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1 | Approved? | Date of approval | Group | Course Number | Course Name | Credits | School/ College | Brief Course Description | NOTES | ||||||||
2 | See notes --> | * | * | * | If a computational science course is not listed here, please submit the course for review. (For CSE/ECE, please also check EECS and vice versa) | * | * | This course list is for the Graduate Certificate in Computational Discovery & Engineering, not for any other MICDE program. Courses listed here are not necessarily approved for course requirements for the Ph.D. in Scientific Computing or the Graduate Certificate in Computational Neuroscience. Each program has a separate course review process. For questions about courses for these programs, email micde-phd@umich.edu or micde-neuro@umich.edu. | See the Special Topics tab for information about specific sections of "Special Topics" courses | ||||||||
3 | Approved | methodology | AEROSP 510 | Finite Elements in Mechanical and Structural Analysis I | 3 | College of Engineering | Prereq: AEROSP 315 (3 credits) Introductory level. Finite element solutions for structural dynamics and nonlinear problems. Normal modes, forced vibrations, Euler buckling (bifurcations), large deflections, nonlinear elasticity, transient heat conduction. Computer laboratory based on a general purpose finite element code. | ||||||||||
4 | Approved | methodology | AEROSP 511 | Finite Elements in Mechanical and Structural Analysis II | 3 | College of Engineering | Prereq: AEROSP 510 or MECHENG 505. (3 credits) Introduction to fundamental principles and latest developments in aerosol science. The dependence of aerosol composition and size distributions on the underlying atmospheric thermodynamics, dynamics, chemistry, and physics will be presented. Recent observations and theoretical treatments are used to illustrate aspects of aerosol science that are poorly quantified at present | ||||||||||
5 | Approved | methodology | AEROSP 523 / MECHENG 523 | Computational Fluid Dynamics I | 3 | College of Engineering | Prereq: AEROSP 325 or preceded or accompanied by MECHENG 520. (3 credits) Physical and mathematical foundations of computational fluid mechanics with emphasis on applications. Solution methods for model equations and the Euler and the Navier-Stokes equations. The finite volume formulation of the equations. Classification of partial differential equations and solution techniques. Truncation errors, stability, conservation, and monotonicity. (cross-listed with MECHENG 523) | ||||||||||
6 | Approved | application | AEROSP 528 / NAVARCH 527 / NERS 547 | Computational Fluid Dynamics for Industrial Applications | 3 | College of Engineering | Advisory Prereq: NERS 344, MECHENG 320, CEE 325 or equivalent. (3 credits) Theoretical background on turbulence and modeling for single-phase and two-phase flow, and practical experience on using CFD codes. Evaluate simulations of 3-D flows, applicability/limitations of turbulence models, mesh generation and mesh convergence, numerical methods for solution of Navier-Stokes equation, theoretical exercises, computational project and presentation. Cross-listed with NAVARCH 527 and AEROSP 528. | ||||||||||
7 | Approved | methodology | AEROSP 550 / CEE 571 / EECS 560 / MECHENG 564 | Linear Systems Theory | 4 | College of Engineering | Linear spaces and linear operators. Bases, subspaces, eigenvalues and eigenvectors, canonical forms. Linear differential and difference equations. Mathematical representations: state equations, transfer functions, impulse response, matrix fraction and polynomial descriptions. System-theoretic concepts: causality, controllability, observability, realizations, canonical decomposition, stability. | crosslisted with CEE 571/EECS 560/MECHENG 564. | |||||||||
8 | Approved | 1/13/2026 | methodology | AEROSP 551 / EECS 562 | Nonlinear Systems and Control | 3 | College of Engineering | Introduction to the analysis and design of nonlinear systems and non- linear control systems. Stability analysis using Lyapunov, input-output and asymptotic methods. Design of stabilizing controllers using a variety of methods selected from linearization, absolute stability theory, vibrational control, sliding modes and feedback linearization. | |||||||||
9 | Approved | methodology | AEROSP 567 | Inference, Estimation, and Learning | 3 | College of Engineering | Theory and algorithms for synthesizing models and data for general applications across science and engineering. Topics include algorithms for maximum likelihood estimation, Bayesian inference, and regression for static inference problems and for estimation in dynamical systems. Theoretical foundations of the algorithms and projects that focus on implementation. | ||||||||||
10 | Approved | application | AEROSP 588 | Multidisciplinary Design Optimization | 3 | College of Engineering | Prerequisite: MATH 419 or equivalent, MATH 371 or equivalent, graduate standing. (3 credits) Introduction to numerical optimization and its application to the design of aerospace systems, including: mathematical formulation of multidisciplinary design problems, overview of gradient-based and gradient-free algorithms, optimality conditions (unconstrained and constrained, Pareto optimality), sensitivity analysis and multidisciplinary problem decomposition. No background in aerospace is required. | ||||||||||
11 | Approved | methodology | AEROSP 623 | Computational Fluid Dynamics II | 3 | College of Engineering | Prereq: AEROSP 523 or equivalent, substantial computer programming experience, and AEROSP 520. (3 credits) Advanced mathematical and physical concepts in computational fluid dynamics, with applications to one- and two-dimensional compressible flow. Euler and Navier-Stokes equations, numerical flux functions, boundary conditions, monotonicity, marching in time, marching to a steady state, grid generation. | ||||||||||
