Mathematics

Mathematics allows you to uncover patterns, solve problems, and make sense of complex systems. You will study core topics like calculus, linear algebra, and probability, while also exploring how numerical methods and computer tools help solve real-world challenges. These courses build your analytical thinking and problem-solving skills for use in science, engineering, and data-driven fields. Whether you’re modeling dynamic systems or analyzing data, mathematics gives you the language to describe and understand the world.

Opening up Mathematics courses

Within Mathematics, you can take any of the 100-level courses without taking any of the gateways. The 200 and 300-level courses can be accessed through the Mathematical Methods gateway course.

Courses in Mathematics

Gateway

Mathematical Methods

Introduces linear algebra (vectors, matrices, eigenvalues) and calculus (limits, differentiation, integration) to construct and solve equations. Provides problem‑solving skills applicable across disciplines.

200-level

Advanced Calculus

This course builds on elementary calculus, extending concepts like differentiation, integration to multiple dimensions, differential equations. This course also includes some analysis involving complex-valued functions. Students will deepen their analytical skills and solve problems both by hand and using computer algebra software—preparing them for advanced applications in mathematics, science, and data analysis.

200-level

Linear Algebra

This course introduces key concepts in linear algebra, such as systems of equations, vectors and matrices, and linear spaces, with a strong emphasis on visual and conceptual understanding. These ideas are widely applied across fields—from economics and physics to computer science and robotics. Students will develop their skills by solving numerous exercises, both by hand and using computer algebra software. This hands-on approach supports practical skills alongside theoretical understanding.

200-level

Computational & Numerical Mathematics

Many mathematical problems do not have analytical solutions. They require a numerical algorithmic solution strategy. This course introduces key methods in computational and numerical mathematics, including root-finding, interpolation, numerical differentiation and integration, and solving differential equations. Emphasis is placed on understanding algorithmic accuracy, stability, and efficiency. Students will use computer algebra software extensively to apply these techniques to many exercises.

300-level

Probability & Statistics

This course provides a solid foundation in mathematical statistics. The course discusses probability theory, discrete and continuous distributions, including joint distributions for two (or more) random variables, sample statistics and parameter estimation. Students will solve many problems analytically and use computer algebra software to simulate and validate results—developing both theoretical understanding and practical skills essential for data science.

300-level

Linear Systems

This course focuses on the analysis of linear systems from an engineering perspective. The course explores multiple ways to represent systems — such as through linear differential equations, transfer functions, state-space representation and signal-flow diagrams — and discusses how to convert between these characterizations. Emphasis is placed on understanding the structure and behavior of systems, laying the groundwork for applications in control, signal processing, and modeling.

Also consider these options:

Data Science & Intelligent Systems

The other fields within the Data Science & Intelligent Systems cluster.

Data Science & Intelligent Systems

Explore Philosophy!

To delve into the logic, reasoning, and foundations behind the numbers.

Philosophy

Explore Law!

To apply logical thinking and precision to complex legal systems and arguments.

Law

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The UCR Program Builder is designed to help you easily plan your academic program. Step by step, the tool guides you through selecting courses, building a balanced curriculum, and meeting UCR’s academic requirements.

Try the Program Builder

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Mathematics

Mathematics

Opening up Mathematics courses

Courses in Mathematics

Courses in Mathematics

Mathematical Methods

Mathematical Methods

Advanced Calculus

Advanced Calculus

Linear Algebra

Linear Algebra

Computational & Numerical Mathematics

Computational & Numerical Mathematics

Probability & Statistics

Probability & Statistics

Linear Systems

Linear Systems

Also consider these options:

Also consider these options:

Data Science & Intelligent Systems

Data Science & Intelligent Systems

Explore Philosophy!

Explore Philosophy!

Explore Law!

Explore Law!