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Algebra 2

We are used to describing the world around us in terms of three dimensions: width, height, and depth. We might also discuss the fourth dimension: time. However, in mathematics and physics, there are many more dimensions in the universe. Our N-Dimensional Vectors course introduces the concept of N-Space and how we define the components of N-Vectors. We explore Dot Product Properties and how to calculate Distance in N-Space. We will also introduce an important inequality, The Cauchy-Schwarz Inequality, which has applications in N-Dimensional Vectors and more.

- N-Space
- N-Vectors
- Vector Expressions
- Evaluating Vector Expressions
- Unit Vectors
- The Norm of a Vector
- Calculating the Norm of a Vector
- Distance in N-Space
- Determining Distance in N-Space
- Dot Product Properties
- The Dot Product of N-Vectors
- Finding the Dot Product of Vectors in N-Space
- Orthogonal Vectors
- Orthogonal Projection
- Determining an Orthogonal Vector Projection
- The Triangle Inequality
- Applying the Triangle Inequality
- The Cauchy-Schwarz Inequality
- Applying the Cauchy-Schwarz Inequality

Study fundamental topics in college-level algebra with emphasis on application.

Grasp core concepts of statistics such as probability distributions, approximations, and hypothesis-testing.

Pathways are a sequence of tutorials that help you learn a whole subject area, one concept at a time. Choose from multiple teachers and teaching styles.

The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 27 of Sophia's online courses for college credit. These courses are eligible to transfer to many different colleges and universities.