Notes
Choose a course to start.
CSCI2520
CSCI2520: Data structures
Data-structure notes.
Chapter 0
Programming foundations
Language and memory tools used throughout the data-structure notes.
Chapter 1
ADT and operation semantics
From ADT contracts to stack/queue behavior and dictionary-style hashing operations.
Chapter 2
Lists and recursion
Recursive list contracts, head-tail reasoning, and representation-aware operation cost.
Chapter 3
Complexity and sorting
Asymptotic growth, cost comparison, and sorting-oriented complexity reasoning.
Chapter 4
Trees and BSTs
Binary tree traversal, reconstruction, and binary-search-tree operations.
Chapter 5
Graphs
Graph representations and traversals, minimum spanning trees, shortest paths, and topological ordering.
Chapter 6
Heaps and greedy coding
Binary heaps, priority queues, Huffman coding, and heap-based multiway merging.
7 Chapter · 14 Sections
Series overviewMATH1025
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.
Chapter 0-1
Foundations and early methods
Foundational symbolic language and core transformations used across the course.
Chapter 2-3
Proof and inequalities
Induction, order reasoning, rational inequalities, absolute value, and first classical inequalities.
Chapter 4
Binomial theorem
Factorials, permutations, combinations, Pascal's identity, and coefficient extraction from binomial expansions.
Chapter 5
Sequences
Sequences as functions, recursive construction, arithmetic and geometric progressions, finite sums, and first applied recurrences.
Chapter 6
Complex numbers
Complex arithmetic, conjugates, modulus, polar and exponential forms, roots of unity, and complex-plane geometry.
Chapter 7
Integer methods
Divisibility, primes, gcd computations, Bezout identities, and integer linear equations.
Chapter 8
Polynomial methods
Polynomial arithmetic, division with remainder, polynomial gcds, irreducibility, rational functions, partial fractions, and Vieta formulas.
Chapter 9
Vectors and geometry
Vectors, norms, inner products, projections, cross products, and area and volume geometry.
Chapter 10
Lines, planes, and curves
Lines and planes, distances and projections, and parametrized curves with velocity and speed.
Chapter 11
Conic sections
Focal definitions, tangents and reflection, optional coordinate classification, and exact conic loci and parametric applications.
10 Chapter · 21 Sections
Series overviewMATH1030
MATH1030: Linear 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.
Chapter 1
Systems of equations
Learn to read equations as full solution sets.
Chapter 2
Matrices and elimination
Build matrix intuition and use row reduction with purpose.
Chapter 3
Matrix algebra
Matrix arithmetic, multiplication, transpose, special and elementary matrices, and block structure.
Chapter 4
Solution structure
Homogeneous systems, null spaces, and the shape of full solution sets.
Chapter 5
Invertibility
Understand when a matrix can be undone and why that matters.
Chapter 6
Vector spaces
Move from matrix procedures to the structure of spaces, span, independence, and basis.
Chapter 7
Determinants
Determinants, cofactor formulas, and the structural algebra that connects row operations, transpose, and invertibility.
Chapter 8
Eigenvalues and diagonalization
Eigenvalues, eigenspaces, similarity, and diagonalization as the next structural layer after determinants.
Chapter 9
Inner products and orthogonality
Inner products, orthogonality, orthonormal bases, and Gram-Schmidt as the geometric layer after eigenvalues.
9 Chapter · 35 Sections
Series overviewMATH1090
MATH1090: Set 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.
Chapter 1
Logic
Reasoning tools for statements, connectives, and quantifiers.
Chapter 2
Sets and relations
Basic set language, functions, and relations.
Chapter 3
Numbers by construction
How natural numbers, integers, and rationals are built, and where Q still falls short.
Chapter 4
Order and completeness
Total order, bounds, supremum and infimum, and the completeness gap between Q and R.
Chapter 5
Sequences and first limits
Sequences, Cauchy convergence, and the first delta-epsilon treatment of function limits.
Chapter 6
Big sets
Cardinality, countability, Cantor's theorem, choice principles, intervals, Cantor set, density, and well-ordering.
Chapter 7
Sets with structure
Binary operations and the first algebraic structures built on top of sets.
7 Chapter · 23 Sections
Series overview