12 | Contact MICDE | methodology | AEROSP 729 & 740 | Special Topics (selected) | Refer to course guide | College of Engineering | Please ask us about using a special topic class as its content changes frequently. Previously approved topics include: Machine Learning for Science; Parameter Inference and State Estimation | See the Special Topics tab for information about specific sections of "Special Topics" courses | |||||||||
13 | Approved | methodology | ASTRO 406 | Computational Astrophysics | 3 | LSA | Prereq: Math 216 plus prior or current enrollment in Physics 240, and some knowledge of programming; or instructor’s permission. (3 credits) Develop practical working knowledge of the numerical methods most widely used in current research. For each method we briefly discuss the underlying theory and then put it into practice by coding and using numerical routines for specific research applications. | ||||||||||
14 | Approved | 6/12/2025 | methodology | ASTRO 501 | Modern Astronomical Techniques | ||||||||||||
15 | Approved | 6/12/2025 | application | ASTRO 533 | The Structure and Content of Galaxies | ||||||||||||
16 | Approved | 6/12/2025 | application | ASTRO 534 | The Extragalactic Universe | ||||||||||||
17 | Approved | methodology | BIOCHEM 551 / PATH 551 / BIOMEDE 551 / BIOINF 552 / CHEM 551 | Proteome Informatics | 3 | Michigan Medicine | Introduction to proteomics, mass spectrometry, peptide identification and protein inference, statistical methods and computational algorithms, post-translational modifications, genome annotation and alternative splicing, quantitative proteomics and differential protein expression analysis, protein-protein interaction networks and protein complexes, data mining and analysis of large-scale data sets, clinical applications, related technologies such a metabolomics and protein arrays, data integration and systems biology. Prerequisites: Bio Chem and calculus. | ||||||||||
18 | Approved | application | BIOINF 463 / BIOPHYS 463 / MATH 463 | Math Modeling in Biology | 3 | LSA | Cross-listed with BIOINF 463/BIOPHYS 463. Prereq: Math 214, 217, 417, or 419; and 216, 286, or 316 (3 credits) The complexities of the biological sciences make interdisciplinary involvement essential and the increasing use of mathematics in biology is inevitable as biology becomes more quantitative. Mathematical biology is a fast growing and exciting modern application of mathematics that has gained world- wide recognition. In this course, mathematical models that suggest possible mechanisms that may underlie specific biological processes are developed and analyzed. Another major emphasis of the course is illustrating how these models can be used to predict what may follow under currently untested conditions. The course moves from classical to contemporary models at the population, organ, cellular, and molecular levels. The goals of this course are: (i) Critical understanding of the use of differential equation methods in mathematical biology and (ii) Exposure to specialized mathematical and computational techniques which are required to study ordinary differential equations that arise in mathematical biology. By the end of this course students will be able to derive, interpret, solve, understand, discuss, and critique discrete and differential equation models of biological systems. | ||||||||||
19 | Approved | methodology | BIOINF 501 | Mathematical Foundations for Bioinformatics | 3 | Michigan Medicine | Prereq: Calc II or equivalent (3 credits) The course provides a review of some of the fundamental mathematical techniques commonly used in bioinformatics and biomedical research. These include: 1) principles of multi-variable calculus, and complex numbers/functions, 2) foundations of linear algebra, such as linear spaces, eigen values and vectors, singular value decomposition, spectral graph theory and Markov chains, 3) differential equations and their usage in biomedical system, which includes topic such as existence and uniqueness of solutions, two dimensional linear systems, bifurcations in one and two dimensional systems and cellular dynamics, and 4) optimization methods, such as free and constrained optimization, Lagrange multipliers, data denoising using optimization and heuristic methods. MATLAB, R and Python will be introduced as tools to simulate/implement the mathematical ideas. | ||||||||||
20 | Approved | 10/30/2025 | application | BIOINF 524 | Foundations of Bioinformatics and Systems Biology | ||||||||||||
21 | Approved | 5/5/2025 | methodology/ application | BIOINF 540 / MATH 540 | Mathematics of Biological Networks | 3 | Michigan Medicine | Data-guided modeling, analysis, and visualization of networks is critical for understanding and controlling biological processes. With the appropriate methods, we can explore many questions including: • How do cells respond to internal and external stimuli, and how can we intervene or reprogram them? • How do cellular proteins interact with one another? • How do cell and tissue functions emerge from dynamical forces within (genome) and between cells? | |||||||||
22 | Approved | 11/14/2025 | application | BIOINF 545 / BIOSTAT 646 / STATS 545 | High-throughput Molecular Genomic and Epigenomic Data Analysis | This course will cover statistical methods used to analyze data in experimental molecular biology, with an emphasis on gene and protein expression array data. Topics: data acquisition, databases, low level processing, normalization, quality control, statistical inference (group comparisons, cyclicity, survival), multiple comparisons, statistical learning algorithms, clustering visualization, and case studies. | |||||||||||
23 | Approved | methodology | BIOINF 547 / MATH 547 / STATS 547 | Mathematics of Data | 3 | Michigan Medicine | Basic introduction to data representation as vectors, matrices (graphs, networks), and tensors, geometric methods for dimension reduction (manifold learning, diffusion maps, t-distributed stochastic neighbor embedding (t-SNE), etc.) and topological data reduction (introduction to computational homology groups, etc.). Application-based approach to spectral graph theory, address the combinatorial meaning of eigenvalues and eigenvectors of matrices associated with graphs, and discuss extensions to tensors [1, 2]. The course will also provide an introduction to the application of dynamical systems theory to data [3, 4]. | ||||||||||
