BSc in Applied Mathematics, Statistics, and Data Science

MATH 011 – Precalculus (4-0-4)

This course is an introduction to university mathematics. This is a developmental pre-freshman level course covering basic mathematics and pre-calculus. The emphasis in this course is on problem solving, rather than theory. Topics include college algebra, functions, polynomial and rational functions, exponential and logarithmic functions, as well as trigonometry.

MATH 101 – Fundamentals of Mathematical Reasoning (3-0-3)

This course provides a foundation in logical and mathematical reasoning. It develops first year university  students’ structured logical thinking and mathematical rigor. The course introduces methods of proof, basic concepts and properties of real numbers, relations and functions. The course also presents an introduction to combinatorics, set theory and number theory.

MATH 111 – Calculus I (4-0-4)

This course introduces students to the theory and techniques of single variable differential and integral calculus. The emphasis is on problem solving. Topics include studying the exponential, logarithmic, trigonometric, and polynomial functions. Their limits, continuity, derivatives, and extrema are studied. Integration is introduced and students learn to compute the area under a curve as well as volumes by slicing, disks, washers, and cylindrical shells.

MATH 112 – Calculus II (4-0-4)
Prerequisite: MATH111

This is a second semester calculus course for students who have previously been introduced to the basic ideas of differential and integral calculus. The emphasis in this course is on problem solving, rather than theory. Topics include integration techniques, parametric equations, infinite series, an introduction to vectors and vector-valued functions, as well as an introduction to functions of several variables and double integrals.

MATH 204 – Linear Algebra (3-0-3)
Prerequisite: MATH112

This course introduces properties of matrices, determinants, and solution techniques for systems of linear equations. The course presents basic properties of vector spaces, subspaces, linear independence, span, basis, and coordinates. Students study linear transformations and their matrix representations. The course examines eigenvalues, eigenvectors, and diagonalization. Finally, Euclidean inner product, orthogonality, and the Gram-Schmidt process are presented.

MATH 206 – Differential Equations (3-0-3)
Prerequisite: MATH112

This is a first course in ordinary differential equations. The topics covered in this course include first-order and second-order differential equations, series solutions, and the Laplace transform. Solution techniques are applied to engineering and science problems.

MATH 211 – Differential Equations and Linear Algebra (4-0-4)
Prerequisite: MATH112

This course introduces ordinary differential equations with linear algebra. The course covers basic topics of linear algebra, including linear systems, basic properties of matrices, vector spaces, and eigenvalues and eigenvectors. The course also covers solution techniques for first-order differential equations, higher-order linear equations with constant coefficients, linear and almost linear systems of differential equations, and Laplace transforms.

MATH 224 – Real Analysis I (4-0-4)
Prerequisite: MATH101, MATH112

This course gives students a thorough understanding of essential concepts in analysis such as real numbers, limits, continuity, and convergence of sequences and series. The course also covers a rigorous definition of derivative and construction of the Riemann integral and their properties including the Fundamental Theorem of Calculus. Students are required to read and write proofs using a precise knowledge of definitions and theorems.

MATH 231 – Calculus III (3-0-3)
Prerequisite: MATH112

This course covers differential and integral calculus for multivariable functions. First, students learn calculus tools such as partial derivatives, directional derivatives, gradients and how to apply them to analyze functions and solve constrained optimization problems. Subsequently, multiple integrals and their applications to calculate areas, volumes, mass  and center of mass will be discussed. The course concludes with topics from vector calculus and key theorems such as Green’s theorem, Stokes’ theorem, and Gauss’s theorem.

MATH 232 – Engineering Mathematics (3-0-3)
Prerequisite: MATH112

This course introduces students to selected topics from mathematical analysis with engineering applications.  The first part is a calculus part which covers the definition of functions of several variables and their domain and range. Also, the course discusses limits, continuity, partial derivatives, gradient vectors, and multiple integrals for functions of several variables. The second part of the course deals with Fourier analysis including complex numbers, Fourier series, Fourier integrals, and Fourier transforms.

MATH 234 – Discrete Mathematics (3-0-3)
Prerequisite: MATH112

This course introduces students to logic and mathematical reasoning to prove elementary theorems in number theory and set  theory. The course starts with a discussion of propositional and predicate calculus, followed by basic proving and counting techniques. Subsequently, operations on sets, functions and cardinality are presented. The course concludes with selected topics in graph theory, number theory and Boolean Algebra.

