Courses tagged with "Taking derivatives" (363)

Geometry comes from the Greek roots geo-, meaning Earth, and metron, meaning measure. Thus, geometry literally means the process of measuring the Earth. In a more mathematical sense, this course looks at geometric figures that we see in everyday life to understand the patterns in their attributes and how their measures relate to these patterns. It expands on the basic geometric concepts learned in previous math courses, through the applications of these concepts in new contexts. You will learn to develop formal proofs that support patterns and rules of geometric figures previously investigated, including congruent and similar figures, triangles, quadrilaterals, and circles. From here, the course expands on your knowledge about triangles and the Pythagorean theorem, introducing trigonometry of both right triangles and general triangles. The course will help you develop links between the attributes of two-dimensional and three-dimensional figures; help you develop formulas for calculating the volume of prisms…

This course is designed to prepare Saylor’s consulting educators to build K-12 subject courses that are aligned with the Common Core State Standards in English Language Arts & Literacy in History/Social Studies, Science and Technical Subjects and Mathematics.  You will begin this course by gaining an overview of what the set of Common Core State Standards is, why Saylor is focused on developing courses around the Common Core State Standards, and the main benchmarks for ensuring that a course is compliant with the Common Core State Standards.  In unit 2 of this course, you will look at the Common Core State Standards in detail and identify key takeaways from them.  In unit 3 of this course, you will explore how to develop content that meets the Common Core State Standards and how to integrate the standards through the development of learning assignments based on specific texts and activities.  In unit 4 of this course, you will take a look at the different assessment strategies often used for Common Core…

Bioorganic chemistry studies the chemistry of organic biomolecules.  It is a rapidly growing interdisciplinary field that combines organic chemistry and biochemistry.  Please recall that organic chemistry investigates all molecules that contain carbon and hydrogen, and biochemistry focuses on the network of molecular pathways in the cell.  Bioorganic chemistry employs organic chemistry to explain how enzymes catalyze the reactions of metabolic pathways and why metabolites react the way they do.  Bioorganic chemistry aims to expand organic-chemical research on structures, synthesis, and kinetics in a biological direction. This one-semester course will cover several advanced chemistry topics and will discuss the chemistry behind biological processes.  The course begins by introducing you to the mechanisms behind the most common biological chemical reactions (Unit 1).  You will then take a closer look at the metabolic processes of biomolecules.  You will apply your knowledge of the structural feature…

Real Analysis II is the sequel to Saylor’s Real Analysis I, and together these two courses constitute the foundations of real analysis in mathematics. In this course, you will build on key concepts presented in Real Analysis I, particularly the study of the real number system and real-valued functions defined on all or part (usually intervals) of the real number line. The main objective of MA241 [1] was to introduce you to the concept and theory of differential and integral calculus as well as the mathematical analysis techniques that allow us to understand and solve various problems at the heart of sciencenamely, questions in the fields of physics, economics, chemistry, biology, and engineering. In this course, you will build on these techniques with the goal of applying them to the solution of more complex mathematical problems. As long as a problem can be modeled as a functional relation between two quantities, each of which can be expressed as a set of real numbers, the techniques used for real-value…

Cryptography is essentially the science of writing in secret code.  In data and telecommunications, cryptography has specific security requirements, such as authentication, privacy or confidentiality, integrity, and non-repudiation.  To meet these security requirements, we employ secret key (or symmetric) cryptography, public-key (or asymmetric) cryptography, and hash functions. In the first part of the course, we will review a number of different ciphers that were used before World War II.  These ciphers would be easily broken nowadays, since cryptography has advanced quickly over the past couple of decades with the advent of modern computers.  We will cover block cipher algorithms and describe the advanced encryption standard for a symmetric-key encryption adopted by the U.S. government.  We will also learn about the important MD5 and SHA-1 hash functions as well as the message authentication code. This course will focus on public key cryptography, which is best exemplified by the RSA algorithm (na…

Principles of Microeconomics belongs to the CLEP® PREP suite of Saylor courses. This version of ECON101 will help you master the subject of microeconomics and will help prepare you to take the CLEP® exam in microeconomics [1]. The purpose of this course is to provide you with a basic understanding of the principles of microeconomics. At its core, the study of economics deals with the choices and decisions that have to be made in order to manage scarce resources available to us. Microeconomics is the branch of economics that pertains to decisions made at the individual level, i.e., by individual consumers or individual firms after evaluating resources, costs, and tradeoffs. When we talk about the economy, we are referring to the marketplace or system in which these choices interact with one another. In this course, you will learn how and why these decisions are made and how they affect one another in the economy. Each of the following units has been designed as a building block, where the concepts you le…

