This course will explore a variety of mathematical models including models from algebra, geometry, pre-calculus and calculus. In addition, models from the COMAP international modeling contest will be discussed. Excel will be used extensively to analyze some models and the modeling program Stella will also be demonstrated. The course is appropriate for the teacher who wishes to add more sophisticated modeling problems to his current course or wishes to design a modeling course. In addition to the course handout, additional models and ideas will be included on CD.
Learn how to use the function-graphing features in The Geometer's Sketchpad, version 4. You can now explore, animate, and analyze functions of algebra and trigonometry. Learn how to build and animate parameters within functions. You can use Cartesian or polar grids. You will also look at the conic sections and various ways to construct them. You will explore numerous classroom-ready tasks. There are some great new possibilities for teaching algebra and trigonometry.
With the support of technology, all high-school students – even those in non-AP statistics courses - can learn about sampling distributions, randomness, confidence intervals and the logic of inference. In this problem- and simulation-based course, participants will use manipulatives, TI-84 calculators and Fathom to make sense of these key ideas. No prior experience teaching statistics or with any of this technology is needed.
For some, the thought of bringing technology into the classroom is met with excitement. For an educator who prefers chalk and chalkboard, using computers can be intimidating. This course will give techno-phobic teachers real ways to implement technology. Each day we will use a different tool: PowerPoint, Excel, the Internet, and Podcasting. Ideas for using each tool will be presented gently to prevent intimidation. The goal is to convert teachers who fear technology into teachers who embrace it.
Using The Geometer's Sketchpad, the TI-84 and TI-Nspire, all high school students can explore topics covered in a calculus course without actually knowing any calculus. We will work through activities related to topics such as the fundamental notion of change, max-min problems, related-rate problems, area under a curve and arc length. This course will be of interest to teachers looking for ways of making their algebra, geometry and precalculus courses more interesting and deepening students’ understanding of mathematics. No experience with The Sketchpad, the TI-84 or TI-Nspire is necessary.
Fathom is well known as a program for data analysis, but it also useful in exploring the big ideas of algebra. The program can dramatize and connect the concepts of functions, variation, graphing, and modeling, all within a data-rich environment. This course will be an introductory one, for teachers with little or no experience with Fathom. The content will draw from the conventional topics of algebra I and algebra II. The goal of the course is for the participants to gain enough experience so that they can continue to explore the teaching possibilities on their own.
There are certain concepts in physics that are especially difficult for students. Participants will develop ways to teach such concepts through problem-solving activities. We will focus on mechanics and electricity, two main topics in AP Physics C. However, you do not have to be an AP Physics teacher to enjoy the course and to make use of it in your classroom. The discussion and the problems will emphasize the concepts, not high-level mathematics.
Many of the students we teach find it difficult to grasp mathematical concepts at the level of abstraction we expect. They see no relevance in what they are asked to do and are unwillimg to learn mathematical processes in an isolated and unrelated context. Despite this, these students can solve problems. This course presents activities using standard software packages and internet access to enable students to provide solutions to practical problems. There will also be the option to explore this type of integration of mathematical ideas in our traditional classrooms with more able students.
This course is designed for those who want to have some fun learning about how to write codes and break codes. The course will incorporate making your own Code-O-Graph, cracking the Enigma machine, orienteering, making a math trail (which others will need to follow), puzzles, and bar codes. It will include activities that can be used in the mathematics classroom to motivate students to reflect upon the major breakthroughs in mathematics in history. We will use Simon Singh's BBC code-breaking program, and learn about the DaVinci trail through London.
This workshop uses real-world data to promote algebraic thinking. Want to teach green algebra? Use Worldwatch environmental data to build mathematical models and make predictions for the future. Use motion detectors to create piecewise-defined functions and fit transformed absolute-value functions to the collected data. Between promoting environmental awareness and getting students up and moving while learning mathematics, you can reach a much broader range of students and get them excited about learning algebra and precalculus.
Geometry Expressions is a new software tool which generates algebraic expressions directly from a dynamic geometry model. Learn how to use this tool in mathematical discovery and problem solving both on its own and in conjunction with CAS. The class itself will be conducted in a discovery-learning format. Come re-experience the thrill of discovering new mathematics. Investigations will include: geometry and central-post irrigation, splines and telescope optics, discovering theorems in elementary differential geometry. No prior experience with CAS or geometry software is necessary.