MATH 242 – Introduction to Probability and Statistics (3-0-3)
Prerequisite: MATH112

This course introduces students to basic probability models and statistical methods for data analysis. The course will cover introductory probability theory, discrete and continuous probability distributions, elements of descriptive statistics, and different statistical inference methods such as estimation for the mean and the variance, hypothesis testing for the mean and the variance.

MATH 243 – Probability and Statistical Inference (3-0-3)

Prerequisite: MATH112

This course provides a mathematically rigorous introduction to probability theory and inferential statistics.  Numerous real-world applications are presented throughout the course. After covering random variables/ vectors, expectation/variance, and limit theorems, students are introduced to inferential statistics, including point estimation and interval estimation in the presence of nuisance parameters, and simple hypothesis testing.

MATH 244 – Probability (3-0-3)
Prerequisite: MATH101, MATH112

This course introduces the mathematical theory of probability at an undergraduate level of rigor. The course covers basic concepts of axiomatic probability and conditional probability, random variables/vectors and their distribution, moments, and various models of random variables. Students will also study classical probability inequalities and limit theorems in large sample theory.

MATH 251 – Operations Research I (4-0-4)
Prerequisite:   MATH204, or MATH211

This course introduces operations research and deterministic mathematical modeling with a focus on linear programming. Topics include graphical interpretation of linear optimization problems, simplex method, duality sensitivity analysis and general solution strategies. Emphasis is given to modeling industry problems and interpretation of the solutions obtained. Students learn to use modern modeling languages and software to find optimal solutions for large-scale problems.

MATH 252 – Introduction to Applied Statistics (3-0-3)
Prerequisite: MATH112

This course introduces students to basic probability and statistical methods. The course will cover descriptive statistics, random variables, basic discrete and continuous distributions, point and interval estimation, tests of hypotheses, regression and basic design of experiments. Applications to biosciences and engineering will be given throughout the course.

MATH 295 – Special Topics in Mathematics (3-0-3)

MATH 296 – Directed Studies (3-0-3)

MATH 315 – Advanced Linear Algebra with Applications to Data Science (3-0-3)
Prerequisite: MATH204, or MATH211, or MATH204

This course presents the mathematical structure of vector spaces and multilinear transformations. The axioms of vector spaces are introduced along with the notion of basis and dimension. Properties of dual spaces and multilinear transformations are studied. Eigenvalues and eigenvectors theorems are used to diagonalize matrices. Adjoint, self-adjoint, normal and unitary operators on pre-Hilbert spaces are constructed. Applications of these concepts to data science are emphasized throughout the course.

MATH 316 – Partial Differential Equations (3-0-3)
 Prerequisite: MATH211, or (MATH206, MATH204)

This course presents the mathematical theory of partial differential equations (PDEs) in classical formulation. First order quasi-linear PDEs are solved by the method of characteristics. Second order quasi-linear PDEs are classified and then solved by the method of separation of variables. Solutions to PDEs are interpreted in physical and engineering contexts.

MATH 317 – Nonparametric Statistics (3-0-3)
Prerequisite: MATH345, MATH346

This course presents the theory and practical tools from classical nonparametric statistics. Students learn to determine the suitability of parametric versus nonparametric methods, with an emphasis on applying procedures for testing hypotheses. This course discusses correlation and regression in a nonparametric setting. Students are trained to select and use software to perform nonparametric estimation and hypothesis testing on data.

MATH 318 – Statistical Learning (3-0-3)
Prerequisite: MATH345, MATH231, MATH346

This course introduces statistical learning methods with emphasis on analysis of categorical data and application to real data sets. Students learn different types of regression models (linear, logistic and nonparametric). Classification methods (discriminant analysis and support vector machines) are presented along with dimensionality reduction techniques (principal component analysis and clustering). Resampling techniques and model selection methods are also discussed.

MATH 319 – Numerical Analysis I (3-0-3)
Prerequisite: (MATH346, or COSC114), (MATH211, or (MATH206, MATH204))

This course introduces students to the theory and applications of numerical approximation techniques. Students are introduced to error analysis, numerical solutions of nonlinear algebraic equations, interpolation and least squares approximations. Additionally, the course presents numerical tools of integration and differentiation required for the numerical solutions of ordinary differential equations and eigenvalue problems. Emphasis is placed on implementing efficient computational methods in MATLAB.

