61. Key Curriculum Press | The Tool Kit Of Dynamics Activities Series The Best Resources You ll Find for Teaching These Contemporary Topics! fractals A Tool Kit of Dynamics activities 256 pages 155953-355-2 http://www.keypress.com/catalog/products/supplementals/Prod_ToolKit.html

Home Customer Service Ordering Information Contact Us ... Site Map State Resources Choose Your State... Alabama Alaska Arizona Arkansas Colorado Connecticut Delaware District of Columbia Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Lousiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oregon Oklahoma Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming Resource Centers The Geometer's Sketchpad Fathom Dynamic Data TinkerPlots Discovering Algebra ... Statistics in Action Professional Development In Partnership with You Summer Institutes Custom Workshops Implementation Workshops General Information Ordering Information Customer Service Contact Us Meet Our Authors ... Press Room Other Key Sites Key College Publishing KCP Technologies Keymath.com Supplementals : The Tool Kit of Dynamics Activities Series The Tool Kit of Dynamics Activities Series The Best Resources You'll Find for Teaching These Contemporary Topics! Growing out of a five-year research project sponsored by the National Science Foundation (NSF), our

62. The Geometer's Sketchpad® - 2004 NCTM Annual Meeting Mathematical Curves Conics, Spirals, fractals (activities and Applications) Bemidji State University has a course that looks at teaching mathematics in http://www.keypress.com/sketchpad/general_resources/user_groups/nctm_2004/index.

Getting Started Product Information How to Order Curriculum Modules ... user groups nctm 2004 Report from the 2004 NCTM Annual Meeting Philadelphia, PA April 2004 The Geometer's Sketchpad featured prominently at the National Council of Teachers of Mathematics 82nd Annual Meeting in Philadelphia. Members and research advisors of KCP Technologies made several presentations; material from those talks is available below . In all, twenty-two different presentation sessions featured Sketchpad ; the abstracts of these sessions are available here . Finally, information on the NCTM meeting of the Sketchpad User Group is also available Featured Sketchpad Presentations Dynamic Geometry and Young Learners Presenters: Nathalie Sinclair, Nick Jackiw The Geometer's Sketchpad now offers primary school teachers many opportunities to deepen their students' understanding of important mathematical ideas across the curriculum. In addition to the many geometry-related possibilities, we will share powerful activities and models for developing students' number sense, their understanding of measurement, and their prealgebraic thinking. Presentation Materials: Sketch Using Sketchpad to Explore Number and Early Algebra Concepts Presenters: Daniel Scher, Nathalie Sinclair

63. Mathematician Robert Devaney - Knox College News Alumni activities and Services Contact College Advancement Alumni Hall Lectures April 2425 on chaos theory and fractal geometry http://www.knox.edu/x4061.xml

Fast Facts Why Knox Visit Our History ... News Archive April 2003 Mathematician Robert Devaney Lectures April 24-25 on chaos theory and fractal geometry April 15, 2003 GALESBURG Robert Devaney, professor of mathematics at Boston University and an internationally-known expert on fractal geometry and chaos theory, will give a lecture, "Chaos Games and Fractal Images," at 7 p.m., Thursday, April 24, in Room A-110 of the Umbeck Science-Mathematics Center, Knox College, Galesburg, Illinois. He will give a second talk, "Fractal Geometry of the Mandelbrot Set," at 12 noon, Friday, April 25, in Room A-219 of the Umbeck Center. Both events are free and open to the public. The Thursday lecture, which is intended for general audiences, will discuss Devaney's work in chaos theory mathematical functions that do not follow any regular patterns. The Friday lecture, which assumes some familiarity with high-school pre-calculus, will examine mathematical formulas, known as fractals, that create irregular patterns similar to those found in natural objects. Devaney has written ten books and more than 70 research papers, and has given more than 1,000 lectures worldwide. He has also created computer-based tools and games that teach chaos theory, fractal geometry and dynamical systems. He has received regional and national teaching awards from the Mathematical Association of America, the Teacher/Scholar Award from Boston University, and the Director's Award for Distinguished Teaching Scholars from the National Science Foundation.

