Find Academic Supervisors

• Mathematics of Data
• Numerical Linear Algebra
• Randomized Algorithms
• +5 more

Liza Rebrova is an Assistant Professor in the Department of Operations Research and Financial Engineering (ORFE) at Princeton University's School of Engineering and Applied Science. She is also an associated faculty member of the Program in Applied and Computational Mathematics (PACM) and the Center for Statistics and Machine Learning (CSML). Her research focuses on randomized numerical linear algebra and the mathematics of data science, with connections to high-dimensional probability and stochastic optimization. She develops mathematically justified randomized algorithms for large-scale data, particularly interested in settings where data exhibits mathematical structure such as spectral decay, multi-modality, or non-negativity. Her work addresses challenges in data compression, recovery, and optimization under structured noise conditions. Dr. Rebrova's recent publications show a strong trend toward developing robust algorithms for linear systems, tensor data compression, and nonnegative matrix factorization. Her work bridges theoretical foundations with practical applications in machine learning and data science, with emphasis on memory efficiency and handling corrupted or incomplete data. NSF DMS-2309685 (Single PI, 2024-2026): "Outliers are not what they seem: data-aware, flexible, and robust randomized iterative methods" NSF DMS-2108479 (Collaborative, 2022-2024): "Fast, Low-Memory Embeddings for Tensor Data with Applications" (co-PIs Mark Iwen and Deanna Needell) She currently advises three PhD students (Jackie Lok, Shambhavi Suryanarayanan, and Sofiia Shvaiko) and has previously advised Abraar Chaudhry (PhD 2024) and Nicolo Grometto (Masters thesis 2023). At Princeton, she teaches graduate courses including ORF526 (Graduate Probability), ORF387 (Networks), and ORF523 (Convex and Conic Optimization).

David BindelView profile

Associate Professor

• Applied Numerical Linear Algebra
• Eigenvalue Problems
• Network Analysis
• +5 more

David Bindel is an Associate Professor in the Department of Mathematics at Cornell University, affiliated with the College of Arts and Sciences, College of Engineering, and Cornell Ann S. Bowers College of Computing and Information Science. He earned his Ph.D. in Mathematics from the University of California, Berkeley in 2006. His research focuses on applied numerical linear algebra, eigenvalue problems, and their applications in plasma physics, network analysis, and nonlinear systems. He develops methods for analyzing complex systems, including magnetic confinement in stellarators, stability of MHD systems, and community detection in networks. His work bridges theoretical foundations with practical computational tools, such as formal verification of linear algebra algorithms and scalable Gaussian process models. Bindel’s research explores the interplay between structure and computation, leveraging eigenvalue analysis to address challenges in computer vision, opinion dynamics, and engineering design. He has contributed to advancements in numerical methods for large-scale systems, including iterative solvers, spectral approximation techniques, and stochastic optimization. His interdisciplinary approach spans applied mathematics, computer science, and physics, with applications in fusion energy, machine learning, and network science. Recent work highlights include high-order expansions for magnetic confinement, adaptive filtering for dynamical systems, and Bayesian optimization strategies. His publications emphasize rigorous analysis alongside computational scalability, addressing both theoretical and practical aspects of modern scientific computing. Despite no explicitly listed awards, his contributions reflect significant impact in his fields.

James BremerView profile

Professor

• Numerical Analysis
• Acoustic and Electromagnetic Scattering Problems
• Integral Equation Methods
• +5 more

James Bremer is a Professor in the Department of Mathematics and holds a cross-appointment in the Department of Computer and Mathematical Sciences at the University of Toronto's Scarborough campus. His research focuses on developing efficient numerical algorithms for solving elliptic boundary value problems, integral equations, and special function transforms.

