# EMF Mathematics Courses

## The Most Advanced Math Curriculum!

Each course introduces mathematical ideas not found in standard curriculum and allows students to explore these ideas in depth. Completing just one course helps students develop logical reasoning and abstract thinking skills and each additional course has a cumulative effect.

These 15 courses help students complete all High School Math, except calculus, thus giving them a tremendous advantage over their peers.

###### 1.Operational Systems

###### USD 59.95 44.95

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. Course Outline

###### 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. Course Outline

###### 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. Course Outline

###### 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. Course Outline

###### 5. Mappings

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. Course Outline

###### 6. The Rational Numbers

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. Course Outline

###### Decimals and an Application of the Rational Numbers

This course builds upon knowledge of the rational numbers to introduce decimal numbers and their properties, arithmetic operations on decimals, and position 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. Armed with a deeper understanding of decimals, decimal approximations, and percentages, students conclude the course with a case study of a fictional world in which mathematics is necessary to analyze a social and political issue. Course Outline

###### Probability I

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 EMF's most technologically ambitious course yet 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. Course Outline

###### Number Theory I

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. Course Outline

###### 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. Course Outline

## Experience EMF through sample contents here.

The study hours needed to complete each course varies considerably. The first course consists of more than 70 engaging exercises. Talented, well motivated students can complete this course with approximately 35 hours of study. Enrollment in each EMF course / module is for a period of three months.

#### Please take the FREE Aptitude Test

While the test is not mandatory, we encourage parents to take advantage of this test because a child's experience with EMF will be far more positive and effective if courses are taken when he or she is ready.