Courses & Tuition

Courses

EMF recognizes that certain fundamental concepts elegantly unify the various branches of mathematics. EMF first teaches these concepts and then builds on that foundation to explore modern mathematics.

1. Operational Systems
   This course covers modular arithmetic using secret codes and online games. Learn about operational systems and their properties (commutativity, associativity, neutral elements, invertibility) by building interactive machines and evaluating non-numeric operations. Get a solid introduction to the concepts of least common multiple and greatest common divisor, as well as to the geometric notions of midpoint and reflection.
2. The Integers
   This course introduces positive and negative integers with an unusual elevator and mysteriously disappearing nuts. Learn about adding, subtracting, multiplying and ordering integers by building interactive number lines and driving a balloon-popping car. Students are exposed to various theorems about integer relationships and carefully guided through the first steps of how to make a well-reasoned and logical argument in support thereof.
3. Sets, Subsets and Set Operations
   This course introduces the building blocks of set theory, which provides the basic language in which most mathematical texts are written. "Set" is what mathematicians call a collection of objects; it's a tiny word but a powerful concept as you will see. Learn about set properties and relationships involving sets with whimsical videos and the increasingly challenging String Game. Through mind-stretching, interactive exercises, students cover fundamental concepts such as elements, roster names, the empty set, subsets, Venn diagrams, intersection, union, set difference and complement, and the Pascal Formula.
4. Ordered n-Tuples
   This course considers what happens when order is imposed upon a collection of objects. Building on concepts introduced in Operational Systems, interactive features such as taxi driver navigation and the rock-paper-scissors game give context to the properties of Cartesian product sets. An intuitive study of open sentences in two variables and the graphing of their solutions plant the seeds for future courses in Algebra. Students deepen their understanding of various mathematical operations as these concepts are extended componentwise to sets of ordered n-tuples.
5. Mappings
   This course examines relationships between the elements of two sets. Students explore various types of mappings, including permutations, with interactive ball sorters, slide rules and clever animations. Elementary combinatorial exercises lay the foundation for advanced concepts in Algebra, Geometry and Probability. Applying the properties of function composition, students delve into fractions and percentages in a mathematically rigorous and intuitive way.
6. The Rationals
   This course builds on topics covered in previous courses in order to examine the rational numbers, commonly referred to as fractions, as a natural extension of the integers. The course uses detailed narrations and interactive number lines and coordinate planes to cover the absolute value function, the properties of operations on rational numbers, how they are ordered, and that they are densely packed, not evenly spaced as the integers are. Students learn how to solve equations of rational numbers through the foundational concept of mappings instead of with rote algebraic manipulation. Using interactive proof-builders, students also advance to the next step in learning how to construct well-reasoned and logical arguments.
7. The Decimals
   This course builds upon knowledge of the rational numbers to introduce decimal numbers and their properties, arithmetic operations on decimals, and positional notation for decimals. Students learn to compute various decimal approximations of rational numbers and to evaluate errors in approximation. The course revisits percentages in relation to decimals and arithmetic operations on percentages. Students then apply what they have learned about decimals, decimal approximations, and percentages in the study of rates (that is, ratios of measured quantities), the slopes of straight lines, a case study of a fictional world in which mathematics is necessary to analyze a social and political issue, and an extended introduction to elementary descriptive statistics.
8. Probability
   This course provides an introduction to elementary probability theory and covers one-stage, two-stage, and multistage random experiments, the Product Rule, counting subsets, combinatorics, and random digit generators. This is one of EMF's most technologically ambitious courses with over half the pages containing an interactive device, narrated animation, or virtual classroom. Using these tools students learn about, replicate, or analyze the outcomes of a wide variety of random experiments online. The course concludes with an exploration of one of the most important methods in probability — Monte Carlo simulation — and two famous questions — the birthday problem and the Monty Hall puzzle.
9. Number Theory
   An exploration of numbers for their own fascinating sake is a joy that every young person should experience. This course provides that opportunity by investigating some of the most intriguing and timeless questions in Number Theory. Along the way, students learn about prime and composite numbers, prime factorization, and number bases as well as examining elegant ideas such as Euclid's Lemma, the Sieve of Eratosthenes, and the Fundamental Theorem of Arithmetic. Students expand their logical reasoning skills with an introduction to the powerful proof technique of mathematical induction. Interactive exercises help students practice their proof-writing skills with simpler conclusions, while animated narrations enhance rigorous yet accessible proofs of more significant results such as the multiplicativeness of Euler's totient function.
10. Algebra: Groups, Rings and Fields
    This course focuses on the study of algebra, in particular the kind of algebra that is usually learned by mathematics majors at university. As an incidental matter, students who complete the EMF algebra series will be able to solve any high school algebra problem with ease but, more importantly, will be well-prepared to study the high-level mathematics that is at the heart of important disciplines such as public-key cryptography and particle physics. Building on a solid understanding of operational systems, this course introduces groups, rings, and fields and their mathematical properties. While typical high school algebra students are limited to applying these rules mechanically to solve numeric equations, EMF students are guided to their own intuitive "discovery" of these behaviors through interactive exercises involving numeric and non-numeric mathematical structures. Students continue to sharpen their logical reasoning skills by proving several of these properties using EMF's proof-building technology.
11. Algebra: Relations, Mappings, Equations
