Mathematics Courses
Comprehensive mathematics tutoring for all levels, from first-year calculus to advanced graduate topics. We offer expert instruction for UBC mathematics courses.
First Year
Differential Calculus
Introduction to limits, continuity, derivatives, and their applications including optimization and curve sketching.
Integral Calculus
Fundamentals of integration, techniques of integration, applications to area, volume, and differential equations.
Linear Algebra
Systems of linear equations, matrices, vector spaces, determinants, eigenvalues, and eigenvectors.
Calculus for Life Sciences
Calculus concepts tailored for life sciences students, including exponential and logarithmic functions, and their biological applications.
Calculus for Physical Sciences
Calculus with emphasis on physical applications, including trigonometric functions, series, and differential equations.
Second Year
Multivariable Calculus
Functions of several variables, partial derivatives, multiple integrals, line and surface integrals, and vector calculus.
Ordinary Differential Equations
First and second order differential equations, systems of differential equations, and applications to modeling.
Linear Algebra II
Advanced topics in linear algebra including inner products, orthogonality, diagonalization, and Jordan canonical form.
Introduction to Real Analysis
Rigorous treatment of limits, continuity, differentiation, and integration with emphasis on proofs and mathematical rigor.
Discrete Mathematics
Logic, set theory, combinatorics, graph theory, and mathematical reasoning with applications to computer science.
Probability
Probability spaces, random variables, distributions, expectation, variance, and introduction to statistical inference.
Statistics
Descriptive statistics, probability distributions, hypothesis testing, confidence intervals, and regression analysis.
Third Year
Advanced Calculus
Rigorous treatment of multivariable calculus, including inverse and implicit function theorems, and optimization.
Complex Analysis
Complex numbers, analytic functions, Cauchy's theorem, residues, and applications to real integrals.
Abstract Algebra
Groups, rings, and fields with emphasis on group theory, including subgroups, homomorphisms, and quotient groups.
Number Theory
Divisibility, prime numbers, modular arithmetic, Diophantine equations, and applications to cryptography.
Topology
Topological spaces, continuity, compactness, connectedness, and fundamental concepts of modern geometry.
Differential Geometry
Curves and surfaces in space, curvature, geodesics, and introduction to manifolds and Riemannian geometry.
Numerical Analysis
Numerical methods for solving equations, interpolation, numerical integration and differentiation, and error analysis.
Mathematical Modeling
Construction and analysis of mathematical models for real-world problems using differential equations and optimization.
Partial Differential Equations
Classification of PDEs, separation of variables, Fourier series, and solutions to heat, wave, and Laplace equations.
Mathematical Statistics
Advanced statistical inference, maximum likelihood estimation, hypothesis testing, and Bayesian statistics.
Fourth Year
Real Analysis
Measure theory, Lebesgue integration, functional analysis, and advanced topics in analysis.
Algebraic Structures
Advanced topics in abstract algebra including Galois theory, modules, and algebraic number theory.
Functional Analysis
Banach and Hilbert spaces, linear operators, spectral theory, and applications to differential equations.
Differential Topology
Manifolds, tangent spaces, vector fields, differential forms, and integration on manifolds.
Commutative Algebra
Rings and modules, localization, completion, dimension theory, and connections to algebraic geometry.
Algebraic Topology
Fundamental groups, covering spaces, homology and cohomology theory, and applications.
Mathematical Physics
Mathematical methods in physics including Fourier analysis, special functions, and group theory applications.
Optimization Theory
Linear and nonlinear optimization, convex analysis, duality theory, and algorithms for optimization.
Stochastic Processes
Markov chains, Poisson processes, Brownian motion, and applications to finance and queueing theory.
Graph Theory
Advanced topics in graph theory including connectivity, planarity, coloring, and extremal graph theory.