University Mathematics
Build rigorous foundations for STEM, computing, economics, and advanced mathematical study.
Choose a university math course
Each course connects a unit map, guided practice, a complete test, and the calculator best suited to the subject.
College Algebra
Develop fluent symbolic and graphical reasoning for college STEM work.
6 connected units: begin with Equations and inequalities, build through Rational models, and finish with Systems.
Calculus I
Study limits, derivatives, and applications of instantaneous change.
7 connected units: begin with Limits and continuity, build through Implicit differentiation, and finish with Antiderivatives.
Calculus II
Develop integration methods, sequences, series, and parametric reasoning.
7 connected units: begin with Integration techniques, build through Sequences, and finish with Parametric and polar curves.
Multivariable Calculus
Analyze functions, derivatives, and integrals in higher dimensions.
7 connected units: begin with Vectors and space, build through Vector fields, and finish with Green, Stokes, and divergence theorems.
Linear Algebra
Understand vector spaces, matrices, linear maps, and eigenstructure.
7 connected units: begin with Systems and elimination, build through Vector spaces, and finish with Orthogonality.
Differential Equations
Model change with first-order, higher-order, and systems methods.
7 connected units: begin with Separable equations, build through Laplace transforms, and finish with Qualitative analysis.
Discrete Mathematics
Build proof skills through logic, combinatorics, relations, and graphs.
7 connected units: begin with Logic, build through Counting, and finish with Number theory.
Probability
Model uncertainty with random variables and distributions.
7 connected units: begin with Probability axioms, build through Continuous variables, and finish with Limit theorems.
Mathematical Statistics
Connect probability models to estimation, testing, and inference.
7 connected units: begin with Sampling distributions, build through Hypothesis tests, and finish with Bayesian foundations.
Numerical Methods
Approximate mathematical problems while tracking error and stability.
7 connected units: begin with Floating-point error, build through Numerical differentiation, and finish with ODE solvers.
Real Analysis
Make calculus rigorous through limits, continuity, sequences, and proof.
7 connected units: begin with Real numbers, build through Continuity, and finish with Metric spaces.
Abstract Algebra
Study algebraic structures through groups, rings, fields, and homomorphisms.
7 connected units: begin with Groups, build through Quotient groups, and finish with Field extensions.
Practise any university mathematics course
Each set generates unlimited questions by unit, with a worked answer after every one.
- College Algebra practice questions
- Calculus I practice questions
- Calculus II practice questions
- Multivariable Calculus practice questions
- Linear Algebra practice questions
- Differential Equations practice questions
- Discrete Mathematics practice questions
- Probability practice questions
- Mathematical Statistics practice questions
- Numerical Methods practice questions
- Real Analysis practice questions
- Abstract Algebra practice questions
Build knowledge in a dependable order
University mathematics connects computation to models, proof, abstraction, and careful statements of conditions.
Check the prerequisite
Review the definitions and earlier results that the course assumes before starting a proof or calculation.
Learn the central relationship
A definition names the objects; a theorem or formula explains how those objects are connected.
Use more than one representation
Words, symbols, tables, graphs, diagrams, data, and code can show the same mathematical idea from different sides.
Test independent recall
Practice and course tests show whether you can select, complete, and verify a method without copying an example.
Common questions
What maths do I need before starting Calculus I?
Comfort with algebra and functions matters more than any calculus preview: factoring, exponent and log rules, and reading a function's domain. Most people who struggle with Calculus I are struggling with the algebra inside the calculus.
Is university maths just harder school maths?
It is a different task. School maths mostly asks you to execute a method; university maths asks you to justify why the method is allowed, which is why proof and conditions matter so much more.
Which course covers proofs?
Discrete Mathematics introduces proof techniques directly, and Real Analysis and Abstract Algebra assume you can already write one. Start with Discrete Mathematics if proof is new to you.