Mathematics

The Mathematics undergraduate program at the California Institute of Technology offers a rigorous and comprehensive education in pure and applied mathematics, designed to prepare students for a wide range of careers in academia, industry, and research. The curriculum emphasizes not only core mathematical principles such as algebra, analysis, geometry, and topology but also fosters critical thinking, problem-solving skills, and an appreciation for the beauty and elegance of mathematical concepts. Students have the opportunity to engage in advanced coursework and research projects under the guidance of renowned faculty members who are leaders in their fields. The program encourages exploration of interdisciplinary applications of mathematics in areas such as physics, computer science, engineering, and economics, thus providing students with a versatile skill set applicable to various scientific and technical industries. Caltech's small class sizes and collaborative environment promote close interaction between students and faculty, allowing for personalized mentorship and a conducive atmosphere for intellectual growth. In addition to classroom learning, students can participate in seminars, workshops, and conferences that connect them with ongoing mathematical research and developments. The program aims to develop a deep understanding of fundamental mathematical theories while also fostering innovation and creativity. Graduates of the program are well-equipped to pursue advanced studies or careers in academia, data science, technology development, or finance. Emphasizing both theoretical knowledge and practical application, the Mathematics major at Caltech is designed to cultivate analytical prowess, quantitative reasoning, and a lifelong passion for discovery.

Course Content

• Introduction to Abstract Algebra
• Introduction to Discrete Mathematics
• Problem Solving in Calculus
• Oral Presentation
• How to Solve It
• Frontiers in Mathematics
• Senior Thesis
• Independent Reading
• Zhou, GDifferential Equations
• Differential Equations
• Introduction to Abstract Algebra
• Classical Analysis
• Introduction to Geometry and Topology
• Analysis
• Topics in Analysis
• Mathematical Logic and Axiomatic Set Theory
• Abstract Algebra
• Combinatorial Analysis
• Information Theory
• Algebraic Geometry
• Probability
• Representation Theory
• Algebraic and Differential Topology
• Number Theory
• Introduction to Continuous Logic
• Mathematical Finance

Requirements

TOEFL paper-based test score 550

TOEFL iBT® test 80

• Common Application with Caltech Questions
• $75 application fee or fee waiver (Common App waiver or Caltech-specific waiver)
• SAT with writing or ACT with writing
• SAT Subject Test in Mathematics Level 2
• 1 SAT science subject test: biology (ecological), biology (molecular), chemistry, or physics
• 1 math or science teacher evaluation
• 1 humanities or social sciences teacher evaluation
• Secondary School Report
• Academic transcripts

In addition to the two required teacher evaluations, you are welcome to submit an evaluation from a mentor or supervisor who knows you in a different context. If you have published a scientific research paper, you may submit the full paper to Caltech. Instructions on how to submit these papers will be included in your application confirmation email.

No work experience is required.

All undergraduate financial aid is awarded based on need. Annually, nearly 60 percent of undergraduates receive aid under Caltech's policy to provide all U.S. citizens and permanent residents with the support required to meet 100 percent of their families' demonstrated need.

The Mathematics undergraduate program at the California Institute of Technology (Caltech) is renowned for its rigorous curriculum, distinguished faculty, and vibrant research community. This program provides students with a comprehensive foundation in pure and applied mathematics, encourages independent research, and prepares graduates for careers in academia, industry, and government. The curriculum encompasses a wide range of mathematical disciplines, including algebra, analysis, differential equations, topology, geometry, and mathematical logic, as well as specialized courses in applied areas such as statistics, numerical analysis, and mathematical physics. Students have the opportunity to engage in collaborative research projects, often working closely with faculty members who are leading experts in their fields. The program emphasizes both theoretical understanding and practical problem-solving skills, fostering a deep appreciation for the beauty and utility of mathematics. Caltech's close-knit academic environment facilitates mentorship and personalized advising, supporting students' academic and professional development. The institution also provides resources such as advanced computational tools, seminars, workshops, and conferences to enrich the learning experience. Graduates of the program frequently pursue PhDs in top graduate schools or secure positions in industry, leveraging their strong analytical skills and broad mathematical knowledge. The Mathematics program at Caltech exemplifies a commitment to excellence and innovation, preparing students to contribute meaningfully to a world increasingly driven by data, technology, and scientific discovery.