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Mathematics · first-year foundations
1000-level
MATH1025
Preparatory mathematics
Develop the algebraic and geometric tools used in university mathematics: proof and inequalities, complex numbers, sequences, polynomials, vectors and conic sections. Start with precise algebra, then learn to choose and justify a method.10 chapters · 21 sections · EN / 繁 / 简MATH1030Linear algebra I
Start with systems of equations and row reduction, then connect matrix calculation to span, independence, basis and dimension. Determinants, eigenvectors and inner products reveal the algebraic and geometric structure behind those calculations.9 chapters · 35 sections · EN / 繁 / 简MATH1090Set theory
Build precise mathematical reasoning from logic and sets, then construct the number systems, understand completeness and limits, and compare infinite sets. Begin with propositions and work toward proofs that depend on clearly stated assumptions.7 chapters · 23 sections · EN / 繁 / 简MATH1010Calculus I
Limits, derivatives, integration and applications.6 chapters · 15 sections · EN / 繁 / 简MATH1020General Mathematics
Functions, geometry, series, counting and probability.6 chapters · 16 sections · EN / 繁 / 简MATH1550Matrices and linear algebra
Matrix methods, real vector spaces, spectral structure and rank-aware approximation.6 chapters · 29 sections · EN / 繁 / 简MATH1630Linear algebra
Linear maps, determinants, eigenvalues, orthogonality and matrix factorizations.6 chapters · 6 sections · EN / 繁 / 简MATH1050Foundation of Modern Mathematics
Logic, proof, number systems, sets and their applications.6 chapters · 15 sections · EN / 繁 / 简MATH1520Calculus for scientific applications
Elementary functions, limits, differentiation, integration and ordinary differential equations; probability is historical enrichment.5 chapters · 5 sections · EN / 繁 / 简Mathematics · second year and beyond
2000–3000-level
MATH2010
Advanced calculus I
Develop multivariable calculus from Euclidean geometry and limits to continuity, differentiability, Jacobian matrices, and the chain rule.4 chapters · 14 sections · EN / 繁 / 简MATH3320Foundation of Data Analytics
Regression and validation, sparse approximation, spectral and learned dimensionality reduction, matrix completion, quadratic optimization, and clustering from center objectives to density hierarchies.6 chapters · 18 sections · EN / 繁 / 简MATH2046Advanced linear algebra
Abstract linear structure, polynomial operators, canonical forms and bilinear geometry.5 chapters · 5 sections · EN / 繁 / 简MATH2050Mathematical analysis
Real numbers, sequences, continuity, compactness and cardinality.4 chapters · 12 sections · EN / 繁 / 简MATH2060Mathematical analysis II
Differentiation, integration, sequences and series of functions, and elementary-function constructions.15 chapters · 15 sections · EN / 繁 / 简MATH2230Complex variables
Complex differentiation, elementary maps, contour methods, series and residues.7 chapters · 8 sections · EN / 繁 / 简MATH2066Introductory Real Analysis
Differentiability, proper and improper Riemann integration, all-order Taylor formulas, uniform convergence, parameter integrals, double series and analytic constructions, with proofs and complete solutions.6 chapters · 12 sections · EN / 繁 / 简MATH2020Advanced calculus II
Proper multiple integrals, rigorous coordinate changes, and vector integral theorems with their actual proof domains.5 chapters · 15 sections · EN / 繁 / 简MATH2040Linear algebra II
Finite-dimensional structural linear algebra, with precise field conditions, complete polynomial and Jordan proofs, worked examples and solved practice.4 chapters · 11 sections · EN / 繁 / 简MATH2221Mathematics Laboratory II
MATLAB-oriented computational mathematics laboratories.8 chapters · 8 sections · EN / 繁 / 简MATH2070Algebraic Structures
Groups and their quotients, rings, polynomial quotients and field extensions, and Boolean algebra.3 chapters · 7 sections · EN / 繁 / 简MATH2076Introduction to Algebra
Congruence and groups, quotient structures, polynomial rings and field extensions, and Boolean algebra for logic.3 chapters · 10 sections · EN / 繁 / 简Computer science
CSCI
CSCI2520