This College Algebra course will cover fundamental concepts of algebra required to interpret a variety of functions and equations. Topics within this course include: linear, quadratic, polynomial, rational, exponential, inverse functions and their graphs, linear inequalities, and linear systems of equations. Students who successfully complete this course will demonstrate increased ability in problem-solving and logical thinking.

Este curso está concebido como una preparación mínima necesaria para los primeros cursos de ingeniería y otros estudios en los que se imparten matemáticas. En él trabajaremos: El concepto de conjunto y sus operaciones La notación matemática elemental Los diferentes tipos de números: naturales, enteros, racionales, irracionales y reales Finalmente aprenderás los conceptos básicos necesarios sobre números complejos

Created specifically for those who are new to the study of probability, or for those who are seeking an approachable review of core concepts prior to enrolling in a college-level statistics course, Fat Chance prioritizes the development of a mathematical mode of thought over rote memorization of terms and formulae. Through highly visual lessons and guided practice, this course explores the quantitative reasoning behind probability and the cumulative nature of mathematics by tracing probability and statistics back to a foundation in the principles of counting. In Modules 1 and 2, you will be introduced to basic counting skills that you will build upon throughout the course. In Module 3, you will apply those skills to simple problems in probability. In Modules 4 through 6, you will explore how those ideas and techniques can be adapted to answer a greater range of probability problems. Lastly, in Module 7, you will be introduced to statistics through the notion of expected value, variance, and the normal distribution. You will see how to use these ideas to approximate probabilities in situations where it is difficult to calculate their exact values.

How did Newton describe the orbits of the planets? To do this, he created calculus. But he used a different coordinate system more appropriate for planetary motion. We will learn to shift our perspective to do calculus with parameterized curves and polar coordinates. And then we will dive deep into exploring the infinite to gain a deeper understanding and powerful descriptions of functions. How does a computer make accurate computations? Absolute precision does not exist in the real world, and computers cannot handle infinitesimals or infinity. Fortunately, just as we approximate numbers using the decimal system, we can approximate functions using series of much simpler functions. These approximations provide a powerful framework for scientific computing and still give highly accurate results. They allow us to solve all sorts of engineering problems based on models of our world represented in the language of calculus. Changing Perspectives Parametric Equations Polar Coordinates Series and Polynomial Approximations Series and Convergence Taylor Series and Power Series The three modules in this series are being offered as an XSeries on edX. Please visit Single Variable Calculus XSeries Program Page to learn more and to enroll in the modules. This course, in combination with Parts 1 and 2, covers the AP* Calculus BC curriculum. Learn more about our High School and AP* Exam Preparation Courses This course was funded in part by the Wertheimer Fund. *Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.

In this course, we go beyond the calculus textbook, working with practitioners in social, life and physical sciences to understand how calculus and mathematical models play a role in their work. Through a series of case studies, you’ll learn: How standardized test makers use functions to analyze the difficulty of test questions; How economists model interaction of price and demand using rates of change, in a historical case of subway ridership; How an x-ray is different from a CT-scan, and what this has to do with integrals; How biologists use differential equation models to predict when populations will experience dramatic changes, such as extinction or outbreaks; How the Lotka-Volterra predator-prey model was created to answer a biological puzzle; How statisticians use functions to model data, like income distributions, and how integrals measure chance; How Einstein’s Energy Equation, E=mc2 is an approximation to a more complicated equation. With real practitioners as your guide, you’ll explore these situations in a hands-on way: looking at data and graphs, writing equations, doing calculus computations, and making educated guesses and predictions. This course provides a unique supplement to a course in single-variable calculus. Key topics include application of derivatives, integrals and differential equations, mathematical models and parameters. This course is for anyone who has completed or is currently taking a single-variable calculus course (differential and integral), at the high school (AP or IB) or college/university level. You will need to be familiar with the basics of derivatives, integrals, and differential equations, as well as functions involving polynomials, exponentials, and logarithms. This is a course to learn applications of calculus to other fields, and NOT a course to learn the basics of calculus. Whether you’re a student who has just finished an introductory Calculus course or a teacher looking for more authentic examples for your classroom, there is something for you to learn here, and we hope you’ll join us!

