# Online courses directory (90)

This course provides a brief review of introductory algebra topics. Topics to be covered include integer operations, order of operations, perimeter and area, fractions and decimals, scientific notation, ratios and rates, conversions, percents, algebraic expressions, linear equations, the Pythagorean theorem, and graphing.

This mini-course is intended for students who would like a refresher on the basics of linear algebra. The course attempts to provide the motivation for "why" linear algebra is important in addition to "what" linear algebra is. Students will learn concepts in linear algebra by applying them in computer programs. At the end of the course, you will have coded your own personal library of linear algebra functions that you can use to solve real-world problems.

The goal of this course is to give you solid foundations for developing, analyzing, and implementing parallel and locality-efficient algorithms. This course focuses on theoretical underpinnings. To give a practical feeling for how algorithms map to and behave on real systems, we will supplement algorithmic theory with hands-on exercises on modern HPC systems, such as Cilk Plus or OpenMP on shared memory nodes, CUDA for graphics co-processors (GPUs), and MPI and PGAS models for distributed memory systems. This course is a graduate-level introduction to scalable parallel algorithms. “Scale” really refers to two things: efficient as the problem size grows, and efficient as the system size (measured in numbers of cores or compute nodes) grows. To really scale your algorithm in both of these senses, you need to be smart about reducing asymptotic complexity the way you’ve done for sequential algorithms since CS 101; but you also need to think about reducing communication and data movement. This course is about the basic algorithmic techniques you’ll need to do so. The techniques you’ll encounter covers the main algorithm design and analysis ideas for three major classes of machines: for multicore and many core shared memory machines, via the work-span model; for distributed memory machines like clusters and supercomputers, via network models; and for sequential or parallel machines with deep memory hierarchies (e.g., caches). You will see these techniques applied to fundamental problems, like sorting, search on trees and graphs, and linear algebra, among others. The practical aspect of this course is implementing the algorithms and techniques you’ll learn to run on real parallel and distributed systems, so you can check whether what appears to work well in theory also translates into practice. (Programming models you’ll use include Cilk Plus, OpenMP, and MPI, and possibly others.)

This class presents the fundamental probability and statistical concepts used in elementary data analysis. It will be taught at an introductory level for students with junior or senior college-level mathematical training including a working knowledge of calculus. A small amount of linear algebra and programming are useful for the class, but not required.

Mathematical Methods for Quantitative Finance covers topics from calculus and linear algebra that are fundamental for the study of mathematical finance. Students successfully completing this course will be mathematically well prepared to study quantitative finance at the graduate level.

