Quantum Mathematics Institute

Explore the Fundamentals

Mathematics is the language in which the patterns of the natural world are written. Orbits of planets, spread of disease, behavior of markets, and the design of cryptographic protocols all rest on quantitative structure. The Quantum Mathematics Institute teaches that structure directly: from the algebra of vectors to the limits that found calculus, we build understanding from first principles rather than from memorized recipes.

Browse Courses

Featured Courses

Our core sequence moves from the tools of calculus and linear algebra to the abstract ideas that organize modern mathematics. Every course is taught by a research mathematician and ships with a complete set of free problem sets and solutions.

beginner

Calculus I

Limits, continuity, derivatives, and definite integrals. You will meet the FTC and learn why a rate of change accumulates into a total.

Math 1014 credits

beginner

Linear Algebra

Vector spaces, linear transformations, matrices, and eigenvalues. This is the structural skeleton shared by data science and quantum mechanics.

Math 1204 credits

intermediate

Probability and Statistics

Random variables, expectation, variance, and the central limit theorem, extended into hypothesis tests and confidence intervals for the sciences.

Stat 2103 credits

beginner

Discrete Mathematics

Logic, proof techniques, counting, and graph theory. These tools give the precise vocabulary required by algorithms, combinatorics, and cryptography.

Math 1303 credits

Core Topics

A directory of the areas we teach in depth. Each entry links to the course page where the topic is covered.

Differential Equations

Graph Theory

Numerical Methods

Try a Sample Question

A short check on the power rule, the workhorse derivative formula from single-variable calculus. Select an option to see the reasoning.

Using the power rule, what is the derivative of f(x) = 3x^4?

Choose an option to see the reasoning.

Practice Problem Generator

A short bank of calculus and algebra questions to keep the fundamentals sharp. Generate a fresh problem, work it out on paper, then reveal the worked answer.

Daily Drill

Press "New problem" to generate a question.

problems generated

answers revealed

Frequently Asked Questions

What courses does the institute offer?

We offer thirteen semester length courses, from first-year Calculus and Linear Algebra through Real Analysis, Abstract Algebra, Topology, and Number Theory at the advanced level. A full list with levels and descriptions appears on the Course Catalog page.

How much does it cost to study here?

The right to learn is never gated. All lecture notes, worked problem sets, solutions, and past papers in the resource library are free. Paid tuition covers live teaching time, hand marking, and personal feedback for enrolled students.

What are the prerequisites for taking a course?

Beginner courses assume high school algebra and geometry. Intermediate courses require Calculus I and Linear Algebra or their equivalents, which we verify with a placement quiz. Advanced courses require the relevant intermediate sequence plus a passing score on a proof-writing assessment.

Do you issue certificates or credits?

Yes. Students who complete a course with a passing mark on its problem sets and final paper receive a certificate of completion stating the course and the grade earned. The institute is recognized by the Council for Independent Mathematical Studies.

How do I contact the institute with a question?

Use the contact form on the Contact page, or write to office@qmi-institute.org for general questions and admissions@qmi-institute.org for admissions and placement. We reply within two working days.

How do lessons work for enrolled students?

Groups of at most twenty meet weekly in an interactive seminar where definitions are tested and proofs are built on the board. Each course sets weekly written problem sets that are marked by hand with line-level comments, with full solutions released a week later.