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# Courses

All of our courses are comprehensive and standards-based, typically covering hundreds of individual topics. Each course kicks off with an adaptive diagnostic exam that creates a custom-fit experience by identifying any missing prerequisite knowledge and any course material the student may already know.

Our lowest entry point is 5th Grade Math, which would be an appropriate starting point for any student who's mastered fraction arithmetic with "like" denominators. The next step in the sequence would be Prealgebra. This course bridges the gap between elementary-school arithmetic and middle-school algebra and geometry.

Learn how to perform arithmetic with negative numbers, fractions, and decimals. Solve real-world problems involving measurement, data, and geometry.

### Prealgebra

Further your understanding of arithmetic and geometry, learn about variables, and solve linear equations, inequalities, and systems.

### Prealgebra vs. 6th-8th Grade Math

The Prealgebra course covers the same content as the standard 6th-8th grade math courses, only in a more streamlined format. A student who can manage a B+ or better in their grade-level courses without outside intervention, or who regularly scores at least “proficient” on standardized math assessments, would be a good candidate for the Prealgebra course.

## High School Courses

The integrated courses cover the same material as the traditional course sequence, however, it interleaves the progression of concepts in a way that is more efficient and more fun for the student.

### Geometry

Learn how to compute length, area, and volume for a wide variety of objects. Discover relationships between angles and side lengths in right triangles.

### Algebra II

Master the algebra of advanced functions including quadratics, logarithms, trigonometry, and more. Dive deep into the theory of polynomials.

### Precalculus

Learn advanced trigonometry and core concepts in probability and statistics. Encounter objects from higher math including complex numbers, vectors, and matrices.

### Integrated Math I

Level up your algebra skills, learn about functions and graphing, and solve problems in geometry and real-world modeling.

### Integrated Math II

Master the algebra of advanced functions including quadratics, logarithms, trigonometry, and more. Learn core concepts in probability and statistics.

### Integrated Math III

Dive deep into the algebra of polynomials and advanced trigonometry. Encounter objects from higher math including complex numbers, vectors, and matrices.

One of the primary shortcomings of the traditional sequence is that many Algebra I skills typically have to be re-learned in Algebra II after the student has taken a year off for Geometry. Since the Integrated Math sequence sidesteps this problem, the same material can be covered in three years instead of four.

## AP Courses

AP Calculus AB and AP Calculus BC are high school advanced placement courses intended to prepare students for the respective College Board AP Exams. While AP Calculus BC is meant to represent the material covered in the two-semester university calculus sequence Calculus I and Calculus II, AP Calculus AB is a less comprehensive treatment, covering about 70% of the material.

### AP Calculus AB

Learn about limits, continuity, derivatives, indefinite and definite integrals and how to apply these concepts in a variety of contexts.

### AP Calculus BC

Master the fundamentals of single-variable calculus including with vectors, parametric and polar equations. Learn how to apply tests of convergence to infinite series and to approximate functions using Taylor series.

## Mathematical Foundations

The Mathematical Foundations sequence is aimed at adult learners interested in pursuing advanced university courses, but lack the necessary foundational knowledge. Whether you're starting off again with the basics or just need to brush up on your calculus, this is the fastest and most efficient way to get up to speed.

### Mathematical Foundations I

Solidify your arithmetic, learn about variables and graphs, level up your algebra, and learn the essentials of geometry.

### Mathematical Foundations II

Master the algebra of advanced functions including quadratics, logarithms, and trigonometry. Dive deep into the theory of polynomials, learn the basics of limits, derivatives, and integrals from calculus, and explore a variety of concepts from higher math including complex numbers, vectors, probability, and statistics.

### Mathematical Foundations III

Learn advanced calculus techniques for computing limits, derivatives, and integrals, and apply calculus to solve problems in the context of related rates, optimization, particle motion, and differential equations. Dive deeper into complex numbers, vectors, matrices, parametric and polar curves, probability, and statistics.

## University Courses

Our university courses are modeled after the rigorous, semester-length courses offered at elite universities, and in many cases, go a few steps beyond. These courses are comprehensive and cover every major topic reasonably included in an undergraduate treatment of the subject.

### Calculus I

Learn the mathematics of change that underlies science and engineering. Master limits, derivatives, and the basics of integration.

### Calculus II

Further your understanding of calculus: master advanced integration techniques, model real-world situations using differential equations, and more.

### Linear Algebra

Dive deep into the math behind vectors and matrices. Learn a wide assortment of computational methods and conceptual connections that unify into an elegant whole.

### Mathematics for Machine Learning

Learn the key skills and concepts from linear algebra, multivariable calculus, and probability & statistics that you need to know in order to understand and implement core machine learning algorithms. This course will prepare you for a university-level machine learning course that covers topics such as gradient descent, neural networks and backpropagation, support vector machines, extensions of linear regression (e.g. logistic and lasso regression), naive Bayes classifiers, principal component analysis, matrix factorization methods, and Gaussian mixture models.

### Multivariable CalculusComing soon...

Generalize your understanding of calculus to vector-valued functions and functions of multiple variables.

### Differential EquationsComing soon...

Master a variety of techniques for solving equations that arise when using calculus to model real-world situations.

### Probability & StatisticsComing soon...

Learn the mathematics of chance and use it to draw precise conclusions about possible outcomes of uncertain events. Analyze real-world data using mathematically rigorous techniques.

### Methods of ProofComing soon...

Build fluency with sets and logic, the most fundamental structures and operations in mathematics. Learn what a proof is and master a variety of techniques for proving mathematical statements.

### Discrete MathematicsComing soon...

Learn mathematical techniques for reasoning about quantities that are discrete rather than continuous. Encounter graphs, algorithms, and other areas of math that are widely applicable in computer science.

### Abstract AlgebraComing soon...

Dive deep into the core relationships that govern how mathematical objects interact with one another. Learn to identify algebraic structures and apply mathematical reasoning to arrive at general conclusions.

## Comprehensive Curriculum

Our extensive course catalog covers the full range of content, from elementary arithmetic to upper-division undergraduate mathematics, and everything in between.