Matrix Algebra underlies many of the current tools for experimental design and the analysis of high-dimensional data. In this introductory online course in data analysis, we will use matrix algebra to represent the linear models that commonly used to model differences between experimental units. We perform statistical inference on these differences. Throughout the course we will use the R programming language to perform matrix operations. Given the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. You will need to know some basic stats for this course. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts. These courses make up two Professional Certificates and are self-paced: Data Analysis for Life Sciences: PH525.1x: Statistics and R for the Life Sciences PH525.2x: Introduction to Linear Models and Matrix Algebra PH525.3x: Statistical Inference and Modeling for High-throughput Experiments PH525.4x: High-Dimensional Data Analysis Genomics Data Analysis: PH525.5x: Introduction to Bioconductor PH525.6x: Case Studies in Functional Genomics PH525.7x: Advanced Bioconductor This class was supported in part by NIH grant R25GM114818.

Introduction to the mathematical concept of networks, and to two important optimization problems on networks: the transshipment problem and the shortest path problem. Short introduction to the modeling power of discrete optimization, with reference to classical problems. Introduction to the branch and bound algorithm, and the concept of cuts.

Differential equations are the mathematical language we use to describe the world around us. Most phenomena can be modeled not by single differential equations, but by systems of interacting differential equations. These systems may consist of many equations. In this course, we will learn how to use linear algebra to solve systems of more than 2 differential equations. We will also learn to use MATLAB to assist us. We will use systems of equations and matrices to explore: The original page ranking systems used by Google, Balancing chemical reaction equations, Tuned mass dampers and other coupled oscillators, Threeor more species competing for resources in an ecosystem, The trajectory of a rider on a zipline. The five modules in this seriesare being offered as an XSeries on edX. Please visit the Differential EquationsXSeries Program Page to learn more and to enroll in the modules. *Zipline photo by teanitiki on Flickr (CC BY-SA 2.0)

More than 2000 years ago, long before rockets were launched into orbit or explorers sailed around the globe, a Greek mathematician measured the size of the Earth using nothing more than a few facts about lines, angles, and circles. This course will start at the very beginnings of geometry, answering questions like "How big is an angle?" and "What are parallel lines?" and proceed up through advanced theorems and proofs about 2D and 3D shapes. Along the way, you'll learn a few different ways to find the area of a triangle, you'll discover a shortcut for counting the number of stones in the Great Pyramid of Giza, and you'll even come up with your own estimate for the size of the Earth. In this course, you'll be able to choose your own path within each lesson, and you can jump between lessons to quickly review earlier material. GeometryX covers a standard curriculum in high school geometry, and CCSS (common core) alignment is indicated where applicable. Learn more about our High School and AP* Exam Preparation Courses This course was funded in part by the Wertheimer Fund.

Preparing for the AP Calculus AB exam requires a deep understanding of many different topics in calculus as well as an understanding of the AP exam and the types of questions it asks. This course is Part 1 of our XSeries: AP Calculus AB and it is designed to prepare you for the AP exam. In Part 2, you will use and apply the meaning and interpretations of derivatives from Part 1 to the integral, antiderivatives and differential equations. You will learn some applications of integrals including finding volumes of solids and solids of revolution, volumes with known cross sections and applications to Velocity-Time graphs. We will close with an introduction to differential equations and see how they are used. As you work through this course, you will find lecture videos taught by expert AP calculus teachers, practice multiple choice questions and free response questions that are similar to what you will encounter on the AP exam and tutorial videos that show you step-by-step how to solve problems. By the end of the course, you should be ready to take on the AP exam!