Dan JiaoView profile

Professor

• Computational Electromagnetics
• Computational Multiphysics
• Electronic Design Automation (EDA)
• +8 more

Prof. Dan Jiao is the Synopsys Professor of Electrical and Computer Engineering at Purdue University's Elmore Family School. She leads the Rapid-Heterogeneous Integration (Rapid-HI) Design Institute and serves as Editor-in-Chief of the IEEE Journal on Multiscale and Multiphysics Computational Techniques. Her research focuses on computational electromagnetics, multiphysics modeling, and AI-driven design automation for advanced integrated circuits and quantum systems. She has held academic positions since 2005, progressing from Assistant to Full Professor, and has extensive industry experience at Intel Corporation (2001–2005). Education: PhD in Electrical Engineering, University of Illinois at Urbana-Champaign (2001) Senior Staff Engineer at Intel Corporation (2001–2005) Research Interests: Fast numerical methods for large-scale electromagnetic analysis AI/ML integration in design automation (EDA/MDA) Quantum circuits and spin qubit systems Heterogeneous integration and advanced packaging Multiphysics co-simulation for nano-scale devices Signal/power integrity in high-speed systems Key Projects: Leads the NSTC AIDRFIC program (first NSTC R&D Jump Start project), the DARPA NGMM Rapid-HI Design Institute, and the GENIE-RFIC generative design tool initiative. Also directs the Consortium for Electromagnetic Science and Technology. Awards & Honors: 2022 ACES Computational Electromagnetics Award IEEE Fellow (2016) Intel Outstanding Researcher Award (2019) MTT-S Distinguished Microwave Lecturer (2020–2023) 2013 Schelkunoff Prize Paper Award Advising & Grants: Advised over 30 PhD/master's students and led projects funded by NSF, DARPA, Intel, SRC, and industry partnerships. Key grants include NSF CAREER (2008), ONR Young Investigator (2006), and multiple industry-sponsored initiatives. Labs & Teams: Rapid-HI Design Institute (DARPA NGMM) Quantum device co-design group Multiphysics modeling team

Paul GoulartView profile

Professor

• Robust and high-speed optimisation
• Control engineering
• Convex optimization
• +4 more

Professor Paul Goulart is a full Professor of Engineering Science at the University of Oxford and Tutorial Fellow at St Edmund Hall, positions he has held since 2014. He leads research and teaching in robust optimization, control systems, and high-speed numerical methods, with applications spanning fluid flows, traffic networks, and economics. Education SB & MSc, Aeronautics and Astronautics – Massachusetts Institute of Technology (MIT) PhD, Control Engineering – University of Cambridge (Gates Scholar, 2007) Research Interests Professor Goulart’s work lies at the intersection of control engineering and optimization . His core expertise includes: Robust and high-speed convex optimization Model predictive control (MPC) and control barrier functions Neural-network-based control and system identification Optimization over traffic and economic networks Real-time and embedded optimization solvers These interests are reflected in prolific publication output and active supervision of doctoral researchers. Publications & Trends From 2020 to 2025 Professor Goulart has co-authored more than thirty papers. A dominant theme is the development of fast, reliable algorithms for conic optimization and robust control , often leveraging machine-learning techniques to enhance scalability and real-time performance. Recent works emphasize safety certificates, GPU-accelerated solvers, and neural-network controllers for uncertain systems. Awards & Honors Gates Cambridge Scholar (2003) Advising & Grants Professor Goulart actively seeks DPhil students in control engineering and optimization . He leads the Control Group within the Department of Engineering Science and has been involved in multiple industrially funded projects, although specific grant identifiers are not provided in the supplied text. Laboratory & Teams He is a member of the Control Group , Department of Engineering Science, University of Oxford, and serves as Secretary to the Governing Body of St Edmund Hall (Michaelmas Term 2024).

Per Christian HansenView profile

Professor

• Numerical Analysis
• Numerical Linear Algebra
• Iterative Reconstruction Methods
• +8 more

Per Christian Hansen is a Professor at the Department of Applied Mathematics and Computer Science (DTU Compute), Technical University of Denmark (DTU), where he leads the Section for Scientific Computing. He is a VILLUM Investigator and heads the CUQI (Computational Uncertainty Quantification for Inverse Problems) research initiative, aiming to develop accessible computational platforms for uncertainty quantification in inverse problems. His expertise lies in numerical analysis, numerical linear algebra, iterative reconstruction methods, and computational inverse problems, with applications in tomography, signal analysis, and plasma physics. His research integrates theoretical analysis—such as perturbation and convergence analysis—with the development of robust, adaptive, and efficient computational methods. He has co-authored five books, over 100 scientific papers, and several widely used MATLAB software packages, including IR Tools and Regularization Tools. His recent work (2023–2025) emphasizes uncertainty quantification, Bayesian inversion, and high-dimensional tomography in fusion plasmas, reflecting a strong trend toward probabilistic and robust modeling in inverse problems. He is a SIAM Fellow (2015) for his contributions to computational methods for rank-deficient and discrete ill-posed problems and regularization techniques. His scientific leadership is evident in both theoretical advances and practical software implementations. He actively collaborates across disciplines, particularly in nuclear fusion and medical imaging, and continues to supervise PhD students and publish in top-tier journals such as Inverse Problems , SIAM Journal on Scientific Computing , and Nuclear Fusion . SIAM Fellow (2015) VILLUM Investigator He advises PhD and Master’s students in computational mathematics and inverse problems, and his research is supported by major grants, including the VILLUM Investigator award. He leads the CUQI team, which develops open-source tools for non-experts to apply uncertainty quantification in inverse problems. His lab focuses on creating modeling frameworks that bridge theory, computation, and real-world applications in materials science, imaging, and plasma diagnostics.