Use the power of algebra to understand and interpret points and lines (something we typically do in geometry). This will include slope and the equation of a line. Descartes and Cartesian Coordinates. The Coordinate Plane. Plot ordered pairs. Graphing points exercise. Graphing points. Quadrants of Coordinate Plane. Graphing points and naming quadrants exercise. Graphing points and naming quadrants. Points on the coordinate plane. Points on the coordinate plane. Coordinate plane word problems exercise. Coordinate plane word problems. Reflecting points exercise. Reflecting points. Ordered pair solutions of equations. Ordered Pair Solutions of Equations 2. Determining a linear equation by trying out values from a table. Equations from tables. Plotting (x,y) relationships. Graphs of Linear Equations. Application problem with graph. Ordered pair solutions to linear equations. Interpreting Linear Graphs. Exploring linear relationships. Recognizing Linear Functions. Interpreting linear relationships. Graphing lines 1. Recognizing Linear Functions. Linear and nonlinear functions (example 1). Linear and nonlinear functions (example 2). Linear and nonlinear functions (example 3). Linear and nonlinear functions. Graphing using X and Y intercepts. Graphing Using Intercepts. X and Y intercepts. X and Y intercepts 2. Solving for the x-intercept. Finding x intercept of a line. Finding intercepts for a linear function from a table. Linear function intercepts. Interpreting intercepts of linear functions. Interpreting and finding intercepts of linear functions. Analyzing and identifying proportional relationships ex1. Analyzing and identifying proportional relationships ex2. Analyzing and identifying proportional relationships ex3. Analyzing and identifying proportional relationships. Comparing proportional relationships. Constructing an equation for a proportional relationship. Constructing and comparing proportional relationships. Graphing proportional relationships example. Graphing proportional relationships example 2. Graphing proportional relationships example 3. Graphing proportional relationships. Comparing rates. Representing and comparing rates. Rates and proportional relationships. Rate problem with fractions 1. Unit cost with fractions 1. Rate problems 1. Slope of a line. Slope of a Line 2. Slope and Rate of Change. Graphical Slope of a Line. Slope of a Line 3. Slope Example. Hairier Slope of Line. Identifying slope of a line. Slope and Y-intercept Intuition. Line graph intuition. Algebra: Slope. Algebra: Slope 2. Algebra: Slope 3. Graphing a line in slope intercept form. Converting to slope-intercept form. Graphing linear equations. Fitting a Line to Data. Comparing linear functions 1. Comparing linear functions 2. Comparing linear functions 3. Comparing linear functions. Interpreting features of linear functions example. Interpreting features of linear functions example 2. Interpreting features of linear functions. Comparing linear functions applications 1. Comparing linear functions applications 2. Comparing linear functions applications 3. Comparing linear functions applications. Constructing a linear function word problem. Constructing and interpreting a linear function. Constructing linear graphs. Constructing and interpreting linear functions. Multiple examples of constructing linear equations in slope-intercept form. Constructing equations in slope-intercept form from graphs. Constructing linear equations to solve word problems. Linear equation from slope and a point. Finding a linear equation given a point and slope. Equation of a line from fractional slope and point. Constructing the equation of a line given two points. Finding y intercept given slope and point. Solving for the y-intercept. Slope intercept form from table. Slope intercept form. Idea behind point slope form. Linear Equations in Point Slope Form. Point slope form. Linear Equations in Standard Form. Point-slope and standard form. Converting between slope-intercept and standard form. Converting from point slope to slope intercept form. Converting between point-slope and slope-intercept. Finding the equation of a line. Midpoint formula. Midpoint formula. The Pythagorean theorem intro. Pythagorean theorem. Distance Formula. Distance formula. Perpendicular Line Slope. Equations of Parallel and Perpendicular Lines. Parallel Line Equation. Parallel Lines. Parallel Lines 2. Parallel lines 3. Perpendicular Lines. Perpendicular lines 2. Equations of parallel and perpendicular lines. Distance between a point and a line. Distance between point and line. Algebra: Slope and Y-intercept intuition. Algebra: Equation of a line. CA Algebra I: Slope and Y-intercept. Graphing Inequalities. Solving and graphing linear inequalities in two variables 1. Graphing Linear Inequalities in Two Variables Example 2. Graphing Inequalities 2. Graphing linear inequalities in two variables 3. Graphs of inequalities. Graphing linear inequalities. Graphing Inequalities 1. Graphing and solving linear inequalities. CA Algebra I: Graphing Inequalities. Similar triangles to prove that the slope is constant for a line. Slope and triangle similarity 1. Slope and triangle similarity 2. Slope and triangle similarity 3. Slope and triangle similarity 4. Slope and triangle similarity. Average Rate of Change Example 1). Average Rate of Change Example 2). Average Rate of Change Example 3). Average rate of change when function defined by equation. Average rate of change. Descartes and Cartesian Coordinates. The Coordinate Plane. Plot ordered pairs. Graphing points exercise. Graphing points. Quadrants of Coordinate Plane. Graphing points and naming quadrants exercise. Graphing points and naming quadrants. Points on the coordinate plane. Points on the coordinate plane. Coordinate plane word problems exercise. Coordinate plane word problems. Reflecting points exercise. Reflecting points. Ordered pair solutions of equations. Ordered Pair Solutions of Equations 2. Determining a linear equation by trying out values from a table. Equations from tables. Plotting (x,y) relationships. Graphs of Linear Equations. Application problem with graph. Ordered pair solutions to linear equations. Interpreting Linear Graphs. Exploring linear relationships. Recognizing Linear Functions. Interpreting linear relationships. Graphing lines 1. Recognizing Linear Functions. Linear and nonlinear functions (example 1). Linear and nonlinear functions (example 2). Linear and nonlinear functions (example 3). Linear and nonlinear functions. Graphing using X and Y intercepts. Graphing Using Intercepts. X and Y intercepts. X and Y intercepts 2. Solving for the x-intercept. Finding x intercept of a line. Finding intercepts for a linear function from a table. Linear function intercepts. Interpreting intercepts of linear functions. Interpreting and finding intercepts of linear functions. Analyzing and identifying proportional relationships ex1. Analyzing and identifying proportional relationships ex2. Analyzing and identifying proportional relationships ex3. Analyzing and identifying proportional relationships. Comparing proportional relationships. Constructing an equation for a proportional relationship. Constructing and comparing proportional relationships. Graphing proportional relationships example. Graphing proportional relationships example 2. Graphing proportional relationships example 3. Graphing proportional relationships. Comparing rates. Representing and comparing rates. Rates and proportional relationships. Rate problem with fractions 1. Unit cost with fractions 1. Rate problems 1. Slope of a line. Slope of a Line 2. Slope and Rate of Change. Graphical Slope of a Line. Slope of a Line 3. Slope Example. Hairier Slope of Line. Identifying slope of a line. Slope and Y-intercept Intuition. Line graph intuition. Algebra: Slope. Algebra: Slope 2. Algebra: Slope 3. Graphing a line in slope intercept form. Converting to slope-intercept form. Graphing linear equations. Fitting a Line to Data. Comparing linear functions 1. Comparing linear functions 2. Comparing linear functions 3. Comparing linear functions. Interpreting features of linear functions example. Interpreting features of linear functions example 2. Interpreting features of linear functions. Comparing linear functions applications 1. Comparing linear functions applications 2. Comparing linear functions applications 3. Comparing linear functions applications. Constructing a linear function word problem. Constructing and interpreting a linear function. Constructing linear graphs. Constructing and interpreting linear functions. Multiple examples of constructing linear equations in slope-intercept form. Constructing equations in slope-intercept form from graphs. Constructing linear equations to solve word problems. Linear equation from slope and a point. Finding a linear equation given a point and slope. Equation of a line from fractional slope and point. Constructing the equation of a line given two points. Finding y intercept given slope and point. Solving for the y-intercept. Slope intercept form from table. Slope intercept form. Idea behind point slope form. Linear Equations in Point Slope Form. Point slope form. Linear Equations in Standard Form. Point-slope and standard form. Converting between slope-intercept and standard form. Converting from point slope to slope intercept form. Converting between point-slope and slope-intercept. Finding the equation of a line. Midpoint formula. Midpoint formula. The Pythagorean theorem intro. Pythagorean theorem. Distance Formula. Distance formula. Perpendicular Line Slope. Equations of Parallel and Perpendicular Lines. Parallel Line Equation. Parallel Lines. Parallel Lines 2. Parallel lines 3. Perpendicular Lines. Perpendicular lines 2. Equations of parallel and perpendicular lines. Distance between a point and a line. Distance between point and line. Algebra: Slope and Y-intercept intuition. Algebra: Equation of a line. CA Algebra I: Slope and Y-intercept. Graphing Inequalities. Solving and graphing linear inequalities in two variables 1. Graphing Linear Inequalities in Two Variables Example 2. Graphing Inequalities 2. Graphing linear inequalities in two variables 3. Graphs of inequalities. Graphing linear inequalities. Graphing Inequalities 1. Graphing and solving linear inequalities. CA Algebra I: Graphing Inequalities. Similar triangles to prove that the slope is constant for a line. Slope and triangle similarity 1. Slope and triangle similarity 2. Slope and triangle similarity 3. Slope and triangle similarity 4. Slope and triangle similarity. Average Rate of Change Example 1). Average Rate of Change Example 2). Average Rate of Change Example 3). Average rate of change when function defined by equation. Average rate of change.

Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets. Students appreciate our unique approach to teaching linear algebra because:

- It’s visual.
- It connects hand calculations, mathematical abstractions, and computer programming.
- It illustrates the development of mathematical theory.
- It’s applicable.

In this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you'll also get more! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors. In addition, you will get a glimpse of cutting edge research on the development of linear algebra libraries, which are used throughout computational science.

MATLAB licenses will be made available to the participants free of charge for the duration of the course.

**This summer version of the course will be released at an accelerated pace. Each of the three releases will consist of four ”Weeks” plus an exam . There will be suggested due dates, but only the end of the course is a true deadline.**

We invite you to LAFF with us!

**FAQs**

**What is the estimated effort for the course? **

About 8 hrs/week.

**How much does it cost to take the course?**

You can choose! Auditing the course is free. If you want to challenge yourself by earning a Verified Certificate of Achievement, the contributions start at $50.

**Will the text for the videos be available?**

Yes. All of our videos will have transcripts synced to the videos.

**Are notes available for download?**

PDF versions of our notes will be available for free download from the edX platform during the course. Compiled notes are currently available at www.ulaff.net.

**Do I need to watch the videos live?**

No. You watch the videos at your leisure.

**Can I contact the Instructor or Teaching Assistants?**

Yes, but not directly. The discussion forums are the appropriate venue for questions about the course. The instructors will monitor the discussion forums and try to respond to the most important questions; in many cases response from other students and peers will be adequate and faster.

**Is this course related to a campus course of The University of Texas at Austin?**

Yes. This course corresponds to the Division of Statistics and Scientific Computing titled “SDS329C: Practical Linear Algebra”, one option for satisfying the linear algebra requirement for the undergraduate degree in computer science.

