For Talented Secondary School Students
Is Now Available Online.

"This curriculum does a wonderful job of captivating young minds and provoking within them a lifelong thirst for learning, producing graduates with unusually mature insight into mathematics."Professor Emeritus Vincent Haag
Franklin & Marshall College 
"My son cannot stop talking about the mathematical ideas he is learning. He is choosing to do EMF over Minecraft!"Nan Rosenberry
EMF Parent 
"The days of learning math by repetition are a thing of the past. Although the EMF program is selfstudy, it has the oneonone feeling of having an instructor and at a very fair price. As a parent I give EMF an A+."Jorge Sardinas
EMF Parent 
"As a homeschooling mom I can tell you EMF is our favorite curriculum — challenging and interesting!"Michelle Unger
EMF Parent 
"My son thought he did not like mathematics till he started EMF. Now, it is his most favorite subject. EMF has helped him gain confidence, develop discipline, and encourage his younger sister to appreciate mathematical thinking."Poornima Meenakshisundaram
EMF Parent 
"I was taking a practice test for the timed AMC8 exam when I came across a problem involving nonstandard mathematics. Thanks to EMF, I was already familiar with these ideas and solved the problem a lot faster."Peyton Robertson
EMF Student 
"As a homeschooler, our son is an avid user of online educational resources. I recently asked him to pick his favorite online course. He answered, 'most definitely EMF, by a wide margin'."Arvinder Oswal
EMF Parent 
"EMF does more than teach; it inspires. Using the ideas I learned from EMF, I was able to show the students I tutor that math is truly fun!"Hossain Turjo
EMF Student 
"The way of thinking about a problem that I learned from your program is something I use every day. I think I am a better physician because of the years I spent in EM."Cara O'Brien, M.D. and EM Alumna
while a Resident at Duke University 
"After many years of boredom in elementary school, I finally felt challenged. EM was also wonderful preparation for my future schooling."Tuni Kundu, Ph.D. and EM Alumna
while a Mechanical Engineer at Fluor 
"The content and the pedagogy are of the highest quality and I recommend it without reservation."Professor Emeritus Gerald R. Rising
State University of New York at Buffalo 
"I still remember remarking to a friend in middle school that, after coming out of each EM class, I felt smarter! I still marvel that I was exposed to such a wealth of mathematics at such a young age."Rochelle Pereira, Ph.D. and EM Alumna
while Assistant Professor of Mathematics at The College of St. Catherine 
"There is no doubt that the Elements of Mathematics curriculum gave me the logical thinking skills and mental framework that inspired and enabled me to develop the Chocolate Fix puzzle system."Mark Engelberg, EM Alumnus
Inventor of ThinkFun's Chocolate Fix logic game 
"I have since graduated from Yale College and Harvard Law, and I can honestly say that my EM classes were the most challenging academic experiences of my life."Ellen Moskowitz, J.D. and EM Alumna
while at Ropes & Gray 
"Our program in mathematics is the strongest in the nation and for [an EM student] to be able to jump in with our best students and perform at the highest level is ample testimony of the strength of the program."Professor Andrew M. Gleason
Harvard University 
"EM was the greatest program ever imagined  and there is no way I could have stayed in teaching 46 years had it not been for the EM program."Leona Penner
Retired EM Teacher
Welcome!
Elements of Mathematics: Foundations is a carefully planned sequence of selfstudy, online courses for wellmotivated secondary school students with superior verbal and analytical skills.
The Elements of Mathematics: Foundations curriculum allows talented students to complete all of middle and high school mathematics up to calculus, in approximately three years.
Each course in the Elements of Mathematics: Foundations series introduces mathematical ideas not found in the standard US curriculum and allows students to explore these ideas in depth. Each course presents the beautiful and fun side of mathematics. Completing just one course helps students develop logical reasoning and abstract thinking skills that they may not otherwise, and each additional course has a cumulative effect.
