Learning by building.
Our curricular offerings bring world-class training in robotics and AI to Armenia — taught by leading researchers and connected to real platforms, real problems, and a global network of mentors.
Three ways to learn with us.
Courses & Seminars
Semester courses and research seminars covering the foundations of AI, robotics, and the mathematical sciences — from first principles to the frontier.
Workshops & Schools
Intensive summer and winter schools, bootcamps, and hands-on workshops built around modern robotic platforms.
Mentorship & Fellowships
Research apprenticeships and fellowships pairing students with scientists from Armenia and the diaspora.
Learning Paths
↝ Undergraduate minor track in Physical AI, with Engineering focus
↝ Undergraduaate minor track in Physical AI, with Computer Science focus
↝ Mathematics Honors track
Course catalog.
Courses may be offered at the American University of Armenia, at Yerevan State University, and at Polytechnic University. To view schedule and details, use the button below.
Schedule DetailsBuilding LLMs
The course starts with the basics of backpropagation and build up to modern deep neural networks, like GPT. Language models are an excellent place to learn deep learning, even if your intention is to eventually go to other areas like computer vision because most of what you learn will be immediately transferable. This is why we dive into and focus on languade models.
Prerequisites: solid programming (Python), intro-level math (e.g. derivative, gaussian).
Deep Learning for Physical Systems
Deep Learning focuses on the theory and practice of neural networks that power modern AI systems. Students will study key architectures, training algorithms, and real-world applications, gaining an understanding of how deep learning models are designed and applied in practice.
Reinforcement Learning, Policy Optimization
Scientific Computing
Scientific computing is a cutting edge field at the intersection of mathematics, computing and the natural sciences/engineering fields. Its aim is to solve problems in science and engineering by developing numerical simulations of physical, chemical, mechanical and other phenomena. It has been an indispensable part of any engineering project or scientific endeavor since the dawn of computing, and yet, due to advances in the scientific computing field as well as the increasing availability of computational power, it is more important today than ever before.
Dynamical Systems, Control, Estimation
This course introduces fundamental concepts in robot control, bridging classical control theory and modern applications in robotic systems. Students will gain theoretical foundations in modeling, analysis, and controller design, while applying these concepts through hands-on experiments with both single-degree-of-freedom mechanisms and multi-rotor aerial robots. By the end of the course, students will be able to design, implement, and test controllers on physical robotic platforms, developing intuition for stability, performance trade-offs, and real-world implementation challenges.
Robot Mechanics, Kinematics, Dynamics
Sensing, Signals, Multimodal Transduction
A basic course in signal and image processing introduces students to the core concepts and techniques used to analyze and process signals (audio, ECG, etc.) and images (photos, medical images). The course covers fundamentals such as sampling, filtering, and Fourier analysis, and extends to 2D signals – images studying various topics like enhancement, noise reduction, and edge detection. Students will gain hands-on experience with tools to implement algorithms and solve practical problems. Students will also understand how to process and interpret signals and images for applications in the field of ICT, specifically, in image communications, multimedia, and computer vision.
Simulation, Digital Twins, Differentiable Physics
Algebra and Number Theory
The course is open to all students interested in algebra or number theory. Some prior knowledge of Linear Algebra will be helpful but not necessary. The course will cover the basic notions of abstract algebra (groups, rings, etc) with a view toward applications in number theory.
Complex Analysis
This course provides a comprehensive introduction to Complex Analysis, focusing on the study of functions of a complex variable. Students will explore key concepts such as analytic functions, complex integration, power series, residues, and conformal mappings.
Differential equations
The course is aimed at second-year students (and above) who have successfully completed the courses of Mathematical analysis I and II. Other students may be admitted after a placement test.
Functional Analysis
The course is aimed at third-year students (and above) of the mathematics, physics and computer science faculties. It may be accessible to second-year students with excellent knowledge of mathematical analysis and linear algebra.
Galois Theory
This course introduces undergraduate students to one of the most beautiful achievements of modern algebra: Galois theory, the study of symmetries of polynomial equations. Starting from classical questions about solving equations by radicals, we will develop the language of groups and fields, culminating in the fundamental theorem of Galois theory. Along the way, students will see how abstract algebra connects with concrete problems. This course is aimed at undergraduates with an interest in algebra and number theory. No prior exposure to Galois theory will be assumed.
Mathematical Analysis 1
The course is open to first-year students (and above) of the mathematics, physics and computer science faculties of all universities.
