set of thematic concerns; still others understand it as a literary mode, in which contemporary authors like Stephen King continue to write. In this course, you will explore these and other definitions as you read a number of novels (and have the option to screen a film), attempting to define for yourself the term “Gothic.” You will supplement your studies with critical literature on the Gothic novel and literary mode, critiquing and adapting the approaches and theories as you see fit. You will begin the course with an overview of approaches to the literary Gothic and an outline of its stereotypical characteristics and elements. You will then progress through the course by examining Gothic novels (and an optional film) in three thematic categories (which, as you will see, often overlap): Gothic Spaces, the Monstrous Other, and Gender and Sexuality. The Gothic novel is at one and the same time a specific English literary event and a set of literary qualities that persist in American and European novels and films to the present day. The Gothic era of English literature begins with the novelist Horace Walpole (1717-1797) and the 1765 publication of The Castle of Otranto: A Gothic Story. Some scholars suggest that the last great novel of the era is Melmoth the Wanderer by Charles Robert Maturin (1782-1824); it was published in 1820. The literary Gothic, on the other hand, refers to a set of themes and conventions, whose roots and sensibilities originate in the English Gothic novels of the late eighteenth and early nineteenth century. After 1820, books and later films are described as Gothic because their creators have adapted and expanded the plots, narrative devices, and themes of the Gothic era of English literature, bringing new life to the genre by reflecting on contemporary political, social, and economic issues. What all Gothic literature and film have in common is the exploration of contemporary taboos, creating an atmosphere of terror. The taboo subjects change over time, but the fear and trembling that they invoke do not.
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