Linear algebra
1–2Linear algebra trains the habits mathematics depends on — not trivia for exams, but reusable technique for later studios, labs or clinics.
A mathematics curriculum is a sequence, not a shopping list. Early courses build shared vocabulary; middle years introduce methods; the final stretch demands a project that can fail in public.
Elective freedom varies: some systems lock professional accreditation hours; others allow wide minors. The courses below are the common spine, not every university's catalogue.
Core courses
Real analysis
1–2Real analysis trains the habits mathematics depends on — not trivia for exams, but reusable technique for later studios, labs or clinics.
Abstract algebra
1–2Abstract algebra trains the habits mathematics depends on — not trivia for exams, but reusable technique for later studios, labs or clinics.
Topology
2–3Topology trains the habits mathematics depends on — not trivia for exams, but reusable technique for later studios, labs or clinics.
Probability
2–3Probability trains the habits mathematics depends on — not trivia for exams, but reusable technique for later studios, labs or clinics.
Differential equations
2–3Differential equations trains the habits mathematics depends on — not trivia for exams, but reusable technique for later studios, labs or clinics.
Number theory
3–4Number theory trains the habits mathematics depends on — not trivia for exams, but reusable technique for later studios, labs or clinics.
Geometry
3–4Geometry trains the habits mathematics depends on — not trivia for exams, but reusable technique for later studios, labs or clinics.
Common tracks
Pure maths
A pure maths emphasis usually appears after foundations, when students choose seminars, labs or studios that deepen one problem family inside mathematics.
Applied maths
A applied maths emphasis usually appears after foundations, when students choose seminars, labs or studios that deepen one problem family inside mathematics.
Statistics
A statistics emphasis usually appears after foundations, when students choose seminars, labs or studios that deepen one problem family inside mathematics.
Mathematical physics
A mathematical physics emphasis usually appears after foundations, when students choose seminars, labs or studios that deepen one problem family inside mathematics.
Skill map
Proof writing98
Abstraction96
Problem decomposition90
Computation62
Teaching clarity58
Persistence92
Proof writing
Proof writing is practised weekly in mathematics programmes; the percentage is relative strength among skills on this page, not a grade.
Abstraction
Abstraction is practised weekly in mathematics programmes; the percentage is relative strength among skills on this page, not a grade.
Problem decomposition
Problem decomposition is practised weekly in mathematics programmes; the percentage is relative strength among skills on this page, not a grade.
Computation
Computation is practised weekly in mathematics programmes; the percentage is relative strength among skills on this page, not a grade.
Teaching clarity
Teaching clarity is practised weekly in mathematics programmes; the percentage is relative strength among skills on this page, not a grade.
Persistence
Persistence is practised weekly in mathematics programmes; the percentage is relative strength among skills on this page, not a grade.
How you learn
Lectures & readings
Large-group framing plus primary texts or problem sets that define the week's vocabulary.
Labs / studios / clinics
Supervised practice where mistakes are expected and feedback is specific.
Seminars
Small-group argument; silence is expensive because the group notices.
Capstone / thesis
A public synthesis — defence, exhibition, clinic portfolio or engineered prototype.
Treat the catalogue as a map of practised skills, not a brand promise. The department that grades hard and returns work fast usually teaches more than the one that advertises prestige alone.
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