#Y0A#Math
Course
MA1 A
Term
Spring 2026
Schedule
Mon / Wed Lecture + Fri Recitation
Lessons
2
Course overview
We open with vectors in R² and R³, the concrete, drawable objects, and use geometry (lines, planes, cross products, curvilinear coordinates) to build the intuition that makes the algebra feel inevitable. From there the course moves into linear systems, matrix operations, determinants, rank, and the classification of matrices by equivalence and similarity, finishing with orthogonal and unitary structure.
- Start geometric: vectors, linear combinations, independence, and the geometry of lines, planes, and solids before touching a single matrix.
- Build the full algebraic toolkit: elimination, matrix algebra, determinants, Jordan normal form, and orthogonal decompositions.
- Connect both halves so you can read a theorem, draw the picture, and compute the answer, whichever the problem demands.
Weekly rhythm
- Read the lesson page first and work through the examples in order.
- Open the linked alternate video only if you want a second explanation or a different pace.
- Do the exercises, then recitation or lab immediately after the notes so the ideas turn into practice.
- Attempt the homework last, without jumping straight to solutions.
Course themes
- Vectors, linear combinations, independence, and spanning: the vocabulary everything else is written in.
- Geometry in R² and R³: lines, planes, cross products, triple products, and curvilinear coordinates.
- Matrix algebra, elementary operations, and invertibility: the machinery for solving and classifying linear systems.
- Determinants, rank, equivalence, Smith normal form, and the structure theorems that sort matrices up to similarity.
- Orthogonal and unitary transformations: the geometry-preserving maps that tie the algebraic and geometric halves together.
Prerequisites & corequisites
No prerequisites.
- Corequisite: MCE A (Mathematical Thinking and Python)
- Corequisite: MA1 B (Calculus I)
- Corequisite: PH1 A (Mechanics)
Course direction
The course is teaching you to see linear algebra as one subject with two faces, geometric and algebraic, and to move between them without losing your footing.
References
Outside notes, textbooks, or course pages worth keeping around.