MATH 320 – Mathematical Foundations of General Relativity (3-0-3)
Prerequisite: (MATH211, or (MATH204, MATH206)), MATH231

This course introduces students to the tools of modern differential geometry, focusing on Riemannian and Lorentzian geometries. The course also covers covariant derivatives, tensors, curvature, and geodesic curves with emphasis on modern coordinate-free methods of computation. It presents physical models of general relativity, such as black holes, gravitational lensing and cosmological models.

MATH 321 – Applied Statistics for Engineers (3-0-3)
Prerequisite: MATH242 or MATH243

The course introduces key statistical methods and models used in engineering applications. Emphasis is on both theoretical underpinnings and practical applications, preparing students to analyze data using statistical techniques. Topics include fundamental statistical concepts, various regression models, analysis of variance, and more advanced multivariate techniques.

MATH 331 – Stochastic Processes (3-0-3)
Prerequisite: (MATH204 or MATH211), (MATH242 or MATH243 or MATH244), (MATH346 or ESMA341 or COSC101)

This course introduces stochastic processes and their applications. Topics covered include discrete and continuous time Markov processes, branching processes, Poisson process and basic queuing models. Students learn to use stochastic processes to model and analyze problems in engineering, biology and finance.

MATH 333 – Applied Engineering Mathematics (3-0-3)
Prerequisite: (MATH211 or (MATH206, MATH204)), COSC114

This course provides students with the numerical and analytical methods to solve mathematical models  appearing in engineering science including, but not limited to, nonlinear equations, systems of algebraic  equations, extrapolation, and ordinary differential equations. Applications will include wave motion and heat conduction. The course includes writing computer codes.

MATH 345 – Mathematical Statistics (3-0-3)
 Prerequisite: MATH242 or MATH243 or MATH244

This course provides a rigorous introduction to classical statistics. Probabilistic concepts and tools are used to present inferential statistics methods, including sampling distributions, parametric point estimators and their properties, interval estimation, hypothesis testing and regression models. Students study some elements of Bayesian statistics.

MATH 346 – Mathematical and Statistical Software (3-0-3)
Prerequisite: COSC114, (MATH204 or MATH211), (MATH242 or MATH243 or MATH244)

This course introduces mathematical and statistical programming using the MATLAB and R programming languages. The topics covered span a variety of topics in data science and numerical computation, including tidy data, exploratory data analysis, plotting, and symbolic computation.

MATH 352 – Complex Functions (3-0-3)
Prerequisite: MATH231

This course provides students with a sound knowledge of analytic functions of a complex variable, infinite series in the complex plane and theory of residues in relation to Fourier integrals and transforms. The students are introduced to several applications in engineering and science.

MATH 377 – Undergraduate Research (3-0-3)

This course provides an opportunity for students, working individually or in small groups, to develop an enhanced understanding and application of specific research methods and/or creative practices. The course assists students to enhance their education and become integrated into the KU community by actively and successfully engaging in research, creative, and/or scholarly projects under the supervision of a faculty member. This course serves as a free or technical elective.

MATH 391 – Direct Studies (3-0-3)

This course gives an upper level undergraduate student the opportunity to participate in an individual or group project, study, or research activity under the supervision of a faculty member. A formal report is required.

MATH 395 – Special Topics in Mathematics (4-0-4)

This course covers the fundamental principles of the theory of manifolds. In the first part of the course,  the notions of topological space, continuity, compactness, boundedness, connectedness and convergence are introduced. Most topics focus on the study of smooth functions, vector fields and differential forms. An overview of integration on manifolds and the De Rham cohomology are also considered.

MATH 399 – Internship (1-0-1)
Prerequisite: SDAS300 or GENS300

The internship provides students with practical, on-the-job experience. It is academically supervised by a faculty member and professionally supervised by the company’s designated internship supervisor who provides feedback to the university about the student’s progress. The duration of the internship is a minimum of 8 consecutive weeks, and is graded on a Pass/Fail basis.

MATH 410 – Introduction to Topology (3-0-3)
Prerequisite: MATH231, MATH224

This course will introduce students to basic principles of point set topology. The course covers topological spaces, homeomorphisms, compactness, connectedness and metric spaces. It also prepares the students to undertake advanced courses in mathematics, such as algebraic topology, normed spaces and differential geometry

MATH 411 – Modern Algebra (3-0-3)
Prerequisite: MATH315 or MATH224

This course introduces basic concepts and properties of fundamental elements of modern algebra. Fundamental theorems are used to explain properties of groups, rings, and fields. Students read and write proofs using a precise knowledge of definitions and theorems. This course also presents applications of permutation groups to explain symmetries of regular polygons in geometry.

