This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature.

Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This course aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding, and includes many applications in engineering, physics, biology, operations research and finance.

This class addresses the representation, analysis, and design of discrete time signals and systems. The major concepts covered include: Discrete-time processing of continuous-time signals; decimation, interpolation, and sampling rate conversion; flowgraph structures for DT systems; time-and frequency-domain design techniques for recursive (IIR) and non-recursive (FIR) filters; linear prediction; discrete Fourier transform, FFT algorithm; short-time Fourier analysis and filter banks; multirate techniques; Hilbert transforms; Cepstral analysis and various applications.
Acknowledgements
I would like to express my thanks to Thomas Baran, Myung Jin Choi, and Xiaomeng Shi for compiling the lecture notes on this site from my individual lectures and handouts and their class notes during the semesters that they were students in the course. These lecture notes, the text book and included problem sets and solutions will hopefully be helpful as you learn and explore the topic of Discrete-Time Signal Processing.

A large proportion of contemporary research on organizations, strategy and management relies on quantitative research methods. This course is designed to provide an introduction to some of the most commonly used quantitative techniques, including logit/probit models, count models, event history models, and pooled cross-section techniques.

Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems.

The aim of this course is to highlight some technical aspects of the classical tradition in architecture that have so far received only sporadic attention. It is well known that quantification has always been an essential component of classical design: proportional systems in particular have been keenly investigated. But the actual technical tools whereby quantitative precision was conceived, represented, transmitted, and implemented in pre-modern architecture remain mostly unexplored. By showing that a dialectical relationship between architectural theory and data-processing technologies was as crucial in the past as it is today, this course hopes to promote a more historically aware understanding of the current computer-induced transformations in architectural design.

This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes.

The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages. This includes systems with finite or infinite state spaces, as well as perfectly or imperfectly observed systems. We will also discuss approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.

The course addresses dynamic systems, i.e., systems that evolve with time. Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions.
We will analyze the response of these systems to inputs and initial conditions. It is of particular interest to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. We will learn how to design (control) systems that ensure desirable properties (e.g., stability, performance) of the interconnection with a given dynamic system.

Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Kinematics. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange’s equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems.

This class is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics include kinematics; force-momentum formulation for systems of particles and rigid bodies in planar motion; work-energy concepts; virtual displacements and virtual work; Lagrange’s equations for systems of particles and rigid bodies in planar motion; linearization of equations of motion; linear stability analysis of mechanical systems; free and forced vibration of linear multi-degree of freedom models of mechanical systems; and matrix eigenvalue problems. The class includes an introduction to numerical methods and using MATLAB® to solve dynamics and vibrations problems.
This version of the class stresses kinematics and builds around a strict but powerful approach to kinematic formulation which is different from the approach presented in Spring 2007. Our notation was adapted from that of Professor Kane of Stanford University.

Upon successful completion of this course, students will be able to:

Create lumped parameter models (expressed as ODEs) of simple dynamic systems in the electrical and mechanical energy domains
Make quantitative estimates of model parameters from experimental measurements
Obtain the time-domain response of linear systems to initial conditions and/or common forcing functions (specifically; impulse, step and ramp input) by both analytical and computational methods
Obtain the frequency-domain response of linear systems to sinusoidal inputs
Compensate the transient response of dynamic systems using feedback techniques
Design, implement and test an active control system to achieve a desired performance measure

Mastery of these topics will be assessed via homework, quizzes/exams, and lab assignments.

The DMT Clearinghouse is a registry for online learning resources about research data management. Initial seed funding was provided by the U.S. Geological Survey's Community for Data Integration. Subsequent funding has been granted by an Institute of Museum and Library Services National Leadership Grant (LG-70-18-0092-18). Developed in collaboration with the Earth Sciences Information Partnership (ESIP) Federation, and DataONE, with subsequent support from the University of New Mexico Libraries Research Data Services, the DMT Clearinghouse is available for searching, browsing, and submitting information about learning resources on data management topics. DMT Clearinghouse FeaturesThe Search Interface allows users to find learning resources by entering terms, names of people and organizations, dates, and keywords. The Browse Interface allows users to view the entire list of learning resources, and to filter by educational framework. An educational framework is a plan or set of steps that defines or collects the content using clear, definable standards about what the student should know and understand. For purposes of the DMT Clearinghouse, a given learning resource may be associated with a community-defined standard for data management, for example:USGS Science Support FrameworkDataONE Data Life CycleESIP Data Management Short Course for Scientists The Digital Preservation NetworkInternational Council for Science (ICSU) World Data System (WDS) Training Resource GuideFAIR Data Principles The Submission Form allows users to enter information about learning resources that they would like to see included in the DMT Clearinghouse. A user log in is not required to submit a resource with key, required information. To add more information about a learning resource than just that required, please log in or create an account (click "Log In at the upper right side of the screen.) NOTE: Submissions will be published to the DMT Clearinghouse following an editorial review to ensure the resource meets quality and selection criteria for inclusion.. You may be contacted for more information about your submission, if needed. Your contact information will not be made available publicly without your permission. For questions or feedback, please contact clearinghouseEd@esipfed.org.

Introduction to econometric models and techniques, simultaneous equations, program evaluation, emphasizing regression. Advanced topics include instrumental variables, panel data methods, measurement error, and limited dependent variable models. May not count toward HASS requirement.

This text is an introductory treatment on the junior level for a two-semester electrical engineering course starting from the Coulomb-Lorentz force law on a point charge. The theory is extended by the continuous superposition of solutions from previously developed simpler problems leading to the general integral and differential field laws. Often the same problem is solved by different methods so that the advantages and limitations of each approach becomes clear. Sample problems and their solutions are presented for each new concept with great emphasis placed on classical models of physical phenomena such as polarization, conduction, and magnetization. A large variety of related problems that reinforce the text material are included at the end of each chapter for exercise and homework.

6.632 is a graduate subject on electromagnetic wave theory, emphasizing mathematical approaches, problem solving, and physical interpretation. Topics covered include: waves in media, equivalence principle, duality and complementarity, Huygens’ principle, Fresnel and Fraunhofer diffraction, dyadic Green’s functions, Lorentz transformation, and Maxwell-Minkowski theory. Examples deal with limiting cases of Maxwell’s theory and diffraction and scattering of electromagnetic waves.

This open course for Elementary Statistics was created through a Round Ten Textbook Transformation Grant:

https://oer.galileo.usg.edu/mathematics-collections/39/

The open course contains ancillary materials for OpenStax Introductory Statistics:

https://openstax.org/details/books/introductory-statistics

Included in the course are introductions to each lesson, lecture slides, videos, and problem questions. Topics include:

Types of Data
Sampling Techniques
Qualitative Data
Frequency Distributions
Descriptive Statistics
Variation and Position
Confidence Intervals
Hypothesis Testing
Chi-Square Goodness of Fit
Linear Regression
Variance ANOVA

This course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography. While this is an introductory course, we will (gently) work our way up to some fairly advanced material, including an overview of the proof of Fermat’s last theorem.

This intensive micro-subject provides the necessary skills in Microsoft® Excel spreadsheet modeling for ESD.71 Engineering Systems Analysis for Design. Its purpose is to bring entering students up to speed on some of the advanced techniques that we routinely use in analysis. It is motivated by our experience that many students only have an introductory knowledge of Excel, and thus waste a lot of time thrashing about unproductively. Many people think they know Excel, but overlook many efficient tools, such as Data Table and Goal Seek. It is also useful for a variety of other subjects.

This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations.