multiplication, Gaussian elimination, Row
transformations, row exchanges, triangular factors,
Inverses, transposes, solving Ax=b, A=LU
decomposition.
Vector Spaces: Vector spaces, subspaces, solving
Ax=0 and Ax=b, Linear independence, Basis, bases
and dimension. Four fundamental subspaces of a
matrix. Linear Transformations.
Orthogonality: Orthogonal vectors, orthogonal
subspaces, Projections onto lines, projections onto
subspaces and least squares, Gram-Schmidt.
Example: Fast Fourier Transform, Fourier series.
Determinants: Introductions, properties of the
Determinant, Formulas for the
Determinant,Applications.
Eigenvalues and Eigenvectors: Diagonalization
of Matrix, Powers A^k, Complex Matrices, Similarity
Transformation, *Difference Equations and powers
A^k, *Differential Equations and e^{At}.
Positive Definite Matrices: Minima, Maxima,
Saddle points, Tests for Positive definiteness,
Singular Value Decomposition SVD.
*Matrix norm, Condition number, Iterative methods
for Ax=b, Linear Programming
*represents optional topics.
● Row exchanges, Triangular factors,
LU=b,inverses, transposes, intro to vector space,
solving Ax=0
● Solving Ax=b, linear independence , basis,
dimension, four subspaces. Orthogonality
definition, projections onto lines
● Projections onto subspaces, Least squares
minimization, orthogonal bases, Gram-Schmidt,
FFT, Fourier transforms
● Determinants, Properties, formulas, applications,
area, volume etc.
● Eigenvalues and e-vectors:diagonalization,
Complex matrices,similarity transformations. *
A^k, e^{At}
● Positive Definite Matrices, minima-maxima,
saddle pt, tests of psd, SVD,
● Reserved for overflow. Additional topics: Matrix
norm, condition no, Linear Programming
Machine
Learning for
Cyber Security
1. Articulate and explain which problems in
Cyber Security may be solvable with
Machine Learning.
2. Understand and implement machine
learning algorithms and models for Cyber
Security problems such as malware
analysis, intrusion detection, spam filtering,
fraud detection, online behavior analysis
etc.
3. Get basic hands-on experience with
● Basic Probability theory and Distributions
● Linear Regression (uni- and multi-variate) and
Logistic Regression
● Basic Classification Techniques
○ Bayesian Classification
○ Other Classification Techniques
● Unsupervised Learning
○ Spectral Embedding, Manifold detection
and Anomaly Detection
● Supervised Learning