Private Universe Project in Mathematics: Workshop 4: Thinking Like a Mathematician

What does a mathematician do? What does it mean to think like a mathematician? This program parallels what a mathematician does in real life with the creative thinking of students.,How a Mathematician Approaches Problems - Fern Hunt, a mathematician at the National Institute for Standards and Technology, is seen as she collaborates with colleagues to solve difficult technical problems. Using the metaphor of the childrens game Towers of Hanoi, she explains her approach to solving problems. 15 m

Chemical Equilibrium in the Gas Phase

This website describes gas phase equilibrium chemistry and provides a tutorial on key concepts like LeChatelier's principal and includes on-line exercises in which the reader can check their understanding. Calculations of equilibrium constants expressed in terms of pressure and concentration are presented. This site will be most useful for high school and introductory university Chemistry courses in which students are developing an understanding of equilibrium chemistry.

Middle School Portal: Math and Science Pathways (MSP2)

Six days a week, a new math problem is posted on this Web site to intrigue and challenge grade school students. Each Daily Brain has a different theme, considering some mathematical perspective of science, history, geography, and more. After solving the problem, or for a little help, students can look at a step-by-step solution that is also posted online. All old Daily Brains are kept in an archive, and as of May 2003, they numbered around 400. The problems are mostly intended for students betwe

Middle School Portal: Math and Science Pathways (MSP2)

Located at the University of Wales, the Centre for the Popularisation of Mathematics brings a more artistic side to the often plainly presented subject. Several online exhibits and galleries illustrate sculptures and knots that have a basis in math. One of the most interesting and famous mathematical sculptures is the Mobius Band. The centre gives a description of the Mobius Band and its significance, as well as instructions on how to create one and interesting experiments to try. Many other scu

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

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

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