MATH 412 – Optimization (3-0-3)
Prerequisite: (MATH204 or MATH211), MATH231

This course introduces main optimization techniques and their applications in physics, engineering, economics and social sciences. After covering unconstrained optimization algorithms, the course focuses on methods to solve linear and nonlinear constrained optimization problems. A special focus on convex optimization and on recent machine learning algorithms complete the course.

MATH 413 – Game Theory (3-0-3)
Prerequisite: MATH315

This course provides an extended treatment of methods and applications of game theory at an advanced undergraduate level. A distinction between competitive and cooperative games is presented, and mathematical theory of games and game theoretic analysis are applied. Applications in social sciences, economics and industry are developed from basic principles relying on saddle point theory and Nash equilibria concepts.

MATH 414 – Advanced Discrete Mathematics (3-0-3)
Prerequisite:   MATH315, MATH101

This course offers an in-depth discussion of fundamental discrete mathematics topics. The course starts by exploring binary relations, surjective and injective functions and cardinality, including Schröder–Bernstein theorem. Subsequently, modular arithmetic and its applications in cryptography are presented, as well as Boolean algebras and their connections to logic and set theory. The course concludes with selected topics from graph theory and knot theory.

MATH 415 – Design of Experiments (3-0-3)
Prerequisite: MATH318 or ISYE311 or ISYE321

This course offers a review of various types of designs of experiments and their applications in different  engineering fields. The course introduces analysis of variance, followed by an introduction to block designs, full factorial designs, 2-level full factorial and fractional factorial designs. Moreover, Taguchi methods and response surface methods are discussed.

MATH 416 – Sample Survey Design and Analysis (3-0-3)

Prerequisite: MATH346, MATH345
Corequisite: MATH318

This course introduces the main techniques involved in survey design and analysis. The main sampling techniques are covered. The course reviews the main methods used in the analysis of surveys, such as regression, factor analysis and principal component analysis. Students design, pilot, and implement a survey, and then they select and use statistical software to analyze the results.

MATH 417 – Measure and Probability Theory (3-0-3)
Prerequisite: MATH244, MATH224

This course introduces the fundamentals of measure and integration theory and progresses onto probability from a measure-theoretic point of view. It develops the Lebesgue integral along with the associated limit theorems. The course covers the Radon-Nikodym theorem and its applications to basic probability theory. This course also presents various forms of the central limit theorem, along with the theory of conditional expectation on sigma fields.

MATH 419 – Numerical Analysis II (3-0-3)
Prerequisite: MATH316, MATH319

This course presents the theoretical and practical methods for numerical solution of ordinary and partial  differential equations. It explores Runge-Kutta and multistep methods, as well as stability theory, stiff  equations and boundary value problems. A short introduction to Galerkin approximations and finite element methods is also presented.

MATH 423 – Financial Risk Analysis (3-0-3)
Prerequisite: (MATH242 or MATH243 or MATH244), MATH412

This course provides an overview of the main theoretical concepts underlying the analysis of financial risk. The course presents applications of theoretical concepts in practice in a variety of financial contexts. Additionally, students learn to solve risk analysis problems numerically using optimization methods and numerical simulations.

MATH 424 – Optimal Control Theory (3-0-3)
Prerequisite: MATH316, MATH412, MATH346

This course provides an introduction to the basics of optimal control theory (deterministic and stochastic)  through examples. The course further builds on standard differential linear system and optimization under  constraints, to explore issues related to real-world problems modeled by differential equations.

MATH 425 – Financial Portfolio Management (3-0-3)
Prerequisite: MATH345, MATH412

This course introduces relevant financial management problems that are solved and analyzed using optimization techniques. These techniques are applied to several case studies using linear and nonlinear programming, dynamic programming, and stochastic programming. Financial topics covered include asset-liability management, option pricing and hedging, risk management, and portfolio selection.

MATH 426 – Finance in Discrete Time (3-0-3)
Prerequisite: MATH346, MATH231, (MATH243 or MATH345 or MATH242)

The course gives a modern overview of the main concepts of mathematical finance using discrete-time stochastic models. The course focuses on the Cox-Ross-Rubinstein (binomial) model. Topics include no-arbitrage pricing of financial derivatives, replication, hedging, self-financed portfolios, risk-neutral valuation, stopping times, and portfolio optimization. As the main application, European and American options in discrete time are studied, and the numerical algorithms for their pricing are presented.