As with many serious intellectual pursuits, succeeding in Elements of Mathematics: Foundations is as much about persevering through challenge as it is about learning new ideas. Parents of a prospective student should read the following with their child:
Elements of Mathematics: Foundations
Elements of Mathematics: Foundations is a series of interactive, selfstudy math courses designed specifically for bright secondary school students that goes well beyond the typical gifted math class offered in schools or online. It is not an accelerated version of the standard US mathematics curriculum.
Based on the Intuitive Background books of the Elements of Mathematics (EM) series developed over many years by an international team of mathematicians, Elements of Mathematics: Foundations is a selfcontained, selfstudy program that allows the talented student to complete all of middle and high school mathematics up to calculus before leaving middle school.
The Elements of Mathematics: Foundations curriculum embodies the idea that mathematics is a comprehensive body of knowledge rather than a collection of unrelated topics. Running through this deep discipline are certain fundamental concepts that elegantly unify the various branches.
Students who develop an intuitive understanding of these core concepts and an appreciation for how they are woven throughout mathematics have a nearly insurmountable advantage in advanced classes over peers who do not.
Elements of Mathematics: Foundations provides deep and lasting insight, and students who have completed the EM courses have progressed to study college level courses in high school and graduate level classes upon arrival at college.
Is Elements of Mathematics: Foundations right for your child? EMF takes a sophisticated approach to mathematics that students would not normally encounter until college. Regardless of whether your child has just finished elementary school or has already completed algebra and geometry courses, the answer depends on the individual student. The free aptitude test is a valuable tool that parents can use to help them make this determination.
The Elements of Mathematics: Foundations online courses are based on the Intuitive Background books of the Elements of Mathematics (EM) series. EM is the result of a collaborative effort of an international team of eminent mathematicians and mathematics educators.
Through more than a decade of research and development, these scholars created an original curriculum that is fun and engaging while maintaining a level of mathematical rigor found only at the university level. Aimed solely at talented middle and high school students and unconstrained by the need to follow a standardsbased curriculum, EM focused on providing precocious students with a deep understanding of mathematical structure.
Along the way, the Intuitive Background curriculum covered all of middle and high school mathematics up to calculus before the end of middle school. After completing the Intuitive Background books, students would continue in the EM series, which covered a significant portion of a college undergraduate mathematics degree by the end of high school. The formal logic segment of the EM curriculum is already available online at www.eimacs.com as part of the Advanced Mathematical Logic track.
The Elements of Mathematics: Foundations courses are offered by the Institute of Mathematics and Computer Science (IMACS) through its distance learning division, eIMACS.
Our online math and computer science courses are developed by the IMACS Curriculum Development Group, which draws on an average of over 25 years' experience that includes extensive time teaching gifted children in a classroom setting.
Based in Plantation, Florida, IMACS was established in 1993 and maintains local teaching centers in Florida, North Carolina, Missouri, and Connecticut. Over 4,500 students from across the US and around the world study our widelyacclaimed curricula for precocious students.
EMF Aptitude Test
If you are unsure whether your child is ready to begin the first EMF course, IMACS recommends that you encourage him or her to take the EMF Aptitude Test. This test is designed to help you and your child decide if he or she is ready for and would enjoy the EMF courses.
The EMF Aptitude Test is not like the tests typically given in schools. First, it deals with a subject that your child has almost certainly never studied before. Second, it is designed to gauge thinking skills and intellectual maturity, not knowledge; thus the questions are actually a series of puzzles. Third, some of the later questions will be challenging, and prospective students should not be discouraged if they are unable to solve all the puzzles. In fact, an excellent score can be achieved without answering all the questions.
The EMF Aptitude Test can be taken at your convenience with no fee and no obligation. All you need is:
 internet access;
 compatible Web browser (see Getting Started on left menu bar);
 desktop or laptop computer;
 paper and pencil; and
 30 minutes of uninterrupted time when your child can give the test his or her best effort.
