Applied and Computational Mathematics
Why Study Applied and Computational Mathematics?
While mathematicians might contemplate whether solving an equation is possible, students in Caltech's Bachelor of Science (BS) in Applied and Computational Mathematics (ACM) degree program first observe a real-world phenomena, model an equation to explain it, and investigate how quickly and efficiently a computation can be performed—can we solve this in seconds? Years?
This practical, goal-oriented approach empowers you to craft mathematical models that simulate fluid dynamics, predict weather patterns, or optimize financial strategies, pushing boundaries across disciplines. By weaving together rigorous mathematical training with computer programming, the ACM major translates abstract mathematical objects like matrices and differential equations into concrete solutions for today's scientific and societal puzzles.
Why Applied and Computational Mathematics at Caltech?
In Caltech's applied and computational mathematics major, you'll tackle challenging problems through unique mathematical approaches with the freedom to explore the limits of what's possible through computing. Create tangible solutions by modeling differential equations that tilt a drone's arm, studying linear transformations' influence on computer graphics, or predicting political or economic outcomes.
What sets our program apart is the integration of mathematics with other disciplines and the freedom to study and research according to your interests. Taking interdisciplinary courses like "Understanding China Through Finance," alongside advanced math classes, you'll step into the shoes of policymakers using quantitative methods to analyze international relations and trade dynamics—preparing you to engage with complex global issues from an advanced mathematical perspective.
What You'll Learn
The ACM program curriculum builds on core calculus and applied linear algebra, teaching you how linear and non-linear systems work and how to use calculations in real-world situations, like manipulating computer pixels. You'll progress through additional complex analysis coursework, learning to analyze ordinary and partial differential equations and improving or refining algorithms with methods such as reduction.
Balancing robust math preparation with computer training, ACM majors gain the computational prowess to physicalize mathematical concepts while pushing their mathematical abilities. Specialize the degree in tracks including Statistical and Machine Learning, Robotics, Mechanics, or Fluid Dynamics, and explore courses like Hedge Funds, which analyzes investment strategies from both historical and mathematical perspectives. This approach prepares you to create models for interdisciplinary solutions, like programming AI to improve a biomedical device.
View the Caltech catalog for degree requirements and curriculum information.
Who You'll Learn From
Work directly with over 80 renowned faculty in the Division of Engineering and Applied Sciences and collaborate with experts from business, economics, engineering, and political science who apply mathematical modeling to their fields. In small class sizes, faculty foster direct mentorship with students and connect them with research and internship opportunities, no matter the field of interest.
If you love solving the most challenging problems and being resilient and unrelenting about it, Caltech is the place for you. You're not going to be thrown one plus one to solve, but some crazy integral that will take days or even weeks to solve.
Career Possibilities
In today's world, where computing is essential to pair with high-level quantitative skills, the applied and computational mathematics degree opens doors to diverse career paths. Graduates can pursue graduate school in mathematics, computer science, economics, or engineering or apply their skills in industry, research, or policy roles, such as:
- Biomedical technology
- Quantitative finance
- Data science and machine learning
- Scientific computing
- Policy analysis and consulting
- Software engineering and algorithm development
- Academic research and teaching
Curriculum Components and Prerequisites
The ACM major curriculum builds on Caltech's core mathematics courses to develop strong foundations in applied and computational mathematics. It is customizable via tracks in Learning & Vision, Graphics, Robotics & Engineering, Environmental Science, Business & Finance, or Mechanics. Curriculum components include:
- Fundamentals of mathematics, programming, and scientific communication
- Scientific fundamentals across biology, bioengineering, chemistry, mechanical engineering, and physics
- ACM core in methods, linear algebra, probability, and numerical analysis
- ACM elective courses in statistics, analysis, or mathematical modeling
Pursue a Bachelor's in Applied and Computational Mathematics at Caltech
Join Caltech's applied and computational mathematics major program to translate abstract insights into solutions for complex real-world problems. Whether you're passionate about pursuing high-level quantitative research, creating more efficient infrastructure, or analyzing financial markets, ACM provides rigorous quantitative and computational skills to turn your mathematical talent into meaningful impact.