MATH 431 – Discrete Mathematical Models in Biology (3-0-3)
Prerequisite: (MATH346 or COSC114), (MATH206 or MATH211), (MATH242 or MATH243 or MATH345)

This course applies mathematical theory and techniques to biological and biomedical applications with an emphasis on discrete mathematical modelling. The course introduces discrete deterministic/probabilistic modelling methods, such as difference equations, cellular automata or surface-energy models, agent-based models and network models. Cell migration and growth dynamics of bacterial colonies, tumors and epidemiology are explored..

MATH 432 – Continuous Mathematical Models in Biology (3-0-3)
Prerequisite: MATH231, (MATH206 or MATH211), MATH346

This course explores mathematical modeling in biological systems, covering population dynamics, disease modeling, and reaction-diffusion equations. Students learn to use tools such as phase portraits, bifurcation diagrams, and stability analysis. Advanced topics include traveling waves, molecular diffusion, and advection-diffusion. The course also examines enzyme kinetics, tissue formation, and cancer modeling. These models provide insights into complex biological processes.

MATH 435 – Mathematical Imaging (3-0-3)
Prerequisite: (COSC114 or MATH346), (MATH204 or MATH211), (MATH242 or MATH243 or MATH244)

This course provides a comprehensive treatment of the mathematical techniques used in imaging science. The course focuses on image reconstruction and analysis techniques. Students will learn popular methods such as filtered back projection, iterative reconstruction, image segmentation and compressed sensing. Emphasis is placed on understanding the mathematical foundations behind these techniques and their implementation in applications such as medical and porous media imaging.

MATH 468 – Teaching Key Concepts in Mathematics (3-0-3)
Prerequisite: MATH467

This is the second course in a two-part sequence on introductory Mathematics Education intended for  future teachers. This course focuses on analyzing science pedagogy and practices for developing formative and summative assessments. This course also includes the development of practical investigation skills and teamwork issues. The course will include various reading tasks, class activities, and microteaching, involving practical work and other assignments.

MATH 475 – Model Calibration and Uncertainty Quantification (3-0-3)
Prerequisite: (COSC114 or MATH346), (MATH204 or MATH211), (MATH242 or MATH243), (or (MATH244, MATH319)

This course introduces students to uncertainty quantification for physical and biological models. Course topics include parameter selection techniques, sensitivity analysis, and frequentist and Bayesian model calibration. Propagation of uncertainties in the models is studied along with the construction of surrogate models and stochastic spectral methods. Applications include climate, engineering, biological and biomedical phenomena.

MATH 477 – Undergraduate Research (3-0-3)

This course provides an opportunity for students, working individually or in small groups, to develop an enhanced understanding and application of specific research methods and/or creative practices. The course assists students to enhance their education and become integrated into the KU community by actively and successfully engaging in research, creative, and/or scholarly projects under the supervision of a faculty member. This course serves as a free or technical elective.

MATH 485 – Nonlinear Dynamics (3-0-3)
Prerequisite: (MATH211, (or MATH206, MATH204)), MATH231

This course introduces students to applications of nonlinear dynamical systems. Students learn to qualitatively describe the behavior of a solution of a dynamical system and identify various types of bifurcations in one- and two-dimensional systems. Moreover, students analyze limit cycles and their stability. Finally, this course offers students basic knowledge of Hamiltonian systems and integrability.

MATH 491 – Direct Studies

This course gives an upper level undergraduate student the opportunity to participate in an individual or group project, study, or research activity under the supervision of a faculty member. A formal report is required.

MATH 495 – Selected Topics (3-0-3)

MATH 497 – Senior Research Project I (3-0-3)

Over the course of two semesters, students conduct a supervised research project. Projects involve the  theoretical or computational investigation of a mathematical concept, the construction and solution of  a model of a real-world problem, or the reading, understanding and expansion of an existing scholarly  publication. Students summarize the final results of the research in the form of a written report as well as a public oral presentation.

MATH 498 – Senior Research Project II (3-0-3)
Prerequisite: MATH497

Over the course of two semesters, students conduct a supervised research project. Projects involve the  theoretical or computational investigation of a mathematical concept, the construction and solution of  a model of a real-world problem, or the reading, understanding and expansion of an existing scholarly  publication. Students summarize the final results of the research in the form of a written report as well as a public oral presentation.