| Topic | Formula/Command | Example |
|---|---|---|
| Set Theory | ||
| Union of Sets | union(A, B) |
A = {1, 2, 3}; B = {3, 4, 5}; |
| Intersection of Sets | intersect(A, B) |
A = {1, 2, 3}; B = {3, 4, 5}; |
| Complement of a Set | complement(A, U) |
A = {1, 2, 3}; U = {1, 2, 3, 4, 5}; |
| Cartesian Product | cartesian(A, B) |
A = {1, 2}; B = {'x', 'y'}; |
| Combinatorics | ||
| Factorial | factorial(n) |
n = 5; |
| Permutations | nchoosek(n, k) |
n = 5; k = 3; |
| Combinations | npermutek(n, k) |
n = 5; k = 2; |
| Probability | ||
| Probability of an Event | P(event) = (number of favorable outcomes) / (total number of outcomes) |
favorable = 3; total = 6; P = favorable / total; |
| Expected Value (Discrete Random Variable) | E(X) = Σ(x * P(X=x)) |
X = [1, 2, 3]; P = [0.2, 0.3, 0.5]; |
| Graph Theory | ||
| Degree of a Vertex | degree(vertex) |
vertex = 3; |
| Adjacency Matrix | adjacency_matrix(graph) |
graph = [0, 1, 0; 1, 0, 1; 0, 1, 0]; |
| Shortest Path (Dijkstra's Algorithm) | Implement as needed | |
| Number Theory | ||
| Greatest Common Divisor (GCD) | gcd(a, b) |
a = 12; b = 18; |
| Least Common Multiple (LCM) | lcm(a, b) |
a = 12; b = 18; |
| Prime Check | Implement as needed | n = 17; |
| Logic | ||
| Logical AND | and(A, B) |
A = true; B = false; |
| Logical OR | or(A, B) |
A = true; B = false; |
| Logical NOT | not(A) |
A = true; |
| Proof Techniques | ||
| Proof by Contradiction | Implement as needed | |
| Mathematical Induction | Implement as needed | |
| Algorithms | ||
| Euclidean Algorithm (GCD) | Implement as needed | |
| Binary Search | Implement as needed |
Please note that for certain mathematical operations and proof techniques, MATLAB provides built-in functions and commands to use directly. For algorithms, you may need to implement them based on your specific requirements.