Courses tagged with "Taking derivatives" (363)

The advent of computers transformed science.  Large, complicated datasets that once took researchers years to manually analyze could suddenly be analyzed within a week using computer software.  Nowadays, scientists can use computers to produce several hypotheses as to how a particular phenomenon works, create computer models using the parameters of each hypothesis, input data, and see which hypothetical model produces an output that most closely mirrors reality. Computational biology refers to the use of computers to automate data analysis or model hypotheses in the field of biology.  With computational biology, researchers apply mathematics to biological phenomena, use computer programming and algorithms to artificially create or model the phenomena, and draw from statistics in order to interpret the findings.  In this course, you will learn the basic principles and procedures of computational biology.  You will also learn various ways in which you can apply computational biology to molecular and cell…

We live in an increasingly globalized world.  Technology enables us to do business just as easily with our neighbors as with a businessperson thousands of miles away from us.  Knowing how to navigate cultural differences is an increasingly valuable skill that will make you a more valuable employee.  Encounters among members of different cultures frequently fail simply because of basic cultural differences, such as the importance of time, proper greetings, or even the use of eye contact.  This course is designed to help you identify how to become a better communicator in these sorts of cross-cultural situations.  You will learn about barriers to successful communication that involve cultural differences.  You will also learn more about your own communication style and how it can be developed to facilitate more successful intercultural encounters. Though some of this course addresses a Western/U.S. perspective, much of the course focuses on characteristics of specific cultures and how generally one cultur…

This course is a continuation of the first-semester course titled CS101: Introduction to Computer Science I [1]. It will introduce you to a number of more advanced Computer Science topics, laying a strong foundation for future academic study in the discipline. We will begin with a comparison between Java - the programming language utilized last semester - and C++, another popular, industry-standard programming language. We will then discuss the fundamental building blocks of Object-Oriented Programming, reviewing what we learned last semester and familiarizing ourselves with some more advanced programming concepts. The remaining course units will be devoted to various advanced topics, including the Standard Template Library, Exceptions, Recursion, Searching and Sorting, and Template Classes. By the end of the class, you will have a solid understanding of Java and C++ programming, as well as a familiarity with the major issues that programmers routinely address in a professional setting. [1] http://www.saylor.

This course is designed to introduce you to the study of Calculus.  You will learn concrete applications of how calculus is used and, more importantly, why it works.  Calculus is not a new discipline; it has been around since the days of Archimedes.  However, Isaac Newton and Gottfried Leibniz, two 17th-century European mathematicians concurrently working on the same intellectual discovery hundreds of miles apart, were responsible for developing the field as we know it today.  This brings us to our first question, what is today's Calculus?  In its simplest terms, calculus is the study of functions, rates of change, and continuity.  While you may have cultivated a basic understanding of functions in previous math courses, in this course you will come to a more advanced understanding of their complexity, learning to take a closer look at their behaviors and nuances. In this course, we will address three major topics: limits, derivatives, and integrals, as well as study their respective foundations and a…

Many consider William Shakespeare the greatest dramatisteven the greatest writerof all time.  His impact on Western culture and language is unmistakable, but his works have also been continuously read and performed around the world, illustrating his global significance.  Over the course of this semester, we will attempt to determine why his works have become so widely revered, or why they seem, to quote Ben Jonson, “not for an age, but for all time.” We will begin by familiarizing ourselves with Elizabethan theatre, language, and culturethe world in which Shakespeare lived and breathed.  We will then conduct close readings of a number of Shakespeare’s most acclaimed plays, progressing through his dramatic works by categorizing them in three groups: comedies, tragedies, and histories.  Finally, we will turn to some of his poetry, which Shakespeare (perhaps surprisingly) considered superior to his plays.  By the end of this course, you will have developed a strong understanding of Shakespeare’s w…

This course will introduce you to the fundamentals of probability theory and random processes. The theory of probability was originally developed in the 17th century by two great French mathematicians, Blaise Pascal and Pierre de Fermat, to understand gambling. Today, the theory of probability has found many applications in science and engineering. Engineers use data from manufacturing processes to sample characteristics of product quality in order to improve the products being produced. Pharmaceutical companies perform experiments to determine the effect of a drug on humans and use the results to make decisions about treatment of illnesses, while economists observe the state of the economy over periods of time and use the information to forecast the economic future. In this course, you will learn the basic terminology and concepts of probability theory, including random experiments, sample spaces, discrete distribution, probability density function, expected values, and conditional probability. You will al…

