10 College Math Courses for High School Students

For high school students passionate about mathematics, diving into flexible college-level courses can be a good way to engage with the subject during the school year. 

College math courses for high school students go beyond the standard school syllabus, offering exposure to advanced concepts and critical thinking skills that lay the foundation for future academic and career success. They can serve as a solid foundation for future research projects or internships.

You can get a head start in your field of interest and build a portfolio that acts as concrete evidence of learning. The knowledge and skills gained via such courses can help you start your research project or a startup company after college, or serve as a good base for your college applications. 

Some of the courses below are virtual, and offer college credit as well!

Below, we have listed 10 college math courses for high school students.

1. HarvardX: STAT110x – Introduction to Probability

Location: Virtual (EdX)

Cost: $209

Application Deadline: Rolling basis

Program Dates: Self-paced

Eligibility: No strict prerequisites, familiarity with school-level algebra is recommended

This 10-week course on EdX provides an introduction to probability, equipping you with the necessary tools to understand data and uncertainty across fields such as science, engineering, finance, and economics. It covers topics such as counting, story proofs, random variables, distributions, limit theorems, Markov chains, averages, the law of large numbers, etc. You can also interact with other students during this course thanks to EdX’s discussion forums and discuss topics such as statistical inference, stochastic process, randomized algorithms, and more. 

2. MITx: 18.01x – Calculus 1A: Differentiation

Location: Virtual (EdX)

Cost: Free

Application Deadline: Rolling basis

Program Dates: Self-paced

Eligibility: No strict prerequisites, familiarity with school-level algebra and trigonometry is recommended

This program explains differential calculus, along with its definition, computation, and application of derivatives to solve real-world problems. You will learn how to evaluate limits numerically and graphically, calculate the derivative of any function, hand sketch many functions, make linear and quadratic approximations of functions, and apply derivatives to maximize and minimize functions and find related rates. You can visualize concepts and use a sketch tool to understand graphics better via ‘Mathlets,’ and be part of discussion forums in this course. 

3. Stanford Online: CME 100 – Vector Calculus for Engineers

Location: Virtual

Cost: $1,514 per credit unit.

Application Deadline: Rolling basis

Program Dates: Self-paced

Eligibility: Strong background in single-variable calculus | Prior completion of either MATH21 - Calculus or prior earning of a score of 5 on the AP Calculus BC exam

This course comprehensively explores vector calculus and its applications in engineering by incorporating computation and visualization using MATLAB. You will learn differential vector calculus, including vector-valued functions and partial derivatives, integral vector calculus covering multiple, line, and surface integrals, along with an introduction to linear algebra. This course also features online discussion forums with fellow students. You will gain strong analytical and problem-solving skills essential for various engineering fields and completing this advanced mathematics course from Stanford can help your college applications. 

4. HarvardX: PH525.2x – Data Science: Inference and Modeling

Location: Virtual (EdX)

Cost: $149

Application Deadline: Rolling basis

Program Dates: Self-paced

Eligibility: No strict prerequisites, familiarity with basic programming concepts and probability

This EdX course introduces statistical inference and modeling using electron forecasting as a case study. You will learn to define estimates and margins of error, apply models to aggregate data, and the basics of Bayesian statistics and predictive modeling using R programming language. The course also includes discussion forums for interacting with peers and instructors. By the end of the course, you will develop a strong foundation in data analysis and statistical thinking and have a strong understanding of confidence intervals and p-values. 

5. MITx: 6.431x – Probability: The Science of Uncertainty

Location: Virtual (EdX)

Cost: $300

Application Deadline: Rolling basis

Program Dates: Self-paced

Eligibility: No strict prerequisites, background in basic probability and mathematical reasoning is recommended

This course provides an introduction to probabilistic models, random processes, and statistical inference helping you to analyze uncertainty in real-world scenarios. It covers topics such as probability models, Bayesian inference, Poisson processes, Markov chains, and classical statistics. You engage in interactive sessions where you discuss problem sets to deepen your understanding and develop skills such as mathematical reasoning, data analysis, and statistical modeling, which are highly valued in the fields of finance, engineering and artificial intelligence. The probabilistic models covered in this program do not rely on the traditional ‘theorem-proof’ format, but an intuitive, rigorous and mathematically precise manner.

