Limits and continuity of functions of a single variable. Differentiability. Techniques of differentiation. Implicit differentiation. Local extrema, first and second derivative tests for local extrema. Concavity and inflection points. Curve sketching. Applied extrema problems. The Mean Value Theorem and applications.
Pre-requisites: One year preparatory mathematics or equivalent
Definite and indefinite integrals of functions of a single variable. Fundamental Theorem of Calculus. Techniques of integration. Hyperbolic functions. Applications of the definite integral to area, volume, arc length and surface of revolution. Improper integrals. Sequences and series: convergence tests, integral, comparison, ratio and root tests. Alternating series. Absolute and conditional convergence. Power series. Taylor and Maclaurin series.
Pre-requisites: MATH 101
Polar coordinates, polar curves, area in polar coordinates. Vectors, lines, planes and surfaces. Cylindrical and spherical coordinates. Functions of two and three variables, limits and continuity. Partial derivatives, directional derivatives. Extrema of functions of two variables. Double integrals, double integrals in polar coordinates. Triple integrals, triple integrals in cylindrical and spherical coordinates.
Pre-requisites: MATH 102
Systems of linear equations. Vector spaces Rn: subspaces, bases, dimensions. Rank of matrices. Eigenvalues and eigenvectors. Similar matrices. Diagonalizable matrices. Matrix exponential. First order differential equations: separable, linear, exact, substitution methods. Applications to linear models of first order. The homogeneous differential equations with constant coefficients. Wronskian. Nonhomogeneous differential equations. Methods of undetermined coefficients and variation of parameters. Systems of differential equations. Non-homogeneous systems. Series solutions.
Pre-requisites: MATH 102
Propositional Logic, Propositional Equivalence, Predicates and Quantifiers, Nested Quantifiers, Rules of Inference; Methods of Proof, Divisibility and the Fundamental Theorem of Arithmetic; Sets, Set Operations, Cardinality of Sets; Functions; Recurrence Relations, Solving Recurrence Relations, Equivalence Relations and Congruences, Sequences and Summations; Mathematical Induction, Strong Induction, Recursive Definitions and Structural Induction, Well-Ordering Principle; Basics of Counting, Pigeonhole Principle, Permutations and Combinations, Binomial Coefficients.
Pre-requisites: MATH 101
Note: Not to be taken with ICS253
Mathematics framework for machine learning, mathematical foundations and computational principles of machine learning underlying modern learning algorithms, least squares methods, support vector machines, linear and nonlinear principal component analysis, neural networks, connections between deep learning and differential equations. Integration of theory with Python-based implementation to bridge mathematical models and practical algorithms.
Pre-requisites: (MATH 225 or MATH 208), STAT 201, and ISE 291
Special functions. Bessel's functions and Legendre polynomials. Vector analysis including vector fields, divergence, curl, line and surface integrals, Green's, Gauss' and Stokes' theorems. Sturm-Liouville theory. Laplace transforms. Fourier series and transforms. Introduction to partial differential equations and boundary value problems in rectangular, cylindrical and spherical coordinates.
Pre-requisites: Math 201 , MATH 208
Development of mathematical models for engineering and applied sciences with emphasis on real-world systems, deterministic, discrete, and stochastic models, introductory data-driven modeling approaches models formulation from physical principles, analysis of system behavior, models’ validation considering data, assumptions, uncertainty, and errors, dimensional analysis and scaling laws, dynamical systems, conservation laws, partial differential equations, and probabilistic modeling with basic reliability concepts, use of computational tools (MATLAB/Python) for simulation, visualization, and model evaluation.
Pre-requisites: MATH 333, and STAT 201
Numerical linear algebra with emphasis on computational methods for solving matrix problems arising in scientific computing and data-driven applications, Matrix factorizations, least squares, singular value decomposition, conditioning, eigenvalue problems, iterative methods, efficient implementation and practical use in high-dimensional settings, including applications in data analysis and machine learning.
Pre-requisites: MATH 371 or CIE 301 or MATH 225 or MATH 208
Students are required to spend one summer working in industry prior to the term in which they expect to graduate. Students are required to submit a report and make a presentation on their summer training experience and the knowledge gained. The student may do his summer training by doing research and other academic activities
Pre-requisites: ENGL 214, Junior Standing, Approval of the Department
This is the first part of a two-semester capstone project designed for senior mathematics students. Under the supervision of a faculty member, students work on a research topic in mathematics, either suggested by the faculty member or chosen by the students. Students conduct a review of relevant literature, prepare a proposal outlining the project’s scope, objectives, and proposed methodology. The course emphasizes critical thinking, problem solving skills, and the applications of mathematical concepts and methods learned in previous courses.
