This problem provides an opportunity to experiment with modeling real data. Populations are often modeled with exponential functions and in this particular case we see that, over the last 200 years, the rate of population growth accelerated rapidly, reaching a peak a little after the middle of the 20th century and now it is slowing down.

This task rquires students to determine if linear functions would be useful to model relationships presented in a data table.

Spreadsheets Across the Curriculum module. Students build spreadsheets to model the growth in population of a species of birds introduced to an isolated island in New Zealand.

The fundamental concepts, and approaches of aerospace engineering, are highlighted through lectures on aeronautics, astronautics, and design. Active learning aerospace modules make use of information technology. Student teams are immersed in a hands-on, lighter-than-air (LTA) vehicle design project, where they design, build, and fly radio-controlled LTA vehicles. The connections between theory and practice are realized in the design exercises. Required design reviews precede the LTA race competition. The performance, weight, and principal characteristics of the LTA vehicles are estimated and illustrated using physics, mathematics, and chemistry known to freshmen, the emphasis being on the application of this knowledge to aerospace engineering and design rather than on exposure to new science and mathematics.

Word Count: 72364

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

Word Count: 30407

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

This ebook provides a unique pedagogical approach to teaching the fundamentals of communication systems using interactive graphics and in-line questions. The material opens with describing the transformation of bits into digital baseband waveforms. Double-sideband suppressed carrier modulation and quadrature modulation then provide the foundation for the discussions of Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), M-ary Quadrature Amplitude Modulation (M-QAM), M-ary Phase Shift Keying (MPSK), and the basic theory of Orthogonal Frequency Division Multiplexing (OFDM). Traditional analog modulation systems are also described. Systems trade-offs, including link budgets, are emphasized. Interactive graphics allow the students to engage with and visualize communication systems concepts. Interactivity and in-line review questions enables students to rapidly examine system tradeoffs and design alternatives. The topics covered build upon each other culminating with an introduction to the implementation of OFDM transmitters and receivers, the ubiquitous technology used in WiFi, 4G and 5G communication systems.

This class uses revolutionary programmable interactivity to combine material from three fields – Computer Science + Mathematics + Applications – creating an engaging, efficient learning solution to prepare students to be sophisticated and intuitive thinkers, programmers, and solution providers for the modern interconnected online world.
Upon completion, students are well trained to be scientific “trilinguals,” seeing and experimenting with mathematics interactively as math is meant to be seen, and ready to participate and contribute to open source development of large projects and ecosystems.

An introductory course on teaching and learning science and mathematics in a variety of K-12 settings. Topics include education and media, education reform, the history of education, simulations, games, and the digital divide.

Functional analysis helps us study and solve both linear and nonlinear problems posed on a normed space that is no longer finite-dimensional, a situation that arises very naturally in many concrete problems. Topics include normed spaces, completeness, functionals, the Hahn-Banach Theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of Lᵖ spaces; Hilbert spaces; compact and self-adjoint operators; and the Spectral Theorem.

Game theory is an excellent topic for a non-majors quantitative course as it develops mathematical models to understand human behavior in social, political, and economic settings. The variety of applications can appeal to a broad range of students. Additionally, students can learn mathematics through playing games, something many choose to do in their spare time! This text also includes an exploration of the ideas of game theory through the rich context of popular culture. It contains sections on applications of the concepts to popular culture. It suggests films, television shows, and novels with themes from game theory. The questions in each of these sections are intended to serve as essay prompts for writing assignments.

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions. The task lends itself to an extended discussion comparing the differences that students have found and relating them back to the equation and the graph of the two functions.

30-page illustrated guide to fundamentals of measurement. This is intended to be a clear, comprehensive overview of effective measurement technique. Intended for advanced high school or introductory college level students. Includes worked examples and problems.

This course provides a basic introduction to metric spaces. It covers metrics, open and closed sets, continuous functions (in the topological sense), function spaces, completeness, and compactness.

6.336J is an introduction to computational techniques for the simulation of a large variety of engineering and physical systems. Applications are drawn from aerospace, mechanical, electrical, chemical and biological engineering, and materials science. Topics include: mathematical formulations; network problems; sparse direct and iterative matrix solution techniques; Newton methods for nonlinear problems; discretization methods for ordinary, time-periodic and partial differential equations, fast methods for partial differential and integral equations, techniques for dynamical system model reduction and approaches for molecular dynamics.
This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5211 (Introduction to Numerical Simulation).

lecture slides for a calculus-based course in Introduction to Probability & Statistics; suitable for sophomore or junior level of an undergraduate program

This course provides an elementary introduction to probability and statistics with applications. Topics include basic combinatorics, random variables, probability distributions, Bayesian inference, hypothesis testing, confidence intervals, and linear regression.
These same course materials, including interactive components (online reading questions and problem checkers) are available on MIT’s Open Learning Library, which is free to use. You have the option to enroll and track your progress, or you can view and use the materials without enrolling.

The microscopic world is full of phenomena very different from what we see in everyday life. Some of those phenomena can only be explained using quantum mechanics. This activity introduces basic quantum mechanics concepts about electrons that are essential to understanding modern and future technology, especially nanotechnology. Start by exploring probability distribution, then discover the behavior of electrons with a series of simulations.

Introduction to Statistical Physics introduces the concepts and formalism at the foundations of statistical physics. By the end of the course, students should understand qualitative and quantitative definitions of entropy, the implications of the laws of thermodynamics, and why the Boltzmann distribution is important in modeling systems at finite temperature. In terms of skills, students should have increased their familiarity with mathematical methods in the physical science, learned how to write short programs to simulate random events, and become more adept at articulating their understanding of physics.
This course was offered as part of MITES Summer, a six-week, residential STEM experience for rising high school seniors. MIT Introduction to Technology, Engineering, and Science (MITES) provides transformative experiences that bolster confidence, create lifelong community, and build an exciting, challenging foundation in STEM for highly motivated 7th–12th grade students from diverse and underrepresented backgrounds.

An Excel-Based Approach

Short Description:
Introduction to Statistics: An Excel-Based Approach introduces students to the concepts and applications of statistics, with a focus on using Excel to perform statistical calculations. The book is written at an introductory level, designed for students in fields other than mathematics or engineering, but who require a fundamental understanding of statistics. The text emphasizes understanding and application of statistical tools over theory, but some knowledge of algebra is required.

Long Description:
Introduction to Statistics: An Excel-Based Approach introduces students to the concepts and applications of statistics, with a focus on using Excel to perform statistical calculations. The book is written at an introductory level, designed for students in fields other than mathematics or engineering, but who require a fundamental understanding of statistics. The text emphasizes understanding and application of statistical tools over theory, but some knowledge of algebra is required.

Word Count: 175351

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)