Middle School Portal: Math and Science Pathways (MSP2)
M.C. Escher is a widely known and popular artist whose work depicts complex, and often impossible, geometrical patterns. This Web site examines the mathematics behind his drawings. Many examples of Escher's work are given, illustrating mathematical principles such as the shape and the logic of space. Tessellations and polyhedra are common building blocks of the drawings. It is quite interesting to see how basic designs are transformed into the intricacies depicted by Escher. The material is cert
Approximating pi
This web page features mathematical information about Archimedes' successful approach to finding an approximation to pi and an interactive manipulative that replicates the approach. The user can approximate pi as a number between the lengths of the perimeters of two polygons, one inscribed inside a circle and one circumscribed around the circle. The number of sides for the polygons may be increased to 96 with the value for pi always being between the two approximations. Similarities and differen
Middle School Portal: Math and Science Pathways (MSP2)
In this online activity, students analyze predictions made by sportswriters about which basketball teams will win to determine which teams are playing each other. The Getting Started link describes how to set up a table to organize the given information. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The solution illustrates and explains three different ways to successfully organize information, includ
Movie money : do movies make money?
The initial question for this online activity asks students to determine if showing movies makes money for theater owners. Given information about box office receipts, the percentage of receipts that theater owners pay to movie distributors, and overhead costs, students answer the question by making calculations and organizing information in a suggested table. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasi
Middle School Portal: Math and Science Pathways (MSP2)
This online activity offers students a chance to analyze data stated as percentages to draw conclusions about the similarity of five archeological sites. Students analyze the data by making a table of the differences for each pair of sites by subtracting the smaller percentage from the larger for each of five types of evidence. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The activity features a solu
Middle School Portal: Math and Science Pathways (MSP2)
This online activity challenges students to determine which of four different size grape juice cans labeled with the grape juice concentration would have the strongest grape taste. The activity is one of 80 mathematical challenges featured on the Figure This! web site emphasizing real-world uses of mathematics. The Hint suggests forming ratios that are fractions to compare quantities. Two ways of answering the initial question are illustrated with tables. Related questions have students consider
Mathematical Methods of Engineering Analysis
Mathematical Methods of Engineering Analysis
Middle School Portal: Math and Science Pathways (MSP2)
This web site offers families, teachers, and tutors 80 mathematical challenges helpful for encouraging problem solving with students in grades 6 to 8. The math challenges focus on concepts and objects found in everyday life, such as how fast your heart beats, what shape container holds the most popcorn, and how much of me shows in a mirror. Each challenge contains an initial problem with a solution hint, a complete explanation of the answer, and additional problems related to the same challenge.
Middle School Portal: Math and Science Pathways (MSP2)
This challenge asks students to determine possible ways for combining stamps costing 15 and 33 cents to total 1 dollar 77 cents. It notes that this type of problem is similar to a process used for creating security codes. This online student activity is part of the Figure This! collection of 80 mathematical challenges. Students are encouraged to make a chart as they explore possible number combinations. The answer page describes and illustrates four different approaches to finding the solution,
From Algorithms to Z-Scores: Probabilistic and Statistical Modeling in Computer Science
The materials here form a textbook for a course in mathematical probability and statistics for computer science students. Computer science examples are used throughout, in areas such as: computer networks; data and text mining; computer security; remote sensing; computer performance evaluation; software engineering; data management; etc.
Mathematics Under the Microscope
This book inevitably asks the question "How does the mathematical brain work?" The author tries to reflect on the explosive development of mathematical cognition, an emerging branch of neurophysiology which purports to locate structures and processes in the human brain responsible for mathematical thinking. PDF file.
Deviation between the sliding direction of the chip over the tool and the direction of the friction
Pure oblique cutting experiments with conventional cutting tools as well as ultra-sharp tools have been carried out under a wide range of cutting conditions using a linear slide based cutting set-up. The chip flow direction was measured using the 3D Digital Image Correlation (DIC) technique of high-speed stereoscopic images and the frictional force direction was determined from forces. It is estimated that the error in chip flow angle measurements using DIC, was approximately ±1°, as was the e
Building a testbed for mini quadrotor unmanned aerial vehicle with protective shroud
Potential applications of small rotorcraft unmanned aerial vehicles (UAVs) range from military missions to exploration of the planet Mars (Patrick C. O’Brien, 2003). Tasks such as exploration of unknown territories, formation flying, intelligence gathering etc, require UAV to be capable of flying very close to other flying or steady objects. Exposed rotary wings limit rotorcraft vehicle’s capability to fly in proximity of other objects. In some applications, such as rescue operation, urban w
Piezoelectric interfacial phenomena biosensor (A)
In numerous biomedical applications, it is vital to observe the activity of various biological systems such as cells, proteins or bacteria in solution, and their interaction with different natural and artificial interfaces. Monitoring sedimentation of cells or antibodies, their adhesion to the surfaces of different levels of biocompability, or the study of the impact of the drugs on cells or bacteria is of vital importance for biomedical and pharmaceutical applications. Currently, there is no in
Looking at Learning ... Again, Part 2: Workshop 2. Mathematics: A Community Focus
With Dr. Marta Civil. As teachers, we often make assumptions about the knowledge children are exposed to at home. Sometimes it seems that we focus on only reading and writing,Dr. Civil contends that we need to look more carefully at the mathematical potential of the home and that it is essential that schools learn to be more flexible and knowledgeable about students home environments. See and hear from Dr. Civil, the teachers she works with, and a long-standing parent mathematics group, and fo
SP.2H3 Ancient Philosophy and Mathematics (MIT)
Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquir
Discovering Diversity - David
David, assistant professor of hospitality management, shares personal teaching experiences and discusses the importance of fostering diversity in and out of the classroom.
Mathematical analysis
This is a module framework. It can be viewed online or downloaded as a zip file. As taught in 2007-2008 and 2009-2010. This module introduces mathematical analysis building upon the experience of limits of sequences and properties of real numbers and on calculus. It includes limits and continuity of functions between Euclidean spaces, differentiation and integration. A variety of very important new concepts are introduced by investigating the properties of numerous examples, and developing the a
Lecture 24 - 11/17/2010
Lecture 24
Virtual Maths, Shapes Space and Measure, Surface of a semi cylinder template
Diagram and template for using a semi-cylinder to calculate area
