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Modular Knowledge Base
Central repository of reusable knowledge units consumed by olverae sub-sites.
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Open knowledge base →
Browse every knowledge unit by subject tag, with search.
/modules
Open test bank →
Past papers and practice questions by course.
/testbank
Open coding problems →
Practice coding problems online with autotest; sign in to run & submit.
/cp
Open breadboard challenges →
Build a circuit to spec in the simulator; auto-graded.
/challenges
Mathematics · Math Foundations
Solving Linear Equations
~8 min
Mathematics · Math Foundations
Solving 2- and 3-Variable Linear Systems (Elimination / Cramer's Rule)
~15 min
Mathematics · Math Foundations
Complex Numbers (Modulus, Argument, Arithmetic)
~12 min
Mathematics · Calculus
Derivatives: Concepts and Basic Rules
~12 min
Mathematics · Calculus
Indefinite and Definite Integrals
~12 min
Mathematics · Calculus
First-Order Ordinary Differential Equations
~15 min
Mathematics · Calculus
Properties and Graph of the Exponential Function eˣ
~8 min
Mathematics · Math Foundations
Reading Function Graphs (v-t, i-t)
~8 min
Electrical · Circuit Fundamentals
Breadboard Basics
~10 min
Mathematics · Linear Algebra
Vector Spaces & Subspaces
~25 min
Mathematics · Linear Algebra
Linear Transformations & Change of Basis
~25 min
Mathematics · Linear Algebra
Inner Products, Orthogonalisation & QR
~30 min
Mathematics · Linear Algebra
Least Squares Approximation
~25 min
Mathematics · Linear Algebra
Determinants
~20 min
Mathematics · Linear Algebra
Eigenvalues, Eigenvectors & Diagonalisation
~30 min
Mathematics · Linear Algebra
Symmetric Matrices & Quadratic Forms
~25 min
Mathematics · Linear Algebra
Jordan Forms & Generalised Eigenspaces
~30 min
Mathematics · Linear Algebra
Matrix Exponentials
~25 min
Mathematics · Linear Algebra
Systems of Linear ODEs
~30 min
Mathematics · Statistics
Descriptive Statistics
~20 min
Mathematics · Statistics
Random Variables
~25 min
Mathematics · Statistics
Special Probability Distributions
~30 min
Mathematics · Statistics
Sampling Distributions & the CLT
~25 min
Mathematics · Statistics
Confidence Intervals
~25 min
Mathematics · Statistics
Hypothesis Testing
~30 min
Mathematics · Statistics
Inference for Two Means
~25 min
Mathematics · Statistics
Simple Linear Regression
~30 min
Mathematics · Statistics
Analysis of Variance (ANOVA)
~30 min
Mathematics · Linear Algebra
Vectors in Rⁿ & the Dot Product
~18 min
Mathematics · Linear Algebra
Matrix Algebra: Multiplication, Transpose, Inverse
~20 min
Mathematics · Statistics
Counting & Combinatorics
~15 min
Mathematics · Statistics
Probability Basics: Sample Spaces, Events, Conditional Probability
~22 min
Mathematics · Statistics
MATH2099 · 描述统计
~10 min
Mathematics · Statistics
MATH2099 · 随机变量的期望
~10 min
Mathematics · Statistics
MATH2099 · 五个特殊分布
~10 min
Mathematics · Statistics
MATH2099 · 抽样分布与 CLT
~10 min
Mathematics · Statistics
MATH2099 · 置信区间与比例
~10 min
Computing · Algorithms
Shell Sort
~9 min
Computing · Algorithms
Counting Sort
~8 min
Computing · Algorithms
Bipartite Graph (2-Coloring Test)
~9 min
Computing · Algorithms
Big-O & Time Complexity Analysis
~16 min
Computing · Data Structures
Graph Representation (adjacency matrix/list)
~16 min
Computing · Algorithms
Euler & Hamilton Paths/Circuits
~16 min
Computing · Algorithms
Shortest Path
~16 min
Computing · C Programming
Abstract Data Types
~10 min
Computing · Algorithms
Topological Sort
~14 min
Computing · Data Structures
Priority Queue
~12 min
Computing · Algorithms
Stable Sort
~9 min
Computing · Algorithms
Binary Search
~11 min
Computing · Data Structures
Stacks
~16 min
Computing · Data Structures
Queues
~16 min
Computing · Data Structures
Tree Traversal (pre/in/post/level order)
~16 min
Computing · Data Structures
2-3-4 Trees
~16 min
Computing · Data Structures
Tries
~16 min
Computing · Algorithms
Recursion
~16 min
Computing · Algorithms
Sorting Algorithms
~16 min
Computing · Data Structures
Arrays
~16 min
Computing · Data Structures
Linked Lists
~16 min
Computing · Data Structures
Binary Trees
~16 min
Computing · Data Structures
Binary Search Tree (BST)
~16 min
Computing · Data Structures
AVL Trees (self-balancing, rotations)
~16 min
Computing · Data Structures
Hash Tables
~16 min
Computing · Data Structures
Heaps / Priority Queues
~16 min
Computing · Algorithms
Depth-First Search (DFS)
~16 min
Computing · Algorithms
Breadth-First Search (BFS)
~16 min
Computing · Algorithms
Minimum Spanning Tree (Prim/Kruskal)
~16 min
Computing · C Programming
Pointers
~12 min