Click here to sign up for the EMF Aptitude Test.
Getting Started

Step 1: Prerequisites
The prerequisites are as follows:
 Your child should be of middle school age. Learn more »
As with any program for gifted and talented students, it is difficult to offer exact guidelines for the ideal age at which to study EMF. At a minimum, students must have mastered all of elementary school math. Students who have completed algebra and/or geometry courses will find some of the material familiar although approached from a very different, more sophisticated standpoint.
 Your child must be motivated, independent, and talented.
 He or she must also have excellent reading skills as students will need to comprehend text explanations of mathematical concepts.
 Before starting EMF, your child must have completed all of elementary school math, and must be fluent in arithmetic operations of multipledigit numbers, including long division.
EMF courses are designed for students with a high level of intellectual maturity. To complete EMF in a selfstudy manner, students will need solid executive functioning skills as well. To help parents determine their child's level of readiness, IMACS created a free online aptitude test for prospective students to take prior to enrolling in the first course.
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.
See Step 3 below for more information on the aptitude test.
 Your child should be of middle school age. Learn more »

Step 2: Browser
EMF is supported on the free Chrome and Firefox browsers. In addition to laptops and desktops, EMF is compatible with iPads, Android tablets, and touchscreen computers. However, some features are easier to use with a mouse or other pointing device. EMF is not compatible with smartphones.

Step 3: Sign up!
Sign up securely by clicking here. After completing the registration process, you will receive an email with instructions on how to take the aptitude test as well as how to enroll in the first course, Operational Systems.
Courses
Each course in the Elements of Mathematics: Foundations series introduces important ideas not covered by the standard US math curriculum. Each course contains carefully crafted exercises that guide students through the process of mathematical discovery. Challenging problems encourage creative thinking and a healthy level of intellectual struggle.
In this way, each course avoids the "tellthendrill" approach and allows students to experience the joy of finding things out for themselves.
 Operational Systems Learn more »
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 nonnumeric 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.
 The Integers Learn more »
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 balloonpopping car. Students are exposed to various theorems about integer relationships and carefully guided through the first steps of how to make a wellreasoned and logical argument in support thereof.
 Sets, Subsets and Set Operations Learn more »
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 mindstretching, 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.
 Ordered nTuples Learn more »
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 rockpaperscissors 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 ntuples.
 Mappings Learn more »
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.
 The Rationals Learn more »
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 proofbuilders, students also advance to the next step in learning how to construct wellreasoned and logical arguments.
 The Decimals Learn more »
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.
 Probability Learn more »
This course provides an introduction to elementary probability theory and covers onestage, twostage, 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.
 Number Theory Learn more »
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 proofwriting 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.
 Algebra: Groups, Rings and Fields Learn more »
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 wellprepared to study the highlevel mathematics that is at the heart of important disciplines such as publickey 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 nonnumeric mathematical structures. Students continue to sharpen their logical reasoning skills by proving several of these properties using EMF's proofbuilding technology.
 Algebra: Relations, Mappings and Equations over Fields Learn more »
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.
 Algebra: Relational and Ordered Operational Systems Learn more »
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 indepth 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.
 Real Functions I Learn more »
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 indepth derivation of the quadratic formula — typical high school algebra students are merely asked to memorize this formula — after which EMF students will be wellversed 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.
 Real Functions II Learn more »
This course begins with an introduction to sequences and series, including indepth 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' proofwriting skills, Real Functions II marks the completion of the transition from outline proofs to paragraph proofs.
 Geometry: Incidence and Transformations Learn more »
This course begins the formal study of Euclidean geometry in EMF. Working in the threedimensional context of space, the twodimensional context of planes, and the onedimensional context of lines, students investigate familiar geometrical figures and a variety of ways of transforming them. In the first half of the course, realworld 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 twocolumn high school proof in complexity, sophistication, and consequence.
