### Probability

**EE 503**

- Countable and Uncountable Sets, Outcomes, Events, Probabilities
- Conditional Probabilities, Independence
- Counting, Playing Cards and Balls and Bins
- Baye’s Rule, Random Variables, CDFs and PDFs
- Functions of Random Variables, Expectations, Iterated Expectations
- Law of Large Numbers
- Central Limit Theorem and Gaussians
- Hypothesis Testing, Minimum Mean Square Distortion
- Discrete Time Markov Chains
- Discrete Time Queues, Simulation
- Continuous Time Chains
- Poisson Processes, M/M/1, Renewal Theory

### Random processes

**EE 562**

- Definition of random processes: random variables, random vectors, random sequences, random waveforms, etc.
- Second order statistics: Properties of correlation functions
- Covariance matrix factorization, eigenvalues, eigenvectors, causal factoring and whitening concepts
- Gaussian processes
- Simple hypothesis tests
- Linear minimum-mean-square-error estimation, orthogonality principle
- Linear operations on random processes, convergence concepts: convolution, integration, differentiation
- Frequency domain analysis: time invariant linear operations
- Energy spectra, power spectra, white noise approximations
- Linear transformations of wide-sense stationary random processes, spectral factorization, and applications
- Poisson distributed events in time, Campbell’s theorem
- Karhuenen-Loeve expansions on finite intervals
- Narrowband process representations
- Time averages, ergodicity

### Linear algebra

**EE 510**

- Systems of Linear Equations
- Review of Elementary Linear Algebra, Algebraic Structures
- Vector Spaces
- Normed and Inner Product Spaces
- Linear Transformations
- Linear Transformations and Orthogonality
- The Moore-Penrose Pseudo-Inverse, Linear Least Squares Problems
- Eigenvalues and Eigenvectors
- Singular Value Decomposition
- Review of Multivariable Calculus, Bilinear and Quadratic Forms
- Application: Optimization
- Application: Analysis of Linear Dynamical Systems
- Application: Stability Analysis of Dynamical Systems
- Tensor Analysis

### Signals, Systems, and Comms

**EE 467**

**EE 301**

- Time-Domain Analysis of Continuous-Time Systems
- Laplace Transform (Continuous Time)
- Fourier Series and Fourier Transform (Continuous Time)
- Time-Domain Analysis of Discrete-Time Systems
- Discrete-Time Fourier Analysis
- z-Transform (z-Transform)

### Electricity and Magnetism

**EE 370**

- Calculate voltages, currents, waves, and impedance in transmission lines
- Time and phasors domain analysis
- Maxwell's equations and calculations of the energy of electromagnetic fields
- Electric and magnetic fields of plane waves
- Dipole antennas and their characteristics
- Wireless communication and understanding receive power