How MAT137 and MAT157 Were Replaced

The two replacements at a glance

Old full-year course	New fall half	New winter half
MAT137Y1 — Calculus! (with proofs)	MAT148H1 — Calculus I with Proofs	MAT149H1 — Calculus II with Proofs
MAT157Y1 — Analysis I	MAT158H1 — Analysis 1A	MAT159H1 — Analysis 1B

MAT138H1 (Introduction to Proofs) is the proof-skills companion for both streams. It is optional alongside the calculus stream and recommended concurrently with the analysis stream.

The calculus stream (former MAT137Y1)

MAT148H1 — Calculus I with Proofs

Hours: 36L/12T.
Topics: logic, quantifiers, sets, mathematical induction, limits, continuity, mean value theorem, transcendental functions, inverse function theorem, differentiation.
Approach: conceptual, computation plus problem solving, proofs introduced.
Prerequisite: high school calculus.
Exclusions: MAT137Y1, MAT137Y5, MAT137H5, MAT139H5, MATA30H3, MATA31H3.

MAT149H1 — Calculus II with Proofs

Hours: 36L/12T.
Topics: integration and applications, fundamental theorem of calculus, improper integrals, sequences and series, power series, Taylor's theorem.
Prerequisite: MAT148H1, or MAT135H1/MAT130H1 (min 70%), or MAT158H1.
Exclusions: MAT137Y1 and its variants, MATA37H3.

The analysis stream (former MAT157Y1)

MAT158H1 — Analysis 1A

Hours: 36L/12T.
Topics: elementary logic, limits, continuity, least upper bounds, intermediate and extreme value theorems, derivatives, mean value theorem, inverse function theorem, integrals, fundamental theorem, elementary transcendental functions.
Approach: theoretical, proof-first. Mandatory for the Mathematics Specialist and related specialist programs.
Prerequisite: high school calculus. MAT138H1 recommended concurrently.
Exclusions: MAT157Y1, MAT157Y5, MAT157H5.

MAT159H1 — Analysis 1B

Hours: 36L/12T.
Topics: integrals, fundamental theorem, elementary transcendental functions, integration techniques, Taylor's theorem, series, uniform convergence, power series.
Prerequisite: MAT158H1, or MAT148H1 (min 70%), or MAT157H5.
Exclusions: MAT157Y1, MAT157Y5, MAT159H5.

Why split the courses

Half-credit format gives flexibility: clearer fall/winter checkpoints instead of one all-or-nothing year.
It allows switching streams at the midpoint. The prerequisites are written to cross over: MAT149H1 accepts MAT158H1, and MAT159H1 accepts MAT148H1 at 70%. So a student can start in analysis (MAT158H1) and step down to the calculus second half, or start in calculus and, if strong, move up.
Entry and exit are cleaner for students who change programs after first term.

What this means for the stream choice

The split does not change the core decision. The calculus stream (148/149) is the rigorous-but-sane default for most quantitative fields. The analysis stream (158/159) is the hard track for students set on mathematics, and is mandatory for the Mathematics Specialist. For a stats-specialist, PhD-bound student, 158/159 is the right call; see the Comprehensive Guide, section 2.