    This course continues the study of abstract algebra by introducing the fundamental notion of a relation and its properties. Whereas the previous course in the EMF algebra series focused on combining elements of a set with operations, this course investigates ways of relating elements of a set, one to another. Mappings, a key mathematical construct studied earlier in EMF, are then described as special types of relations. By expanding ideas and techniques introduced in the fifth and sixth EMF courses to the general context of any field, students learn to solve linear, quadratic and rational equations with mappings by calling upon the powerful properties of relations covered in the first part of this course. As with all EMF courses, students are exposed to mathematical ideas typically not seen until college and continue to gain experience building proofs of important results.
12. Algebra: Relational and Ordered Operational Systems
    This course ties together the previous two courses and completes the study of abstract algebra in EMF. Students learn how groups, rings and fields can be combined with certain kinds of relations to form new structures, specifically relational systems and ordered systems. Within such systems, techniques for solving inequalities are given a much more in-depth treatment than has been possible in earlier courses. Skeleton proofs are provided of various properties of ordered groups, rings, and fields, and students are asked to complete them and then to apply these properties to easily solve inequalities over these systems.
13. Real Functions I
    This course introduces the real number system as an extension of the ordered field of rational numbers and goes on to investigate certain fundamental classes of functions on the real numbers. After learning about the real numbers and their properties, students prove that the set of real functions with function addition and multiplication form a ring. Armed with this fact, various ring properties covered in earlier EMF courses, and powerful online graphing tools, students investigate systems of first degree equations and inequalities on the real numbers. The course then turns to analyzing quadratic equations and inequalities, first graphically and then by factorization and completing the square. The analysis culminates with an in-depth derivation of the quadratic formula — typical high school algebra students are merely asked to memorize this formula — after which EMF students will be well-versed in methods for solving first and second degree equations and inequalities, as well as understanding why these methods work. Real Functions I wraps up with second look at statistics, including the normal distribution, and an introduction to trigonometry. Throughout the course, students put their understanding and skills to work on realistic, complex problems that underscore algebra's usefulness in the real world.
14. Real Functions II
    This course begins with an introduction to sequences and series, including in-depth coverage of arithmetic and geometric sequences and series. Students continue to expand their knowledge of real polynomial functions such as integer and rational power functions, exponential and logarithmic functions, the absolute value function, rational functions, and asymptotes. The course builds on material from Sets, Mappings, and Probability to explore the Binomial Theorem, a fundamental result with uses as varied as the distribution of IP addresses and financial modeling. Practical applications, including two extensive case studies in statistics, continue to demonstrate algebra's usefulness in the real world. The course culminates with an introduction to the field of complex numbers as a field extension of the real field and to polynomial functions over the complex field. Throughout, EMF students will prove many of the results about real and complex functions that typical high school students are only asked to memorize and apply. With respect to developing students' proof-writing skills, Real Functions II marks the completion of the transition from outline proofs to paragraph proofs.
15. Geometry: Incidence and Transformations
    This course begins the formal study of Euclidean geometry in EMF. Working in the three-dimensional context of space, the two-dimensional context of planes, and the one-dimensional context of lines, students investigate familiar geometrical figures and a variety of ways of transforming them. In the first half of the course, real-world experiences with physical objects are used to inform the mathematically rigorous construction of analogous geometric objects and the properties they should have. The second half of the course builds on concepts from Sets and Mappings in order to explore transformations — reflections, translations, rotations, and magnifications — as mappings on sets of points. Students prove numerous results that are typically taken as given in high school geometry as they ascertain which of these transformations are permutations and which permutations preserve betweenness, collinearity, angle measure, distance, and circular orientation. As this is EMF, the proofs that students complete go well beyond the basic two-column high school proof in complexity, sophistication, and consequence.
16. Geometry: Congruence and Similarity
    This course continues the study of Euclidean geometry in EMF. Students begin by investigating congruent figures in order to extend their knowledge of reflections, translations, rotations, and glide-reflections, together known as isometries. They then prove that these "rigid motion" mappings form a group. Equipped with their understanding of group properties from EMF's abstract algebra courses, students spend the first part of this course exploring congruence and symmetry, including properties of congruent triangles and a classification of polygons in terms of their symmetry groups. The second part of the course focuses on magnifications and their properties. Students explore what happens when magnifications are composed with themselves and with isometries and discover that these compositions, known as similitudes, also form a group. The third part of the course provides an in-depth study of circle geometry incorporating multiple applications from the first two parts. Because EMF teaches mathematics as a unified body of knowledge rather than a collection of unrelated topics, students come to realize a fundamental connection between algebra and geometry that most traditional school math students will never know.
17. Geometry: Coordinates and Measurement     
    This course concludes the study of Euclidean geometry in EMF, with a focus on measurement in two and three dimensions: of area, volume, distance, taxi-distance, conic sections; introduces vector spaces; and reexamines isometries in the context of coordinate systems.
18. Precalculus Coda     
    This course brings together various topics covered in earlier EMF courses and expands upon that material with an extensive study of vectors in the real number plane and space, linear transformations (including orthogonal mappings), and matrices and their application in solving systems of equations. Together these topics comprise a typical Precalculus course and provide a detailed understanding of the basic principles behind The Calculus.