This course provides students with an introduction to the core technologies used to communicate information on the Web: Hypertext Markup Language (HTML) and Cascading Style Sheets (CSS).  Whether managing an employer's website, producing an online resume, or starting a web-based business, knowing the fundamentals of how information is structured and presented on the internet is a crucial skill for the contemporary workplace. Today, many technologies exist to facilitate the creation and management of websites, including development environments like Adobe Dreamweaver and Content Management Systems like WordPress and Joomla!  Even though mastery of the basics of HTML and CSS is easily attainable, these labor-saving technologies have discouraged many professionals from learning crucial coding skills.  With a basic understanding of how HTML code is created and transformed, professionals are better able to produce or transform websites according to precise specifications, whether they use a fully-featured dev…

In BIO101 [1], you were introduced to biology on a microscopic scale when you learned about the functions of molecules, genes, and cells.  In this course, you will learn about biological changes that happen on a very large scale, across entire populations of organisms and over the course of millions of years, in the form of evolution and ecology.  Evolution, the process by which different species of organisms have developed and diversified from earlier forms, has been a central theme in the field of biology ever since Darwin first published his theories about it.  Mounting evidence from many different branches of science all point to the fact that species have experienced a gradual but definite physical change.  In this course, we will learn about evolution and theories that stem from evolution. We will also learn about ecology, the study of the interactions between different types of organisms and their surroundings.  Changes in surroundings will force organisms to adapt and changeoften in terms of th…

This course is designed to introduce you to the study of calculus. You will learn concrete applications of how calculus is used and, more importantly, why it works. Calculus is not a new discipline; it has been around since the days of Archimedes. However, Isaac Newton and Gottfried Leibniz, two seventeenth-century European mathematicians concurrently working on the same intellectual discovery hundreds of miles apart, were responsible for developing the field as we know it today. This brings us to our first question, what is today’s calculus? In its simplest terms, calculus is the study of functions, rates of change, and continuity. While you may have cultivated a basic understanding of functions in previous math courses, in this course you will come to a more advanced understanding of their complexity, learning to take a closer look at their behaviors and nuances. In this course, we will address three major topics: limits, derivatives, and integrals, as well as study their respective foundations and appl…

Advertising is an integral part of our modern, media-dominated society. While many of us have a love-hate relationship with the industry, advertising can be wonderfully entertaining. However, is advertising a necessary evil? Does it make meaningful contributions to our society? With the incredible growth of social media, now is a particularly exciting time to explore the fascinating world of advertising. The purpose of this course is to lead students in an exploration of fundamental advertising principles and the role advertising plays in the promotional mix. You will learn where advertising fits in the Marketing Mix, also known as the four Ps: Product, Price, Place, and Promotion. Although some consider all promotion synonymous with advertising, you will learn the unique characteristics that separate advertising from other forms of promotional communication. You will revisit some familiar marketing concepts within a new framework, approaching the subject from the advertiser’s perspective. Our text us…

As a student of economics, you must study the history of economic thought to understand why individuals, firms, and governments make certain choices. Economists try to answer three basic questions: what to produce, how to produce it, and for whom. The history of economic thought represents a wide diversity of theories within the discipline, but all economists address these three basic questions. As you learn more about the history of economic thought, you may realize that policies presented as great innovations today are founded upon centuries-old writings. You will learn that without a clear sense of the discussions and debates that took place among economists of the past, the modern economist lacks a complete perspective. By examining the history of economic thought, you will be able to categorize and classify thoughts and ideas and will begin to understand how to think like an economist. Economics is both a social science and a business subject; accordingly, economic thinking affects everything from art t…

Linear algebra is the study of vector spaces and linear mappings between them.  In this course, we will begin by reviewing topics you learned in Linear Algebra I, starting with linear equations, followed by a review of vectors and matrices in the context of linear equations.  The review will refresh your knowledge of the fundamentals of vectors and of matrix theory, how to perform operations on matrices, and how to solve systems of equations.  After the review, you should be able to understand complex numbers from algebraic and geometric viewpoints to the fundamental theorem of algebra.  Next, we will focus on eigenvalues and eigenvectors.  Today, these have applications in such diverse fields as computer science (Google's PageRank algorithm), physics (quantum mechanics, vibration analysis, etc.), economics (equilibrium states of Markov models), and more.  We will end with the spectral theorem, which provides a decomposition of the vector space on which operators act, and singular-value decomposition, w…

This course is designed for the novice who has little or no word processing experience.  The course provides an introduction to word processing.  You will explore word processing skills while also learning to create a basic business letter and a business memo.  Although the resources in this course use Microsoft Word 2010, it should be noted that all of the basic skills and tasks that you will be asked  can be done on any word processing program.  If you stay flexible enough in your own word processing program to search out the commands and icons on whatever software you are using, you will succeed.  The most current version of Microsoft Word was selected, because it would be most beneficial to the job seeker.  In addition most colleges, universities, and some public libraries are using a newer version of Word.  You can complete this course using any word processing software, but if you are using an older version of Word, you may also want to seek out a resource where you can interact with the newer v…