 Geometry: Congruence and Similarity Learn more »
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 glidereflections, 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 indepth 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.
 Geometry: Coordinates and Measurement Coming soon! »
 Precalculus Coda
In addition to the regular courses above, EMF includes the following supplemental short courses that become available to EMF students at no charge following the completion of certain specified EMF courses:
 PreAlgebra Supplement Learn more »
This short course explains topics, terminology, and notation that are taught in a typical school prealgebra 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 wellprepared to take any school prealgebra test and succeed in a traditional school algebra 1 course.
 Abstract Algebra Readiness Supplement Learn more »
This short course tests a student's readiness for EMF courses 1014, 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 Supplement Learn more »
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 wellprepared to take any school algebra 1 test and succeed in a traditional school algebra 2 course.
 Algebra 2 Supplement Learn more »
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 wellprepared to take any school algebra 2 test and succeed in traditional advanced high school math courses.
 Geometry Supplement
New! Students interested in prealgebra may also consider PreAlgebra Plus, which includes the first nine EMF courses and first two supplemental short courses.
To experience EMF through interactive sample pages, click on the Sample Content box in the left margin of this page.
EMF covers PreAlgebra, Algebra 1 & 2, Geometry, Precalculus and universitylevel topics such as Logic, Set Theory, Number Theory, Abstract Algebra, and Topology.
View and download a printable a copy of EMF At a Glance.
Learn more about EMF's prealgebra course, PreAlgebra Plus.
Download printable pacing guides for PreAlgebra Plus (includes EMF0109) and EMF1014.
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Each enrollment is for a period of 90 days.
 Operational Systems $59.95
 The Integers $59.95
 Sets, Subsets and Set Operations $59.95
 Ordered nTuples $59.95
 Mappings $59.95
 The Rationals $59.95
 The Decimals $59.95
 Probability$59.95
 Number Theory$59.95
 Algebra: Groups, Rings and Fields$59.95
 Algebra: Relations, Mappings and Equations over Fields$59.95
 Algebra: Relational and Ordered Operational Systems$59.95
 Real Functions I$59.95
 Real Functions II$59.95
 Geometry: Incidence and Transformations$59.95
 Geometry: Congruence and Similarity$59.95
 Geometry: Coordinates and MeasurementComing soon!
 Precalculus Coda
In addition to the regular courses above, EMF includes supplemental short courses that become available to EMF students at no charge following the completion of certain specified EMF courses:
 PreAlgebra: follows EMF7 or EMF9, and prepares students for EndOfCourse PreAlgebra exam.
 Abstract Algebra Readiness: follows EMF9, and prepares students for the EMF Abstract Algebra courses EMF10, 11 and 12.
 Algebra 1: follows EMF13 or EMF14, and prepares students for an EndOfCourse Algebra 1 exam.
 Algebra 2: follows EMF14, and prepares students for an EndOfCourse Algebra 2 exam.
 Geometry: follows EMF17, and prepares students for an EndOfCourse Geometry exam.
Course Offerings 
Total Tuition 
Enroll in EMF Courses 116 individually at $59.95 per course 
$959.20 
Enroll in EMF Course 1 ($59.95), EMF Continuation Pack 24 ($154.95), EMF Continuation Pack 57 ($154.95), EMF Continuation Pack 810 ($154.95), EMF Continuation Pack 1113 ($154.95), EMF Continuation Pack 1416 ($154.95) 
$834.70 
Enroll in EMF Course Pack 16 
$815.95 
Enroll in PreAlgebra Plus 
$360.00 
FAQ (Frequently Asked Questions)
 What is IMACS?
IMACS is the Institute for Mathematics and Computer Science, an independent teaching and educational research institute that specializes in courses for mathematically talented students.
 How do I know if my child is ready for EMF?