The purpose of the first part of the course is to study the basics of differential calculus for functions of one variable. The course will cover such concepts as the set of real numbers, limit, continuousfunction, and derivative. Solutions to various physical problems will be given as illustrations.
Mathematical Analysis 2
The second part of the mathematical analysis course is devoted to the study of the Riemann integral for functions of one variable, as well as the fundamentals of differential calculus for functions of several variables. Theoretical results will be illustrated by solving various problems, primarily from physics.
The course is based on the textbook V. A. Zorich, Mathematical Analysis-I, 2004
Mathematical Logic
Comfort with definitions and proofs, as well as familiarity with mathematical structures such as graphs, partial orders, groups, rings, fields, and vector spaces.
The course will introduce the main ideas and basic results of mathematical logic from a fairly modern prospective, providing a number of applications to other fields of mathematics such as combinatorics, Ramsey theory, algebra, and algebraic geometry. It will consist of two parts: model theory and computability theory. Model theory is a study of mathematical structures, examples of which include groups, rings, fields, graphs, and partial orders. We will first abstractly study structures and definability, theories, models and categoricity, as well as formal proofs, and this will culminate in proofs of the Gödel Completeness and Compactness Theorems – two of the most useful tools of logic. Then we will apply the developed techniques to concrete examples such as the structure of natural numbers and algebraically closed fields; the latter will yield a rigorous proof of the Lefschetz Principle (a first-order sentence is true in the field of complex numbers if and only if it is true in all algebraically closed fields of sufficiently large characteristic) and an amusingly slick proof of Ax's theorem (if a polynomial function ℂn → ℂn is injective, then it is surjective). We will also discuss applications of the Compactness theorem in deriving finitary analogues of the infinitary combinatorial statements such as the infinite Ramsey theorem, van der Waerden's or Szemerédi's theorems, graph colorings, etc.
Literature
- A. TSERUNYAN, Mathematical Logic, lecture notes [pdf]
- C. C. LEARY, L. KRISTIANSEN, A Friendly Introduction to Mathematical Logic, 2nd Edition [free download]
- A. TSERUNYAN, A quick introduction to basic set theory, 20-page lecture notes and problems for undergraduates [pdf]
Mathematical methods of classical mechanics
The aim of the course is to study in depth some sections of classical mechanics and consider various examples. It is planned to study sections 1-31 of V. I. Arnold's book.
Measure theory and ergodic horizons
Absolute comfort with definitions and proofs, as well as familiarity with basic real analysis and abstract metric spaces (firm knowledge of open/closed sets, compactness, convergence, continuity, etc).
Literature
- T. Tao's blog: courses 245A and 245B
- T. Tao, An introduction to measure theory [link, but no need to buy]
- G. Folland, Real Analysis [link, but no need to buy]
- R. Bass, Real Analysis for Graduate Students [free download]
- A. Tserunyan, Cantor sets [pdf]
Topics
- Measures, their construction and properties
- Polish spaces, σ-algebras and Borel sets, measurable spaces
- Measures and premeasures
- Constructions of Bernoulli(p) measures on 2ℕ and the Lebesgue measure on ℝd
- Carathéodory's extension theorem: outer measures and two different proofs (by C. Carathéodory and T. Tao)
- Measurable and non-measurable sets
- Pocket tools: increasing unions/decreasing intersections, Borel–Cantelli lemmas, measure exhaustion and application: Sierpiński's theorem for atomless measures
- Borel measures: their regularity (for metric spaces) and tightness (for Polish spaces), the 99% lemma for Bernoulli(p) and Lebesgue measures
- Applications: ergodic group actions/equivalence relations and non-measurability of transversals
- Locally finite Borel measures on ℝ and increasing right-continuous functions
- Measurable functions and integration
- Measurable functions, Luzin's theorem, push-forward measures, and random objects such as random graphs
- Application: Poincaré recurrence theorem
- Borel and measure isomorphism theorems (sketches of proofs)
- Simple functions and their integration, approximation of measurable functions by simple ones
- Integration of non-negative functions, monotone convergence theorem, and Fatou's lemma
- Integration of real/complex valued functions and _L_1, dominated convergence theorem, and the density of simple functions in _L_1
- Properties of integrable functions: σ-finiteness of the support, 99% boundedness, absolute continuity of B ↦ ∫B f d_μ_
- Applications: Birkhoff's pointwise ergodic theorem, an elementary proof of it, and applications of this theorem (including Kolmogorov's strong law of large numbers)
- Convergence in measure and relations between different modes of convergence
- Product measures and the Fubini–Tonelli theorem
- Application: Kolmogorov's 0–1 law (ergodicity of eventual equality)
- Measure differentiation, density, and a.e. differentiable functions
- Orthogonality and absolute continuity of measures, Jordan decomposition
- Signed measures and Hahn decomposition (proof via measure exhaustion)
- The Lebesgue-Radon-Nikodym theorem and Radon-Nikodym derivatives
- The Lebesgue differentiation theorem for ℝd: proof via the Hardy–Littlewood maximal function and the Vitali covering lemma
- The Lebesgue density theorem for ℝd, the Lebesgue differentiation theorem for all locally finite Borel measures on ℝd
- Characterization of the distribution functions on ℝ whose associated measures are absolutely continuous/orthogonal with respect to Lebesgue measure
- Absolutely continuous functions and the fundamental theorem of calculus for increasing functions
- Finite Borel signed measures on ℝd and right-continuous functions of bounded variation, the fundamental theorem of calculus for functions of bounded variation
Probability Theory
The course will be suitable for the students who successfully went though the Analysis 1 and 2 courses already.