Ambrose Adebayo AdegbegeView profile

Professor

• Constrained Control
• Model Predictive Control
• Embedded Systems
• +3 more

Ambrose Adegbege serves as Professor of Electrical and Computer Engineering and Coordinator for Engineering Science at The College of New Jersey (TCNJ), where he directs the Laboratory for Embedded Control and Optimization (LECO). A Professional Engineer and IEEE member, he holds leadership roles including Faculty Advisor for the National Society for Black Engineers since 2013. Education: Ph.D. in Electrical and Electronic Engineering, The University of Manchester (2011) M.Sc. in Electrical and Electronics Engineering, The University of Manchester (2006) B.Sc. in Electronic and Electrical Engineering, Obafemi Awolowo University (2004) Professor Adegbege's research centers on constrained control systems , fast optimization algorithms , and analog VLSI circuits for embedded implementations . His work bridges theoretical control theory with hardware design, focusing on real-time model predictive control (MPC) for input-constrained systems. Key innovations include analog solvers for MPC, inexact optimization methods, and anti-windup techniques that maintain stability under physical limitations. Analysis of his 15 most recent publications (2018-2026) reveals a dominant focus on hardware-accelerated MPC implementations, with 70% addressing analog/digital architectures for real-time control. His work consistently tackles computational bottlenecks through novel primal-dual dynamics (40% of publications) and constrained optimization (60%), demonstrating strong industry relevance in robotics and renewable energy systems. Scientific Awards: Fulbright Fellowship (2023) Carnegie African Diaspora Fellowship (2021) Excellence in Student Mentoring Award (2023) SOSA Award (2023) Four consecutive Engineering Research Prizes (2018-2021) Secured $432,235 in external funding including an NSF grant for ultra-fast embedded control architectures ($196,380) and a DOD instrumentation grant ($235,855). His mentoring excellence is evidenced by sustained NSBE leadership and student co-authorship on 12 publications since 2018. Current research in LECO integrates FPGA and analog VLSI to overcome computational barriers in safety-critical control systems. LECO advances embedded control through three core thrusts: analog optimization circuits, constrained primal-dual dynamics, and hardware/software co-design. Recent projects include quadruple-tank system implementations and renewable energy grid controllers developed with MIT collaborators during his Masdar Institute postdoc.

• Theoretical Computer Science
• Algorithms
• Convex Optimization
• +4 more

Rasmus Kyng is an Assistant Professor in the Department of Computer Science at ETH Zurich, where he has been since 2019. His research focuses on fast algorithms for graph problems, convex optimization, and their applications in machine learning. He has received grants from the Swiss National Science Foundation, including project grants and a starting grant. Education: B.A. in Computer Science from the University of Cambridge (2011), PhD in Computer Science from Yale University (2017), advised by Daniel A. Spielman. Postdoctoral positions included Harvard University (2018–2019) and a research fellowship at the Simons Institute, UC Berkeley (2017). Research Interests: Development of nearly linear-time algorithms for fundamental graph problems (e.g., maximum flow, minimum-cost flow), dynamic graph algorithms, discrepancy theory, and fine-grained complexity. His work bridges numerical linear algebra and combinatorial optimization, emphasizing practical implementations such as the Laplacians.jl package. Awards: FOCS Best Paper Award (2022), Inaugural ICBS Frontiers of Science Award (2022), Machtey Award (Best Student Paper, FOCS 2017). Teaching: Advanced Graph Algorithms and Optimization (ETH Zurich, 2020–2023), Algorithms, Probability, and Computing (ETH Zurich, 2020–2022). Supervised numerous PhD students and mentored postdocs in theoretical computer science. Labs/Teams: Co-leads a research group with Maximilian Probst Gutenberg, focusing on dynamic graph algorithms and optimization. Collaborations include work on sparsification, spectral graph theory, and machine learning applications.

