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A High School Course For Mathematicians

The IMACS University Mathematical Logic Course is based on the Elements of Mathematics series of textbooks. These were initially developed in the 1960’s and 70’s by an international team of eminent mathematicians to be both rigorous and engaging for talented high school students, and mathematicians at IMACS have refined them in light of several decades teaching experience.

The curriculum begins with topics covered in the logic courses typically required of a college major in mathematics, engineering, computer science or philosophy. It then goes on to introduce more advanced techniques in mathematical logic and reasoning.

Program Details

Enrollment requires recommendation from an IMACS instructor or success in an aptitude test .
Students work at their own pace and meet with an instructor in weekly classes.
Classes have at most 12 students.
Classes are 120 minutes in duration.
It is expected that students work independently between classes.
Classes are split into four 8-week sessions per year. New enrollments are accepted throughout the year, spaces pending.
Students access live classes and the IMACS Store via their personal Student Portal .
Students who miss a class may schedule a make-up class in any week of the same session.
Parents use the Parent Portal to enroll students; arrange make-up classes; review student IMACS points; access credit card profiles, accounts, invoices and calendars; and contact IMACS instructors and administrators.

Tell Me More

We have answered the most common questions that parents have in the FAQ section below. The program is not for every student, not even for every student of precocious talent. But for some students, the University Mathematical Logic experience is life changing. Please contact us if you are interested in this program for your child.

University Mathematical Logic

A University-level Logic Course

Providing an advanced introduction to formal logic and mathematical proof, but designed for the most talented secondary school students, it is the envy of university mathematics courses everywhere!

Logic for Mathematicians

Proposition, Predicate and Axiomatic Logic

Three advanced courses cover propositional logic, a predicate logic sufficient to formalize all basic set theory, and an introduction to axiomatic set theory. To learn more, study the FAQs below, or contact us today .

Frequently Asked Questions

Q uestion:

What topics are covered?

A nswer:

Students take University Mathematical Logic courses in the following sequence:

Logic for Mathematics I : An introduction to propositional logic, a branch of modern mathematics that provides the foundation for formal and rigorous mathematical proofs.

Logic for Mathematics II : An introduction to predicate logic, a so-called “first-order logic” sufficient to formalize all of set theory, which provides the basic language in which most mathematical texts are written.

Logic for Mathematics III : An introduction to axiomatic set theory, which plays a central role in modern mathematics and is fundamental to understanding math at its most sophisticated levels.

Q uestion:

What is a typical outcome for students?

A nswer:

Students who complete this curriculum have developed superior abstract reasoning abilities that make all future classes requiring critical thinking significantly easier.

Because of the ease with which former students handle mathematical reasoning, some go on to complete PhD’s in mathematics. But whatever path they choose — and alums include not just mathematicians but computer scientists, engineers, philosophers, doctors and lawyers — it is smoothed by the advanced logic and analytical skill covered by the University Mathematical Logic course.

Q uestion:

How do I know if my child is ready for an IMACS University Level Class?

A nswer:

Students must take an aptitude test before enrolling in one of these classes.

Q uestion:

Can my child start in Logic for Mathematics II?

A nswer:

Almost certainly No. This is a unique curriculum and students must start from the beginning. However, because it is self-paced, stronger students may find that they’re moving rather quickly.

Q uestion:

Are IMACS University-Level courses right for my child?

A nswer:

Many students enroll in our university-level courses because, regardless of age, they are ready for an academic challenge suited to their advanced abilities. Traditional schools often lack the resources or flexibility to meet the intellectual needs of these talented, young children.

IMACS university-level courses provide an academic challenge worthy of the brightest students. Your child will truly take pride in his or her ability to solve advanced computer science, logic, and math problems.

When a student completes a course, an official transcript is provided that reports the student’s final grade, along with a detailed description of the course content. For those who do well in our program, we provide strong, individually tailored letters of recommendations for college applications.

The educational foundations students build through our program help them outperform the expectations of their parents, teachers and professors.

For the rest of their lives, whether in school, at work or at play, IMACS graduates simply think better.