Spreadsheets Across the Curriculum module/Geology of National Parks course. Students study how discharge per unit area varies with elevation in the high country of Glacier National Park from USGS hydrograph data from Swiftcurrent Creek and its tributary Grinnell Creek..

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In this model eliciting activity (MEA), students are hired by a travel magazine to determine if two airlines that fly into Chicago are equally reliable. They examine data of flight arrival delay times for both airlines flying out of the same city. They first identify measures that can be used to compare the two airlines. Working in small groups, the students decide the size of a meaningful difference between the airlines for each measure and use that information to determine a rule that for deciding if one airline is more reliable than another. The students apply their rule to flight arrival delay data for the two airlines from four additional departure cities, and use the results to write a report to the magazine editor on whether or not one airline is more reliable than the other. This activity can serve as an introduction to ideas of central tendency and variability, and prepares students for formal approaches to comparing groups.

This assignment exposes students to data on economic growth and development as commonly measured by per capita GDP and the Human Development Index (HDI) for 100 countries of the world. There is a big debate about how good an indicator HDI is compared to GDP per capita as a measure of development.

The following topics are covered in the course: complex algebra and functions; analyticity; contour integration, Cauchy’s theorem; singularities, Taylor and Laurent series; residues, evaluation of integrals; multivalued functions, potential theory in two dimensions; Fourier analysis and Laplace transforms.

Complex analysis is a basic tool with a great many practical applications to the solution of physical problems. It revolves around complex analytic functions—functions that have a complex derivative. Unlike calculus using real variables, the mere existence of a complex derivative has strong implications for the properties of the function. Applications reviewed in this class include harmonic functions, two dimensional fluid flow, easy methods for computing (seemingly) hard integrals, Laplace transforms, and Fourier transforms with applications to engineering and physics.

6.004 offers an introduction to the engineering of digital systems. Starting with MOS transistors, the course develops a series of building blocks — logic gates, combinational and sequential circuits, finite-state machines, computers and finally complete systems. Both hardware and software mechanisms are explored through a series of design examples.
6.004 is required material for any EECS undergraduate who wants to understand (and ultimately design) digital systems. A good grasp of the material is essential for later courses in digital design, computer architecture and systems. The problem sets and lab exercises are intended to give students “hands-on” experience in designing digital systems; each student completes a gate-level design for a reduced instruction set computer (RISC) processor during the semester.

All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.

The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures.

This course provides the fundamental computational toolbox for solving science and engineering problems. Topics include review of linear algebra, applications to networks, structures, estimation, finite difference and finite element solutions of differential equations, Laplace’s equation and potential flow, boundary-value problems, Fourier series, the discrete Fourier transform, and convolution. We will also explore many topics in AI and machine learning throughout the course.

An in-class statistics activity for computing and interpreting the standard deviation from a sample.

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environmental Applications (1.017) and Uncertainty in Engineering (1.010), are being jointly offered and taught as a single course.

This posting explains the concept of a function, the notation, domain and range of a function, and the basic ways to define a function.

From the University of Florida Department of Mathematics, this is the second volume in a three volume presentation of calculus from a concepts perspective. The emphasis is on learning the concepts behind the theories, not the rote completion of problems.

Using highly interactive learning design, this Concepts in Statistics course provides students with a strong understanding of fundamental principles that guide the study of statistical inference. Drawing from Open Learning Initiative (OLI) source content, this course’s simulations and lab-style synthesis activities invite hands-on exploration of statistical concepts. Students learn to summarize data graphically and numerically; examine relationships among quantitative data; understand the role of probability and probability distributions; link probability to statistical inference; and conduct foundational statistical calculations and analyses.