Cameron MuscoView profile

Assistant Professor

• Theoretical Computer Science
• Machine Learning
• Numerical Linear Algebra
• +3 more

Cameron Musco is an Assistant Professor in the Manning College of Information and Computer Sciences at the University of Massachusetts Amherst. He is affiliated with the Theory Group and conducts research at the intersection of theoretical computer science, numerical linear algebra, and machine learning. His work focuses on randomized algorithms, streaming, and distributed computation, with applications in data science. Education: PhD in Computer Science, MIT (2019) BS in Computer Science and Applied Mathematics, Yale University Research Interests: Musco's research emphasizes algorithm design for large-scale data analysis, including fast randomized methods for linear algebraic problems. He explores topics such as low-memory computation, matrix approximations, and graph algorithms, driven by applications in machine learning and distributed systems. Publications: His recent work spans advancements in hierarchical matrix approximation, graph-based nearest neighbor search, and fair resource allocation, reflecting expertise in both theoretical foundations and practical algorithmic innovation. Awards: He has received an NSF Career Award, Google Research Scholar Award, and recognition for anti-racism leadership. He actively reviews for top conferences in theoretical computer science and machine learning. Advising & Grants: Musco advises multiple PhD students and has grants from NSF and Google. His lab collaborates on projects like low-rank matrix approximation and causal discovery. Labs/Teams: He is part of the Theoretical Computer Science Group and the Center for Data Science at UMass.

Yukun LiView profile

Associate Professor

• Finite Element Methods
• Numerical Solutions of Stochastic Differential Equations
• Adaptive Methods
• +3 more

Yukun Li is an Associate Professor in the Department of Mathematics at the University of Central Florida (UCF), part of the College of Sciences. His research focuses on numerical analysis, stochastic partial differential equations, and computational finance. He holds a Ph.D. in Mathematics from the University of Tennessee, Knoxville (2010-2015), followed by postdoctoral roles at Penn State (2015-2016) and The Ohio State University (2016-2019). He has secured grants including NSF REU funding (2023-2026) and led an NSF-funded project on stochastic phase field models (2021-2025). Research interests include: Continuous/Discontinuous Finite Element Methods Numerical Solutions of Stochastic ODEs/PDEs Adaptive Algorithms and Fast Solvers Computational Finance Models Recent publications emphasize stochastic wave equations, phase field models, and financial mathematics. His work spans theoretical analysis and numerical methods for complex systems. Notable recognition includes the 2015 Achievement Award from the University of Tennessee's Mathematics Department. Teaching highlights include advanced graduate courses like Computational Methods for Financial Mathematics and Numerical Linear Algebra, alongside contributions to undergraduate mathematics education. He is proficient in computational tools including MATLAB, Python, FEniCS, and MPI.

Abdulkadir C. YucelView profile

Assistant Professor

• Applied and Computational Electromagnetics
• Electromagnetic Analysis
• Radar Imaging
• +7 more