Supplements

The following supplemental short courses become available to EMF students at no charge following the completion of certain specified EMF courses.

• Pre-Algebra
  This short course explains topics, terminology, and notation that are taught in a typical school Pre-Algebra class by relating them to the more advanced language and concepts taught in EMF. Students who successfully complete the first seven EMF courses, this supplement, and recommended practice tests will be well-prepared to take any school Pre-Algebra test and succeed in a traditional school Algebra 1 course.
• Abstract Algebra Readiness
  This short course tests a student's readiness for EMF courses 10-14, which focus on Abstract Algebra. Students who complete the first nine EMF courses should use this supplement to review the important ideas covered in those courses as these ideas provide the mathematical tools necessary to master the EMF Abstract Algebra courses.
• Algebra 1
  This short course explains topics, terminology, and notation that are taught in a typical school Algebra 1 class by relating them to the more advanced language and concepts taught in EMF. Students who successfully complete the first 13 EMF courses, this supplement, and recommended practice tests will be well-prepared to take any school Algebra 1 test and succeed in a traditional school Algebra 2 course.
• Algebra 2
  This short course explains topics, terminology, and notation that are taught in a typical school Algebra 2 class by relating them to the more advanced language and concepts taught in EMF. Students who successfully complete the first 14 EMF courses, this supplement, and recommended practice tests will be well-prepared to take any school Algebra 2 test and succeed in traditional advanced high school math courses.
• Geometry
  This short course explains topics, terminology, and notation that are taught in a typical school Geometry class by relating them to the more advanced language and concepts taught in EMF. Students who successfully complete the first 17 EMF courses, this supplement, and recommended practice tests will be well-prepared to take any school Geometry test and succeed in traditional advanced high school math courses.
• Precalculus Readiness
  This short course tests a students readiness for EMF's Precalculus Coda course. Students who complete the first 17 EMF may use this supplement to review the important ideas covered in those courses before advancing to the Precalculus Coda course.
• Precalculus
  This short course will explain topics, terminology, and notation that are taught in a typical school Precalculus class by relating them to the more advanced language and concepts taught in EMF. Students who successfully complete the entire EMF program, this supplement, and recommended practice tests will be well-prepared to take any school Precalculus test and succeed in an Advanced Placement Calculus class.