We will model explorations with the TI-84 that help students improve their understanding of functions, inverse relations, parametric equations, data analysis, motion problems, simulations, applications of polynomial functions, and other topics. We will also use CBRs to do explorations and experiments. Participants will leave with a written set of explorations and activities. We welcome all levels of experience with the TI-84. Novice users are encouraged to attend the Sunday morning workshop: Learn How to Navigate the Keyboard.
We will use explorations with the TI-84 that help students improve their understanding of exponential, logistic, and trigonometric functions, vectors, parametric and polar equations, limits, rates of change, and analytic geometry. We will also use CBRs to do explorations and experiments. Participants will leave with a written set of explorations and activities. If there is interest, we will explore the additional resources using the TI-84 Inspire and study problem solving preparation for the free response questions on the AP Calculus exam. We welcome all levels of experience with the TI-84.
This course will provide a thorough introduction to The Geometer's Sketchpad covering all the important features of it. No prior experience will be assumed. Participants will learn both basic and advanced features of version 4. Emphasis will be on learning to use The Geometer's Sketchpad effectively in geometry classes, designing labs and exploration activities, using the software for classroom demonstrations and explanations. Macintosh and PC CD’s with extensive examples of labs and explorations will be provided.
This course will begin with visualization and conjecture building and proceed to deductive reasoning. We will use The Geometer's Sketchpad to explore real-world problems that were developed in a joint project with Russian mathematicians. The materials provide an opportunity for students to explore multiple theorems and concepts and allow for multiple representations (algebraic, coordinate, geometric). The dynamics of teamwork and the undeniable benefits of collaborative learning will be emphasized. No prior Sketchpad experience is necessary.
PowerPoint presentations can make a teacher’s life easier, especially in combination with other technology. The weak note taker, the visual learner and the absentee student all benefit. Presentations are consistent between sections and you will be able to connect with your students in a more meaningful way. This course is for a teacher with minimal experience with PowerPoint. Bring ideas for your own lessons.
Why use textbook data when you can use real data? For example, when will women run faster than men in the Olympics? Using Fathom, Excel, and the TI-84, algebra and precalculus can be enriched with the vast amount of real data available on the Internet. We will model data to linear, quadratic, exponential, power, piecewise and even some logistic functions. A variety of activities will be provided for algebra I, algebra II and precalculus. Some of the activities will use regression. Attendees will gain ideas on sources of data and activities that encourage students to find their own data.
Let's spice up our precalculus curriculum with some amazing labs. We will use Excel, The Geometer's Sketchpad, and the TI-84 to explore some of the fun concepts of precalculus through great problems and interesting constructions. We will also take some time to discuss what needs to be in a precalculus course in light of the current state of technology.
Some problems are good because they teach a particular concept well and some are good because of the really interesting mathematical techniques they use. Participants will be looking at five problems that are good for both of these reasons and because they can be carried throughout the course of a student’s mathematics study from elementary-level mathematics to calculus. Participants will use spreadsheet applications and The Geometer’s Sketchpad in their explorations.
This course is intended for all chemistry teachers who think they do not remember much physics, but wish they did. The course will present several physics topics that are of interest to chemistry teachers: the structure of the atom and basics of quantum theory, photons and photoelectric effect, isotopes, elementary particles, nuclear science, transmutations, kinetics, energy considerations in nuclear reactions, thermodynamics and gas laws, electricity and electrochemistry. The participants will also be given specific curriculum ideas and a list of Internet sources for labs and simulations.
Participants will gain a conceptual and mathematical understanding of the physics used in the secondary-school curriculum. We'll study concepts and problem solving, without laboratories. If you had physics a long time ago and remember little to nothing or have never had a physics class, this is for you! Stress level for this class is rated as ZERO! Topics include: measurement and uncertainty, dimensional analysis, kinematics (motion) in one and two dimensions, dynamics (forces) and circular motion will be covered in depth. Work/energy and momentum will be covered if time permits.
Learn how to transform your teaching into an exciting, fresh approach. The course will focus on the art of teaching and how it can be revitalized with a tablet, including preparing for class by creating digital whiteboards, teaching with tablet-oriented software, and posting notes. Participants will become thoroughly familiar with OneNote - Microsoft's primary note-taking software, as well as FluidMath and other tablet-oriented software. Examples are easily transferable to any math or science class. If participants do not have their own Tablet PC, one will be provided.