24 | Approved | methodology | BIOINF 551 / CHEM 551 / BIOCHEM 551 / PATH 551 / BIOMEDE 551 | Proteome Informatics | 3 | Michigan Medicine | Introduction to proteomics, mass spectrometry, peptide identification and protein inference, statistical methods and computational algorithms, post-translational modifications, genome annotation and alternative splicing, quantitative proteomics and differential protein expression analysis, protein-protein interaction networks and protein complexes, data mining and analysis of large-scale data sets, clinical applications, related technologies such a metabolomics and protein arrays, data integration and systems biology. Prerequisites: Bio Chem and calculus. | ||||||||||
25 | Approved | application | BIOINF 563 / MATH 563 | Advanced Mathematical Methods for the Biological Sciences | 3 | LSA | Prereq:Math 217, 417, or 419 and Math 450 or 454. (3 credits) Natural systems behave in a way that reflects an underlying spatial pattern. This course focuses on discovering the way in which spatial variation influences the motion, dispersion, and persistence of species. The concepts underlying spatially dependent processes and the partial differential equations which model them will be discussed in a general manner with specific applications taken from molecular, cellular, and population biology. This course is centered on modeling in three major areas i) Models of Motion: Diffusion, Convection, Chemotaxis, and Haptotaxis; ii) Biological Pattern Formation; and iii) Delay-differential Equations and Age-structured Models. | ||||||||||
26 | Approved | 10/30/2025 | application | BIOINF 575 | Programming Laboratory in Bioinformatics | ||||||||||||
27 | Approved | application | BIOINF 580 | Introduction to Signal Processing and Machine Learning in Biomedical Sciences | 3 | Michigan Medicine | The course covers signal processing and machine learning methods with an emphasis on their applications in healthcare. Students will need a basic understanding in linear algebra for this course. Topics include: 1) transforms and feature entraction – Fourier transform, wavelet transformation, fundamentals of information in theory. 2) Introduction to machine learning – clustering vs classification, Naïve Bayes, Classification and regression trees. Random forest, support vector machines, introduction to neural networks, and sparse learning. 3) applications in medicine and biology. | ||||||||||
28 | Approved | 7/10/2023 | methodology/ application | BIOINF 590 | Image Processing and Advanced Machine Learning for Cancer Bioinformatics | 3 | Michigan Medicine | This course intends to build on the fundamentals of signal processing and machine learning to explore concepts from these areas in the context of cancer bioinformatics. Motivating examples from cancer genomics, cancer imaging and drug discovery will be used to examine these principles. The course will comprise instructor-led lectures, student lectures, and course projects. Pre-requisite: BIOINF 580 or instructor consent. | |||||||||
29 | Approved | methodology | BIOINF 593 | Machine Learning in Computational Biology | 3 | Michigan Medicine | This course introduces the foundational machine learning techniques used in computational biology and describes their applications to biological data. The course emphasizes theoretical foundations and practical implementation of the techniques, in addition to the biological background needed for computational biology applications. Expertise in programming, calculus, linear algebra, and probability are required. | ||||||||||
30 | Approved | 5/5/2025 | methodology | BIOINF 595 | Machine Learning for Drug Discovery | ||||||||||||
31 | Approved | methodology | BIOMEDE 503 | Statistical Methods For Biomedical Engineering | 3 | College of Engineering | Prereq: Graduate standing or permission of instructor. (3 credits)This course will cover descriptive statistics, probability theory, distributions for discrete and continuous variables, hypothesis testing and analysis of variance, as well as more advanced topics. We will make connections with real problems from engineering, biology and medicine, and computational tools will be used for examples and assignments. | ||||||||||
32 | Approved | application | BIOMEDE 516 / ECE 516 | Medical Imaging Systems | College of Engineering | We'll examine, from a systems perspective, the techniques used to form internal images of (living) human bodies. These imaging systems are used for tasks ranging from cancer detection to basic biophysical and cognitive research, and include planar X-ray and gamma-ray (nuclear medicine) imaging, X-ray tomography, ultrasound, single-photon tomography, positron emission tomography, and magnetic resonance imaging (MRI). | |||||||||||
33 | Approved | 12/15/2025 | application | BIOMEDE 537 | Computational Tools for Genomic Technologies | 3 | College of Engineering | ||||||||||
34 | Approved | methodology | BIOMEDE 551 / BIOINF 552 / CHEM 552 / BIOCHEM 552 / PATH 551 | Proteome Informatics | 3 | Michigan Medicine | Introduction to proteomics, mass spectrometry, peptide identification and protein inference, statistical methods and computational algorithms, post-translational modifications, genome annotation and alternative splicing, quantitative proteomics and differential protein expression analysis, protein-protein interaction networks and protein complexes, data mining and analysis of large-scale data sets, clinical applications, related technologies such a metabolomics and protein arrays, data integration and systems biology. Prerequisites: Bio Chem and calculus. | ||||||||||
