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University of Toronto: mathematics and statistics

Course guides for the University of Toronto's mathematics and statistics courses. Each guide follows the course chapter by chapter: definitions, theorems with the reasoning spelled out, worked examples, pitfalls and practice questions with answers.

Start with the path through the program or how MAT137 and MAT157 were replaced.

Mathematics

Course Title Year Chapters What it covers
MAT137 Calculus with Proofs Year 1 14 The proof-based calculus on-ramp: logic, limits, derivatives, integrals, sequences, and series.
MAT158H1 Analysis 1A Year 1 11 Rigorous first-semester analysis, built from completeness of the real numbers through the Fundamental Theorem of Calculus.
MAT159H1 Analysis 1B Year 1 7 The second analysis course: improper integrals, Taylor's theorem, series, uniform convergence, and power series.
MAT240H1 Algebra I Year 1 10 Proof-based linear algebra over arbitrary fields, from vector spaces and linear maps to diagonalization.
MAT247H1 Algebra II Year 2 10 Theoretical linear algebra: inner products, adjoints, the spectral theorem, and canonical forms.
MAT257Y1 Analysis II Year 2 14 Specialist multivariable analysis: topology of R^n, differentiation, integration, forms, manifolds, and Stokes' theorem.

Beside the math

Course Title Subject Chapters
PHY131H1 Introduction to Physics I Physics 10
PHY132H1 Introduction to Physics II Physics 10
CSC108H1 Introduction to Computer Programming Computer Science 10
CSC148H1 Introduction to Computer Science Computer Science 10
ENG140Y1 Literature for our Time English 10

Still to be written

These courses are listed so the whole program can be seen at once; their guides come later.

Algebra (6)
Course Title Year
MAT301H1 Groups and Symmetries Year 3
MAT347Y1 Groups, Rings and Fields Year 3
MAT401H1 Polynomial Equations and Fields Year 4
MAT445H1 Representation Theory Year 4
MAT448H1 Introduction to Commutative Algebra and Algebraic Geometry Year 4
MAT449H1 Algebraic Curves Year 4
Analysis (12)
Course Title Year
MAT237Y1 Multivariable Calculus with Proofs Year 2
MAT334H1 Complex Variables Year 3
MAT336H1 Elements of Analysis Year 3
MAT337H1 Introduction to Real Analysis Year 3
MAT351Y1 Partial Differential Equations Year 3
MAT354H1 Complex Analysis I Year 3
MAT357H1 Foundations of Real Analysis Year 3
MAT436H1 Introduction to Linear Operators Year 4
MAT437H1 K-Theory and C* Algebras Year 4
MAT454H1 Complex Analysis II Year 4
MAT457H1 Advanced Real Analysis I Year 4
MAT458H1 Advanced Real Analysis II Year 4
Applied Math (12)
Course Title Year
APM236H1 Applications of Linear Programming Year 2
MAT244H1 Introduction to Ordinary Differential Equations Year 2
MAT267H1 Advanced Ordinary Differential Equations Year 2
APM346H1 Partial Differential Equations Year 3
APM348H1 Mathematical Modelling Year 3
APM421H1 Mathematical Foundations of Quantum Mechanics and Quantum Information Theory Year 4
APM426H1 General Relativity Year 4
APM441H1 Asymptotic and Perturbation Methods Year 4
APM446H1 Applied Nonlinear Equations Year 4
MAT461H1 Hamiltonian Mechanics Year 4
APM462H1 Nonlinear Optimization Year 4
APM466H1 Mathematical Theory of Finance Year 4
Data Science (1)
Course Title Year
MAT245H1 Mathematical Methods in Data Science Year 2
Discrete Math (3)
Course Title Year
MAT332H1 Introduction to Graph Theory Year 3
MAT344H1 Introduction to Combinatorics Year 3
APM461H1 Combinatorial Methods Year 4
Dynamical Systems (1)
Course Title Year
MAT335H1 Chaos, Fractals and Dynamics Year 3
Foundation (5)
Course Title Year
MAT223H1 Linear Algebra I Year 2
MAT224H1 Linear Algebra II Year 2
MAT235H1 Vector Calculus I Year 2
MAT236H1 Vector Calculus II Year 2
MAT246H1 Concepts in Abstract Mathematics Year 2
Geometry (5)
Course Title Year
MAT363H1 Geometry of Curves and Surfaces Year 3
MAT367H1 Differential Geometry Year 3
MAT402H1 Classical Geometries Year 4
MAT403H1 Classical Geometries II Year 4
MAT464H1 Riemannian Geometry Year 4
Logic (2)
Course Title Year
MAT309H1 Introduction to Mathematical Logic Year 3
MAT409H1 Set Theory Year 4
Number Theory (3)
Course Title Year
MAT315H1 Introduction to Number Theory Year 3
MAT415H1 Algebraic Number Theory Year 4
MAT417H1 Analytic Number Theory Year 4
Probability (5)
Course Title Year
MAT370H1 Introduction to Mathematical Probability Year 3
MAT377H1 Mathematical Probability Theory Year 3
STA347H1 Probability Year 3
STA357H1 Theoretical Probability Year 3
STA447H1 Stochastic Processes Year 4
Seminar (3)
Course Title Year
MAT475H1 Problem Solving Seminar Year 4
MAT477H1 Seminar in Mathematics Year 4
MAT478H1 Seminar in Mathematics Year 4
Statistics (29)
Course Title Year
STA237H1 Probability, Statistics and Data Analysis I Year 2
STA238H1 Probability, Statistics and Data Analysis II Year 2
STA247H1 Probability with Computer Applications Year 2
STA248H1 Statistics for Computer Scientists Year 2
STA255H1 Statistical Theory Year 2
STA257H1 Probability and Statistics I Year 2
STA261H1 Probability and Statistics II Year 2
STA302H1 Methods of Data Analysis I Year 3
STA303H1 Methods of Data Analysis II Year 3
STA304H1 Surveys, Sampling and Observational Data Year 3
STA305H1 Design and Analysis of Experiments Year 3
STA313H1 Data Visualization Year 3
STA314H1 Statistical Methods for Machine Learning I Year 3
STA355H1 Theory of Statistical Practice Year 3
STA365H1 Applied Bayesian Statistics Year 3
STA410H1 Statistical Computation Year 4
STA414H1 Statistical Methods for Machine Learning II Year 4
STA422H1 Theory of Statistical Inference Year 4
STA437H1 Methods for Multivariate Data Year 4
STA442H1 Methods of Applied Statistics Year 4
STA450H1 Topics in Statistics Year 4
STA452H1 Mathematical Statistics I Year 4
STA453H1 Mathematical Statistics II Year 4
STA457H1 Time Series Analysis Year 4
STA465H1 Spatial Data Analysis Year 4
STA475H1 Survival Analysis Year 4
STA480H1 Fundamentals of Statistical Genetics Year 4
STA490Y1 Statistical Consultation, Communication, and Collaboration Year 4
STA492H1 Seminar in Statistical Science Year 4
Topology (2)
Course Title Year
MAT327H1 Introduction to Topology Year 3
MAT425H1 Differential Topology Year 4