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How to help high schoolers prep for college-level math

By: Brandpoint

(BPT) - College-bound students already have some avenues for advancing their studies of crucial subjects, such as pursuing college-level courses while in high school. Students with demonstrated interest in STEM subjects need a solid foundation to reach their full potential. Advanced mathematics is required for these students to be able to understand the natural world, analyze data, perform systematic observation and modeling - all crucial skills for their future studies and careers in fields including the natural sciences, engineering, computer science and more.

To attain an advanced foundation in mathematics, students can pursue vigorous courses while they're still in high school. Stanford University-Level Online Immersive (ULO-I) offers challenging online mathematics courses to students worldwide.

"ULO-I classes are designed to provide resources for advanced high school students to proceed well beyond what their schools can offer," said Dr. Rafe Mazzeo, Cassius Lamb Kirk Professor of Mathematics at Stanford University and Faculty Director of Stanford Online High School.

What is Stanford Pre-Collegiate University-Level Online Immersive?

ULO-I courses offer university-level mathematics to high school students anywhere in the world via two different intensive, semester-long courses. The course format is partially synchronous, with students listening to two to three recorded Stanford faculty lectures per week. They will also attend two synchronous online sessions, during which the course instructor will expand on material and facilitate group discussion and work. Students should expect five hours of live online class time and up to four hours of homework per week.

Just as with any advanced coursework, successful participation in this program can help students present themselves as strong candidates to any college, but it does not guarantee admission to or transfer credit at any university.

Multivariable Calculus and Linear Algebra

Launched last year, this course is based on recently developed curriculum for first-year Stanford students that can help prepare students who are already well-prepared in single variable calculus for further studies in engineering, computer science, data science, natural sciences and theoretical mathematics. The Multivariable Calculus and Linear Algebra course was the first offering in the ULO-I program.

"For Multivariable Calculus and Linear Algebra, we use a high-level curriculum that was developed in the Stanford University Mathematics department to prepare Stanford undergraduate students for math, data science, AI, engineering and all other quantitative disciplines," said Mazzeo. "Linear algebra and the optimization techniques introduced in this course are fundamental for almost every application of math, particularly in data science and AI. This course is also a prerequisite for many Stanford computer science and engineering courses."

Students who have completed the course will be well prepared to take classes in ordinary differential equations and more advanced linear algebra.

Discrete Mathematics

This course conveys the fundamental theory, structures and techniques of discrete mathematics. Discrete mathematics is an extremely broad and diverse subject, with a variety of connections to other branches of mathematics (including number theory, abstract algebra and others), and applications to fields outside of mathematics (including computer science, optimization, operations research and engineering).

This challenging course provides an ideal environment for students to improve and deepen their abilities to observe patterns, engage in mathematical reasoning, formulate conjectures and construct rigorous mathematical proofs.

Discrete Mathematics will teach students how to prove results and solve problems that may be somewhat different from those they have experienced prior to this course. Students will develop the foundations and mathematical maturity necessary to be broadly successful in higher-level mathematics (and other fields).

Students taking one of these courses will earn five units of Stanford University Continuing Studies credit. Schools, universities and districts have different policies regarding transfer of credits issued by Continuing Studies Programs. Credits for University-Level Online courses are most commonly used to place out of required courses (at the discretion of the receiving program). Prospective students should inquire with their institutions regarding their credit policies.

How to apply

High school students can apply to these courses now through January 6, 2025 for the spring semester, which begins Monday, January 27, 2025 and runs until May 16, 2025. Applicants are required to submit a transcript and other documents, depending on the chosen course. They must also submit a recommendation letter from a math instructor.

To learn more about these courses and to apply, visit ULO-I.Stanford.edu.

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