Undergraduate Courses
Graduate Courses
Summer Courses
Classes are usually structured as follows:
- One and a half weekly hours of teaching:
Focused on the 4 C’s of learning:
1. Creativity
2. Critical thinking
3. Collaboration
4. Communication
- One weekly hour of quiz:
Alternating between a theory quiz and a programming quiz -
Each class is also comprised of a midterm and a final project. The projects have very
loosely description and are meant to give the students the opportunity to develop
teamwork and presentation skills.
Course Syllabus
Signal and System
Follows the book: Haykin, Simon, and Barry Van Veen. Signals and systems. John Wiley & Sons, 2007.
Topics covered:
- Continuous-time and discrete-time signals
- Linear time invariant systems
- Time Domain Analysis
- Discrete & Continuous Convolution
- Fourier Series
- Fourier Transformation
- Sampling
- Discrete (and Fast) Fourier Transforms
- Laplace transform
- Z Transform
Introduction to communication and system
Follows the book: Proakis, John G., et al. Communication systems engineering. Vol. 2. New Jersey: Prentice Hall, 1994.
Topics covered:
- Signal representations and Fourier transforms
- Amplitude modulation, frequency translation
- Angle modulation: PM, FM, PLL, non-linear effects
- Multiplexing, superheterodyne receivers, signals through systems
- Probability & random processes, statistics, correlations, spectral density
- Noise and its characterization, effects on analog modulation
- A/D, sampling theorem, PAM, quantization and PCM
- Baseband digital signaling, matched filter, error probability
- ISI, Nyquist criterion, comparison of baseband digital signaling schemes
Ordinary differential equations
Follows the book: Boyce, William E., Richard C. DiPrima, and Douglas B. Meade. Elementary differential equations and boundary value problems. Vol. 9. New York: Wiley, 1992.
.Topics covered:
- Direction fields , classification of differential equations
- First order differential equations
- Autonomous equations and population dynamics
- Second order linear differential equations
- Method of undetermined coefficients
- Higher order linear equations
- The Laplace Transform
- 4 Differential equations with discontinuous forcing functions
- Systems of two linear differential equations
- Linear systems of differential equations
Numerical Analysis
Follows the book: Burden, Richard L., and J. Douglas Faires. “Numerical Analysis, Brooks.” Cole, Belmont, CA (1997).
Topics covered:
- Preliminaries of Computing
- Basic concepts: round-off errors
- Numerical solution of Nonlinear Equations
- Bisection method, fixed-point iteration, Newton’s method.
- Error analysis for Iterative Methods.
- Computing roots of polynomials.
- Interpolation and Polynomial Approximation
- Lagrange Polynomial
- Divided Differences
- Hermite Interpolation
- Numerical integration and differentiation
- Trapezoidal rule, etc., Gaussian quadrature and Euler-Maclaurin formula. Direct methods for solving linear systems, numerical factorization
Lab on Python for data science and machine learning
Folow the book: Intro to Python for Computer Science and Data Science: Learning to Program with AI, Big Data and The Cloud by Paul J. Deitel , and Harvey Deitel
Topics covered:
- Fundamental programming concepts
- File IO and exception handling
- Algorithms and recursion
- Python libraries and Data collection
- Mathematical and scientific computing
- Data manipulation and visualization
- Machine learning
Information Theory
Follows the book: Alajaji, Fady, and Po-Ning Chen. An Introduction to Single-User Information Theory. Springer, 2018.
Topics covered:
- Information measures (entropy, divergence, mutual information)
- Lossless data compression:
- Lossy data compression:
- Channel coding
- Binary hypothesis testing:
Multi-terminal information theory
Follows the book: Kramer, Gerhard. “Topics in multi-user information theory.” Foundations and Trends® in Communications and Information Theory 4.4–5 (2008): 265-444.
Topics covered:
- Review channel coding theory and rate distortion theory.
- Multi-access channels.
- Distributed source coding: Slepian-Wolf, Wyner-Ziv, Berger-Tung.
- Gelfand-Pinsker theorem and Costa’s dirty paper coding.
- Broadcast channels: Marton’s region and dirty paper precoding.
- Mac channel
- Interference channel
Machine learning theory
Follows the book: Nesterov, Yurii. Introductory lectures on convex optimization: A basic course. Vol. 87. Springer Science & Business Media, 2013.
Topics covered:
- Gradient descent, Convexity, first-order methods
- Subgradient method, Generalized gradient descent, Acceleration
- Newton’s Method, Duality
- Matrix differentials
- Linear Programming
- Duality, KKT conditions
- ADMM, Mirror descent, Quadratic programs, cone programs
- SVMs; Interior point methods
Convex Optimization
Follows the book: Boyd, Stephen, and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004.
Topics covered:
- Affine and convex sets
- Generalized inequalities
- Separating and supporting hyperplanes
- Dual cones and generalized inequalities
- Convex functions: properties and examples
- Operations that preserve convexity
- The conjugate function
- Quasiconvex functions
- Log-concave and log-convex functions
- Optimization problems
- Convex optimization
- Linear optimization problems
- Quadratic optimization problems
- Geometric programming
- Generalized inequality constraints
- Vector optimization
- Duality
- The Lagrange dual function
- The Lagrange dual problem
- Optimality conditions
Machine Learning Theory
Follows the book: Understanding Machine Learning: From Theory to Algorithms Shai Ben-David and Shai Shalev-Shwartz
Topics covered:
- Introduction, learning theory and statistical learning theory
- VC theory
- PAC model
- Metric spaces, Convex sets, supporting hyperplanes
- Duality theory, Lagrangian
- Primal & Dual problem, Strong convexity, Lipschitz continuity
- Duality theory and KKT conditions