Mathematics I · ADIN001NABB · Corvinus University of Budapest
Fall semester 2026–27, with Gyula Magyarkuti. Slides, quiz dates, the weekly schedule, and a lab where you can push matrices around and see what they do.
Course
The syllabus can be downloaded here. The most important parts are summarised below.
Four quizzes worth 5 points each, plus a final written exam worth 30. That makes 50 points in total.
total = (q₁, q₂, q₃, q₄, e) · (1, 1, 1, 1, 1) ≤ 50
Schedule
Each week links to its slides. The green links jump to a lab experiment for that topic.
Lab
Five small games, one for each big idea of the course. Each has a free-play mode and a challenge mode. Scores stay in your own browser and nothing here is graded.
Weeks 3, 4, 6, 8, 9
A 2×2 matrix is decided by where it sends the two basis vectors. Its first column is where î lands, its second is where ĵ lands. Drag the arrow tips or type numbers. The gold square shows the determinant as an area, and dashed lines mark the eigenvectors.
Weeks 1, 2
Level 1Land on the gold ring using only u and v. Pick α and β so that αu + βv hits the target. Watch out for traps: if u and v are parallel, they only span a line, and the target may be out of reach. Every three hits takes you up a level.
Weeks 1, 5, 6
A random 3×3 system, worked in exact fractions. In Quiz me mode you choose each row operation, and a wrong choice tells you what it would break. In Watch mode you just step through. The green cell is the pivot and the gold row is the one that just changed.
The system
Augmented matrix
Next row operation?
What shape is this?
The picture is hidden until you answer.
Weeks 7, 9
Q(x, y) = a·x² + 2b·xy + c·y², seen from above. Green is where Q is positive, rose where it is negative, and the lines are contour lines. Sylvester’s criterion reads the shape off the leading principal minors. The dashed lines are the eigenvectors of the symmetric matrix, and they are always perpendicular.
Weeks 3, 9
In the wild
Week 9 · eigenvectors
P·r = 1·r
The original ranking of web pages is the eigenvector for eigenvalue 1 of a huge matrix of link probabilities.
Week 6 · inverse matrix
x = (I − A)⁻¹·d
How much each sector must produce to meet final demand d. This input–output model won Wassily Leontief the 1973 Nobel Prize in economics.
Week 7 · quadratic forms
σ² = wᵀ·Σ·w
The variance of a portfolio with weights w is a quadratic form in the covariance matrix Σ. It is positive semidefinite, because a variance can’t be negative.
Week 3 · matrix product
v′ = M·v
Each rotation, zoom and camera move is a matrix multiplication, applied to millions of vertices per frame on the graphics card.