Network Science - Applied Mathematics
Academic Certificate in Network Science
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Professor Ralucca Gera, Ph.D.
260 Spanagel Hall,
Applied Mathematics Department
Naval Postgraduate School
Phone: (831) 656-2230
Fax: (831) 656-2355
The Academic Certificate in Network Science provides education in the use of mathematical methods for the analysis, understanding, and exploitation of complex networks. Network Science has emerged as an area critical to the success of the mission of the Navy and the Department of Defense because of the central role it plays in cyber-security, network-centric warfare, and other related areas of critical interest. A thorough understanding of the underlying mathematics is essential for the correct interpretation and further development of practical methods, models, and approaches to problems involving complex networks. The certificate program is designed to provide that very background. Upon successful completion of the course work, students will be awarded a certificate of accomplishment in keeping with standard practices of the Naval Postgraduate School.
Requirements for Entry
Prospective students must have taken a discrete mathematics class at NPS (or equivalent from other institutions): MA1025, MA 2025, or MA3025. Please email Prof. Gera for more information.
Program entry dates are flexible and students who wish to pursue this certificate should coordinate with the program manager. Generally students enter start it in the Fall quarter, as MA4027 is offered every Fall, and MA4404 is offered every Winter (the electives are offered throughout the year).
Variable, usually 2-3 quarters. Once you enrolled in the courses, please use this link to apply for the certificate: Academic Certificate Enrollment Request Form using your primary curriculum, and then adding curriculum 200 for the Network Science Academic Certificate.
MA Academic Certificate Requirements
To earn the academic certificate students must pass all four courses with a C+ (2.3 Quality Point Rating (QPR)) or better in each course and an overall QPR of 3.0 or better. Students earning grades below these standards will need to retake the courses to bring their grades within standards or they will be withdrawn from the program.
(1) MA4027 Graph Theory and Applications (4-0) offered in the Fall quarters
Advanced topics in the theory of graphs and digraphs. Topics include graph coloring, Eulerian and Hamiltonian graphs, perfect graphs, matching and covering, tournaments, and networks. Application areas with DoD/DoN relevance range from mathematics to computer science and operations research, including applications to coding theory, searching and sorting, resource allocation, and network design. Prerequisites: MA3025.
(2) MA4404 Structure and Analysis of Complex Networks (4-0) offered in the Winter quarters
The course focuses on the emerging science of complex networks and their applications, through an introduction to techniques and models for understanding and predicting their behavior. The topics discussed will be building mainly on graph theory concepts, and they will address the mathematics of networks, their applications to the computer networks and social networks, and their use in research. The students will learn the fundamentals of dynamically evolving complex networks, study current research in the field, and apply their knowledge in the analysis of real network systems through a final project. DoD applications include security of critical communication infrastructure.
(3) One of the following courses:
- MA4394 Topics in Network Science (4-0) Offered any quarter that there are enough requests. This course focuses on the emerging field of network science. The students will learn about the ongoing research in the field by listening to conference presentations (prerecorded or in person if possible to attend conferences), and applying the learned knowledge to a research project. If the research project is used towards a funded research, then (1) students' visit to sponsors will be included during the quarter (if feasible) or virtual conversations with sponsors are facilitated, and (2) a final presentation to the sponsor is anticipated upon the completion of the project. There is no set content for students, as they will be exposed to current topics in the network science field at the time. Prerequisites: consent of instructor (Prof. Ralucca Gera).
- MA4400 Cooperation and Competition (4-0) Offered in the Summer quarters The course will develop game theoretic concepts in evaluations of the importance of players in bargaining situations and of elements in networks. Topics covered include cooperative and noncooperative games, bargaining, the Shapley Value, and coalitions. The course will study applications to military problems and applications to economics, political science, and biology. There will be extensive reading from the literature. Prerequisites: MA3042, OA3201, and an introductory course in probability.
- CS4558 Network Traffic Analysis (3-2). Offered in the Fall quarters Explores fundamentals of packet-switched network traffic analysis at the network layer and above as applied to problems in traffic engineering, economics, security, etc. Explores the design and integration of analytic tools and techniques into the fabric of the network including: spatial and temporal anomaly detection, origin-destination matrix estimation, application mix determination, deep-packet inspection, fingerprinting, intrusion detection and insider threat mitigation. Finally, the course covers active defense and offensive methods reliant on traffic analysis. Prerequisites: CS3502 and CS4550 or equivalent.
- OA4202 Network Flows and Graphs (4-0) Offered in the Summer quarters Introduction to formulation and solution of problems involving networks, such as maximum flow, shortest route, minimum cost flows, and PERT/CPM. Elements of graph theory, data structure, algorithms, and computational complexity. Applications to production and inventory, routing, scheduling, network interdiction, and personnel management. Prerequisite: OA3201.
- EC4770 Wireless Communications Network Security (3-2) Examines the impact of the radio frequency environment on the security of wireless communications networks. Specifically, examines security primitives including confidentiality assurance, integrity and authentication and encryption mechanisms and their impact on different network topologies. Various types of ciphers such as block and stream ciphers and their principles/implementation are studied. Basic encryption algorithms including the Data Encryption Standard (DES) and Advanced Encryption Standard (AES) are examined along with various key establishment and authentication protocols. Public Key Cryptography (PKC) and its variants (RSA, Diffie-Hellman) are discussed. Discusses approaches to integrity assurance in the form of cryptographic hash functions. Security protocols for the TCP/IP protocol stack are discussed including the EAP, SSL/TLS and IPSec. Examines all of the above factors in the context of a variety of topologies including personal area networks (PAN-Security in Bluetooth), wireless local area networks (WLAN), metropolitan area networks (MAN-WiMax and LTE), and wide area networks (WAN). Analyzes and compares protocol implementations such as Wired Equivalent Privacy (WEP), Wi-Fi Protected Access (WPA), and the Mobile Application Part (MAP) of Signaling System No. 7 (SS7). Also analyzes security in telephony, including 2G (GSM) and 3G (UMTS). Discuss general aspects of wireless communication vulnerabilities with example attacks. PREREQUISITES: EC2010, EC3710.
- DA4410 Models of Conflict This course deals with the problems faced by a rational decision-maker, trying to maximize some payoff in a social setting. A distinction will be made between Type I behavior (optimization in a game against nature,) Type II (optimization when faced with agents who react against the decision-maker¹s perceived behavior,) Type III (optimizations against strategic agents,) and Type IV (cooperation with other agents). Applications include arms race models, treaty inspections problems, monopolistic behavior, coalition formation, and pursuit games. The computer is used as a modeling tool. PREREQUISITE: DA2410
- DA 4600 Tracking and Disrupting Dark Networks This course focuses at how to illuminate networked adversaries. The course develops a deep understanding on how to use social network analysis metrics (e.g., topology, centrality, cohesion, brokerage) to better understand the relational aspects of dark networks and how to design intervention strategies for disrupting, destabilizing and possibly destroying dark networks. The course's first objective is to teach students how to identify and describe these networks and their dynamics. We use various software packages (e.g. Inflow, e.g. Analyst's Notebook) to aid in the identification and description effort. The second objective is to design intervention strategies to disrupt, destabilize and possibly destroy dark networks once they have been identified and described. Students are expected to focus their interventions at the tactical and operational levels, although some attention is given to the strategic and policy levels.