BUS206 [1] introduced you to the subject of Management Information Systems (MIS). The focus of that initial course was on the nuts and bolts of information systems: how they work, how you create them, how to secure them, and so on. This course is developed to help you understand how information technology can be used as part of an organization’s overall strategy. In this course you will focus on the allocation and use of technology resources across an entire firm as part of the larger organizational strategy. Because firms do not have an unlimited supply of capital, they must decide when and where to deploy new information technology. Firms must not only focus on when to deploy IT, but also if they should deploy IT at all! This brings up the bigger question about technology: Can the use of IT bring a sustainable competitive advantage to an organization? There are those who say, “No”; and others who say, “Of course!”  You will explore the differing opinions out there on this topic in unit 1. In un…

Physics 101 is the first course in the Introduction to Physics sequence. In general, the quest of physics is to develop descriptions of the natural world that correspond  closely to actual observations.  Given this definition, the story behind everything in the universe is  one of physics.  In practice,  the field of physics is more often limited to the discovery and refinement of the basic laws that underlie the behavior of matter and energy.  While biology is founded upon physics, in practice, the study of biology generally assumes that the present understanding of physical laws is accurate.  Chemistry is more closely dependent on physics and   assumes that physical laws provide accurate predictions.  Engineering, for the most part, is applied physics. In this course, we will study physics from the ground up, learning the basic principles of physical laws, their application to the behavior of objects, and the use of the scientific method in driving advances in this knowledge.  This first course o…

CS405 introduces the field of artificial intelligence (AI).  Materials on AI programming, logic, search, game playing, machine learning, natural language understanding, and robotics introduce the student to AI methods, tools, and techniques, their application to computational problems, and their contribution to understanding intelligence.  Because each of these topics could be a course unto itself, the material is introductory and not complete.  Each unit presents the problem a topic addresses, current progress, and approaches to the problem.  The readings include and cite more materials that are referenced in this course, and students are encouraged to use these resources to pursue topics of interest after this course.

This course surveys major topics and theories in the field of Industrial Organization.  As part of the applied microeconomics structure, Industrial Organization uses the basic tools of microeconomic theory and game theory to study the structure and behavior of firms and their strategic interactions with one another in the marketplace.  Industrial Organization also studies the impact that those interactions have on market structure and welfare. Different kinds of market structures (perfect competition, imperfect competition, monopoly, oligopoly, and so forth) present different scenarios in which firms strive to acquire and use market power for their strategic advantage.  While perfect competition and monopoly are two market structures on opposite ends of the spectrum, imperfect competitionwhere a limited number of firms attempt to manipulate their rivals or consumersis a more realistic set-up.  This course will emphasize market structure analysis and the strategic behaviors of competing firms, including…

Only 150 years ago, the empires and states of Northeast Asiafor many centuries far more developed than their contemporaries in most of Asia, and all of Europe, the Americas and Africafound themselves powerless in the face of the military, technological and economic might of the European imperialist powers and the United States. Yet, today, most of these states have once again become key players in the contemporary world order: economically, politically, culturally, and, in many instances, militarily. In this course, we will study how and why the ‘modern’ transformation of Northeast Asia came about, examining both the indigenous and foreign ideas and institutions on which the transformations were based, and comparing how change manifested in different times and places. We will analyze many of the problems faced both domestically and internationally during this transformation, and will evaluate the prospects for the region in the 21st century. In order to do so, we will trace the political, economic and c…

This course is a continuation of Abstract Algebra I: we will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms.  We will also take a look at ring factorization, which will lead us to a discussion of the solutions of polynomials over abstracted structures instead of numbers sets.  We will end the section on rings with a discussion of general lattices, which have both set and logical properties, and a special type of lattice known as Boolean algebra, which plays an important role in probability.  We will also visit an important topic in mathematics that you have likely encountered already: vector spaces.  Vector spaces are central to the study of linear algebra, but because they are extended groups, group theory and geometric methods can be used to study them. Later in this course, we will take a look at more advanced topics and consider several useful theorems and counting methods.  We will end the course by studying Galois theoryone of the most im…

This lab course supplements BIO101 [1]: “Introduction to Molecular and Cellular Biology.”  Although we cannot virtually replicate a true lab experience, this “lab” will allow you to become familiar with scientific thinking and techniques and will enable you to explore of some key principles of molecular and cellular biology. The material in this lab supplement directly relates to the material covered in the lecture and reading portion of the course.  While the lecture and reading portion focuses on big-picture concepts, here we will focus more on visual understanding, manipulation, and practical use of your knowledge.  In each unit, you will work through tutorials related to important scientific concepts, and then will be asked to think creatively about how your knowledge can be put to practical or experimental use. There are also activities devoted to learning important techniques in scientific study, including microscope use, DNA extraction, Polymerase Chain Reaction, and DNA microarrays.  A…