Participants will discuss general problem-solving approaches and solve many unusual physics problems. These brain twisters force students to think creatively and fully utilize their knowledge of physics concepts. Classroom activities will include individual and small-group problem solving and discussions about pedagogy of problem solving and its role in learning physics concepts. The participants will also receive an ample supply of great physics puzzles to bring back to their students and will be familiarized with existing resources on problem solving.
Through classroom exercises chosen from Phillips Exeter Academy's science curriculum and designed with the Harkness teaching philosophy in mind (question, think, discuss, do), participants will see how hands-on lab work can be used to introduce new material, strengthen developing ideas in current material, or bring closure to material at the end of a unit. The theme of the week will be light and we will conduct different labs every day with biology units on cell respiration, photosynthesis, alternation of generations in ferns and moss, and physics units on mechanics and optics.
In this course, particpants will study the natural history of the seacoast area of New Hampshire. We will take field trips to nearby ecosystems, including a kettle bog, a mixed deciduous-coniferous forest, a beaver flowage, and a coastal salt marsh. Participants will collect samples and data on each trip to bring back to the classroom. Laboratory time will be available to work up the data in the afternoons and evenings. Sample exercises, with procedures and materials used, will be distributed to all participants. Level and content will be appropriate for all interested conference participants.
This course offers a kinesthetic method (feet-on rather than hands-on) for teaching geometry and trigonometry concepts. Movement enables students to be wholly engaged in the learning process and encourages cooperative work. Participants will discover properties of radians by walking on the radii and arcs of a big circle, and will do similar work with angle sums of polygons and concurrent lines in a triangle. Participants will walk their way to a definition of circular functions. Graphs, transformations of functions and inverse circular functions can be grasped using kinesthetic activities.
Participants will be introduced to free, easily implemented technologies that engage students, uncover their preconceptions and build their intuition. You will learn to use wikis, blogs, simulations, podcasting, screencasting, and online quizzes effectively in your own classroom. Participants will learn to choose only tools that enhance learning while making teaching easier, more effective and more enjoyable. You will leave this course with a web site for your own classes even though you currently may have no experience beyond basic email and web browsing.
This course will explore what it is that the best teachers know about their students that helps facilitate the learning process. While discussing various topics, including the effect of stress on the brain, neuroplasticity, and the impact of language on the brain, participants will reflect upon their own teaching in a collaborative setting. Participants will then discuss new ways to incorporate recent findings on learning and the brain in the classroom.
We all realize that we have to teach the Pythagorean theorem, but often wonder about the angle-bisector theorem. We question what theorems should we emphasize and which ones should we just mention because they are needed in the flow of theorems that lead to the next theorem. Our geometry books are very rich in content and heavy to carry but do not prioritize. They leave us often wondering what to teach and what not to teach. In this course, participants will analyze the whole scope of the geometry syllabus and gain the confidence to decide whether to include or exclude a particular theorem.
What are Julia sets, where do they come from, why do they look the way they do, and what do they have to do with the Mandelbrot set? Answers are found within precalculus mathematics. It will be assumed that participants are familiar with the arithmetic and geometry of complex numbers. Exploration will be done using the leader's public-domain software.
Participants will experience a multitude of TI-83/84 based activities that are sure to revitalize their algebra and precalculus classes. Topics include: geometric probability, toolkit functions and transformations, parametric equations (conics and projectile motion), two-variable statistics (median-median line), recursive routines, problems involving applications of quadratic and cubic functions. A contextual approach to mathematics will be developed throughout the week. Novice TI-83/84 users are urged to attend the introductory Sunday morning session.
Activities involving motion help develop a deep understanding of the fundamental concepts of algebra, such as slope, patterns, and graphing. Participants will be involved in data-collection activities related to various types of motion that encourage algebraic thinking and skills development for all levels of students. We will use calculators, motion detectors, and TI-Nspire (no experience is necessary), and even explore some applications that are less dependent on technology. We will go beyond typical CBR activities to include examples of parametrics and variations on harmonic motion.
