Below are lists of relevant courses for graduate students of the interdisciplinary program in Applied Math for the Spring semester of 2026. The list is freely assembled by faculty affiliated with the program.
Spring Semester
| Course name + number | Lecturer | Description | Prerequisites |
| Deep Learning and Approximation Theory 196014 | Nadav Dym | The course will be devoted to approximation theory-type questions which are motivated by deep learning. You may be familiar with Weirstrass’s theorem which shows that polynomials are dense in the space of continuous functions. This is the type of results we will often be interested in, but the function spaces will be neural networks rather than polynomials. We will show that Neural Networks can also approximate all continuous functions. We will then discuss results that try to explain why neural networks are `better’ than polynomials for approximation. In the second part of the course we will focus on `invariant approximation’, where we aim to approximate continuous functions invariant to some group action via invariant neural networks- function spaces which have this same invariances. | A course in multivariate calculus. A course on metric spaces such as 104142 will be helpful. We will assume familiarity with notions such as open, closed and compact sets in high dimensions, and uniform convergence of functions |
| Analytical Methods for Differential Equations 01960012 | Lydia Peres Hari, Mathematics | The aim of the course Analytical Methods is to give the students the “standard toolbox” used by all those who deal with continuous Applied Mathematics , such as Mathematical Physics, Theoretical Physics etc.
These are the basic tools for solving differential equations, used by scientists in their everyday work, tools that do not call for the use of Functional Analysis. Our aim is to obtain solutions to differential equations, and not approximations (asymptotic or numeric). This course is aimed for graduate students in Applied Mathematics, Theoretical Mathematics, Physics, Chemistry, as well as various engineering disciplines that make use of differential equations. The course could also be relevant to strong and advanced undergraduate students. |
Calculus, ODEs, PDEs, Complex functions.
(Strong undergraduate students may take the course in parallel to taking PDE and Complex functions). |
| Transport phenomena – Fluid Flows 058127 graduate level | Alex Leshansky, Chemical Engineering | The course covers the fundamentals of low-Reynolds-number flows. It introduces Cartesian tensors (definitions, properties and operations), reviews differential mass and momentum balances, forces and and stresses, rate-of-strain tensors; equations of fluid flow; boundary conditions (rigid surface and free boundary); it further addresses general properties of Stokes (viscous) flows; their fundamental solutions via spherical harmonics and reviews classical problems of viscous flow, such as flow due to a point force, flow around a translating or rotating rigid particle, flow past a fluid droplet and gas bubble; the advanced topics, such as Helmholtz minimum rate-of-dissipation principle; the Reciprocal Theorem; Faxén laws, viscous resistance tensors; Boundary Integral Equations and others are reviewed. The frontal teaching is followed by a mini-project on a specific problem/topic in viscous flows (individual projects, in the format of “guided reading” and presentations) | Calculus, ODE’s, PDE’s, Undergraduate Fluid Mechanics |
| Optimal Control in Flight Systems 1 (00880751) | Christian Grussler,
Aerospace Engineering |
This course for the most part follows the book Luenberg – Optimization by Vector Space Methods, i.e., is a modern mathematically rigorous course on (in)finite-dimensional (non-)convex optimization with application to (control) engineering problems. The course includes topics such as:
The course also covers topics such as:
|
Recommended: Advanced Linear Algebra & Analysis, 00360106 or equivalent; ODE |
| Coding for Storage Systems 02360520 | Ronny Roth, Computer Science | https://webcourse.cs.technion.ac.il/02360520/Spring2025/ (access with Technion username and password), or https://ronny.cswp.cs.technion.ac.il/home/courses/constrained/
The magnetic disk and the optical disk as examples for input-constrained channels. Presentation and analysis of input-constrained channels. Construction methods of encoders. Bounds on the complexity of encoders. Decoding techniques for input-constrained channels.. |
The course assumes background in linear algebra (eigenvalues of a matrix), as well as familiarity with the concept of finite-state machines. The course has practical applications, but it is of theoretical nature. |
| Vision Aided Navigation (SLAM) 086761 |
Vadim Indelman,
Aerospace Engineering and Data and Decision Sciences |
The course focuses on fundamental topics in vision aided navigation (VAN) and simultaneous localization and mapping (SLAM), which are essential for autonomous operation in unknown, uncertain or dynamically changing environments.
