### EE597: Wireless Networks

Wireless networks play an increasingly important role in the world of communications. This course provides an introduction to various current and next generation wireless networking technologies, and undertakes a detailed exploration of fundamental architectural and design principles used at all layers. Related protocols and their performance are studied using formal analytical tools and realistic simulations.

The course discusses cellular networks, WLANs/WiFi, sensor networks, mobile ad-hoc networks and intermittently connected mobile networks. It covers topics from: (i) the Physical Layer: radio propagation, modulation, coding, wideband approaches (CDMA, OFDM), diversity and MIMO, (ii) the Link Layer: low-power listening, Aloha, CSMA-CA, channelized multiple access (TDMA/FDMA/CDMA), power and rate control, single-hop uplink/downlink scheduling, multihop scheduling, (iii) the Network Layer: link metric estimation and neighborhood table management, opportunistic routing, backpressure routing, network coding and cooperative routing, routing with mobility and intermittent contacts, and (iv) the Transport Layer: TCP over wireless, congestion sharing, explicit and precise rate control, utility optimization.

### EE503: Probability for Electrical and Computer Engineers

Probabilistic tools are among the most useful for modelling real systems and doing performance analysis. As a result, they are used extensively in a number of Electrical and Computer Engineering areas. This course provides a solid basis of probability theory and related topics for graduate students in Electrical and Computer Engineering and prepares the students for many of the Electrical and Computer engineering graduate classes that require a strong understanding of probability. The course covers the material from first principles in a more rigorous manner than is typically found in undergraduate probability classes in Engineering. Major topics covered include but are not limited to sets, sigma algebras, probability axioms, discrete and continuous random variables, expectation and moments, functions of multiple random variables, covariance and correlation, conditional probability and expectation, limit theorems, stochastic processes, discrete and continuous time Markov chains, and a brief introduction to queueing theory.

### EE650: Advanced Topics in Computer Networks – Useful mathematical tools for analyzing wired and wireless networks

The Internet has grown from a small scale research network to an immense world wide infrastructure. Analyzing the performance of such a large scale system is a challenging task that requires either extensive/costly experiments, or carefully chosen mathematical tools. At the same time, it has become apparent that wireless networks are going to play an increasingly important role in the world of communications. It is envisioned that in the near future the global network will consist of an Internet-like core and a number of wireless edge-networks like sensor, mobile ad-hoc, delay tolerant, and mesh networks. The goal of this course is to expose graduate students to the mathematical tools that have been successfully used to model and analyze wired networks like the Internet and wireless networks like sensor and ad-hoc ones.

The course will briefly revise basic probability and queueing principles through some examples. It will then present some or all of the following (time permitting) : (i) the use of Lyapunov functions in proving various stability and throughput results for network switches, (ii) some combinatorics used to analyze scheduling mechanisms in switches, (iii) fluid models used in modelling long-lived TCP flows, (iv) random walks on graphs and other random processes used to model mobility in wireless networks and, (v) probabilistic and combinatorial techniques used to analyze contention and routing performance in wireless networks, (vi) basic information theory concepts used to study the capacity of ad-hoc networks, (vi) basic elements of game theory used to devise network pricing schemes, and (vii) the notions of heavy-tailed distributions, self-similarity, and long range dependence that play an important role in the analysis of web and network traces.

For each topic, we will first introduce the corresponding research problem/area (e.g. switching), then we will present the corresponding mathematical tools/analysis (e.g. Lyapunov functions), and finally we will go through recent publications that have successfully applied these tools/analysis.

### EE465: Probabilistic Methods in Computer Systems Modelling

This class has evolved into EE503, see above.