Do you know what you’re watching? What you’re reading? You might think that what comes across your television or web browser, in your newspaper or magazine, or on your movie screen is pretty much the whole message; what you see is what you get. But the content we see, read, and hear is the product of complex forces − economic, governmental, historical, and technological. This course will explore those underlying forces and provide analytical tools to evaluate media critically. An overall goal is to become media literate, to gain an understanding of mass media as cultural industries that seek to influence our behavior and affect our values as a society. Unit 1 aims to define mass communication, mass media, and culture. It also will introduce the core concepts of media literacy and the concept of transmedia, the practice of integrating entertainment experiences across a range of different media platforms. Unit 2 will introduce selected theories that will help in analyzing mass communication and its effect…

This course will teach you the important role that metal ions play in key biological processes.  You will learn that many biological functions are performed at the cellular level by metal ions that are incorporated into the activation sites of proteins and enzymes.  For example, when oxygen is transported through blood in the human body, it is bound to iron ions that are incorporated into the hemoglobin protein.  In order to function properly, these iron ions must be high-spin and in their +2 oxidation state.  As you progress through this course, you will learn about these and other requirements and mechanisms that must be present in order to facilitate critical biological functions. You will begin this course by reviewing the basic principles of inorganic chemistry, biochemistry, and molecular biology.  Following a brief overview of the spectroscopy methods that scientists use in the study of metals that contain protein, you will explore the structures of the most relevant metal centers in biological…

Precalculus I is designed to prepare you for Precalculus II, Calculus, Physics, and higher math and science courses. In this course, the main focus is on five types of functions: linear, polynomial, rational, exponential, and logarithmic. In accompaniment with these functions, you will learn how to solve equations and inequalities, graph, find domains and ranges, combine functions, and solve a multitude of real-world applications. In this course, you will not only be learning new algebraic techniques that are necessary for other math and science courses, but you will be learning to become a critical thinker. You will be able to determine what is the best approach to take such as numerical, graphical, or algebraic to solve a problem given particular information. Then you will investigate and solve the problem, interpret the answer, and determine if it is reasonable. A few examples of applications in this course are determining compound interest, growth of bacteria, decay of a radioactive substance, and the…

Eighth-grade English Language Arts will provide you with a strong foundation for high school. Grounded in Common Core State Standards, the content of this course emphasizes critical reading, writing, and thinking. You will read and analyze high-quality literary and informational texts. You will write original texts in multiple genres. Language and its conventions will be emphasized throughout, and opportunities to examine the spoken word will be provided as well. Whether you choose to pursue higher education or the world of work, or both, you will be expected to have certain basic skills in reading, writing, speaking and listening. While you probably won

Economics is traditionally divided into two parts: microeconomics and macroeconomics. The main purpose of this course is to introduce you to the principles of macroeconomics. Macroeconomics is the study of how a country’s economy works while trying to discern among good, better, and best choices for improving and/or maintaining a nation’s standard of living and level of economic and societal well-being. Historical and contemporary perspectives on the roles and policies of government are part of the mix of interpretations and alternatives that surround questions of who or what gains and loses the most or least within a relatively small set of key interdependent players. In the broadest view, that set consists of households, consumers, savers, firm owners, investors, agency and elected officials, and global trading partners in which some wear many hats and face price considerations at two levels. Consider one distinction between macroeconomics and microeconomics though prices are taken into account in bot…

English III, American Literature, explores the literature of America from the narratives of the early colonists to the foundational documents of our forefathers, and the literature of our modern times. In English III, you will gain a firm grasp of the various literary periods throughout American history as well as the ability to analyze different genres and styles of notable American authors. As you progress through the course, you will gain an appreciation for American literature and an understanding of how the literature of the day acted as a reflection of the historical period from which it evolved. This course will also give you the opportunity to hone your own writing skills as you identify the characteristics of effective writing for a variety of different purposes and audiences.

