Courses
Math courses
Guided paths from definition to practice: every course has its own order, exercises and exam simulator.
Calculus
Limits, continuity, derivatives, their applications and integrals: the classic path of single-variable calculus, from the idea of approximation to the fundamental theorem.
38concepts
492exercises
≈ 22 hof study approx.
Linear algebra
From systems of equations and matrices to vector spaces, linear transformations, eigenvalues and orthogonality: the shared language of data science, physics and engineering.
31concepts
310exercises
≈ 16 hof study approx.
Probability and statistics
You will learn to measure uncertainty: events, random variables, distributions and the methods for drawing conclusions from data. It supports evidence-based decisions in science, engineering and finance.
32concepts
320exercises
≈ 16 hof study approx.
Differential equations
You will learn to solve equations that relate a function to its derivatives, from first order to systems and the Laplace transform. It is used to model growth, circuits, vibrations and any system that changes in time.
33concepts
330exercises
≈ 17 hof study approx.
Multivariable calculus
Under construction
You will learn to differentiate and integrate functions of several variables, optimize under constraints and compute line and surface integrals up to the theorems of Green, Stokes and divergence. It is used to describe fields, flows and volumes in physics, engineering and data science.
37concepts
370exercises
≈ 19 hof study approx.
Discrete mathematics
You will learn to prove by induction, count configurations, reason with relations and graphs, and solve recurrences and congruences. It is the foundation for computer science, algorithms and cryptography.
33concepts
330exercises
≈ 17 hof study approx.
Elementary number theory
Study the integers in depth: Bézout, congruences and the Chinese remainder theorem, Fermat and Euler, primitive roots, quadratic reciprocity, arithmetic functions, continued fractions and RSA. It is the basis of modern cryptography; Discrete mathematics is recommended first.
37concepts
370exercises
≈ 19 hof study approx.
Modern algebra I
You will learn groups, rings and fields: subgroups, quotients, actions, Sylow theorems, ideals and polynomial factorization. It is the basis of Galois theory, cryptography and algebraic geometry.
47concepts
473exercises
≈ 24 hof study approx.
Enumerative combinatorics
Under construction
Advanced counting techniques are learned: generating functions, partitions, Stirling, Bell and Catalan numbers, symmetry via Burnside and Pólya, posets and extremal methods. They are used to solve enumeration problems and bound combinatorial objects in discrete mathematics, number theory, algebra and probability; it is advisable to have taken Discrete mathematics, Elementary number theory, Modern algebra I, Probability and statistics.
19concepts
190exercises
≈ 10 hof study approx.
Measure theory and integration
Under construction
You learn σ-algebras, Lebesgue measure and integral, their convergence theorems, Lp spaces, and the Fubini-Tonelli and Radon-Nikodym theorems, tools for rigorously formalizing analysis and probability. It helps to have taken Discrete Mathematics, Real Analysis and Set Theory.
7concepts
70exercises
≈ 4 hof study approx.
Continuous optimization
Under construction
You learn the foundations of continuous optimization: convexity, optimality conditions, gradient descent, Newton and quasi-Newton methods, constraints, duality, linear programming and proximal methods, tools for solving minimization problems in science and engineering. It helps to have taken Linear Algebra and Multivariable Calculus.
17concepts
170exercises
≈ 9 hof study approx.
Numerical methods
Under construction
You learn algorithms to approximate roots, linear systems, eigenvalues, interpolants, integrals, derivatives and differential equations, along with the error and stability analysis that determines their reliability. It serves to solve numerically engineering and science problems that have no closed-form solution; it is advisable to have taken Calculus, Differential Equations, Linear Algebra, Real Analysis.
23concepts
250exercises
≈ 12 hof study approx.
Signal processing
Under construction
You learn to represent, filter and analyze continuous and discrete signals using LTI systems, convolution, Fourier series and transforms, sampling, the Z-transform and wavelets, together with random processes and Wiener and Kalman filters. It is used to design filters, digitize signals without losing information and process images, including medical image registration; it helps to have taken Calculus, Complex Analysis, Linear Algebra, Probability and Statistics, Real Analysis.
13concepts
130exercises
≈ 7 hof study approx.
Real analysis
Under construction
Build calculus rigorously: real numbers, sequences, continuity, differentiation and Riemann integration. It prepares you to read and write proofs and to see why calculus works.
32concepts
410exercises
≈ 18 hof study approx.
Complex analysis
Study complex numbers and holomorphic functions: differentiation, contour integration, Laurent series and residues. It helps compute hard real integrals and underpins engineering, physics and number theory.
32concepts
320exercises
≈ 16 hof study approx.
General topology
Under construction
Study metric and topological spaces: open sets, continuity, connectedness and compactness. It gives the common language of analysis, geometry and much of modern mathematics.
32concepts
320exercises
≈ 16 hof study approx.
Set theory
Under construction
Learn the language of sets, functions, cardinals and ordinals, and the axioms that underpin modern mathematics.
30concepts
320exercises
≈ 16 hof study approx.