Andréa GourionEngineering Learning Systems
ENFR
Discuss a pilot

Andréa Gourion · Engineering Learning Systems

Rigorous courses, designed as coherent learning systems.

I help universities turn quantitative and engineering courses into applied, visual and interactive experiences, from course architecture to production-ready learning assets.

Discuss a pilotSee the work
Fig. 01Interactive demo · dot product
Dot product of two vectors and projectionVectors u and v form a 55-degree angle. Their dot product is 6.88.uv55°projection
u⋅v=∥u∥ ∥v∥cos⁡θ\boldsymbol{u}\cdot\boldsymbol{v}=\lVert\boldsymbol{u}\rVert\,\lVert\boldsymbol{v}\rVert\cos\theta12cos⁡ ⁣(55∘)=6.8812\cos\!\left(55^{\circ}\right)=6.88

NoteThe dot product is the length of u multiplied by the signed projection of v onto u.

u⋅v=∥u∥×projection=4×1.72=6.88\begin{aligned}\boldsymbol{u}\cdot\boldsymbol{v}&=\lVert\boldsymbol{u}\rVert\times\text{projection}\\&=4\times1.72=6.88\end{aligned}
u=(40)\boldsymbol{u}=\begin{pmatrix}4\\0\end{pmatrix}v=(1.722.46)\boldsymbol{v}=\begin{pmatrix}1.72\\2.46\end{pmatrix}

Acute angle · positive projection · positive dot product

The angle determines the sign of the dot product.The Kinetic Kernel · public chapter
MTH1008 · course + 2 mini-projectsMTH1102 · 13 decksELE2200 · control + simulationALFA · co-author + 7 casesThe Kinetic Kernel · EN / FR

01 · Project in practice

The figure is not decoration. It is part of the reasoning.

I design usable courses by making notation, geometric intuition, application and interaction reinforce one another. I begin with the subject and end with a system a teaching team can maintain.

Matrix product diagram highlighting one row, one column and their resulting entry.
Fig. 02Matrix multiplication made inspectableMy MTH1008 course notes

For engineering faculties, mathematics departments, online learning units and professional education teams.

02 · Problems absorbed

From fragmented course to transferable system.

01

Fragmented course assets

One maintainable teaching system
02

Abstract quantitative content

Applied cases and visual explanations
03

One-off innovation

A documented system the team can extend

03 · Selected work

Projects that show how I work.

I present five projects that show my practice from different angles: understand the subject, structure the experience and build the assets.

Three planes whose pairwise intersection lines converge at the unique solution (7/3, 8/3, 1).

01 · Course system · Mini-project design · Scientific figures

MTH1008: Algèbre linéaire appliquée

Make a foundational course feel like one coherent instrument.

I brought together course architecture, reproducible figures and a series of applied mini-projects to move from notation to engineering situations.

Course production systemLaTeXTikZPythonMoodle
  • Course architecture
  • Applied cases
  • TikZ
View the case study
MTH1102 slide showing an orange helix on a translucent paraboloid.
FR

This is the original French-language artifact. I have kept it untranslated to preserve the work as it was produced.

02 · 13 signed decks · Multivariable geometry · 2024

MTH1102: Calcul II

Give spatial ideas a consistent visual grammar.

I designed thirteen signed decks that turn curves, coordinate systems, differential elements and surfaces into a sequenced visual course.

Scientific production systemLaTeXTikZPGFPlotsPython
  • Visual system
  • Calculus
  • 3D geometry
View the case study
ELE2200Vertical landing
×2.5
50 m25 m0 mMATLAB / Simulink
0.0 / 20.0 s

03 · Assignment design · MATLAB/Simulink · Interactive simulator

ELE2200: Systèmes et simulation

Turn control theory into one continuous engineering investigation, from equations to landing.

I designed ELE2200’s second assignment around vertical rocket landing, combining PID loops, reduced and complete models, MATLAB/Simulink scaffolds and an interactive web simulator.

Simulation systemMATLABSimulinkCanvasLaTeX
  • Control systems
  • MATLAB/Simulink
  • Interactive simulation
View the case study
The Kinetic KernelDot product

Drag the u and v endpoints

Dot product of two vectors and projectionVectors u and v form a 55-degree angle. Their dot product is 6.88.uv55°
u⋅v=∥u∥ ∥v∥cos⁡θ\boldsymbol{u}\cdot\boldsymbol{v}=\lVert\boldsymbol{u}\rVert\,\lVert\boldsymbol{v}\rVert\cos\theta12cos⁡ ⁣(55∘)=6.8812\cos\!\left(55^{\circ}\right)=6.88

NoteThe dot product is the length of u multiplied by the signed projection of v onto u.

u⋅v=∥u∥×projection=4×1.72=6.88\begin{aligned}\boldsymbol{u}\cdot\boldsymbol{v}&=\lVert\boldsymbol{u}\rVert\times\text{projection}\\&=4\times1.72=6.88\end{aligned}

04 · Interactive product · Bilingual system · Live chapter

The Kinetic Kernel · Linear algebra made manipulable

Make the dot product visible as angle, projection and signed magnitude.

I created a bilingual web learning product where the dot product connects a formal definition to projection, orthogonality and an adjustable geometric state.

Selected technologyReactViteKaTeXSVG
  • Interactive product
  • Bilingual
  • React
View the case study
Five complex fifth roots arranged as a regular pentagon in the complex plane.
FR

This is the original French-language artifact. I have kept it untranslated to preserve the work as it was produced.

05 · Open textbook · Co-author · 7 individually credited cases

ALFA · Applied cases across linear algebra

Move from phenomenon, to model, to algebra, to interpretation.

I co-author this open applied-linear-algebra resource. Seven case studies are individually credited to me, while the visual language for complex numbers remains collective work.

Production systemLaTeX
  • Open textbook
  • Applied cases
  • Editorial system
View the case study

04 · Services

I work from diagnosis through transfer.

Explore services ↗
01

Course transformation

Align outcomes, sequence, activities, assessments and assets around one learning architecture.

02

Applied cases and mini-projects

Turn theory into structured engineering problems with realistic constraints and instructor guidance.

03

Visual and interactive systems

Build scientific figures, decks, simulations and web interactions in one maintainable language.

04

Course platform architecture

Organize content, templates, cohorts and quality checks across the LMS and supporting tools.

05 · Process

I reduce risk through successive reviews.

See the process ↗
  1. 01DiagnoseCourse and system audit
  2. 02ArchitectTarget learning map
  3. 03PrototypeOne representative sequence
  4. 04BuildProduction-ready assets
  5. 05ValidateAcademic, usability and access review
  6. 06TransferDocumentation and handover
Eight-week course transformation pilot

Start with one difficult course, sequence or concept.

I diagnose the current system, prototype a target experience and give your team a concrete basis for the next decision. I define final scope after diagnosis.

Fixed scopeFaculty reviewsHandover documentation
Request a pilot brief

Which course is hardest to make coherent?

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