**Is there a certificate available for completion of this course?**

Online learners who successfully complete LAFF can obtain an edX certificate. This certificate indicates that you have successfully completed the course, but does not include a grade.

**Must I work every problem correctly to receive the certificate?**

No, you are neither required nor expected to complete every problem.

**What textbook do I need for the course?**

There is no textbook. PDF versions of our notes will be available for free download from the edX platform during the course. Compiled notes are currently available at www.ulaff.net.

**What are the principles by which assignment due dates are established?**

There is a window of 19 days between the material release and the due date for the homework of that week. While we encourage you to complete a week’s work before the launch of the next week, we realize that life sometimes gets in the way so we have established a flexible cushion. Please don’t procrastinate. The course closes 25 May 2015. This is to give you nineteen days from the release of the final to complete the course.

**Are there any special system requirements?**

You may need at least 768MB of RAM memory and 2-4GB of free hard drive space. You should be able to successfully access the course using Chrome and Firefox.

This course offers an advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software. Problem sets require some knowledge of MATLAB®.

We will learn the basics of statistical inference in order to understand and compute p-values and confidence intervals, all while analyzing data with R. We provide R programming examples in a way that will help make the connection between concepts and implementation. Problem sets requiring R programming will be used to test understanding and ability to implement basic data analyses. We will use visualization techniques to explore new data sets and determine the most appropriate approach. We will describe robust statistical techniques as alternatives when data do not fit assumptions required by the standard approaches. By using R scripts to analyze data, you will learn the basics of conducting reproducible research.

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. 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 2 XSeries and are self-paced:

PH525.1x: Statistics and R for the Life Sciences

PH525.3x: Statistical Inference and Modeling for High-throughput Experiments

PH525.4x: High-Dimensional Data Analysis

PH525.5x: Introduction to Bioconductor: annotation and analysis of genomes and genomic assays

PH525.6x: High-performance computing for reproducible genomics

PH525.7x: Case studies in functional genomics

This class was supported in part by NIH grant R25GM114818.

HarvardX requires individuals who enroll in its courses on edX to abide by the terms of the edX honor code. HarvardX will take appropriate corrective action in response to violations of the edX honor code, which may include dismissal from the HarvardX course; revocation of any certificates received for the HarvardX course; or other remedies as circumstances warrant. No refunds will be issued in the case of corrective action for such violations. Enrollees who are taking HarvardX courses as part of another program will also be governed by the academic policies of those programs.

HarvardX pursues the science of learning. By registering as an online learner in an HX course, you will also participate in research about learning. Read our research statement to learn more.

Harvard University and HarvardX are committed to maintaining a safe and healthy educational and work environment in which no member of the community is excluded from participation in, denied the benefits of, or subjected to discrimination or harassment in our program. All members of the HarvardX community are expected to abide by Harvard policies on nondiscrimination, including sexual harassment, and the edX Terms of Service. If you have any questions or concerns, please contact harvardx@harvard.edu and/or report your experience through the edX contact form.

This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

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.

Matrix Algebra underlies many of the current tools for experimental design and the analysis of high-dimensional data. In this introductory data analysis course, 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.

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. 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 2 XSeries and are self-paced:

PH525.1x: Statistics and R for the Life Sciences

PH525.3x: Statistical Inference and Modeling for High-throughput Experiments

PH525.4x: High-Dimensional Data Analysis

PH525.5x: Introduction to Bioconductor: annotation and analysis of genomes and genomic assays

PH525.6x: High-performance computing for reproducible genomics

PH525.7x: Case studies in functional genomics

This class was supported in part by NIH grant R25GM114818.

HarvardX requires individuals who enroll in its courses on edX to abide by the terms of the edX honor code. HarvardX will take appropriate corrective action in response to violations of the edX honor code, which may include dismissal from the HarvardX course; revocation of any certificates received for the HarvardX course; or other remedies as circumstances warrant. No refunds will be issued in the case of corrective action for such violations. Enrollees who are taking HarvardX courses as part of another program will also be governed by the academic policies of those programs.

HarvardX pursues the science of learning. By registering as an online learner in an HX course, you will also participate in research about learning. Read our research statement to learn more.

Harvard University and HarvardX are committed to maintaining a safe and healthy educational and work environment in which no member of the community is excluded from participation in, denied the benefits of, or subjected to discrimination or harassment in our program. All members of the HarvardX community are expected to abide by Harvard policies on nondiscrimination, including sexual harassment, and the edX Terms of Service. If you have any questions or concerns, please contact harvardx@harvard.edu and/or report your experience through the edX contact form.

Trusted paper writing service WriteMyPaper.Today will write the papers of any difficulty.