Trimester 08 · Course detail

Senior Research & Baccalaureate Defense

Advanced monographic specialization, an in-silico research dissertation built as a zero-dependency computational engine, and the baccalaureate comprehensive viva voce and oral defense

Credits: 15
Sequence: 8 of 8
Structure: 3 subjects
Status: Full syllabus

Curriculum focus

Advanced monographic specialization, an in-silico research dissertation built as a zero-dependency computational engine, and the baccalaureate comprehensive viva voce and oral defense

Evidence of mastery

In-silico dissertation + 90-minute oral defense before examination panels

Subject 01

Advanced Monographic Specialization Colloquium

Official syllabus code: 3 Credits

A research colloquium at the research frontier: non-linear dispersive systems and solitons, high-dimensional non-convex landscapes with geometric deep learning foundations, and rigorous error analysis for multi-scale digital twins.

Non-Linear Dispersive Systems & Soliton Theory

Non-Linear Dispersive Systems & Soliton Theory (KdV, Non-Linear Schrödinger)

Study the Korteweg–de Vries and non-linear Schrödinger equations, soliton solutions, inverse scattering, and the interplay of dispersion and non-linearity that produces coherent structures.

Non-Convex Landscapes & Digital Twins

High-Dimensional Non-Convex Landscapes & Geometric Deep Learning Foundations

Analyze loss landscapes of high-dimensional non-convex optimization and connect them to the geometric foundations of deep learning — symmetries, equivariance, and graph/network structures.

Rigorous Error Analysis of Multi-Scale Multi-Physics Digital Twins

Develop rigorous a priori and a posteriori error analysis for multi-scale, multi-physics digital twin simulations, quantifying uncertainty across coupled models.

Subject 02

Senior Research In-Silico Dissertation

Official syllabus code: 6 Credits

The dissertation itself: a mathematically specified problem, engineered as a zero-external-dependency computational engine, written up as a monograph formatted to Warsaw/Bologna thesis standards.

Specification & Architecture

Formulation: Mathematical Specification & Boundary Well-Posedness Proof

Formulate the research problem with full mathematical specification and prove well-posedness — existence, uniqueness, and continuous dependence — for its boundary value formulation.

In-Silico Architecture: Zero-External-Dependency Computational Engine

Design and build the computational engine from first principles with zero external dependencies, documenting its architecture, numerics, and verification.

Peer-Review Defense Text: Monograph Formatted to Warsaw/Bologna Thesis Standards

Write the dissertation as a monograph to Warsaw/Bologna thesis standards, structured for peer review and prepared for oral defense.

Subject 03

Baccalaureate Comprehensive Viva Voce & Oral Defense

Official syllabus code: 6 Credits / Registrar Gate

The final gate: a formal defense of the in-silico dissertation followed by theoretical mathematics and theoretical physics & mechanics examination panels — ninety minutes before the AI examination tribunal.

Defense & Examination Panels

Formal Defense of the In-Silico Dissertation & Numerical Telemetry (30 Mins)

Defend the dissertation's mathematical specification, computational engine, and numerical telemetry before the examination tribunal in a thirty-minute formal defense.

The Theoretical Mathematics Examination Panel (Official Warsaw Licencjat Topics) (30 Mins)

Sit the theoretical mathematics panel covering the official Warsaw licencjat examination topics, demonstrating command of the full mathematics sequence.

The Theoretical Physics & Mechanics Examination Panel (30 Mins)

Sit the theoretical physics and mechanics panel, from classical and analytical mechanics through field theory and quantum mechanics.