EMF courses are intended to be selfstudy. To help parents determine their child's level of readiness, IMACS created a free online aptitude test for prospective students to take prior to enrolling in the first course. While the aptitude test is not required for enrollment, parents are strongly encouraged to have their child complete the test because it is designed to help gauge whether EMF is likely to be a good fit for a prospective student.
Whether you decide to have your child take the aptitude test or not, please keep the following prerequisites in mind: Your child should be of middle school age with a high level of intellectual maturity. He or she must have completed all of elementary school math and be fluent in arithmetic operations. Your child must be motivated, independent, and talented with superior analytical skills and excellent reading skills as they will need to comprehend text explanations of mathematical concepts. To complete EMF in a selfstudy manner, students will need solid executive functioning skills as well.
 My child is not considered "mathy", but I see signs of mathematical talent and curiosity. Could EMF be a good fit?
It has been our experience that when people describe a child as "mathy", they typically mean that the child enjoys solving computational math problems, often with aboveaverage speed. EMF uses a broader definition along the lines of what a professional mathematician would consider "mathy" and includes individuals who see beauty in the complexity of patterns, who enjoy tinkering with physical and mental puzzles and games, and who like to ponder big, abstract ideas. This type of creative thinker often finds EMF to be a good fit.
 How does the EMF curriculum compare with other gifted math programs?
Two key characteristics distinguish EMF from most gifted math programs for secondary school students. First, EMF recognizes that certain fundamental concepts elegantly unify the various branches of mathematics. EMF begins by teaching these concepts and then builds on that foundation to explore traditional and modern mathematics. In EMF, math is treated as a cohesive body of knowledge rather than as a sequence of seemingly unrelated topics.
Second, EMF's logic and proofbased approach allows students to experience the excitement and satisfaction of intellectual discovery. EMF follows the method of professional mathematicians — observation, conjecture, proof. Students are guided through carefullysequenced exercises that lead to keen observations, which subsequently give rise to generalized results. EMF also teaches some fundamental techniques of mathematical logic so that students are able to prove many of these results. This approach creates a deep, intuitive understanding of mathematics.
A popular alternative approach used by programs like Art of Problem Solving is to learn mathematics by solving many, many competitionstyle problems. EMF certainly includes problems but under a different pedagogical philosophy: (1) Because gifted students typically need less repetition to learn a concept, EMF trades off having little repetition to go deep into the "why" behind the solutions. (2) EMF's problems are not an end onto themselves but are there to help a student develop mathematical intuition, which later helps them prove many of the important results they learn.
 My talented high school student has already studied algebra and geometry. Is my child too advanced for EMF? Can my child start with a later course?
Your child is not too advanced for EMF. The EMF courses were written by mathematicians to teach modern mathematics to those talented middle and high school students who are capable of benefiting from a sophisticated approach. At times the subject matter will be familiar to older students, but the approach is very different.
All students must begin with the first course — operational systems — because it is unlikely that your child has any experience with these structures (even though they are fundamental to modern algebra). The first course also addresses properties of nonnumeric operational systems, and very few high school students will have experienced these systems. However, a talented high school student would be expected to move through the material at a much faster rate than most younger students because of the higher level of maturity and betterdeveloped study habits.
A very talented high school student who has successfully completed algebra and geometry courses may also be eligible for the Advanced Mathematical Logic courses offered by www.eimacs.com. Click here for a free aptitude test for the AML program.
 How do I register my child to take the aptitude test? Is the test required?
After you complete the registration process for EMF, you will receive an email with instructions on how your child can take the aptitude test as well as how to enroll in the first course, Operational Systems. Taking the test is not required in order enroll in the first course. However, if you are unsure of whether your child is ready for EMF and would find these courses interesting, we strongly encourage you to have your child take the test. The test is designed to measure intellectual maturity, and the information you will gain from the test results may help you make your decision.
 What exactly does "selfstudy" mean?