35 | Approved | application | BIOMEDE 580 / NERS 580 | Computation Projects In Radiation Imaging | 1 | College of Engineering | Prereq: Preceded or accompanied by NERS 481. (1 credit) Computational projects illustrate principles of radiation imaging from NERS 481 (BIOMEDE 481). Students will model the performance of radiation systems as a function of design variables. Results will be in the form of computer displayed images. Students will evaluate results using observer experiments. Series of weekly projects are integrated to describe the performance of imaging systems. Cross-listed with NERS 580. Last offered Winter 2019. | ||||||||||
36 | Approved | application | BIOPHYS 463 / BIOINF 463 / MATH 463 | Math Modeling in Biology | 3 | LSA | Cross-listed with BIOINF 463/BIOPHYS 463. Prereq: Math 214, 217, 417, or 419; and 216, 286, or 316 (3 credits) The complexities of the biological sciences make interdisciplinary involvement essential and the increasing use of mathematics in biology is inevitable as biology becomes more quantitative. Mathematical biology is a fast growing and exciting modern application of mathematics that has gained world- wide recognition. In this course, mathematical models that suggest possible mechanisms that may underlie specific biological processes are developed and analyzed. Another major emphasis of the course is illustrating how these models can be used to predict what may follow under currently untested conditions. The course moves from classical to contemporary models at the population, organ, cellular, and molecular levels. The goals of this course are: (i) Critical understanding of the use of differential equation methods in mathematical biology and (ii) Exposure to specialized mathematical and computational techniques which are required to study ordinary differential equations that arise in mathematical biology. By the end of this course students will be able to derive, interpret, solve, understand, discuss, and critique discrete and differential equation models of biological systems. | ||||||||||
37 | Denied | BIOPHYS 521 | Principles of Biophysical Chemistry | LSA | The course discusses aspects of protein and nucleic acid structure and dynamics, the nature of underlying forces and interactions that control biopolymer processes, and aspects of dynamics in context of function. Emphasis will be laid on theories from thermodynamics and statistical mechanics that form the basis of physical models for processes and processing in these systems. | ||||||||||||
38 | Approved | 8/24/2023 | methodology | BIOSTAT 521 | Applied Biostatistics | 3 | Public Health | Public Health is the study of disease and underlying causes in human populations. Scientific hypotheses in public health are tested by collecting and examining relevant data. Biostatistical analysis provides the means to identify and verify patterns in this data and to interpret the findings in a public health context. In this course, students will learn the basic steps in analyzing public health data, from initial study design to exploratory data analysis to inferential statistics. Specifically, we will cover graphical representations and descriptive statistics for univariate and multivariate data, sampling distributions for statistics, hypothesis testing (including t-tests and chi-square tests), construction of confidence intervals, analysis of contingency tables, and simple and multiple linear regression. Students will learn to apply the concepts covered in class through a semester-long hands-on analysis of real public health data using statistical software. | |||||||||
39 | Denied | 5/20/2025 | BIOSTAT 601 | Probability and Distribution Theory | 4 | ||||||||||||
40 | Denied | 5/20/2025 | BIOSTAT 602 | Biostatistical Inference | 4 | ||||||||||||
41 | Approved | 5/20/2025 | methodology/ application | BIOSTAT 625 | Computing with Big Data | 3 | Public Health | ||||||||||
42 | Approved | 11/14/2025 | application | BIOSTAT 646 / BIOINF 545 / STATS 545 | High-throughput Molecular Genomic and Epigenomic Data Analysis | This course will cover statistical methods used to analyze data in experimental molecular biology, with an emphasis on gene and protein expression array data. Topics: data acquisition, databases, low level processing, normalization, quality control, statistical inference (group comparisons, cyclicity, survival), multiple comparisons, statistical learning algorithms, clustering visualization, and case studies. | |||||||||||
43 | Approved | 5/20/2025 | methodology | BIOSTAT 650 | Theory And Application Of Linear Regression | 4 | Public Health | ||||||||||
44 | Denied | 5/20/2025 | BIOSTAT 651 | Theory And Application Of Generalized Linear Models | 3 | Public Health | |||||||||||
45 | Approved | 5/20/2025 | application | BIOSTAT 653 | Theory And Application Of Longitudinal Analysis | 3 | Public Health | ||||||||||
46 | Denied | 5/20/2025 | BIOSTAT 699 | Seminar in Biostatistics | Public Health | ||||||||||||
47 | Approved | 5/20/2025 | methodology | BIOSTAT 802 | Advanced Inference II | 3 | Public Health | ||||||||||
48 | Approved | 5/20/2025 | application | BIOSTAT 815 | Advanced Topics in Computational Statistics | 3 | Public Health | ||||||||||
49 | Denied | 5/20/2025 | BIOSTAT 885 | Nonparametric Statistics | 3 | Public Health | |||||||||||
50 | Approved | 11/14/2025 | application | CDB 560 | Quantitative Cell Biology | ||||||||||||
51 | Contact MICDE | application | CEE 501 | Special Topics in CEE / MECHENG | 1-4 credits | College of Engineering | See Special Topics tab | See the Special Topics tab for information about specific sections of "Special Topics" courses | |||||||||
52 | Approved | methodology | CEE 510 / NAVARCH 512 | Finite Element Methods In Solid And Structural Mechanics | 3 | College of Engineering | Basic equations of three-dimensional elasticity. Derivation of relevant variational principles. Finite element approximation. Convergence requirements. Isoparametric elements in two and three dimensions. Implementational considerations. Locking phenomena. Problems involving non-linear material behavior. | ||||||||||
