Seminar for mathematics majors. Students present and discuss the subject matter, taken …
Seminar for mathematics majors. Students present and discuss the subject matter, taken from current journals or books and write up exercises. Topic for spring 2003: Elementary topological properties of differentiable manifolds. Topics covered include Sard's theorem, the Thom transversality theorem, vector fields and the Poincare-Hopf theorem, and cohomolgy via differential forms. Prerequisites subject to negotiation with the instructor. Instruction and practice in oral communication provided. In this course, students take turns in giving lectures. For the most part, the lectures are based on Robert Osserman's classic book A Survey of Minimal Surfaces, Dover Phoenix Editions. New York: Dover Publications, May 1, 2002. ISBN: 0486495140.
Students consider human senses and the many everyday human-made sensors so common …
Students consider human senses and the many everyday human-made sensors so common in their lives. They learn about the three components of biosensorsâa special type of sensorâand their functions and importance. With this understanding, students identify various organs in the human body that behave as sensors, such as the pancreas. Using LEGO® MINDSTORMS® NXT robots, provided rbt robot programs and LEGO sensors (light, ultrasonic, sound, touch), students gain first-hand experience with sensors and come to see how engineer-designed sensors play important roles in our daily lives, informing people of their surroundings and ultimately improving our quality of life.
Students are introduced to several types of common medical sensor devices, such …
Students are introduced to several types of common medical sensor devices, such as ear and forehead thermometers, glucometers and wrist blood pressure monitors; they use the latter to measure their blood pressure and pulse rates. Students also measure their heights and weights in order to calculate their BMIs (body mass index). Then they use the collected data to create and analyze scatterplots of the different variables to determine if any relationships exist between the measured variables. Discussions about the trends observed and possible health concerns conclude the activity.
Students design and create sensory integration toys for young children with developmental …
Students design and create sensory integration toys for young children with developmental disabilities an engineering challenge that combines the topics of biomedical engineering, engineering design and human senses. Students learn the steps of the engineering design process (EDP) and how to use it for problem solving. After learning about the human sensory system, student teams apply the EDP to their sensory toy projects. They design and make plans within given project constraints, choose materials, fabricate prototypes, evaluate the prototypes, and give and receive peer feedback. Students experience the entire design-build-test-redesign process and conclude with a class presentation in which they summarize their experiences with the EDP steps and their sensory toy project development.
This modeling task involves several different types of geometric knowledge and problem-solving: …
This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7).
This collection uses primary sources to explore settlement houses during the Progressive …
This collection uses primary sources to explore settlement houses during the Progressive Era. Digital Public Library of America Primary Source Sets are designed to help students develop their critical thinking skills and draw diverse material from libraries, archives, and museums across the United States. Each set includes an overview, ten to fifteen primary sources, links to related resources, and a teaching guide. These sets were created and reviewed by the teachers on the DPLA's Education Advisory Committee.
This task is intended to help model a concrete situation with geometry. …
This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?
This task provides a concrete geometric setting in which to study rigid …
This task provides a concrete geometric setting in which to study rigid transformations of the plane. It is important for students to be able to visualize and execute these transformations and for this purpose it would be beneficial to have manipulatives and it will important that the students be able to label the vertices of the hexagon with which they are working.
The earliest explorers did not have computers or satellites to help them …
The earliest explorers did not have computers or satellites to help them know their exact location. The most accurate tool developed was the sextant to determine latitude and longitude. In this activity, the sextant is introduced and discussed with the class. Students will learn how a sextant can be a reliable tool that is still being used by today's navigators and how computers can help assure accuracy when measuring angles. Also, this activity will show how computers can be used to understand equations even when knowing how to do the math is unknown.
Students investigate the critical nature of foundations as they learn differences between …
Students investigate the critical nature of foundations as they learn differences between shallow and deep foundations, including the concepts of bearing pressure and settlement. Using models representing a shallow foundation and a deep pile foundation, they test, see and feel the effects in a cardboard box test bed composed of layers of pebbles, soil and sand. They also make bearing pressure calculations and recommendations for which type of foundations to use in various engineering scenarios.
Students are introduced to brainstorming and the design process in problem solving …
Students are introduced to brainstorming and the design process in problem solving as it relates to engineering. They perform an activity to develop and understand problem solving with an emphasis on learning from history. Using only paper, straws, tape and paper clips, they create structures that can support the weight of at least one textbook. In their first attempts to build the structures, they build whatever comes to mind. For the second trial, they examine examples of successful buildings from history and try again.
Students gain experience and practice with three types of word problems using …
Students gain experience and practice with three types of word problems using the "Take From" context: result unknown, change unknown, and start unknown.
This task requires students to be able to reason abstractly about fraction …
This task requires students to be able to reason abstractly about fraction multiplication as it would not be realistic for them to solve it using a visual fraction model. Even though the numbers are too messy to draw out an exact picture, this task still provides opportunities for students to reason about their computations to see if they make sense.
Students should think of different ways the cylindrical containers can be set …
Students should think of different ways the cylindrical containers can be set up in a rectangular box. Through the process, students should realize that although some setups may seem different, they result is a box with the same volume. In addition, students should come to the realization (through discussion and/or questioning) that the thickness of a cardboard box is very thin and will have a negligible effect on the calculations.
This is a foundational geometry task designed to provide a route for …
This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle, which is crucial for many further developments in the subject.
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