Selfstudy means that an EMF student is expected to complete these courses without assistance from an instructor. The aptitude test and prerequisites outlined above and on the Getting Started page are designed to help parents determine if their child is ready to begin taking the first EMF course, Operational Systems. Parents are encouraged to give careful consideration to these guidelines before enrolling their child in order to avoid unnecessary frustration from starting the EMF program too soon.
 If EMF courses are selfstudy, what should my child do if he or she needs help understanding the material?
When students are logged into the EMF site they may access the EMF Help Forum. In this forum, EMF students may post questions to be discussed and answered by other students. Questions that cannot be answered satisfactorily by other students are filtered through to experienced instructors and mathematicians who will respond appropriately through the Help Forum. Students, however, are not given direct access to an IMACS instructor.
For each exercise, students may read previously posted Help Forum questions and answers about that exercise by clicking on the green question mark button that appears with that exercise. Students who use the Help Forum are able to rate the helpfulness of answers given and earn "Math Wizard" points for contributing answers subsequently marked as helpful.
To use the EMF Help Forum, students must obey strict rules including rules prohibiting the request or provision of answers and the use of inappropriate language. Students who do not obey these rules will be prohibited from accessing the EMF Help Forum and will not be permitted to enroll in subsequent courses. An EMF student is also free to discuss questions with parents and other individuals.

My child insist on getting everything correct. Are there doovers in EMF?
Yes and No. Certain exercises in EMF allow a student one, and only one, doover if the student's initial answers would receive a score below 50%. The student is given a warning and encouraged to carefully rethink his or her answers.
A student learns as much, if not more, from submitting an imperfect answer and then carefully reading the answer key as he or she does by submitting the correct answer.

If EMF is selfstudy, why has my child not been able to do the work on his own?
Not every child will be able to study the EMF curriculum independently. This can be for a variety of reasons including, but not limited to, starting at too young an age, needing stronger reading skills, lack of intrinsic motivation, underdeveloped study habits, and needing stronger executive functioning skills. In order to excel in EMF most students will need to do some studying, especially prior to taking the incourse tests. Some children who have natural mathematical talent and have done well in standard math courses may still need small to substantial amounts of adult support to succeed in EMF, depending on their maturity. IMACS encourages all parents to regularly monitor their child's progress in EMF and to follow up with their child whenever there are signs of difficulties.
 What should I do if my child is having technical difficulties with the course website?
Please send an email to techsupport@elementsofmathematics.com. Provide a detailed description of the technical problem your child is experiencing. IMACS will work to resolve your issue as quickly as possible. Please note that EMF students should not use this email address to request help with their coursework.
 I think I found a mistake in a course. What should I do?
First use the EMF Help Forum to verify that there is a mistake in the course and not in your understanding. If you really did find a mistake, please email IMACS at techsupport@elementsofmathematics.com with a detailed description of the nature and location of the error.
 Are courses scheduled at specific dates and times?
No. For a given student, a course begins when that student enrolls in that course. Courses may begin at any time during the year. As long as a student is enrolled in an EMF course, he or she will be able to access that course's material 24 hours a day, seven days a week. In addition, a current student will have access to all previous EMF courses in which that student was enrolled. A student may complete coursework at his or her convenience within the enrollment period.
 Can my child download course material to be worked on offline or to be printed and read offline?
No. Due to the interactive nature of EMF course technology, students must do their work online with a live internet connection.
 What is the appropriate pace for working through an EMF course?
The appropriate pace is whatever the student is comfortable with. However, it is best not to go too many days without completing some coursework. A student needs to keep the material fresh in his or her mind since EMF courses move along steadily with little to no repetition. A minimum of at least two or three onehour sessions spread out over a week is recommended.
Likewise, proceeding too quickly through EMF can be detrimental to a student's long term success in the program. Students should bear in mind that there is no prize for finishing first, but significant rewards for those whose meticulousness and dedication leads to a deep and lasting understanding. Students who take the time to read and reread EMF material and to work through the problems slowly and carefully do much better.
