Summer University Prep: Linear Algebra

Course Description

Who is this course for? • Grade 12 graduates starting university in Fall 2026 • Students heading into Math / CS / Engineering / Business / Physics / Data Science • Anyone expecting to take Linear Algebra I in first year and wants a serious head start By the time university begins, students will have already seen the full structure of a typical first-year Linear Algebra course. Why take this course? • Start university with confidence instead of panic • Reduce workload in first year by mastering a full subject in advance • Build a strong foundation for Calculus, Linear Algebra, Data Science, AI, and Machine Learning • Stand out in competitive STEM programs from day one Class Options: • 8–15 Students: $50/hour • 2–6 Students (Small Group): $70/hour • Total: 32 hours (4 hours/week × 8 weeks) Course Modules Module 1 – Vectors & Geometry in ℝ²/ℝ³ • Vectors, length, direction, dot product, projections, lines and planes, angles between vectors. (Foundation for physics, engineering and 3D thinking.) Module 2 – Matrices & Linear Systems • Matrix operations, Gaussian elimination, row-reduced echelon form, inverses, solving large systems efficiently. Module 3 – Vector Spaces & Subspaces • Column space, null space, linear independence, span, basis, dimension – the “grammar” of linear algebra. Module 4 – Determinants & Geometry • Determinants as area/volume scaling, invertibility, singular matrices, geometric meaning. Module 5 – Eigenvalues & Eigenvectors • Characteristic polynomial, diagonalization, geometric meaning of eigenvectors, stability and transformations. Module 6 – Applications & Review • Data and CS applications (e.g., transformations, simple PCA idea), exam-style problems, full course review. Aligned with Real University Courses Content is designed to prepare students for typical first-year Linear Algebra such as: • University of Toronto: MAT223H1 – Linear Algebra I • University of Waterloo: MATH 136 – Linear Algebra 1 for Honours Mathematics • McMaster University: MATH 1B03 – Linear Algebra I • UBC: MATH 152 / MATH 221 – Linear Systems / Matrix Algebra • McGill University: MATH 133 / MATH 223 – Linear Algebra & Geometry / Linear Algebra • University of Alberta: MATH 125 / MATH 127 – Linear Algebra I / Honours Linear Algebra I Students will see the same core topics before their first university lecture.