Math 7341 | Probability 2 | Spring 2025
This course will educate a cohort of applied mathematicians in advanced probabilistic thinking. It will focus on a combination of theory, calculation, and simulation. After a review of the essentials of probability theory, the emphasis is on developing the technical tools needed to build and analyse essential stochastic processes, which are broadly used in mathematical modelling of stochastic phenomena.
Course Description
During this course you will learn:
- A refresher or random variables, the calculus of probability, conditional probabilities and conditional expectations.
- Understand the construction, and core properties, of fundamental stochastic processes including counting processes, renewal processes, continuous time Markov processes, and their modeling applications.
- Understand essential properties of the likelihood of rare events and how to compute approximations to them.
The course will emphasise calculus, probabilistic thinking, and the use of computational environments to inform, simulate, and evaluate results. The course will include problem-solving sessions.
Pre-Requisites
MATH7241 Probability1 or IE6200 Engineering Probability and Statistics. Some familiarity with a computational environment (MATLAB, Python, Octave, etc.)
Course Grading
The grades will be:
- 12% per homework (total 60%).
- Final project 30%.
- Class participation 10%.
Instructor
Ken Duffy
Professor of Mathematics, and Electrical and Computer Engineering
Ken R. Duffy is a Professor of Mathematics and Professor of Electrical and Computer Engineering at Northeastern University. He earned his B.A. and Ph.D. degrees from Trinity College Dublin, Ireland. He was previously a Professor at Maynooth University, Ireland, where he was the Director at the Hamilton Institute, an interdisciplinary research institute focusing on applied mathematics, and a co-Director of the SFI Centre for Research Training in Foundations of Data Science.
His research focuses on probability and statistics, with applications in various engineering and scientific fields. His work in communications has received several awards, including the 2015 Best Paper Award at the IEEE International Conference on Communications, the 2019 IEEE Transactions on Network Science and Engineering Best Paper Award, the Best Research Demo Award at COMSNETS 2022, the Best Demo Award at COMSNETS 2023, and the best paper award from IEEE MILCOM 2024.
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EECE 7332 | Making Networks Reliable: An Introduction to Coding Theory
This course will educate a cohort of engineers capable of selecting, designing, and deploying erasure and error-correcting codes suitable for current and forthcoming technologies to make new networks that are reliable, fast, efficient, and fit for modern purposes.
In our data-driven world, the storage and transport of digital information is a key component underpinning all technologies. Low-latency, high-fidelity access to information is central to enabling algorithms that impact how we work, are entertaining, travel, and, indeed, our healthcare.
Yet all digital data is potentially subject to corruption when stored or communicated, which can have damaging consequences. Erasure and error-correcting codes are widely deployed to enable the accurate recovery of information. Still, new applications, including distributed storage, AR/VR, and V2X, are placing previously unforeseen demands, requiring further innovation to create reliable networks that fit contemporary requirements.
Course Description
During this course you will learn:
- The demands of new applications.
- Recent innovations in coding.
- How erasure and error correction codes and decoders are designed and how they work. How to create software implementations of encoders and decoders to rectify corrupted data.
Course Contents
- The course introduces modern approaches to ensuring reliable network communication and storage, covering theory and use cases.
- After an accessible, engineering-centric introduction to Galois fields, we present erasure coding and decoding, with applications to coding-based protocols that reduce delays over links and networks (network coding), post-quantum security, and speed-up of distributed computation.
- The second part considers error correction, starting with a brief overview of channel capacity. We begin with hard detection, as in storage systems.
- We introduce common codes and decoding using guessing random additive noise decoding (GRAND), which can decode any code.
- We generalize to using detector-generated information (soft information) and show how GRAND can be extended to soft information systems, with examples such as CA-Polar decoding.
- We discuss hardware implementation and realization in silicon.
Pre-Requisites
There are no formal prerequisites, but familiarity with linear algebra and probability is essential, as is familiarity with MATLAB, Python, or equivalent. Reach out to the instructor if you are unsure you meet the requirements.
Course Grading
The grades will be:
- 12% per homework (total 60%).
- Final project 30%.
- Class participation 10%.
Instructor
Ken Duffy
Professor of Electrical and Computer Engineering, and Mathematics
Ken R. Duffy is a Professor of Electrical and Computer Engineering and a Professor of Mathematics at Northeastern University. He earned his B.A. and Ph.D. degrees from Trinity College Dublin, Ireland. He was previously a Professor at Maynooth University, Ireland, where he was the Director at the Hamilton Institute, an interdisciplinary research institute focusing on applied mathematics, and a co-Director of the SFI Centre for Research Training in Foundations of Data Science.
His research focuses on probability and statistics, with applications in various engineering and scientific fields. His work in communications has received several awards, including the 2015 Best Paper Award at the IEEE International Conference on Communications, the 2019 IEEE Transactions on Network Science and Engineering Best Paper Award, the Best Research Demo Award at COMSNETS 2022 and the Best Demo Award at COMSNETS 2023.