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Room for a clear thought

A clear argument starts with a question. Follow each step, check its assumptions and make the reasoning your own.

Courses

20 mathematics and computing courses, with bilingual lessons.

Search these 20 courses by title, code, topic or suggested background.

20 courses in the 2026–27 map

Course lessons are available in English and Chinese; some source materials are in English.

Course list

AX26-MATH-101Undergraduate level

Linear Algebra

Move from solvability of linear systems to orthogonal projection and least-squares derivations, with conditions for uniqueness.

150 estimated hours8 topics

Suggested background
  • Vectors and linear combinations
  • Elementary differentiation

AX26-STAT-201Undergraduate level

Statistical Inference

Choose an inferential method, justify its assumptions, and explain what a numerical result does and does not establish.

200 estimated hours7 topics

Suggested background
  • Random variables
  • Expectation and variance
  • Elementary differentiation

AX26-CS-101Undergraduate level

Algorithm Design

Specify a problem, design an algorithm, prove partial correctness, and give a complexity bound that matches the model of computation used.

150 estimated hours8 topics

Suggested background
  • Basic programming
  • Integer arithmetic
  • Induction

AX26-AI-101Undergraduate level

Supervised Learning

Connect model assumptions to training objectives, local optimisation, and an evaluation that does not leak future information.

150 estimated hours8 topics

Suggested background
  • Vectors and matrix products
  • Differentiation
  • Elementary probability

AX26-CS-201Undergraduate level

Approximation and Randomised Algorithms

Analyse approximation ratios and randomised procedures with explicit algorithms, expectation or concentration, and a clear statement of what NP-hardness still forbids.

200 estimated hours8 topics

Suggested background
  • AX26-CS-101 Algorithm Design
  • Discrete probability
  • Asymptotic notation

AX26-MATH-102Undergraduate level

Real Analysis

Develop ε–N and ε–δ arguments for sequences, continuity, Riemann integration, and interchange of limits.

150 estimated hours8 topics

Suggested background
  • Introductory calculus
  • Quantifiers and proof

AX26-STAT-101Undergraduate level

Probability

Build probability from spaces and random variables through expectation to elementary limit theorems.

150 estimated hours8 topics

Suggested background
  • Introductory calculus
  • Set notation

AX26-MATH-103Undergraduate level

Discrete Mathematics and Proofs

Learn to write direct proofs, contradiction, and induction on sets, counting problems, and elementary graphs.

100 estimated hours6 topics

Suggested background
  • School algebra
  • Willingness to write definitions before examples

AX26-MATH-104Undergraduate level

Groups

Work with groups as axiomatic structures: subgroups, homomorphisms, cosets, and Lagrange, with examples that fail if an axiom is dropped.

100 estimated hours6 topics

Suggested background
  • AX26-MATH-103 Discrete Mathematics and Proofs
  • Equivalence relations

AX26-MATH-105Undergraduate level

Introductory Calculus

Rebuild single-variable differentiation and integration with stated hypotheses, then introduce partial derivatives and multiple integrals.

150 estimated hours7 topics

Suggested background
  • School calculus notation
  • Functions of a real variable

AX26-STAT-301Postgraduate level

Probabilistic Combinatorics

Use the probabilistic method and concentration to prove existence and typical structure results in discrete mathematics.

150 estimated hours7 topics

Suggested background
  • AX26-STAT-101 Probability
  • AX26-MATH-103 Discrete Mathematics and Proofs

AX26-MATH-301Postgraduate level

Combinatorics

Study finite-set combinatorics alongside AXIOVUM-authored graph and counting topics, distinguishing syllabus alignment from our added material.

150 estimated hours7 topics

Suggested background
  • AX26-MATH-103 Discrete Mathematics and Proofs
  • Elementary counting

AX26-MATH-302Postgraduate level

Numerical Linear Algebra

Analyse matrix factorisations and iterative methods with stability, conditioning, and residual language.

150 estimated hours7 topics

Suggested background
  • AX26-MATH-101 Linear Algebra
  • Norms of vectors and matrices

AX26-MATH-303Postgraduate level

Fourier Analysis

Develop Fourier series and transforms at Part C grain, with convergence theorems and applications the synopsis names.

150 estimated hours7 topics

Suggested background
  • AX26-MATH-102 Real Analysis
  • L² inner-product language

AX26-STAT-302Postgraduate level

Stochastic Differential Equations

Introduce Brownian motion, Itô calculus, and SDEs at Part C taught grain, with hypotheses on existence and uniqueness kept explicit.

150 estimated hours6 topics

Suggested background
  • AX26-STAT-101 Probability
  • Ordinary differential equations at undergraduate grain

AX26-MATH-304Postgraduate level

Model Theory

Study structures, theories, and elementary embeddings at Part C grain, with compactness and completeness used as named tools.

150 estimated hours6 topics

Suggested background
  • AX26-MATH-103 Discrete Mathematics and Proofs
  • First-order logic at undergraduate grain

AX26-MATH-305Postgraduate level

Algebraic Topology

Introduce homotopy, fundamental groups, covering methods and selected homology computations with explicit point-set and algebraic prerequisites.