53 | Approved | methodology/ application | CEE 512 | Nonlinear Analysis of Structures | 3 | College of Engineering | CEE 412 or equivalent. (3 credits) Extension of matrix structural analysis to solve geometric and material nonlinear problems in structural engineering. Topics include elastic stability of columns, P-delta effects, large-displacement analysis of cable structures, inelastic analysis of frames using lumped and distributed plasticity models, and solution algorithms for nonlinear systems of equations. | ||||||||||
54 | Approved | methodology | CEE 517 | Reliability of Structures | 3 | College of Engineering | Prerequisite: CEE 270 or equivalent. (3 credits) Fundamental concepts related to structural reliability, safety measures, load models, resistance models, system reliability, optimum safety levels and optimization of design codes. | ||||||||||
55 | Approved | application | CEE 520 | Physical Processes of Land-Surface Hydrology | 3 | College of Engineering | Prereq: CEE 421 or graduate standing. (3 credits) Key elements of land-surface hydrology. Water in the atmosphere; dry adiabatic and pseudoadiabatic processes. Vapor turbulent transfer. Heat fluxes and surface energy budgets. Mass transfer and energy budget methods for estimating evapotranspiration. Soil physical properties; water flow in unsaturated soils; infiltration. Snow hydrology. Runoff generation. Probabilistic approaches to describing spatial variability. Last offered Winter 2017. | ||||||||||
56 | Approved | application | CEE 553 | Infrastruc System Optimization | 3 | College of Engineering | Systems-level approach to the analysis and design of civil infrastructure systems. The fundamental concepts are taught through a series of examples drawn from various infrastructure systems applications. Optimization techniques covered include model building, linear programming, nonlinear programming and the use of algebraic modeling languages. | ||||||||||
57 | Approved | methodology | CEE 571 / AEROSP 550 / EECS 560 / MECHENG 564 | Linear Systems Theory | 4 | College of Engineering | Linear spaces and linear operators. Bases, subspaces, eigenvalues and eigenvectors, canonical forms. Linear differential and difference equations. Mathematical representations: state equations, transfer functions, impulse response, matrix fraction and polynomial descriptions. System-theoretic concepts: causality, controllability, observability, realizations, canonical decomposition, stability. | crosslisted with AEROSP 550/EECS 560/MECHENG 564. | |||||||||
58 | Approved | application | CEE 572 | Dynamic Infrastructure Systems | 3 | College of Engineering | Introduction to the fundamentals of dynamics system theory applied to infrastructure systems including system modeling as well as monitoring and controlling structural, transportation, hydraulic, and electrical grid systems. Continuous-time and discrete-time linear systems are emphasized but elementary concepts in nonlinear systems are also presented. | ||||||||||
59 | Approved | methodology | CHE 505 | Applied Mathematics For Chemical Engineers | 3 | College of Engineering | Prereq: graduate standing. (3 credits) Analytical and numerical techniques applicable to statistical mechanics, transport phenomena, fluid mechanics and reaction engineering. Groups and linear spaces; tensors and linear operators; computational approaches to nonlinear systems and integration; special functions; spectral theory of ordinary and partial differential equations; series expansions; coordinate transformations; complex algebra and analysis; integral transformations. | ||||||||||
60 | Approved | 7/10/2023 | application | CHE 527 | Fluid Flow | 3 | College of Engineering | Applications of fluid dynamics to chemical engineering systems. Theory and practice of laminar and turbulent flow of Newtonian and non-Newtonian fluids in conduits and other equipment. Multi-phase flow. Introduction to the dynamics of suspended particles, drops, bubbles, foams and froth. Selected topics relevant to chemical and other engineering disciplines. | |||||||||
61 | Approved | methodology | CHE 540 | Mathematical Methods For Biological Network Analysis | 3 | College of Engineering | Prereq: senior or graduate standing, permission by instructor. (3 credits) This course focuses on methods and applications. Methods include ordinary differential equations, mathematical programming, Bayesian networks and statistical analysis, etc. Applications to the modeling of various biological systems are discussed and students perform a critical evaluation of current literature as well as hands-on computational projects using high level computing languages. | ||||||||||
62 | Approved | methodology | CHE 554 / MATSCIE 554 | Computational Methods In MATSCIE And CHEM | 3 | College of Engineering | Prereq: Senior level or Graduate Standing. (3 credits) Broad introduction to the methods of numerical problem solving in Materials Science and Chemical Engineering. Topics include numerical techniques, computer algorithms and the formulation and use of computational approaches for the modeling and analysis of phenomena peculiar to these disciplines (cross-listed with CHEM 554) | ||||||||||
63 | Approved | methodology | CHE 557 / MATSCIE 557 | Computational Nanoscience Of Soft Matter | 3 | College of Engineering | Prereq: Differential equations course, and a statistical thermodynamics or statistical mechanics course. (3 credits) Provides an understanding of strategies, methods, capabilities and limitations of computer simulation as it pertains to the modeling and simulation of soft materials at the nanoscale. The course consists of lectures and hands-on, interactive simulation labs using research codes and commercial codes. Ab initio, molecular dynamics, Monte Carlo and mesoscale methods. | ||||||||||
64 | Approved | application | CHE 629 | Complex Fluids | 3 | College of Engineering | Prerequisite: CHE 527. (3 credits). Structure, dynamics, and flow properties of polymers, colloids, liquid crystals and other substances with both liquid and solid-like characteristics. | ||||||||||