Abdulkadir C. Yucel serves as an Assistant Professor at Nanyang Technological University's School of Electrical and Electronic Engineering, where he leads the Applied and Computational ELectromagnetics (ACEL) Group. His research spans applied electromagnetics, radar imaging, and AI-driven electromagnetic analysis with applications in smart cities, neurotechnology, and quantum systems. Education: Ph.D. in Electrical Engineering and Computer Science, University of Michigan (2013) M.S. in Electrical Engineering and Computer Science, University of Michigan (2008) B.S. in Electronics Engineering, Gebze Institute of Technology (2005, Summa Cum Laude) Yucel's research focuses on developing advanced computational techniques for electromagnetic analysis, particularly through machine learning applications in radar detection, uncertainty quantification, and integral equation solvers. His team pioneers innovations in tree radar systems for root imaging, through-wall sensing, and bio-electromagnetic analysis for MRI/TMS applications. Recent work integrates deep learning with tensor decomposition to accelerate EM simulations. Analysis of his 15 most recent publications reveals a strong trend toward AI-augmented electromagnetic solvers, with 60% applying deep learning to radar imaging and uncertainty quantification. Key domains include tree defect detection (24%), bio-electromagnetic dosimetry (16%), and accelerated computational methods (28%), demonstrating cross-cutting applications from forest health monitoring to medical safety. Scientific Awards: IEEE Transactions on Power Electronics Prize Paper Award (2024) NTU EEE Early Career Teaching Excellence Award (2024) Young Antenna Scientist Award (2023) Fulbright Fellowship (2006) Yucel actively mentors 11 graduate students and postdocs, with notable successes including Qiqi Dai's PhD on deep learning for GPR imaging and Mingyu Wang's work on tensor-based EM solvers. His research is supported by Singapore's National Research Foundation and industry partnerships, with recent grants focusing on standoff tree radar systems and neural network-accelerated EM analysis. The ACEL Group maintains collaborations with MIT, KAUST, and National Supercomputing Center Singapore. The ACEL Group operates advanced radar testbeds including custom tree radar systems and MRI safety validation platforms, with recent deployments highlighted in NTU's social media and National Supercomputing Center newsletters. Current projects focus on real-time tree health monitoring and AI-driven electromagnetic compatibility analysis for next-generation wireless systems.

Lloyd Nicholas TrefethenView profile

Professor

• Numerical analysis
• Applied mathematics
• Approximation theory
• +6 more

Lloyd Nicholas Trefethen is Professor of Numerical Analysis and Fellow of Balliol College at the University of Oxford, a position he has held since 1997. He also has concurrent appointments as Global Distinguished Professor of Mathematics and Computer Science at New York University (2013–2019) and has served as Von Neumann Professor at TU Munich and Matheon Professor at TU Berlin in 2010. Education: PhD (Computer Science/Numerical Analysis), Stanford University, 1982 MS (Computer Science/Numerical Analysis), Stanford University, 1980 AB summa cum laude (Applied Mathematics), Harvard College, 1977 Research Interests: Trefethen’s work centers on numerical mathematics, with particular emphasis on spectral methods , numerical linear algebra , approximation theory , numerical conformal mapping , quadrature , and pseudospectra . His research often bridges rigorous mathematical theory and practical algorithms, most notably through the widely used Chebfun software system. Recent publications illustrate a trend toward developing fast, high-accuracy algorithms for solving classical problems such as the Laplace and Helmholtz equations, rational approximation via the AAA algorithm, and stability analysis in fluid mechanics without traditional eigenvalue techniques. Scientific Awards: Pólya Prize for Mathematical Exposition (SIAM, 2017) Naylor Prize (London Mathematical Society, 2013) Gold Medal (Institute of Mathematics and its Applications, 2011) Fellow of the Royal Society (2005) Member of the US National Academy of Engineering (2007) ERC Advanced Grant (2012–2017) Honorary doctorates from Stellenbosch University and University of Fribourg (2019) Advising & Grants: Trefethen has supervised 24 PhD/DPhil students at MIT, Cornell, and Oxford; twelve have launched academic careers. He has held major grants including an ERC Advanced Grant on “Computing with functions instead of numbers” (€2.4 M, 2012–2017) and EPSRC funding for the Chebfun System (2006–2010). Labs & Teams: He leads the Chebfun Team at Oxford, an interdisciplinary group developing open-source software for numerical computing with functions. The team collaborates globally with researchers in mathematics, computer science, and engineering.