Topics to be covered include: Bayesian inference, state of the art SLAM and VAN approaches, and bundle adjustment. Depending on progress, some of the following advanced topics will be also briefly covered: multi-robot cooperative localization and mapping, active SLAM and belief space planning, intro/overview of recent deep learning approaches. |
Random Signals, or Algorithms |
| Fundamentals of Hypersonic Gasdynamics 860800 | Michael Karp,
Aerospace Engineering |
Introduction. Inviscid hypersonic flow. Shock waves and expansion wave relations, approximate calculations of aerodynamic forces, similarity relations. Viscous hypersonic flow: boundary layer equations, hypersonic transition, aerodynamic heating, viscous interactions. Introduction to hot flows: equilibrium, frozen and nonequilibrium flows. | Basic Fluid Mechanics (Viscous and compressible flows) |
| Introduction to Bioinformatics 02360523 | Dvir Aran, Biology & CS | Introduction to Bioinformatics for Computer Science introduces students to biological and medical challenges while teaching core computational and data science techniques. Each lecture begins with real-world biological motivations—including DNA sequencing, gene expression analysis, precision medicine, cancer genomics, and CRISPR technology—followed by relevant computational approaches such as dynamic programming, clustering algorithms, machine learning, statistical inference, and specialized bioinformatics methods. The course covers comparative genomics, gene expression regulation, human genetics, and cutting-edge frontiers in single-cell genomics and genome engineering, while providing hands-on experience with major tools and databases. Through weekly lectures, tutorials, four assignments, and a final project, students develop an integrated understanding of how algorithms advance biomedical research and prepare for impactful careers where computational skills directly contribute to solving health challenges. | Biology 1
Programming |
| Colloidal particles and intermolecular forces 056396 | Ofer Manor, Chemical Engineering | This is an introductory course to the intermolecular interaction between nano- and microparticles in a solvent (colloids) that constitute a world located between molecules and macroscopic structures. In this world, colloidal particles share properties with the two different worlds they border: intermolecular interactions govern the dynamics of colloidal particles and interactions between particles and molecules and between particles themselves, as well as cause macroscopic, readable results, stable suspensions and the collapse of suspensions towards phase separation. In the course, we will learn about intermolecular interactions that translate to interparticle forces, and the use of these interactions to qualitatively and quantitatively describe coagulation kinetics and the stability of colloidal suspensions. In addition, we will learn about electrokinetic measurements of the electrical properties of particles that contribute to the stability of dispersions, and if the time is sufficient about statistical description of many-body interactions between particles (classical density functional theory) that give rise to solvent interactions and interactions between nanoparticles and microparticles, which make additional important interaction mechanisms between colloidal particles. The course grade is based on HW assignments and a final assignment. | Basic knowledge in thermodynamics, calculus, and ODEs |
| Deep learning for physiological signal analysis 3380200 | Joachim A. Behar
Biomedical Engineering |
The task of uncovering novel medical knowledge from complex, large-scale, and high-dimensional physiological patient data collected during medical care is crucial for driving innovation in medicine. This course aims to equip students with the skills to extract valuable medical insights from such data, which is essential for advancing medical breakthroughs. Students will gain an understanding of machine learning applications in the context of physiological time series analysis. We will examine common sources of continuous physiological signals recorded in medical practice and explore deep learning techniques for their analysis. The focus will be on using Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs), including Long Short-Term Memory (LSTM) and Gated Recurrent Units (GRU), to analyze continuous physiological time series. We will introduce recent approaches to self-supervised learning and how the resulting “foundation models” may be leveraged to improve model performance. Finally, emphasis will be placed on strategies for developing models with strong generalization capabilities. | Signals and systemCoding in Python(course for final BSc year and graduates) |
| Mathematical Foundations of Graph Deep Learning 1960016 | Ron Levie | Graph deep learning is a subfield of deep learning that focuses on using neural networks to analyze data represented as graphs. The course will begin with a general introduction to deep learning (no prior background in deep learning is required) and then proceed to develop deep learning methods for graphs. In addition to developing the methodology of graph neural networks (GNNs), the main focus will be on deriving mathematical theory to analyze the capabilities of GNNs. We will analyze properties such as generalization, universal approximation, and expressivity of GNNs. | Calculus, linear algebra, and probability theory. Knowledge in graph theory, point set topology, and functional analysis or measure theory will help, but is not necessary. |
| NONLINEAR VIBRATIONS (0360048) | Oded Gottlieb | Topics *Modeling (overview) and Classification of Nonlinear Systems: (i) review of low-order multi-degree-of-freedom systems (Lagrangian/Hamiltonian) and modal reduction (Galerkin ansatz) of continuous systems (extended Hamilotn’s principle). (ii) autonomous (self-excited) systems vs resonant (internal/combination) non-autonomous systems (external/parametric excitation). *Singular perturbation Methods for Weakly Nonlinear Systems: (i) generalized averaging (averaged Lagrangian), Lindstedt-Poincare’ method vs the multiple-scales method for multibody systems (ODEs) and continuous systems (PDEs). *Numerical Analysis for Strongly Nonlinear Systems: sampling of nonstationary vibrations (Poincare’ sections/spectral analysis), harmonic/spectral balance methods (ODEs). *Local Bifurcation: stability of equilibria (Routh-Hurwitz vs Liapunov functions) and orbital stability of periodic vibrations (Floquet theory), divergence (saddle-node/pitchfork) and flutter (Hopf) in slowly-varying evolution equations. *Global Bifurcation: perturbation of homoclinic (solitons) and heteroclinic (fronts) solutions, domains of attraction (robustness), superstructure in the bifurcation set (universality), sensitivity-to-initial-conditions (Chaos theory), synchronization and chimera states. The objectives of this graduate level course are to: (i) introduce, (ii) develop and (iii) apply the analytical (singular |