Eighth-grade English Language Arts will provide you with a strong foundation for high school. Grounded in Common Core State Standards, the content of this course emphasizes critical reading, writing, and thinking. You will read and analyze high-quality literary and informational texts. You will write original texts in multiple genres. Language and its conventions will be emphasized throughout, and opportunities to examine the spoken word will be provided as well. Whether you choose to pursue higher education or the world of work, or both, you will be expected to have certain basic skills in reading, writing, speaking and listening. While you probably won

English II is the second in a sequence of English courses for high school students. These courses seek to give you the necessary reading, writing, thinking, and research skills to find success in college or the workplace. As the second course, English II challenges you to look deeper within a text for its meaning and provide thoughtful, analytical, and persuasive responses. You will be expected to build literary analysis from the texts as well as outside sources of knowledge. You will first learn to dissect a text for varied levels of meaning, how to interpret this meaning with a critical eye, and how to look beyond the text for its relevance. You will then be expected to read a variety of fiction and nonfiction texts of different lengths, complexities, and genres, and respond to them through questions, annotations, independent research, and essay writing. Texts and assignments will gradually increase in rigor, challenging you to improve the efficacy and complexity of your analysis and writing skills. Bec…

Eighth-grade English Language Arts will provide you with a strong foundation for high school. Grounded in Common Core State Standards, the content of this course emphasizes critical reading, writing, and thinking. You will read and analyze high-quality literary and informational texts. You will write original texts in multiple genres. Language and its conventions will be emphasized throughout, and opportunities to examine the spoken word will be provided as well. Whether you choose to pursue higher education or the world of work, or both, you will be expected to have certain basic skills in reading, writing, speaking and listening. While you probably won’t be expected to write a poem on command, you will have to be able to express yourself clearly when you write and speak. This course includes challenging material which will help you build the skills you need to begin high school. As you progress through your remaining years as a student, you will continue to add and build upon the skills and knowledge yo…

English II is the second in a sequence of English courses for high school students. These courses seek to give you the necessary reading, writing, thinking, and research skills to find success in college or the workplace. As the second course, English II challenges you to look deeper within a text for its meaning and provide thoughtful, analytical, and persuasive responses. You will be expected to build literary analysis from the texts as well as outside sources of knowledge. You will first learn to dissect a text for varied levels of meaning, how to interpret this meaning with a critical eye, and how to look beyond the text for its relevance. You will then be expected to read a variety of fiction and nonfiction texts of different lengths, complexities, and genres, and respond to them through questions, annotations, independent research, and essay writing. Texts and assignments will gradually increase in rigor, challenging you to improve the efficacy and complexity of your analysis and writing skills. Bec…

English III, American Literature, explores the literature of America from the narratives of the early colonists to the foundational documents of our forefathers, and the literature of our modern times. In English III, you will gain a firm grasp of the various literary periods throughout American history as well as the ability to analyze different genres and styles of notable American authors. As you progress through the course, you will gain an appreciation for American literature and an understanding of how the literature of the day acted as a reflection of the historical period from which it evolved. This course will also give you the opportunity to hone your own writing skills as you identify the characteristics of effective writing for a variety of different purposes and audiences.

Geometry comes from the Greek roots geo-, meaning Earth, and metron, meaning measure. Thus, geometry literally means the process of measuring the Earth. In a more mathematical sense, this course looks at geometric figures that we see in everyday life to understand the patterns in their attributes and how their measures relate to these patterns. It expands on the basic geometric concepts learned in previous math courses, through the applications of these concepts in new contexts. You will learn to develop formal proofs that support patterns and rules of geometric figures previously investigated, including congruent and similar figures, triangles, quadrilaterals, and circles. From here, the course expands on your knowledge about triangles and the Pythagorean theorem, introducing trigonometry of both right triangles and general triangles. The course will help you develop links between the attributes of two-dimensional and three-dimensional figures; help you develop formulas for calculating the volume of prisms…

The purpose of this course is to familiarize you with the fundamentals of algebraic expressions, including adding, multiplying, factoring, and simplifying; solving equations and inequalities; performing operations on functions; and performing graphing and basic functional analysis. This course is intended to extend your knowledge beyond the foundational information learned in Algebra I and prepare you for more advanced topics, leading toward trigonometry and calculus. Among the benefits that you will gain from learning the material contained here are adding tools for critical thinking, improving skill sets for use in the sciences, and improving your competitiveness in preparation for college applications. A strong understanding of mathematics is critical toward earning scholarships and gaining admission to many top universities, and the knowledge gained here will help in that regard.

Mathematics comes together in this course. You enter precalculus with an abundant array of experience in mathematics, and this course offers an opportunity to make connections among the big ideas you encountered earlier. It also assists you in developing fluency with the tools used in learning calculus. The focus of this course is the concept of function - it’s with functions that mathematicians and scientists can model the world and make leaps of invention, sending rockets to far planets, determining the future size of populations, and finding the amount of earth to be moved when creating new roads. The unit begins by defining and exploring certain attributes of functions and continues with specific kinds of functions - linear, polynomial, rational, logarithmic, and exponential. In addition to precalculus being important for many fields, the subject is obviously designed to prepare you for calculus, which is the mathematics of things that are changing. Calculus allows us to find areas of strangely curv…