The intent of this course is to explore the capabilities and idiosyncracies of the author's dynamic geometry PC software, which is now twenty-three years young. As time permits, we will animate standard theorems from geometry, create puzzles and dynamic polyhedral nets, synchronize graphs, play idealized billiards, and more. The author also hopes that the audience will propose additional activities that can have an impact in the classroom.
Students thrive on competition. Learn how a game of “World Cup” can help students match polynomial equations to their graphs or how “Geometry Scattegories” ties into the study of points, lines, and planes. The fastest finger round from “Who Wants to be a Millionaire” can be used to reinforce students’ ability to evaluate logs, reason through a triangle proof, or determine probabilities, and nothing is quite like an Algebra II “Math Fire Drill”! Come ready to be creative, have fun, and possibly take home some bragging rights. Only one team will win, but everyone can learn in the process.
Come see how to connect algebra and geometry. Participants will explore problems on a graphing calculator and interactive geometry software of their choice (Cabri II Plus, TI-Nspire, or The Geometer Sketchpad). Explore some great mathematics that will connect algebra and geometry for high-school students. Participants will experience the use of technology to enhance old problems as well as introduce new problems into the high school curriculum.
Explore the newest tools, techniques and technologies that will enhance your classroom experience. We will explore differentiated instruction, with emphasis on integrating technology into your curriculum. Learn about how to use and make Podcasts, Blogs, and Wikisites. Learn how to use simple digital cameras and USB video cameras to reach all your students. We will explore project-based learning and discuss student exhibitions as effective assessment tools. We will explore a variety of Web 2.0 tools that can be incorporated into your classrooms immediately.
Using numerous technologies, the traditional geometry course can be greatly enriched. Participants will learn how to use The Geometer’s Sketchpad, GeoGebra, and Google’s SketchUp, and the Internet to teach topics in new ways. Manipulatives, such as Jovos and Zometools, will be used to supplement the teaching of non-traditional topics. Participants will see a variety of problems that can be used to motivate important geometric concepts and a collection of elegant proofs.
This course will present a variety of sequences, found where we might least expect them, and give opportunities to dig into the mathematics behind them. The analysis of them draws upon a variety of mathematical tools and utilizes some extraordinary thinking. What would happen if Fibonacci proposed his rabbit problem with different conditions? This and other scenarios will be explored in depth: the decimal expansion of 1/89, Pascal’s Triangle and beyond, climbing ladders, tipping waitpeople, switches on a panel, cancer research, alternating and fat subsets, the missing area paradox, and others.
This course will show how 3D geometry can be taught in new and exciting ways using software and manipulatives. Standard topics such as prisms, pyramids, cones, and the Platonic solids will be explored, as well as new and exciting results in tetrahedral geometry, such as the 3D equivalents of the Euler line and the nine-point circle. Participants will gain a working knowledge of two 3D construction programs, Google SketchUp and Cabri 3D. Extensive use will also be made of Zometools.
In our desire to teach algebra to everyone, we must not forget geometry. Participants will explore geometric concepts using an interactive geometry package of their choice (Cabri II Plus, Nspire, or Geometer Sketchpad). Geometry software allows students to explore geometric ideas in a discovery mode. Participants will experience the use of technology to enhance old problems as well as introduce new problems into the high school curriculum.
You can extract DNA from Cheetos! Participants will compare the latest protocols in biotechnology, from Carolina, Bio-Rad, and Edvotek. Participants will review the tricks of the trade, to ensure safety and, more importantly, to get accurate results. In the era of going green, we will pay special attention to those protocols that involve the use of plants and plant products. When participants are not doing experiments, they will explore the latest sites on the Internet and media applications to help solidify their understanding of the concepts behind each lab.
The best way to teach many statistical concepts is to have students see principles in action. In this hands-on course, participants will engage in classroom simulations that explore hypothesis testing, confidence intervals, power, the t-distribution family, and other difficult topics. Most of the simulations will use manipulatives, some the TI-89 (or TI-84). All topics are part of the AP Statistics curriculum.
A tour through ancient and classical mathematics! Ancient Babylon, Egypt, Greece and India are featured stops. Topics include: number systems, counting, Pythagorean theorem, Egyptian arithmetic, literal algebra and early number theory. Development of early geometry - from Thales to Euclid and Archimedes. The three Classical Problems of Antiquity, special curves (via The Geometer's SketchPad) and their solutions! We will focus both on stories about mathematicians and explore the mathematics they created.
