Knowledge map
Each knowledge point appears once. Zoom from the whole system down to a single theorem: what it uses, what uses it, and the counterexamples, lenses and history attached to it.
Relations between theorems have been indexed in 3 of 442 public notes so far. Elsewhere the map shows course and chapter structure only.
Courses
- CSCI2520
Programming foundations, abstract data types with stacks, queues and hashing, lists and recursion, complexity and sorting, trees and binary search trees, graphs, and heaps with greedy coding.
7 chapters14 notes
- CSCI2720
CSCI2720: Building Web Applications
From browser/server foundations and semantic HTML to responsive CSS, JavaScript, forms, Fetch and React.
7 chapters8 notes
- MATH1025
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 chapters21 notes
- MATH1030
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 chapters35 notes3 with relations indexed
- MATH1090
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 chapters23 notes
- MATH2010
Develop multivariable calculus from Euclidean geometry and limits to continuity, differentiability, Jacobian matrices, and the chain rule.
4 chapters14 notes
- MATH3320
MATH3320: Foundation 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 chapters18 notes
- MATH1010
- MATH1020
Functions, geometry, series, counting and probability.
6 chapters16 notes
- MATH1530
MATH1530: Mathematics for Business and Social Sciences
Algebra, trigonometry, vectors, calculus and integrated models.
12 chapters12 notes
- MATH1535
MATH1535: Intermediate Mathematics for Business and Social Sciences
Differential and integral calculus, numerical methods, linear systems, sequences and models.
8 chapters8 notes
- MATH1540
MATH1540: University Mathematics for Financial Studies
Coordinate partial derivatives, total differentiability, the chain rule and local sensitivity models.
18 chapters52 notes
- MATH1550
MATH1550: Methods of Matrices and Linear Algebra
Matrix methods, real vector spaces, spectral structure and rank-aware approximation.
6 chapters29 notes
- MATH1610
MATH1610: Linear Algebra for Advanced Accounting Analytics
Linear systems, identifiability, least squares, allocation, conditioning and matrix algebra.
5 chapters5 notes
- MATH1620
MATH1620: Calculus for Advanced Accounting Analytics
Rates, accumulation, multivariable models and constrained decisions.
6 chapters6 notes
- MATH1630
MATH1630: Linear Algebra and Applications
Linear maps, determinants, eigenvalues, orthogonality and matrix factorizations.
6 chapters6 notes
- MATH2046
MATH2046: Advanced Linear Algebra
Abstract linear structure, polynomial operators, canonical forms and bilinear geometry.
5 chapters5 notes
- MATH2050
MATH2050: Mathematical Analysis I
Real numbers, sequences, continuity, compactness and cardinality.
4 chapters12 notes
- MATH2060
MATH2060: Mathematical Analysis II
Differentiation, integration, sequences and series of functions, and elementary-function constructions.
15 chapters15 notes
- MATH2230
MATH2230: Complex Variables with Applications
Complex differentiation, elementary maps, contour methods, series and residues.
7 chapters8 notes
- MATH1050
MATH1050: Foundation of Modern Mathematics
Logic, proof, number systems, sets and their applications.
6 chapters15 notes
- MATH1510
MATH1510: Calculus for Engineers
Functions, limits, derivatives, integration, series and parametric curves for engineering applications.
7 chapters7 notes
- MATH1520
MATH1520: Calculus for Scientific Applications
Elementary functions, limits, differentiation, integration and ordinary differential equations; probability is historical enrichment.
5 chapters5 notes
- MATH1525
MATH1525: Basic Mathematics for Science and Technology
Build the algebraic and geometric foundations for science and technology: functions, equations, trigonometry, vectors, matrices, sequences, inequalities, polar coordinates and logarithms, with worked examples and complete practice solutions.
9 chapters10 notes
- MATH2066
MATH2066: Introductory 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 chapters12 notes
- MATH2020
MATH2020: Advanced Calculus II
Proper multiple integrals, rigorous coordinate changes, and vector integral theorems with their actual proof domains.
5 chapters15 notes
- MATH2040
Finite-dimensional structural linear algebra, with precise field conditions, complete polynomial and Jordan proofs, worked examples and solved practice.
4 chapters11 notes
- MATH2221
MATH2221: Mathematics Laboratory II
MATLAB-oriented computational mathematics laboratories.
8 chapters8 notes
- MATH2070
MATH2070: Algebraic Structures
Groups and their quotients, rings, polynomial quotients and field extensions, and Boolean algebra.
3 chapters7 notes
- MATH2076
MATH2076: Introduction to Algebra
Congruence and groups, quotient structures, polynomial rings and field extensions, and Boolean algebra for logic.
3 chapters10 notes
- MATH2530
MATH2530: Advanced Calculus (I) for Physical Science and Engineering
Space curves, differentiation and the chain rule, Taylor approximation and extrema, first- and second-order differential equations, and Jacobians in three variables.
7 chapters7 notes
- MATH2550
MATH2550: Quantitative Methods for Earth and Environmental Sciences
Matrices and tensors, differential equations for environmental balance, multiple integration and vector calculus with conservation laws.
13 chapters13 notes
Knowledge points by area
Linear algebra7 knowledge points
- Linear algebraIn MATH1030, MATH1550, MATH1610, MATH1630, MATH2040, & MATH2046
- Systems of linear equationsIn MATH1550 & MATH1630
- Matrix algebraIn MATH1550 & MATH1630
- Vector spacesIn MATH1630, MATH2040, & MATH2046
- Linear transformationsIn MATH1550, MATH1630, MATH2040, & MATH2046
- Eigenvalues and eigenvectorsIn MATH1550 & MATH1630
- Inner productsIn MATH1630, MATH2040, & MATH2046
Multivariable calculus5 knowledge points
- Partial derivativesIn MATH2010
- Multivariable differentiabilityIn MATH2010 & MATH2066
- Local extremaIn MATH2010 & MATH2530
- Multivariable Taylor polynomialsIn MATH2010
- Multiple integralsIn MATH2020 & MATH2550
Calculus1 knowledge point
- Chain ruleIn MATH2010
Optimization3 knowledge points
- Lagrange multipliersIn MATH2010
- OptimizationIn MATH3320
- Gradient descentNot yet linked to a course note
Analysis1 knowledge point
- Implicit function theoremIn MATH2010
Probability2 knowledge points
- Probability foundationsIn MATH3320
- Markov chainsNot yet linked to a course note
Approximation4 knowledge points
- Linear approximationIn MATH3320
- Polynomial approximationIn MATH3320
- High-dimensional approximationIn MATH3320
- Neural-network approximationIn MATH3320
Numerical analysis1 knowledge point
- Proper orthogonal decompositionIn MATH3320
Fourier analysis1 knowledge point
- Fourier seriesNot yet linked to a course note