150 estimated hours6 topics

Suggested background
  • AX26-MATH-102 Real Analysis
  • Group language from AX26-MATH-104
  • Point-set topology: spaces, continuous maps and quotient topology
  • Basic abelian groups, quotient groups and chain-complex notation

AX26-MATH-306Postgraduate level

Further Functional Analysis

Develop Banach-space theorems at Part C grain: Hahn–Banach, uniform boundedness, open mapping, and related dual-space facts the synopsis names.

150 estimated hours6 topics

Suggested background
  • AX26-MATH-102 Real Analysis
  • Normed spaces at Part A grain

AX26-AI-301Postgraduate level

Theories of Deep Learning

Study mathematical theories of deep networks at Part C grain: approximation, optimisation landscapes, and generalisation analyses the synopsis treats.

150 estimated hours6 topics

Suggested background
  • AX26-AI-101 Supervised Learning
  • AX26-MATH-101 Linear Algebra
  • Probability at AX26-STAT-101 grain

AX26-MATH-307Postgraduate level

Category Theory

Explore categories, functors, natural transformations and universal properties, including products and adjunctions.

100 estimated hours6 topics

Suggested background
  • AX26-MATH-104 Groups
  • Comfort with functions, composition, and universal properties as slogans to be made precise
Compare background and study hours
Codes, names, cycles, suggested background, estimated hours and detail links for 20 AXIOVUM courses
Course Code Cycle Suggested background Estimated study hours Course detail
Linear Algebra AX26-MATH-101 Undergraduate level
  • Vectors and linear combinations
  • Elementary differentiation
 150 View syllabus and current access
Statistical Inference AX26-STAT-201 Undergraduate level
  • Random variables
  • Expectation and variance
  • Elementary differentiation
 200 View syllabus and current access
Algorithm Design AX26-CS-101 Undergraduate level
  • Basic programming
  • Integer arithmetic
  • Induction
 150 View syllabus and current access
Supervised Learning AX26-AI-101 Undergraduate level
  • Vectors and matrix products
  • Differentiation
  • Elementary probability
 150 View syllabus and current access
Approximation and Randomised Algorithms AX26-CS-201 Undergraduate level
  • AX26-CS-101 Algorithm Design
  • Discrete probability
  • Asymptotic notation
 200 View syllabus and current access
Real Analysis AX26-MATH-102 Undergraduate level
  • Introductory calculus
  • Quantifiers and proof
 150 View syllabus and current access
Probability AX26-STAT-101 Undergraduate level
  • Introductory calculus
  • Set notation
 150 View syllabus and current access
Discrete Mathematics and Proofs AX26-MATH-103 Undergraduate level
  • School algebra
  • Willingness to write definitions before examples
 100 View syllabus and current access
Groups AX26-MATH-104 Undergraduate level
  • AX26-MATH-103 Discrete Mathematics and Proofs
  • Equivalence relations
 100 View syllabus and current access
Introductory Calculus AX26-MATH-105 Undergraduate level
  • School calculus notation
  • Functions of a real variable
 150 View syllabus and current access
Probabilistic Combinatorics AX26-STAT-301 Postgraduate level
  • AX26-STAT-101 Probability
  • AX26-MATH-103 Discrete Mathematics and Proofs
 150 View syllabus and current access
Combinatorics AX26-MATH-301 Postgraduate level
  • AX26-MATH-103 Discrete Mathematics and Proofs
  • Elementary counting
 150 View syllabus and current access
Numerical Linear Algebra AX26-MATH-302 Postgraduate level
  • AX26-MATH-101 Linear Algebra
  • Norms of vectors and matrices
 150 View syllabus and current access
Fourier Analysis AX26-MATH-303 Postgraduate level
  • AX26-MATH-102 Real Analysis
  • L² inner-product language
 150 View syllabus and current access
Stochastic Differential Equations AX26-STAT-302 Postgraduate level
  • AX26-STAT-101 Probability
  • Ordinary differential equations at undergraduate grain
 150 View syllabus and current access
Model Theory AX26-MATH-304 Postgraduate level
  • AX26-MATH-103 Discrete Mathematics and Proofs
  • First-order logic at undergraduate grain
 150 View syllabus and current access
Algebraic Topology AX26-MATH-305 Postgraduate level
  • AX26-MATH-102 Real Analysis
  • Group language from AX26-MATH-104
  • Point-set topology: spaces, continuous maps and quotient topology
  • Basic abelian groups, quotient groups and chain-complex notation
 150 View syllabus and current access
Further Functional Analysis AX26-MATH-306 Postgraduate level
  • AX26-MATH-102 Real Analysis
  • Normed spaces at Part A grain
 150 View syllabus and current access
Theories of Deep Learning AX26-AI-301 Postgraduate level
  • AX26-AI-101 Supervised Learning
  • AX26-MATH-101 Linear Algebra
  • Probability at AX26-STAT-101 grain
 150 View syllabus and current access
Category Theory AX26-MATH-307 Postgraduate level
  • AX26-MATH-104 Groups
  • Comfort with functions, composition, and universal properties as slogans to be made precise
 100 View syllabus and current access

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