Students who are used to succeeding in math despite jumping from exercise to exercise and ignoring or speedreading the intervening text quickly discover that the same approach does not work in EMF. Students are also expected to take a long time puzzling through the more difficult problems, often by putting pencil to paper, and without giving up too quickly. In other words, EMF rewards patience and persistence.
 Should my child work on EMF if he or she has 15 minutes to spare?
No. Success with the EMF curriculum requires longer stretches of deep focus and concentration. It would be better to use those 15 minutes to help free up a longer block of time later.
 How will I know how my child is doing in the course?
A report card will be emailed each Monday morning. If a student has not made progress in two weeks, report cards are no longer sent until the student answers another exercise.
 How are EMF course scores calculated?
For each course element (exercise, review quiz problem and test problem), IMACS analyzes the available raw scores to determine a level of difficulty. This information is then used to adjust the grading scale for that course element. Think of it as a "curve" if you like. For example, if a student earns 12 out of 16 points on an exercise, this equates to a raw score of 75%, which might result in an adjusted score of 90% for a difficult exercise.
The adjusted scores for exercises and review quiz problems are then accumulated to form an assignment average. Similarly, the adjusted scores for the problems of a given test are accumulated to form an average for that test. If a course has more than one test, the individual test averages are themselves averaged with equal weighting to form a single test average. The course score is then calculated as a weighted average of the assignment average (60% weight) and the test average (40% weight). In view of the demands of this course, any student who obtains a course grade of B or better (83% or higher) should be very proud of his or her achievement.
 As more students complete a course that my child completed already, will my child's course score change?
No. If your child has already completed a course, your child's course score will not be affected by the scores of students who complete that course after your child. IMACS will update the adjusted score algorithm and grade mapping as more students complete a course, but this will affect only students who subsequently complete the course.
 Why does IMACS calculate grades in this way?
As you know, the EMF curriculum is quite different from a standard mathematics course and far more challenging. Some exercise and test questions are such that obtaining a standard "A" grade of 90% is challenging and rarely achieved. For such questions, a "B" grade of 80% is regarded as exemplary. As such, it is difficult to properly reflect EMF student achievement within a standard K12 grading model using raw EMF scores. Nevertheless, parents and students may find it useful to consider performance visàvis a familiar framework, and so the IMACS grading system uses scores that are adjusted to reflect the varying levels of difficulty of exercises and test questions.
 My child completed an EMF course and received a lower average score than he is used to getting. How should we interpret this result?
First, your child is to be commended for completing the EMF course. Remember that this rigorous and demanding program challenges young students to learn and think deeply about complex ideas in mathematics that are rarely introduced outside of a university setting. If a student's final average score is lower than 75%, however, IMACS recommends waiting at least a year before enrolling in the next course. With time, a student who has the natural talent to learn the material may also develop the intellectual maturity, motivation, reading skills and executive functioning skills to excel in EMF on a selfstudy basis.
 Does a student have to take the courses in order, or can some courses be skipped or taken out of order?
The EMF courses must be completed in order and without skipping. These courses are designed to build an intuitive foundation for mathematics through carefully planned steps. While EMF is new to the online environment, the curriculum itself has been in use for over 20 years and is reviewed regularly to determine if updating or reordering sections will improve its effectiveness.
 What if my child completes the EMF series of courses?
He or she will be ready to take calculus classes at the AP level. Students who complete the EMF series with an overall average of 80% or higher may also be eligible for the Advanced Mathematical Logic series of courses. An aptitude test for these universitylevel courses is available at www.eimacs.com.
 What happens if my child does not finish a course within the enrollment period?
Parents may reenroll a student in a course that he or she did not complete within the original enrollment period. Once the course is completed, if the student is enrolled in the next course, any time remaining from the reenrollment period will be added to the new enrollment period for the next course in the sequence at no additional cost.
 If my child completes a course before the enrollment period ends, can he or she start the next course?