The history and development of classical algebra in India, the Middle East and Europe. Topics include: Fibonacci and his rabbits, the abacus, the solution of the cubic equation, early trigonometry, irrationality of pi, analytic geometry and methods of the Calculus. The work of Fermat, Descartes, Wallis, Newton, Leibniz and Euler will be featured. Attention will be paid to the discovery/invention of complex numbers and their hidden connections with trigonometry. We will enjoy stories about mathematicians and explore the mathematics they created.
Revolutions in the concept of number and space! The invention of complex numbers, quaternions, matrices and vectors. The discovery of non-Euclidean geometries. The formalization of notions of infinity and more. The beginnings of modern abstract mathematics through the works of Hamilton, Cayley, Gauss, Lobachevski, Bolyai, Poincare, Cantor and others. We will enjoy stories about mathematicians and explore the mathematics they created.
Participants will be guided through the 30 days of "Potions" lessons that I present to my Calculus BC students every year after the AP test. Students follow a series of recipes in order to "brew potions." The potions are algebraic formulations (mostly involving infinite series but also delving a little bit into infinite products) that have "magical" effects (shrinking, transmutation, etc.). Notebooks are "cauldrons," and graphing calculators are "wands." The class is modeled after Severus Snape's potions class in the Harry Potter books, but participants need not be familiar with the books.
Geometry is perhaps the most important mathematics course in high school. By the time students get to precalculus, however, a great deal of their geometry know-how has gone the way of the slide rule. Let's bring some excitement back into geometry through great problems and great explorations. Let's rediscover what geometry is really all about. Then let's explore some of the geometries that our textbooks never quite get to. Long live triangles!
There are certain lessons that you look forward to during the year because they engage you and your students in rich, meaningful mathematics, they are fun to teach, and they involve the use of technology. Some of mine include: The Tower of Hanoi meets Fractal pop-up cards, toy car races, calculator robot wars, and Pi on the Subway. Spend the week working through these and other activities as we use graphing calculators and computer software to make mathematics come to life for you and your students.
This course will cover the topics in AP Calculus using graphical, numerical and analytic techniques. Topics will primarily be AB with some excursions into BC topics depending on the interest of the participants. The primary tool will be the TI-84 (hence low tech) and will emphasize student discovery as much as possible. The course will be extremely biased — that is, participants will learn how the course leader presents calculus to his students. A good course for those teachers who do have the latest whiz bang technology in their classrooms but who do have the trusty TI-84 (or the TI-83).
Some problems are good because they teach a particular concept well and some are good because of the really interesting mathematical techniques they use. We will be looking at five problems (independent of those in the course 'Just Five Good Problems') that allow students to connect their mathematics together in a meaningful way and enhance their mathematical understanding. We will use spreadsheet applications as well as The Geometer’s Sketchpad. Every participant will leave with five ready-to-use problems that are rich in this multi-level format.
Algebra II comes alive when concepts are developed using board games such as Hi Ho Cherry-O, Cootie, flying balloons, rats in a maze, helicopters, green medicine, flashlights and much, much more. Using TI calculators, Fathom and Vernier sensors, real data will be collected, analyzed, and used to illustrate topics such as recursive functions, matrices, parametric equations and modeling.
A series of activities that are great for use with the TI-Navigator and the TI-84+, but even better with the TI-Nspire CAS. Using the power of wireless networking and the full range of applications available on the TI-Nspire, participants will begin by working through a simple, well known, concrete activity that displays the full pedagogical potential of the Navigator System. Each of these activities then will form a conceptual basis and be extended as the students’ knowledge and skills progress in grades 9 - 12.
The instructor, author of many high school mathematics problems, shares as many of his favorites as time allows, choosing examples from a variety of subject areas and grade levels. For example, on which day of the week is the thirteenth of the month most likely to land? Each participant is encouraged to bring along a favorite problem.
A great course for teachers who are interested in learning about Problem-Based Learning (PBL)! We will discuss my experience of transforming a curriculum from a traditional one to a discourse-driven, technology-oriented and problem-motivated one. Learn how to focus your class on student ideas, discourse, reflection and problem-solving with problems. Discuss research behind the theory of PBL and its support for all students. Although the focus is on geometry, other topics will be discussed.
