Section B.1 Definitions
This section provides a comprehensive list of all formal mathematical definitions in the text.
1 Welcome!
Definition 1.1.4 Algorithm
Definition 1.2.6 Division
Definition 1.2.7 Kid RSA encryption/decryption function
Definition 1.2.10 Greatest Common Divisor
2 Permutations
Definition 2.1.1 Permutation
Definition 2.1.3 Two-line notation
Definition 2.1.6 Permutation composition
Definition 2.1.9 Associative multiplication
Definition 2.1.14 Identity permutation
Definition 2.1.15 Natural powers of a permutation
Definition 2.1.16 Inverse of a permutation
Definition 2.1.20 Groups
Definition 2.1.21 Symmetric Group
Definition 2.1.22 Group isomorphism
Definition 2.1.24 Fixed points and supports of permutations
Definition 2.1.25 Cyclic permutations
Definition 2.1.27 Disjoint cycles
Definition 2.2.1 Object-oriented programming
Definition 2.2.4 Instantiation
3 Simple Cryptography
Definition 3.1.2 Shift cipher
Definition 3.2.8 Derangement
4 Linear Algebra
Definition 4.1.2 Vector space
Definition 4.1.3 The vector space \(\CV{n}\)
Definition 4.1.5 Complex conjugate
Definition 4.1.7 Linear transformation
Definition 4.1.9 Vector space isomorphism
Definition 4.1.11 Inner product
Definition 4.1.12 Standard Hermitian inner product
Definition 4.1.13 Magnitude in \(\CV{n}\)
Definition 4.3.1 Matrix over \(\Comps\)
Definition 4.3.3 Linear combination and span of a set
Definition 4.3.5 Matrix-vector product
Definition 4.3.9 Matrix-matrix product
Definition 4.4.1 Augmented matrices
Definition 4.4.3 Transpose of a matrix
5 Matrix Applications
Definition 5.1.1 System of Linear Equations
Definition 5.1.2 Augmented matrix representation of a SLE
Definition 5.1.3 Row swap operation
Definition 5.1.4 Row scaling operation
Definition 5.1.5 Row elimination operation
Definition 5.1.8 Row-equivalent matrices
Definition 5.1.10 Reduced row-echelon form
Definition 5.1.14 Matrix inverses
Definition 5.3.1 Triangular matrices
6 Graph Theory Algorithms
Definition 6.1.1 Graph
Definition 6.1.4 Adjacent and incident
Definition 6.1.5 Vertex degree
Definition 6.1.6 Subgraphs
Definition 6.1.8 Graph isomorphism
Definition 6.1.9 Graph automorphism
Definition 6.1.11 Paths
Definition 6.1.12 Graph distance
Definition 6.1.13 Cycles in graphs
Definition 6.1.15 Connected graphs
Definition 6.1.16 Components of a graph
Definition 6.1.17 Trees and forests
Definition 6.2.1 Weighted graphs
A Python crash course
Definition A.1.4 Syntax
Definition A.3.5 Mathematical function
Definition A.5.1 Programming function
Definition A.6.16 Semantic errors are bugs