Once a student completes a course, he or she may enroll in and begin the next course in the sequence. Any time remaining from the previous course will be added to the enrollment period for the next course once tuition for the next course is paid. To enroll in the next course, click here and follow the registration and payment process.
 Once my child completes a course, will he or she still have access to the material?
A student may access all completed courses as long as his or her EMF account has not expired. If your child's account has expired, you may reactivate and extend it by enrolling in the next course in the series or by purchasing a 30day extension.
 Is there a way for parents or teachers to receive curriculum support from IMACS other than through the Help Forum?
The EMF curriculum is "mathematician" math as opposed to standard "school" math. Through the work of professional mathematicians and mathematics educators, this advanced material has been made accessible for extremely bright and motivated young students. Individuals capable of providing support to EMF students would need a rare combination of skills: the ability to understand abstract, universitylevel mathematics AND the ability to relate these complex ideas to middle and highschool aged children. Because very few middle and high school teachers have any experience teaching this level of mathematics, it would be challenging to find appropriate curriculum support staff for EMF. Furthermore, the cost to hire such uniquely skilled support staff would necessarily raise the tuition for EMF courses substantially. The goal of IMACS in offering EMF is to provide wide access to our worldclass curriculum in mathematics in a way that is still relatively affordable.
 Will IMACS provide any kind of documentation to show that my child has completed a course?
When a student completes an EMF course, IMACS provides a Student Transcript and a Completion Certificate that may be downloaded through the student's account.
 Is EMF the same as New Math?
While the origins of EMF date back to the heyday of the New Math, the EMF developers both then and now have taken an entirely different approach. They could afford to do so because the target audience for EMF is highly gifted students who have already mastered standard elementary school mathematics and beyond, quickly and effortlessly. Furthermore, New Math was implemented with woefully inadequate teacher training. By contrast, EMF's selfstudy curriculum is written by professional mathematicians who average over 25 years' experience educating gifted children.
 Are you an accredited institution?
While IMACS is not an accredited institution, we have been operating local teaching centers since 1993. During the 10 years prior to that, we taught the EMF curriculum in the Broward County public school district as part of the acclaimed Project MEGSSS program. Regardless of accreditation status, our students find that the most meaningful and enduring benefit from having been in our program is the advantage it gives them in college and in their future careers.
 What is your refund policy?
IMACS is not able to offer refunds on EMF courses due to their low cost.
 What is your "vacation" policy?
Enrollment periods are fixed and may not be paused. However, the length of an enrollment period is designed to give students a reasonable amount of flexibility in consideration of their often active schedules.
 I've read all the material available on the EMF website, but I still have questions that I need answered before enrolling my child. How can I get more information?
Parents interested in enrolling a child in EMF may email specific questions to IMACS at info@elementsofmathematics.com. Please note that EMF students should not use this email address to request help with their coursework.
 I am an educator interested in licensing EMF. How can I get more information?
Visit EMFmath.com/schools for information on licensing EMF.
 How will I know when future EMF courses come online?
IMACS will email parents of current EMF students when new courses come online. You may also "Like" us on Facebook at www.facebook.com/eimacs to receive course updates.
News
Articles, blog posts and press releases about EMF:
Online Math Program for Talented Students Doubles Enrollment in Florida's Broward County Public Schools. District Administration, 23 Oct. 2017.
Gifted Math: A Better Alternative to Acceleration. The IMACS Blog, 17 Nov. 2016.
Broward County Schools to Expand Online Math Program for Gifted Students. THE Journal, 2 Aug. 2016.
Online Gifted Math Program to Grow to Several Hundred Students in Broward County Public Schools. PR Newswire, 2 Aug. 2016.
Not Your Father's Algebra: A New Online Course for Talented Students. The IMACS Blog, 12 Feb. 2015.
IMACS Introduces Elements of Mathematics: Foundations. The IMACS Blog, 25 Oct. 2012.
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