65 | Contact MICDE | methodology/ application | CHE 696 | Special Topics (selected) | 3-4 | College of Engineering | Please ask about using a special topic class as its content constantly change. Previously approved topics include: Applied Data Science for Engineers (crosslisted with MSE - https://micde.umich.edu/wp-content/uploads/sites/6/2020/08/DS-ChE-syllabus_W19.pdf) | See the Special Topics tab for information about specific sections of "Special Topics" courses | |||||||||
66 | Approved | application | CHEM 461 | Physical Chemistry I | 3 | LSA | Prereq: CHEM 260 or 370 or BIOPHYS 370 or PHYSICS 370; and PHYSICS 240 or 235; and MATH 215 or CHEM 262. Should be elected concurrently with CHEM 462. (3 credits).This course provides an introduction to quantum mechanics and its application to chemistry. It is the second of a 3-term sequence in physical chemistry and builds on material introduced in CHEM 260. The Schrodinger Equation is solved in one, two, and three dimensions for important chemical problems. Group theory and quantum chemistry are used to understand chemical bonding and advanced spectroscopy. | ||||||||||
67 | Approved | application | CHEM 462 | Computational Chemistry Laboratory | 1 | LSA | Prereq: MATH 215, and prior or concurrent enrollment in CHEM 461 (1 credit) | ||||||||||
68 | Approved | application | CHEM 463 | Physical Chemistry II | 3 | LSA | Prereq: CHEM 461/462 (3 credits) May not be repeated for credit. No credit granted to those who have completed or are enrolled in CHEM 453. This is the third of a three-term sequence in physical chemistry and focuses on thermodynamics and kinetics. Both classical thermodynamics (entropy, phase, and chemical equilibrium) and statistical thermodynamics are discussed. Fundamental theories underlying chemical kinetics are discussed and solid state structures are introduced. | ||||||||||
69 | Approved | methodology | CHEM 551 / BIOCHEM 551 / PATH 551 / BIOMEDE 551 / BIOINF 551 | Proteome Informatics | 3 | Michigan Medicine | Introduction to proteomics, mass spectrometry, peptide identification and protein inference, statistical methods and computational algorithms, post-translational modifications, genome annotation and alternative splicing, quantitative proteomics and differential protein expression analysis, protein-protein interaction networks and protein complexes, data mining and analysis of large-scale data sets, clinical applications, related technologies such a metabolomics and protein arrays, data integration and systems biology. Prerequisites: Bio Chem and calculus. | ||||||||||
70 | Approved | application | CHEM 571 | Quantum Chemistry | Refer to course guide | LSA | Last offered Fall 2014 | ||||||||||
71 | Approved | application | CHEM 575 | Chemical Thermodynamics | 3 | LSA | Prereq:CHEM 461 (3 credits). May not be repeated for credit. | ||||||||||
72 | Approved | application | CHEM 580 | Molecular Spectra and Structure | 3 | LSA | Prereq: CHEM 570 or permission of instructor (3 credits). May not be repeated for credit. | ||||||||||
73 | Approved | methodology | CLIMATE 407 / SPACE 407 | Mathematical Methods in Geophysics | 4 | College of Engineering | Advised Prereq: MATH 216 (4 credits) Vector calculus and Cartesian tensors; Sturm-Liouville systems, Green’s Functions and solution of boundary value problems; Fourier series, Fourier and Laplace transforms, discrete Fourier transform, fast Fourier transforms, and energy spectra and singular perturbation theory. (SPACE 407) | ||||||||||
74 | Approved | 10/26/2023 | methodology | CLIMATE 423 | Data Analysis and Visualization for Geoscientists | 4 | College of Engineering | Fundamental data science, data and error analysis, data-model comparison tests and metrics, and visualization techniques. By course end, students will be able to produce publication ready scientific data visualization, process data sets using Python, perform large data set analysis, conduct data-model comparisons, and scientifically test hypotheses and interpret results. | |||||||||
75 | Approved | application | CLIMATE 477 / SPACE 477 | Space Weather Modeling | 4 | College of Engineering | Prereq: SPACE 370. Minimum grade of “C” required for enforced prerequisites (4 credits) An introduction to a variety of models of the space environment, including models of the sun, magnetosphere, ring current, ionosphere, thermosphere and ionospheric electrodynamics. Students will learn the origins of different models, what each represents, to run the models and become familiar with the output. | ||||||||||
76 | Approved | methodology | CLIMATE 555 / SPACE 555 | Spectral Methods | 4 | College of Engineering | Advised prereq: MATH 216. ENGR 103 (4 credits) An introduction to numerical methods based on Fourier Series, Chebyshev polynomials and other orthogonal expansions. Although the necessary theory is developed, the emphasis is on algorithms and practical applications in geophysics and engineering, especially fluid mechanics. Many homework assignments will be actual problem-solving on the computer. (SPACE 555) | ||||||||||
77 | Approved | application | CLIMATE 586 | Climate Data Analysis | 3 | College of Engineering | Advised prereq: graduate standing (3 credits) Objective methods are introduced for analyzing climate data with inherent spatial and/or temporal correlation scales. These include time series analysis, pattern recognition techniques, regression, and linear modeling. The emphases are both the usage of such methods and critical evaluation of literature that employ them. | ||||||||||
78 | Approved | 8/24/2023 | methodology | CLIMATE 588 | Regional Scale Climate: Downscaling Techniques and Applications | 4 | College of Engineering | Global change is impacting an increasing number of sectors in science, engineering and policy, creating a need for high-resolution, future climate data used in impact assessments and mitigation plans. Despite the increase in resolution of general circulation models used for climate studies, these model resolutions are not yet consistently fine enough for local and regional scale studies. Therefore, an understanding of the appropriate data tools, including downscaling methods are necessary for local and regional scale applications. The primary objectives of this course are to understand resolution-sensitive climate model processes and types of downscaling techniques, practice data analysis with coding tools, and understand the landscape of climate model d ata for specific applications. | |||||||||
