Bachelor of Mathematics
Master the language of Mathematics in this tertiary level course from the very best free resources available.
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4,723 hours
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Introduction to Proofs
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Introduction to Proofs
Continue with Module 1 — Entering University Mathematics.
About this degree
Degree overview
Curriculum
Degree structure
24 units organised across 3 years.
Year 1
Foundations
8 units
- 1○Introduction to Proofs
Introduction to Proofs lays the foundation for higher mathematics by teaching the language, logic, and reasoning used throughout the discipline. This unit is originally Introduction to Mathematical Proofs (MAT102) by instructor: Dr. Mike Pawliuk for the University of Toronto Mississauga.
123 hours10 lessons - 2○Calculus I
Explore limits, derivatives, and their applications to understanding change and motion.
200 hours13 lessons - 3○Linear Algebra I
Study vectors, matrices, and systems of equations that underpin modern mathematics and science.
200 hours - 4○Discrete Mathematics
Discover the mathematics of algorithms, graphs, combinatorics, and logical reasoning.
200 hours - 5○Calculus II
Extend calculus with integration, infinite series, and advanced techniques for solving real-world problems.
200 hours - 6○Differential Equations
Learn how mathematical equations model dynamic systems such as population growth, motion, and electrical circuits.
200 hours - 7○Statistics I
Build a foundation in probability, data analysis, and statistical reasoning under uncertainty.
200 hours - 8○Mathematical Modelling I
Apply mathematics to create models that describe and solve real-world scientific and engineering problems.
200 hours
Year 2
Core mathematics
8 units
- 9○Multivariable Calculus
Extend calculus to functions of several variables, partial derivatives, and multiple integrals.
200 hours - 10○Real Analysis
Develop a rigorous understanding of calculus through formal definitions, limits, continuity, and convergence.
200 hours - 11○Abstract Algebra I
Explore algebraic structures such as groups, rings, and fields that reveal the symmetry of mathematics.
200 hours - 12○Advanced Probability
Study advanced probability theory, random variables, distributions, and stochastic concepts.
200 hours - 13○Statistics II
Learn how statistical inference, estimation, and hypothesis testing extract meaning from data.
200 hours - 14○Numerical Analysis
Investigate computational methods for solving mathematical problems that cannot be solved exactly.
200 hours - 15○Complex Analysis
Explore the elegant mathematics of complex numbers and functions with applications across physics and engineering.
200 hours - 16○Mathematical Modelling II
Tackle more sophisticated mathematical models involving optimisation, simulation, and differential equations.
200 hours
Year 3
Advanced mathematics
8 units
- 17○Topology
Study the fundamental properties of spaces that remain unchanged through continuous deformation.
200 hours - 18○Functional Analysis
Explore infinite-dimensional vector spaces and operators that form the foundation of modern analysis and quantum mechanics.
200 hours - 19○Abstract Algebra II
Deepen your understanding of advanced algebraic structures and the theory behind modern mathematics.
200 hours - 20○Differential Geometry
Investigate the geometry of curves, surfaces, and manifolds using the tools of calculus and linear algebra.
200 hours - 21○Partial Differential Equations
Learn how equations involving multiple variables describe heat, waves, fluids, and other physical phenomena.
200 hours - 22○Optimization & Operations Research
Solve complex decision-making problems using mathematical optimisation and analytical techniques.
200 hours - 23○Stochastic Processes
Model systems that evolve randomly over time using Markov chains, Brownian motion, and related processes.
200 hours - 24○Capstone: Advanced Mathematical Problem Solving
Integrate your mathematical knowledge by completing a substantial real-world or theoretical project.
200 hours