# Graduate Degree in Computing + Mathematical Sciences

The Computing and Mathematical Sciences (CMS) PhD program is a unique, new, multidisciplinary program at Caltech involving faculty and students from computer science, electrical engineering, applied math, economics, operations research, and even the physical sciences. The program sets high standards for admission and graduation, and boasts a broad collection of world-class faculty (any faculty at Caltech from any of the areas above can advise students).

Disciplines across the information sciences are experiencing an unprecedented convergence. As different areas interact, new fields are emerging. For example, combining Computer Science with...

...Optimization and Statistics has led to machine learning, "big data," and the field of data science.

...Control and Electrical Engineering has led to the smart grid, smart buildings, and the internet of things.

...Physics has led to quantum computing and quantum information theory.

...Economics has led to algorithmic game theory, privacy, and the field of network science.

...Biology and Electrical Engineering has led to bioinformatics, molecular programming, and biomolecular circuits.

Because of this convergence, a new intellectual core is emerging in the information sciences. The core contains material from a spectrum of disciplines: algorithms, networks, machine learning, statistics, optimization, signal processing, and the underlying mathematics. But each area is enriched by the broader context. For instance, the study of algorithms now encompasses the traditional discrete problems of computer science, the continuous problems of applied mathematics, as well as worst-case and average-case perspectives.

The CMS PhD program is designed around the new information science core. This core provides the ideal foundation for future applications across the sciences, engineering, and beyond. Our approach requires the mastery of the following ways of thinking about information science:

**Interpret "information" and "computation" broadly.**We study mechanisms that communicate, store, and process information. These structures might be etched in silicon and called hardware or written in code and called software. But the same mechanisms may be expressed in nucleotides and called DNA. They also arise in our society, where they are called social networks or markets. Our view encompasses all of these manifestations.**Algorithmic thinking is the foundation.**The modern world demands the ability to think algorithmically. Algorithms are not just the basis for advanced computer systems, but they help us understand biological organisms and auction design and more.**Data is central.**Data is being collected at an unprecedented speed and scale. Every area of science and society will be transformed as researchers learn to use this data to develop and test new hypotheses. To unlock this potential, we need to develop reliable algorithms for extracting information and making decisions based on data.**Seek rigor and relevance.**The CMS Program focuses on the theoretical core of information science. We believe that principled and rigorous methods provide the only solid basis for progress. But we also insist on research that is relevant to applications, and we train students to work at the interface of information science and other disciplines.

Students may select a research adviser from any of the 30+ faculty affiliated with the CMS Department, including specialists in Applied & Computational Mathematics, Biological Engineering, Computation & Neural Systems, Computer Science, Control & Dynamical Systems, Economics, Electrical Engineering, Mechanical Engineering, Philosophy, and Physics.

**Graduate Program Details and Requirements**

Requirements for the Computing and Mathematical Sciences graduate program are listed in the current (2021-22) Caltech Catalog, starting on page 411.

Further details and advice can be found here: Navigating the Ph.D. Options in CMS

**Graduate Options Administrator**

Maria Lopez

mlopez@cms.caltech.edu

(626) 395-3034

**Graduate Option Representative**

Joel Tropp

Computing and Mathematical Sciences Option Representative