## Program: Complex Systems Certificate

## Program Description

The field of complex systems is relatively young and evolving, encompassing a wide range of disciplines in the sciences, engineering, computer science, and mathematics. In this context, a “complex system” is defined as an engineered or natural system that is characterized by dynamical properties and unobservable interactions that may not be apparent from observations of its emergent behaviors. Moreover, those dynamics can be intelligent and potentially adversarial. With a strong emphasis on the application of mathematical theory, computational techniques, and modeling in the program, students and faculty will engage in research on complex systems.

The goals of this certificate are to:

- Train and prepare the next-generation scientists and engineers to formulate and solve complex systems problems.
- Advance CSUNâ€™s mission to engage students in creative activities, particularly those from underrepresented in STEM.
- Provide the needed background training for prospective Ph.D. students in complex systems.
- Generate opportunities for industry employees to continue their interdisciplinary education and advance their careers.

This program will prepare students to apply mathematical theory, data-enabled modeling, and computational techniques to the study of complex systems in the natural and engineered world. Coursework will focus on the theoretical foundations of complex systems analysis with an emphasis on applications.

## Program Requirements

### A. Admission Requirements

A master’s degree in STEM fields is required for admission to the certificate program. Students enrolled in the certificate program are eligible to apply to the Ph.D. program. The coursework will be transferred, if admitted. The students in the Ph.D. program will automatically be enrolled in the certificate program and, therefore, will be granted this certificate along with their Ph.D. degree in complex systems.

### B. Course Requirements

Students must complete 19 units in three semesters as follows.

#### Semester 1 (6 units)

##### Select three courses from the following:

CPLX 701 Mathematical Foundations for Complex Systems (2)

CPLX 702 Physics Foundations for Complex Systems (2)

CPLX 703 Chemistry Foundations for Complex Systems (2)

CPLX 704 Biology Foundations for Complex Systems (2)

CPLX 705 Computer Science Foundations for Complex Systems (2)

CPLX 706 Engineer Foundations for Complex Systems (2)

#### Semester 2 (8 units)

##### Complete two additional courses from the above list and the following:

CPLX 710A Complex Systems I (4)

#### Semester 3 (5 units)

##### Complete the following two courses:

CPLX 710B Complex Systems II (4)

CPLX 791 Research Seminar (1)

#### Total Units for the Certificate: 19

## Contact

Department of Mathematics

Chair: Katherine Stevenson

Live Oak Hall (LO) 1300

(818) 677-2721

## Program Learning Outcomes

Students receiving a Complex Systems Certificate will be able to:

- Understand the nature of complex systems.
- Model or mathematically describe complex systems or systems of systems.
- Analyze processes and phenomena with respect to agents, complex systems of agents, or systems of systems using applied mathematical and computational frameworks.
- Demonstrate competency in quantitative and scientific reasoning.
- Demonstrate a depth of understanding of the essential content and principal modes of inquiry in engineering, computer science, and/or the sciences.
- Evaluate research findings and the appropriate literature.