Pre-Algebra Plus

The Pre-Algebra Plus course pack includes EMF Courses 1-9, Pre-Algebra Supplement, and Abstract Algebra Readiness Supplement. Pre-Algebra Plus is suitable for students who are prepared to complete a rigorous and comprehensive pre-algebra course within one academic year.

• Topic List
  • Arithmetic
  • Whole number and integer arithmetic
  • Associativity, commutativity, and distributivity
  • Neutral element and invertibility
  • Exponents and factorials
  • Absolute value

  • Fractions
  • Defining fractions
  • Equivalent fractions and simplest form
  • Fraction arithmetic
  • Mixed numbers
  • Ordering and comparing fractions
  • Property of denseness

  • Decimals and Percents
  • Relation to fractions
  • Decimal arithmetic
  • Rounding, approximation, and error
  • Discounts, interest, and other applications

  • Ratios, Proportions, and Rates
  • Ratios and proportional relationships
  • Graphing proportional relationships
  • Rates and unit conversions

  • Equations and Inequalities
  • Evaluating algebraic expressions
  • Independent and dependent variables
  • Solving linear equations and inequalities
  • Graphing solutions on the number line and plane
  • Slope and intercept
  • Real-world application problems

  • Geometry
  • Triangles, quadrilaterals, and special polygons
  • Perimeter and area
  • The Pythagorean Theorem
  • Segments, lines, and rays
  • Parallel and perpendicular lines
  • Measuring angles
  • 3D shapes, volume, and surface area
  • Circles and circumference

  • Logic and Proofs
  • Boolean logic
  • Proof by cases
  • Proof by contradiction
  • Proof by induction
  • Existence and uniqueness proofs

  • Set Theory
  • Roster names and Venn diagrams
  • Subsets and power sets
  • Union, intersection, and advanced set operations
  • Counting subsets and Pascal's Triangle
  • Cartesian products

  • Number Theory
  • Multiples and least common multiple
  • Divisors and greatest common divisor
  • Divisibility tests
  • Prime and composite numbers
  • Prime factorization
  • The Division Theorem
  • Number bases
  • σ and Φ functions
  • The Fundamental Theorem of Arithmetic

  • Abstract Algebra
  • Modular arithmetic
  • Operational systems
  • Non-numeric operations
  • Relations, functions, and permutations
  • Composition of functions

  • Probability
  • Simple and compound events
  • The Product Rule
  • Counting and combinatorics
  • Theoretical and experimental probabilities

  • Statistics
  • Data charts, tables, and plots
  • Measures of central tendency and variation
  • Modeling and lines of best fit
  • Correlation
  • Random sampling
  • Simulations and the Monte Carlo method
• Pacing Guide
  This printable pacing guide provides weekly benchmarks for completing Pre-Algebra Plus in 300 days. Students who prefer a more flexible pace should consider enrolling in the courses one-by-one or in multi-course bundles, which provide for 810 total days of access.
• Standards Map
  Although the EMF curriculum was not designed with the intention of meeting the Common Core State Standards (CCSS), it does meet the standards and actually goes well beyond them. Students who need evidence of such may refer to this printable standards map from CCSS Grades 6-8 to EMF.

Tuition

Standard Enrollment Options
Note: All new students start with Course 1.

In order to provide an academic opportunity to give students an opportunity to be academically challenged and experience the qualify of an EMF education at no cost, Course 1 is being offered free for 30-day enrollments. Click the ENROLL link for more information.

Individual Course, $59.95 each, 90 days

Course 3-Packs, $154.95 each, 270 days
(Courses 2-4, 5-7, 8-10, 11-13, 14-16)

Pre-Algebra Plus, $360, 300 days
(Courses 1-9)

Algebra Plus, $254.95, 450 days
(Courses 10-14)

Geometry Plus, $154.95, 270 days
(Courses 15-17)

Course Pack 2-18, $879.95*, 1530 days

Course Pack 18, $917.95*, 1620 days
(Courses 1-18)

30-Day Enrollment Period Extension, $25

This printable enrollment options chart shows the most common paths to completing the EMF courses, along with total standard tuition and total available enrollment time.

* Please note that IMACS accept charter funds only for EMF Course Pack 2-18 and EMF Course Pack 18.