79 | Approved | application | CLIMATE 589 | Art of Climate Modeling | 4 | College of Engineering | |||||||||||
80 | Approved | application | CMPLXSYS 425 | Evolution In Silico | 3 | LSA | (3 credits) While every population of living organisms is evolving, not everything that evolves is alive. Nature's success at finding innovative solutions to complex problems has inspired many computational implementations of the evolutionary process. Some of the various implementations we will learn about with hands-on exercises include approaches for solving optimization problems, building controllers and/or bodies for robots, and using computational instances of Darwinian evolution to study fundamental questions in biology. | ||||||||||
81 | Approved | methodology | CMPLXSYS 445 | Introduction to Information Theory for the Natural Sciences | 3 | LSA | This course introduces the basic tools of Information Theory. Entropy, Relative Entropy, and Information, and highlights their utility with applications drawn from various disciplines. After introducing the basics of probability theory and information theory, we explore topics including coding, data compression, channel capacity, thermodynamics, population dynamics, gene transcriptions, network science and more. | ||||||||||
82 | Approved | methodology | CMPLXSYS 511 | Theory of Complex Systems | 3 | LSA | (3 credits) A math-based introduction to the theory and analysis of complex systems. Methods covered include nonlinear dynamics, both discrete and continuous, chaos theory, stochastic processes, game theory, criticality and fractals, and numerical methods. Examples include population dynamics, evolutionary theory, genetic algorithms, epidemiology, simple models of markets, opinion formation models, and cellular automata. | ||||||||||
83 | Approved | methodology/ application | CMPLXSYS 530 | Computer Modeling of Complex Systems | Refer to course guide | LSA | Advised Pre-Req: Enrollment in CSCS Graduate Certificate program or permission of instructor. Introduces students to basic concepts, tools , and issues which arise using computers to model complex systems. Emphasis is placed on the modeling process itself, from model design through implementation to analyzing, documenting, and communicating results. Case studies of computer models of complex systems, including adaptive and non-adaptive complex systems drawn from economics, ecology, immunology, epidemiology, evolutionary biology, political science, and cognitive science. | ||||||||||
84 | Approved | methodology | CMPLXSYS 535 | Network Theory | 3 | LSA | (3 credits) Introduces and develops the mathematical theory of networks, particularly social and technological networks; with applications to important network-driven phenomena in epidemiology of human infections and computer viruses, cascading failure in grids, network resilience and opinion formation. Topics covered: experimental studies of social networks, WWW, internet, information, and biological networks. Cross-listed with PHYS 508. | ||||||||||
85 | Approved | methodology | CSE 548 / SI 649 | Information Visualization | 3 | School of Information | Prereq: SI 506; C- or better or SI 506 waiver and co-requisite: SI 507; C- or better or SI waiver or SI 508; C- or better; or graduate standing (3 credit). Introduction to information visualization. Topics include data and image models, multidimensional and multivariate data, design principles for visualization, hierarchical, network, textual and collaborative visualization, the visualization pipeline, data processing for visualization, visual representations, visualization system interaction design, and impact of perception. Emphasizes construction of systems using graphics application programming interfaces (APIs) and analysis tools. (cross-listed with EECS 548) | ||||||||||
86 | Approved | methodology | CSE 549 / SI 650 | Information Retrieval | 3 | School of Information | Prereq: SI 507 or waiver or graduate standing. (3 credits) Information is everywhere. We encounter it in our everyday lives in the form of E-mail, newspapers, television, the Web, and even in conversations with each other. Information is hidden in a variety of media: text, images, sounds, videos. While casual information consumers can simply enjoy its abundance and appreciate the existence of search engines that can help them find what they want, information professionals are responsible for building the underlying technology that search engines use. Building a search engine involves a lot more than indexing some documents -- information retrieval is the study of the interaction between users and large information environments. It covers concepts such as information need, documents and queries, indexing and searching, retrieval evaluation, multimedia and hypertext search, Web search, as well as bibliographical databases. In this course, students go over some classic concepts of information retrieval and then quickly jump to the current state of the art in the field, where crawlers, spiders, and hard-of-hearing personal butlers roam. (Cross-list with EECS 549) | ||||||||||
87 | Approved | 1/13/2026 | methodology | CSE 576 | Advanced Data Mining | 4 | College of Engineering | This course aims to introduce students to advanced data mining, with emphasis on interconnected data or graphs or networks. Students will become familiar with the challenges of processing large amounts of data, state-of-the-art methods and algorithms for analyzing them, and applications of data mining in various domains. We expect that by the end of the course, students: will have a thorough understanding of the graph mining foundations, and will be able to: critique data mining methods, formulate and solve data mining problems, and analyze large-scale datasets (in distributed and other settings). | |||||||||