Pre-requisites: Senior Standing
This is the second part of a two-semester senior-year capstone project in mathematics. Students continue working on the research project proposed in MATH 413 under the supervision of a faculty member. The course involves implementing mathematical methods, analyzing results, and documenting findings in a formal written report and an oral presentation.
Pre-requisites: MATH 413
Modern cryptography from a provable security perspective, formal security definitions (confidentiality, integrity, authentication), public-key encryption, signatures schemes, message authentication codes (MACs), zero-knowledge proofs, and foundational cryptographic protocols.
Pre-requisites: MATH 210, STAT 201, ICS 202
Foundations of error-correcting codes and their information-theoretic limits, code parameters, Hamming distance, linear codes, finite fields, fundamental bounds on codes, Reed–Solomon codes, channel capacity, Shannon’s theorem, list decoding, and polynomial-based codes including Reed–Muller codes.
Pre-requisites: MATH 210 and (MATH 225 or MATH 208)
Note: Not to be taken with EE 430
Advanced methods for high-dimensional, simulation-based engineering optimization; problem formulation, derivative computation including automatic differentiation, gradient-based optimization algorithms, derivative-free and heuristic methods, surrogate modeling and experimental design, and an introduction to optimization under uncertainty and robust design.
Pre-requisites: (MATH 104 or MATH 201), ICS 104, MATH 373
Presentation and interpretation of data, elementary probability concepts, random variables and probability distributions, binomial, hypergeometric, Poisson, exponential, Weibull, normal and lognormal random variables. Estimation, hypothesis testing for mean, variance and proportion. Simple and multiple linear regression, application to real-life problems. The lab session will be devoted to problem solving using statistics software.
Pre-requisites: MATH 102
Note: Not to be taken with STAT 214 or ISE 205
An introduction to probability, emphasizing the combined use of mathematics and programming. Discrete and continuous families of distributions. Bounds and approximations. Transforms and convergence. Markov chains and Markov Chain Monte Carlo. Dependence, conditioning, Bayesian methods. The multivariate normal, random permutations, symmetry, and order statistics. Use of numerical computation, graphics, simulation, and computer algebra.
Pre-requisites: STAT 201, MATH 208 or MATH 225
An overview of Data driven approach, Data analytics lifecycle. Basic statistics: Variance, Co-variance, Correlation, Confidence interval and Histogram. Data frames, series, slicing, sorting. Relational database with primary and foreign key. SQL implementation in Python. Data acquisition, cleaning, scrubbing, and manipulation. Correlation analysis, PCA, Linear Regression, Gradient descent, Bayesian classifier, Decision tree, K-means clustering, Hierarchical clustering, Big data, and high-dimensional data. Overview of MapReduce and Hadoop.
Pre-requisites: MATH 102 or MATH 106, ICS 104
This course covers the probabilistic foundations of inference in data science. Key topics include frequentist and Bayesian decision-making, maximum likelihood estimation, statistical inference and hypothesis testing, false discovery rate control with ROC analysis, Bayesian hierarchical models, rejection and Gibbs sampling, robust methods like bootstrap confidence intervals and permutation based hypothesis tests, nonparametric methods like kernel density estimation and k-nearest neighbors, machine learning fundamentals including decision trees and ensemble methods, equip students with essential skills for data-driven decision-making.
Pre-requisites: DATA 201
Introduction to the ethical, societal, and contextual issues surrounding data collection, analysis, and use. Examples from real-world applications; implications of data on privacy, equity, accountability, and societal trust. Case studies, discussions, and projects, enhanced critical thinking skills to analyze and address ethical dilemmas in data practices.
Pre-requisites: COE 292
Foundations, technologies, and applications of blockchain systems and cryptocurrencies, distributed ledgers, cryptographic primitives, consensus mechanisms, smart contracts, tokenization, decentralized finance (DeFi), and blockchain applications.
Pre-requisites: COE 292
Theory and practice of Large Language Models including the underlying architectures (transformers, attention mechanisms), training methodologies (pretraining, fine-tuning, instruction-tuning, RLHF), prompt engineering, LLM-based agents, multimodal LLMs, evaluation metrics, deployment, and the ethical and societal challenges of LLMs.
Pre-requisites: DATA 322 or ICS 485
Introduction to Big Data Engineering, practical fundamentals of mining massive data and machine learning with theory to aid intuition building; Introduction to theories, concepts, practical contexts, and algorithms for analyzing very large amounts of data; Emphasis on hands-on, contemporary big data engineering skills applicable in research and industry.
Pre-requisites: MATH 101 or MATH 106, STAT 201