University of Calfornia, Riverside
Mathematics 5 Sequence
The Principles of Calculus
2025 - 2026
University of Calfornia, Riverside
Mathematics 5 Sequence
The Principles of Calculus
2025 - 2026
Coordinator
Contact
Email: weisbart@math.ucr.edu
For our students
Welcome to the The Principles of Calculus, UCR website.
Mathematics 5ABC is the UCR implementation of The Principles of Calculus. Follow the above link to access the course materials on the main website.
The Subject
Newton and Leibniz independently discovered The Calculus in the late 17th century. Over the next 100 years, Euler and many others developed the subject into one of the most important areas of mathematics. It took over another 100 years for mathematicians to develop the logical foundations of the subject.
Our Course
This course is a principle based course. It takes the perspective that to learn a subject in mathematics is to learn to reason using principles in the framework of a sufficiently expressive language. Students will use the language and the reasoning strategies that the course develops to investigate the central ideas of The Calculus. In so doing, they will come to grips with one of the most significant triumphs of human creativity, the mathematical understanding of our place in the solar system.
Scientific Goals
The course begins with the study of unions and intersections of sets. By the end of the year, students will understand how to simulate planetary motion. They will, furthermore, understand all ideas involved in creating such a simulation. They will use a model of planetary motion to determine the relative masses of Earth, Jupiter, and the sun. In 1783, Cavendish measured the gravitational constant of the universe. Students will learn how to use Cavendish's experiment to "weigh" planet Earth.
We hope that you are as excited as we are to begin this adventure!