Notes
Browse rigorous mathematics notes one section at a time. Each page is written as a serious course-note article, with interaction used only where it clarifies a definition, computation, or proof idea, and each section exports as TXT or PDF.
CSCI2520
CSCI2520: Data structures
Structured notes for CSCI2520 data-structure foundations with operation-level reasoning and selective interactive demonstrations.
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 and priority queues
Graph traversals, spanning trees, shortest paths, topological sorting, heaps, and Huffman coding.
6 Chapter · 9 Sections
Series overviewMATH1025
MATH1025: Preparatory mathematics
Preparatory notes for algebraic technique, trigonometry, and proof-aware worked examples.
Chapter 0-1
Foundations and early methods
Foundational symbolic language and core transformations used across the course.
1 Chapter · 2 Sections
Series overviewMATH1030
MATH1030: Linear algebra I
Rigorous linear algebra notes on systems, matrices, structure, and proof, with interaction used only where it clarifies the mathematics.
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 multiplication, transpose, and structural matrix notation.
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 · 25 Sections
Series overviewMATH1090
MATH1090: Set theory
Rigorous course notes on logic, sets, number construction, the real numbers, limits, cardinality, and the first algebraic structures, written in linked sections with careful proofs and examples.
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