知识库

Solving Linear Equations

Solving 2- and 3-Variable Linear Systems (Elimination / Cramer's Rule)

Complex Numbers (Modulus, Argument, Arithmetic)

Derivatives: Concepts and Basic Rules

Indefinite and Definite Integrals

First-Order Ordinary Differential Equations

Properties and Graph of the Exponential Function eˣ

Reading Function Graphs (v-t, i-t)

Breadboard Basics

Vector Spaces & Subspaces

Linear Transformations & Change of Basis

Inner Products, Orthogonalisation & QR

Least Squares Approximation

Determinants

Eigenvalues, Eigenvectors & Diagonalisation

Symmetric Matrices & Quadratic Forms

Jordan Forms & Generalised Eigenspaces

Matrix Exponentials

Systems of Linear ODEs

Descriptive Statistics

Random Variables

Special Probability Distributions

Sampling Distributions & the CLT

Confidence Intervals

Hypothesis Testing

Inference for Two Means

Simple Linear Regression

Analysis of Variance (ANOVA)

Vectors in Rⁿ & the Dot Product

Matrix Algebra: Multiplication, Transpose, Inverse

Counting & Combinatorics

Probability Basics: Sample Spaces, Events, Conditional Probability

MATH2099 · 描述统计

MATH2099 · 随机变量的期望

MATH2099 · 五个特殊分布

MATH2099 · 抽样分布与 CLT

MATH2099 · 置信区间与比例

Shell Sort

Counting Sort

Bipartite Graph (2-Coloring Test)

Big-O & Time Complexity Analysis

Graph Representation (adjacency matrix/list)

Euler & Hamilton Paths/Circuits

Shortest Path

Abstract Data Types

Topological Sort

Priority Queue

Stable Sort

Binary Search

Stacks

Queues

Tree Traversal (pre/in/post/level order)

2-3-4 Trees

Tries

Recursion

Sorting Algorithms

Arrays

Linked Lists

Binary Trees

Binary Search Tree (BST)

AVL Trees (self-balancing, rotations)

Hash Tables

Heaps / Priority Queues

Depth-First Search (DFS)

Breadth-First Search (BFS)

Minimum Spanning Tree (Prim/Kruskal)

Pointers