AP Statistics comes alive when concepts are developed using M&Ms, weird dice, helicopters, animal crackers, inflatable worlds and much, much more. Using TI calculators and Fathom, real data will be collected, analyzed, and used to make inferences. Simulations will be constructed to illustrate key ideas such as The Central Limit Theorem, The Law of Large Numbers, and why we divide by n-1.
You will be instructed with a SMART Board and will learn how to creatively incorporate its features into your classroom: post your daily notes online in color as pdf's; post your actual daily lesson as a video with audio; create videos of your lessons to be used as tutorials. You will be shown how to incorporate the graphing calculator emulators for the 83/84 family (TI-SmartView) and the new emulator for TI-Nspire (CAS and non CAS). It is suggested to bring your own laptop, but it is not a necessity. We will also be using and learning how to use Connect-to-Class and TI-Nspire Navigator.
With all the amazing options available, what technology works best and how do you use these tools most effectively? Through a series of great problems, activities, and applications, participants will utilize laptops, websites, applets, powerpoints, CD-Roms, TI-84's and Smartboard software to explore what you might use in your own classrooms. A day each will be spent using animations, simulations, and visualizations. Strategies, methods, and techniques will be discussed. Although no experience with any of these technologies is required, a willingness to try new things is essential.
This is the 200th anniversary of the birth of Charles Darwin and the 150th anniversary of the book "On the Origin of Species." This course will provide teachers the materials and resources needed to teach evolution in their classrooms. Web-based resources that can be incorporated into the teaching of evolution will be introduced, along with CD-ROM versions of a Virtual Voyage of the Beagle. Hands-on and web-based activities to help students investigate the nature of science and evolution will be presented. This course will focus on evolution and natural selection, the core concept of biology.
This course is designed for teachers who are about to teach statistics for the first time or have taught it for one year and want questions answered. We will explore ways of introducing inference through simulations, as well as using simulations to estimate probability. We will examine online resources and AP problems with their corresponding grading rubrics. Participants should leave this course feeling more confident in their understanding of the fundamental concepts of statistics, in addition to a clearer understanding of the expectations of the AP exam.
This workshop will explore what it means to do geometry on a sphere, cylinder, cone, cube, torus, and Klein Bottle. We will define straight, angle, area and curvature on these surfaces. We will explore to what extent the results of Euclidean geometry can be extended to these surfaces and to what extent they need to be modified. The existence of parallels (or not) and their uniqueness (or not), the angle sum of a triangle on these surfaces are key ideas. You will have in your hands models of all these surfaces to help your intuition.
The focus of this course will be on using photographs and video clips as the basis of engaging mathematical questions for students in algebra, geometry, precalculus, discrete and calculus courses with the goal of connecting mathematics to daily life, design, architecture, public art and commerce. Participants will use new and exciting features of The Geometer's Sketchpad, especially the ability to manipulate and transform photographs. The TI-84 and TI-Nspire will also be used. No experience with these technologies is necessary. A CD of photos and videos will be provided to everyone.
Learn to use the TI-Nspire handheld and the desktop/emulator software. You will be given and shown how to use several TI-Nspire activities for various levels of high school mathematics. You will also be shown how to create your own Nspire activities and how to make this new technology work well for you and your students and how to buy instruction time using Nspire. This course will be instructed with a SMART Board, so you will pick up creative teaching ideas for that as well. And we will be integrating the use of the wireless TI-Nspire Navigator system along with Connect-to-Class. Exciting!
The course will show geometry to be more than memorizing axioms, definitions and theorems. Participants will know there is conjecturing and developing a sense of adventure with geometric figures. They will see how the dynamic nature of The Geometer’s Sketchpad, Cabri Jr, and web-based GeoGebra helps to explore inclusive definitions, transformations, measuring figures, animating drawings, investigating locus situations, special theorems, and connecting geometry to algebra. No prior experience will be assumed. Participants will learn both basic and advanced features of the software or TI-84 App.
This course will introduce the use of model organisms to teach fundamental concepts in biology. Through hands-on exercises involving baker's yeast, the nematode Caenorhabditis elegans, and sea urchins, participants will explore topics such as genetics, metabolism, development, neurobiology, behavior, and environmental science. We will also use the polymerase chain reaction (PCR) to study bacterial infections in the local ant populations. In addition to laboratory experiments, we will discuss the maintenance of the organisms and some of their applications in current biomedical research.
