This course focuses on the fundamentals of computer algorithms, emphasizing methods useful in practice. Upon successful completion of this course, the student will be able to: explain and identify the importance of algorithms in modern computing systems and their place as a technology in the computing industry; indentify algorithms as a pseudo-code to solve some common problems; describe asymptotic notations for bounding algorithm running times from above and below; explain methods for solving recurrences useful in describing running times of recursive algorithms; explain the use of Master Theorem in describing running times of recursive algorithms; describe the divide-and-conquer recursive technique for solving a class of problems; describe sorting algorithms and their runtime complexity analysis; describe the dynamic programming technique for solving a class of problems; describe greedy algorithms and their applications; describe concepts in graph theory, graph-based algorithms, and their analysis; describe tree-based algorithms and their analysis; explain the classification of difficult computer science problems as belonging to P, NP, and NP-hard classes. (Computer Science 303)
16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course will include: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms will include: Variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There will be a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. At the beginning of the course, the students will be given the source of a base code with all the elements of a finite element program which constitute overhead and do not contribute to the learning objectives of this course (assembly and equation-solving methods, etc.). Each assignment will consist of formulating and implementing on this basic platform, the increasingly complex algorithms resulting from the theory given in class, as well as in using the code to numerically solve specific problems. The application to real engineering applications and problems in engineering science will be stressed throughout.
"This course explores electromagnetic phenomena in modern applications, including wireless and optical communications, circuits, computer interconnects and peripherals, microwave communications and radar, antennas, sensors, micro-electromechanical systems, and power generation and transmission. Fundamentals include quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided waves; resonance; acoustic analogs; and forces, power, and energy."
In this course, the student will learn the theoretical and practical aspects of algorithms and Data Structures. The student will also learn to implement Data Structures and algorithms in C/C++, analyze those algorithms, and consider both their worst-case complexity and practical efficiency. Upon successful completion of this course, students will be able to: Identify elementary Data Structures using C/C++ programming languages; Analyze the importance and use of Abstract Data Types (ADTs); Design and implement elementary Data Structures such as arrays, trees, Stacks, Queues, and Hash Tables; Explain best, average, and worst-cases of an algorithm using Big-O notation; Describe the differences between the use of sequential and binary search algorithms. (Computer Science 201)
Given that no consumer grade digital cameras can produce images with more than at most about 12-bits per color channel, and 8-bits per color channel is more common, to manipulate HDR images (of say 32-bits per color channel), one must find a way to "estimate" the 8-bits up to 32-bits. This creation of an HDR image can be accomplished using multiple images at different exposure levels (stops).
The simplest operator used to map an HDR image to an LDR image. For example, the simplest method for how to map a 32-bit range down to an 8-bit range is a basic quantizer.
ZeGenie is a On-Line Interactive Learning Engine designed to help the student through Math material as if with a real human tutor.
All courses are available to students free of charge.
Math materials cover:
Algebra
1. Algebraic Expressions 2. Exponents 3. Quadratic Functions 4. Linear Relations 5. The Pythagorean Theorem 6. The function Basics 7. Functions 8. Absolute Function 9. Square Root Function 10. Step Functions 11. Exponential & Logarithms 12. Factoring 13. System of Equations 14. Conics
Geometry
1. Basics of Geometry 2. Lines, Division Points, Line Equations 3. Triangles and Similarity 4. Circle Theorems 5. Isometries
Trigonometry
1. Introduction to Trigonometry 2. Basic Trigonometric Ratios 3. Law of Sines 4. Law of Cosines 5. Radians 6. Unit Circle 7. Sine Function 8. Cosine Function 9. Tangent Function 10. Trigonometric Identities 11. Solving Trigonometric Functions
First of two-term sequence on modeling, analysis and control of dynamic systems. Mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices. Analytical and computational solution of linear differential equations and state-determined systems. Laplace transforms, transfer functions. Frequency response, Bode plots. Vibrations, modal analysis. Open- and closed-loop control, instability. Time-domain controller design, introduction to frequency-domain control design techniques. Case studies of engineering applications.
NBC's Lester Holt and former NFL running back Deuce McAllister explore kinematics on the playing field. NSF-funded scientists Tony Schmitz from the University of Florida and John Ziegert of Clemson University explain how the kinematic concepts of position, velocity and acceleration can be used to define how a running back moves. "Science of NFL Football" is a 10-part video series funded by the National Science Foundation and produced in partnership with the National Football League.
Subject:
Mathematics and Statistics, Science and Technology
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