88 | Approved | methodology | CSE 586 | Design And Analysis Of Algorithms | 4 | College of Engineering | Prereq: EECS 281 (4 credits) Design of algorithms for nonnumeric problems involving sorting, searching, scheduling, graph theory and geometry. Design techniques such as approximation, branch-and-bound, divide-and-conquer, dynamic programming, greed and randomization applied to polynomial and NP-hard problems. Analysis of time and space utilization. | ||||||||||
89 | Approved | methodology | CSE 587 | Parallel Computing | 4 | College of Engineering | Prereq: EECS 281 and graduate standing (4 credits) The development of programs for parallel computers. Basic concepts such as speedup, load balancing, latency, system taxonomies. Design of algorithms for idealized models. Programming on parallel systems such as shared or distributed memory machines, networks. Grid Computing. Performance analysis. Course includes a substantial term project. | ||||||||||
90 | Approved | methodology | CSE 592 | Artificial Intelligence Foundations | 4 | College of Engineering | Advised prereq: Graduate standing (4 credits) (Credit cannot be obtained for both EECS 492 and EECS 592) An advance introduction to AI emphasizing its theoretical underpinnings. Topics include search, logic, knowledge representation, reasoning planning, decision making under uncertainty, and machine learning.` | ||||||||||
91 | Approved | methodology | CSE 595 / LING 541 / SI 561 | Natural Language Processing | 3 | School of Information | Should be senior standing. (3 credits) Linguistics fundamentals of natural language processing (NLP), part of speech tagging, hidden Markov models, syntax and parsing, lexical semantics, compositional semantics, word sense disambiguation, machine translation. Additional topics such as sentiment analysis, text generation, and deep learning for NLP. Cross-listed with EECS 595. | ||||||||||
92 | Approved | methodology | DATASCI 415 / STATS 415 | Intro to Data Mining | 4 | LSA | Advisory Prereq: MATH 215 and 217, and one of STATS 401, 406, 412 or 426 (4 credits)This course covers the principles of data mining, exploratory analysis and visualization of complex data sets, and predictive modeling. The presentation balances statistical concepts (such as over-fitting data, and interpreting results) and computational issues. Students are exposed to algorithms, computations, and hands-on data analysis in the weekly discussion sessions. | ||||||||||
93 | Approved | methodology | DATASCI 503 / STATS 503 | Statistics Learning II: Multivariate Analysis | 4 | LSA | Prereq: STATS 500 or equivalent (4 credits). The course covers methods for modern multivariate data analysis and statistical learning, including both their theoretical foundations and practical applications. Topics include principal component analysis and other dimension reduction techniques, classification (discriminant analysis, decision trees, nearest neighbor classifiers, logistic partitioning methods, model-based methods), and categorical data analysis. There will be a significant data analysis component. | ||||||||||
94 | Approved | application | DATASCI 507 / STATS 507 | Data Science and Analytics using Python | 3 | LSA | STATS 507 surveys the software tools that are currently popular among data scientists in academia and industry. The course begins with an accelerated introduction to programming in Python. Next, we focus on Python’s scientific computing stack: numpy, scipy, pandas, and scikit-learn. We also cover regular expressions, relational databases, and the UNIX/Linux command line. The final part of the course is an introduction to deep learning using PyTorch. | ||||||||||
95 | Approved | 5/20/2025 | application | DATASCI 531 / STATS 531 | Modeling and Analysis of Time Series Data | LSA | |||||||||||
96 | Approved | methodology | EARTH 468 | Data and Models | 3 | LSA | Prereq: MATH 115 or equivalent (MATH 116, 120, 121, 156, 175, 176, 185, 186, 295, 296) Advised prereq: Knowledge of, or willingness to learn, a programming language (e.g., Matlab, Mathematica) (3 credits) | ||||||||||
97 | Approved | methodology | EARTH 500 | Introduction to Linux Programming | 2 | LSA | (2 credits) | ||||||||||
98 | Approved | methodology | ECE 503 | Introduction To Numerical Electromagnetics | 3 | College of Engineering | Prereq: EECS 330 (3 credits) Introduction to numerical methods in electromagnetics including finite difference, finite element and integral equation methods for static, harmonic and time dependent fields; use of commercial software for analysis and design purposes; applications to open and shielded transmission lines, antennas, cavity resonances and scattering. | EECS 503 | |||||||||
99 | Approved | methodology | ECE 505 | Computational Data Science and Machine Learning | 4 | College of Engineering | Prereq: EECS 301 or MATH 425 or STATS 250 or STATS 412 or STATS 426 or IOE 265 or graduate standing. Minimum grade of C required for enforced prerequisites. (4 credits) (Students who have previously enrolled in 551 or 453 cannot get credit for 505.) Introduction to computational methods for identifying patterns and outliers in large data sets. Topics include the singular and eigenvalue decomposition, independent component analysis, graph analysis, clustering, linear, regularized, sparse and non-linear model fitting, deep, convolutional and recurrent neural networks. Students program methods; lectures and labs emphasize computational thinking and reasoning. | EECS 505 | |||||||||
100 | Approved | application | ECE 516 / BIOMEDE 516 | Medical Imaging Systems | College of Engineering | We'll examine, from a systems perspective, the techniques used to form internal images of (living) human bodies. These imaging systems are used for tasks ranging from cancer detection to basic biophysical and cognitive research, and include planar X-ray and gamma-ray (nuclear medicine) imaging, X-ray tomography, ultrasound, single-photon tomography, positron emission tomography, and magnetic resonance imaging (MRI). | EECS 516 |