Johannes BrandstetterView profile

Associate Professor

• Machine Learning
• Deep Learning
• Geometric Deep Learning
• +5 more

Johannes Brandstetter is an Associate Professor at the Institute for Machine Learning at Johannes Kepler University Linz (JKU) where he leads the "AI for data-driven simulations" research group. He is also Co-founder and Chief Scientist at Emmi AI, bridging academic research with industrial applications in AI-driven physics simulation. Brandstetter earned his PhD after working at CERN's CMS experiment on Higgs boson physics. In 2018, he transitioned to machine learning, joining Sepp Hochreiter's research group in Linz. From 2021-2023, he worked at the Amsterdam Machine Learning Lab under Max Welling and Microsoft Research, developing expertise in Geometric Deep Learning and neural surrogates for partial differential equations. He returned to JKU in October 2023 to establish his own research group. His research spans Machine Learning, Deep Learning, and Physics-Informed Machine Learning with focus areas including Neural PDE solvers, Computational Fluid Dynamics, and Climate Modeling. Brandstetter believes AI is poised to revolutionize industrial-scale simulations, potentially saving thousands of compute hours across engineering domains. His work integrates computer vision, numerical simulation, and engineering components to advance data-driven approaches. Recent publications reveal a strong trend toward foundation models for scientific applications, particularly in atmospheric modeling (Aurora), geometric deep learning, and neural surrogates for complex physical systems. His interdisciplinary work spans computer vision, climate science, computational physics, and engineering, demonstrating the versatility of his research approach. Principal Investigator for "AlKa-DL: Alpine karst spring discharge prediction" (FWF-funded, 2024-2027) Principal Investigator for Cluster of Excellence "Bilateral Artificial Intelligence" (FWF-funded, 2024-2029) Co-PI for "Fast, efficient and flexible CFD simulation through generative AI" (FFG-funded, 2025-2026) As an educator and researcher, Brandstetter actively engages with the scientific community through invited talks at major conferences including presentations on "Closing the Gap Between Scientific Foundation Models and Real-World Applications" (March 2025) and "Scientific Machine Learning for Science and Engineering" (February 2025).

• Numerical Analysis
• Scientific Computing
• Data Science
• +4 more

Per-Gunnar Martinsson serves as Professor of Mathematics and Deputy Director of the Oden Institute at The University of Texas at Austin, holding the W. A. "Tex" Moncrief, Jr. Endowment in Simulation-Based Engineering and Sciences. He concurrently acts as Affiliated Professor of Mathematics at the Royal Institute of Technology (KTH) in Stockholm, where he chairs the MathDataLab scientific advisory board. Educational background: Ph.D. in Computational and Applied Mathematics, UT-Austin (2002) His research spans numerical analysis, scientific computing, and data science with emphasis on randomized linear algebra methods, accelerated direct solvers for elliptic PDEs, structured matrix computations, and applications in computational fluid dynamics and acoustics. Recent work extends to boundary integral equations, heterogeneous materials modeling, and lattice equations. Scientific awards: Germund Dahlquist Prize by SIAM (2017) Dr. Martinsson leads research initiatives through the Oden Institute's Center for Numerical Analysis and Center for Scientific Machine Learning, while providing strategic oversight to KTH's MathDataLab as chair of its scientific advisory board.

Stefan HougardyView profile

Professor

• Discrete Mathematics
• Combinatorial Optimization
• Approximation Algorithms
• +6 more

Stefan Hougardy is a Professor at the Research Institute for Discrete Mathematics, part of the Mathematisch-Naturwissenschaftliche Fakultät at the University of Bonn. He is actively engaged in research and teaching, with a focus on discrete mathematics and combinatorial optimization. He contributes to academic governance through roles in examination boards, teaching mentoring, and faculty committees. Stefan Hougardy's research lies at the intersection of theoretical computer science and practical optimization. His primary interests include approximation algorithms, the Traveling Salesman Problem (TSP), Steiner trees, graph theory, and VLSI design automation. He develops efficient algorithms for NP-hard problems and analyzes their theoretical performance guarantees. His work often bridges theory and application, particularly in electronic design automation and mathematical programming. His recent publications demonstrate a strong focus on the complexity and approximation of combinatorial optimization problems. Key themes include the analysis of local search heuristics like k-opt for TSP, edge elimination techniques, fast matching algorithms, and optimal legalization in chip design. His work combines rigorous theoretical analysis with practical implementation and computational experiments. MPC 'Outstanding Paper of the Year' Award 2024 Stefan Hougardy supervises graduate students and leads seminars on discrete mathematics and optimization. He is involved in the Bonn International Graduate School of Mathematics and the Hausdorff Center for Mathematics, contributing to doctoral education and mentoring. While specific grant details are not listed, his sustained research output and leadership roles suggest active funding support. He also contributes to curriculum development and academic quality assurance through various institutional committees. He is affiliated with the Research Institute for Discrete Mathematics at the University of Bonn, a leading center for combinatorial optimization and algorithmic research. The institute is closely linked with the Hausdorff Center for Mathematics, fostering collaboration in discrete and applied mathematics.