6. Stanford University: MATH 51 – Linear Algebra and Multivariable Calculus

Location: Virtual

Cost: $7,570

Application Deadline: Rolling basis

Program Dates: Self-paced

Eligibility: A conferred bachelor’s degree with a minimum 3.3 GPA | A grade of B+ in a full year of single-variable calculus courses (2 semesters, 3 quarters, or a 5 on the AP Calculus BC exam

This course emphasizes the interconnectedness of two critical mathematical areas - linear algebra and multivariable differential calculus and explains their relevance to machine learning and data science. You will delve into linear algebra concepts such as orthogonality, linear independence, matrix algebra, and eigenvalues, and multivariable calculus topics such as unconstrained optimization via gradients and Hessians, gradient descent and multivariable Chain Rule, and Newton’s Method. The course also prefers computations along with an intuitive understanding of key concepts. You will develop strong analytical and problem-solving skills and can earn up to 5 academic credits at the end of the course.

7. Imperial College London: MATHML – Mathematics for Machine Learning 

Location: Virtual (Coursera)

Cost: $98 (approx.) for course, $399 for Coursera Plus annual subscription

Application Deadline: Rolling basis

Program Dates: Self-paced

Eligibility: No strict prerequisites

This course describes the correlation between foundational mathematics and its applications in machine learning and data science. It covers linear algebra, multivariate calculus, and dimensionality reduction, helping you gain a better understanding of vectors, matrices, optimization techniques, and probability and statistics, all within the context of machine learning. The course also includes video lectures, quizzes, programming assignments, and discussion forums. You will gain analytical, coding, and problem solving, skills often valued in AI, data science and engineering careers, making you an apt candidate for advanced studies. You will receive a Coursera career certificate at the end of the course.

8. Johns Hopkins University: MATHLA – Linear Algebra from Elementary to Advanced

Location: Virtual (Coursera)

Cost: $98 (approx.) for course, $399 for Coursera Plus annual subscription

Application Deadline: Rolling basis

Program Dates: Self-paced

Eligibility: No strict prerequisites

This math course by Johns Hopkins University is a three-course specialization covering undergraduate linear algebra, including vectors, matrices, linear equations, determinants, eigenvalues, symmetric matrices, and quadratic forms. You will be part of lectures, readings, quizzes, and special projects like exploring Markov Chains and Google PageRank, with examples progressing from low to higher dimensions. The course offers discussion forums for peer and instructor interaction. You will develop skills such as problem-solving, mathematical modeling, and matrix analysis, highly valued in data science, AI, machine learning, and economics. 

9. MITx: 18.06x – Linear Algebra – Platform: MIT OpenCourseWare

Location: Virtual 

Cost: Free

Application Deadline: Rolling basis

Program Dates: Self-paced

Eligibility: No strict prerequisites, basic knowledge of vectors, matrices, and three-dimensional coordinate systems

This free course, offered through MIT OpenCourseWare, covers matrix theory and linear algebra, and their applications in physics, economics, engineering, and data science. The topics covered are systems of equations, vector spaces, determinants, eigenvalues, and singular value decomposition. It includes problem-solving videos by MIT instructors, and self-paced learning with comprehensive materials like summary notes and problem sets with solutions. You will engage with lecture videos, readings, problem sets, and computational examples, often using software like MATLAB or Julia, to explore applications such as Fourier transforms and Markov processes. At the end of the course you develop skills in matrix analysis, problem-solving, and computational modeling, which are critical for fields like machine learning and engineering.

10. Stanford Online: CME 102 – Ordinary Differential Equations for Engineers

Location: Virtual 

Cost:  $1,514 per credit unit.

Application Deadline: Rolling basis

Program Dates: Self-paced

Eligibility: Strong background in single-variable calculus | Prior completion of either MATH21 - Calculus or prior earning of a score of 5 on the AP Calculus BC exam

This course by Stanford Online introduces both analytical and numerical methods for solving ordinary differential equations (ODEs) in engineering applications. You will learn to solve linear and nonlinear first-order ODEs, second-order ODEs, and Laplace transforms, alongside numerical techniques using MATLAB, covering finite differences, multi-step methods, and stability analysis. The course focuses on real-world applications, including spring-mass systems, Newton’s laws, and boundary value problems, making it highly relevant for engineering students. You will gain expertise in modeling dynamic systems, a crucial skill for mechanical, aerospace, and electrical engineering careers. 

One other option—the Lumiere Research Scholar Program

If you’re interested in pursuing independent research in math, consider applying to one of the Lumiere Research Scholar Programs, selective online high school programs for students founded with researchers at Harvard and Oxford. Last year, we had over 4,000 students apply for 500 spots in the program! You can find the application form here.

Also check out the Lumiere Research Inclusion Foundation, a non-profit research program for talented, low-income students. Last year, we had 150 students on full need-based financial aid!

Stephen is one of the founders of Lumiere and a Harvard College graduate. He founded Lumiere as a PhD student at Harvard Business School. Lumiere is a selective research program where students work 1-1 with a research mentor to develop an independent research paper.

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