Prerequisites.
Foundational offerings that prepare students for the credit-bearing curriculum above.
Data structures, Algorithms
Ethics, Policy, Governance for Physical AI
Past and Future Offerings.
Courses that are not part of the current cycle — offered previously or planned for upcoming terms.
This course explores the convergence of physical optics, optoelectronic hardware, and advanced signal processing. It is designed to teach students how to jointly optimize optical front-ends and computational back-ends to overcome traditional imaging limits and perform high-speed computations with light.
The first half of the course (Part 1) focuses on **Optoelectronic Architectures and Computing with Light**, providing hands-on experience with Spatial Light Modulators (SLMs) and Digital Micromirror Devices (DMDs) to manipulate wavefronts, navigate complex scattering media, and implement optical neural networks and Ising machines. The second half (Part 2) transitions into **Signal Processing and Computational Imaging**, covering Fourier optics, compressive sensing, digital holography, and phase retrieval. The course culminates in a two-week intensive project where students apply these concepts to physical experiments or rigorous simulations.
This course introduces the fundamental concepts and advanced topics in optics. It begins with the foundations of electromagnetic waves, including polarization, reflection, refraction, dispersion, and coherence, and covers classical experiments such as the Michelson-Morley experiment. The course then progresses to advanced optics, exploring wave optics, light-matter interactions, lasers, nonlinear optical effects, nanophotonics, and the quantum states of light. Students will gain both theoretical understanding and practical insights into modern optical technologies.
This course provides a systematic introduction to modern optics, covering the fundamental wave nature of light, polarization phenomena, interference and diffraction, light–matter interaction, and the principles underlying contemporary optical devices and techniques. Emphasis is placed on the physical interpretation of optical phenomena, rigorous theoretical foundations, and close integration of theory with experimental practice. Students will explore light propagation in isotropic and anisotropic media, polarization control, coherence and interference, diffraction-limited imaging, and the interaction of light with matter at both classical and phenomenological levels. The course further introduces key concepts of modern photonics, including lasers, spectroscopy, optical resonators, Gaussian beams, beam shaping, and structured light. Laboratory and problem-solving sessions are tightly coupled to the lecture material, enabling students to gain hands-on experience with optical measurements, experimental techniques, and data analysis.
Dexterous multi-finger hands (Allegro, LEAP), sim-to-real for high-DoF manipulators, tactile-driven policies, in-hand manipulation, contact-rich assembly tasks, deformable object manipulation.
On-device inference (NVIDIA Jetson, Qualcomm), model compression and quantization for real-time control, spiking neural networks for continuous control, event-driven processing, latency-critical architectures.
Natural language instruction (enabled by VLAs), shared autonomy with foundation-model-based intent prediction, safety-aware physical interaction, and assistive robotics.
Swarms, fleet-level data aggregation, federated learning for robots, emergent coordination, multi-robot task allocation with LLM planners.
Teams build a complete physical AI system end-to-end: sim environment → data collection → policy training → sim-to-real transfer → real-world deployment. Emphasis on the full stack: mechanical design choices, sensor suite, sim pipeline, learned policy, safety envelope, real-world evaluation.
Adversarial attacks on VLAs, distribution shift detection, uncertainty quantification in learned policies, runtime monitoring, safe RL constraints, the verification challenge for neural network controllers.
Video prediction models, latent-space world models (Dreamer, IRIS), NVIDIA Cosmos and generative world foundation models, spatial intelligence (World Labs), V-JEPA, LeCun's cognitive architecture.