64. Math Interactive Workshops -- Workshop #8 Finally, we will touch on the connection between fractals and chaos, A variety of teaching and learning strategies will be modeled and discussed. http://www.learner.org/channel/workshops/math/work_8.html

Workshop #8 The Future of Mathematics: Ferns and Galaxies Content Guide - Andee Rubin Supplies Needed for Workshop #8: 1 die, 1 ruler per pair of participants, worksheets 1-4 pencils, paper, scissors, rulers, calculators, tape, a variety of colored markers About the Workshop What is the theme of the workshop? The advent of new technologies in the mathematics classroom is rapidly changing how, what, and when we teach. Not only do higher-level mathematics become accessible to students at a younger age, but new and fascinating worlds of mathematics can open up to them - in their own classrooms - thanks to the power of computers. We will examine two new mathematical tools, recursion and iteration, and introduce a new geometry, Fractal Geometry, which complements the much older and more familiar Euclidean Geometry. Whom do we see? What happens in the videoclips? We will see many amazing and beautiful things in this workshop. First we will see three different approaches to the creation of a famous fractal, the Sierpinski Triangle. Second, we will see multiple representations of fractals: fractals on paper, on a computer monitor, in nature, and built with manipulatives. Finally, we will touch on the connection between fractals and chaos, and see how beautifully patterned shapes can result from "chaotic" systems. What issues does this workshop address?

65. Geometry Everywhere: Fractal, Math & Form POST VIEWING activities. Day two classroom exercise The chaos Game Third Day activities On the third day finish up all of the fractal projects and http://www.idahoptv.org/ntti/nttilessons/lessons2000/butts.html

Utilization Strategies Lesson Plans Meet the Teachers NTTI WNET ... IdahoPTV by Judy Butts University of Idaho ITV SERIES LIFE BY THE NUMBERS: PATTERNS OF GEOMETRY OVERVIEW This lesson comes after the study of similarity in triangles. The students will be introduced to the idea of self-similarity. They will learn to recognize self-similarity and appreciate how geometry can help natural scientists in their studies. They will watch Life by the Numbers video, Patterns of Geometry, program segment four, New Geometry, in order to develop a deeper understanding of how we can duplicate nature's patterns by using math and iteration of self-similar mathematical elements. The students will all write an analysis of what they have learned about fractals, and how they see an understanding of fractal geometry as tool for the study of natural sciences. Students will be encouraged to do online explorations of fractals on their own in order to discover more applications of fractal geometry to add to their reports. LEARNING OBJECTIVES Students will value the importance of math to the study of the natural sciences, recognizing in fractals a self-similar, iterative geometric process that is everywhere in their natural world.

66. Nutshell Notes Building a Teaching System 2 Teaching in Fractal Patterns Some see teaching as constructive chaos in which varied activities contain an underlying http://carbon.cudenver.edu/public/OTE/nn/vol7/7_2.htm

NUTSHELL NOTES "Teaching tips in a nutshell" - The University of Colorado at Denver's One-page Newsletter for Teaching Excellence 1250 14th St. Room 720 Denver, CO 80217-3364 Phone (303)556-4915 FAX (303)556-2678 Volume 7 Number 2 February, 1999 Building a Teaching System - 2: Teaching in Fractal Patterns In the last issue, we suggested that any syllabus is greatly improved if it is carefully based upon, and even includes critical excerpts from, the author's personal teaching philosophy. We concluded with the admonition to draft this philosophy, then to " paste it above your desk, and consult it before you start every lesson plan and before you go to each class session. Some see teaching as "constructive chaos" in which varied activities contain an underlying purpose that not all students (or peer reviewers) easily see as associated with our learning objectives. Yet, once directed to look beyond limited personal experience (and perhaps our superficial "common sense"), it is possible to see "order in chaos" clearly and wonder why it wasn't seen earlier. About ten years ago, the concept of fractals and implications of "chaos theory" reached the layperson via several popular books. Through them we learned to see order in natural objects such as clouds, trees or coastlines, which we formerly had considered as "irregular," "random" or as having no order. An example might be a winter view of a tree with its outline of leafless branches. At first it looks complex and devoid of order, but we also can see it as built of a variant of the letter "Y" connected repeatedly at different scales. Whether we view the entire tree, a branch, or the veins in a single leaf, the pattern is of the same kind no matter what scale we view it at. We recognize order in such shapes, and we now call such arrangements "fractal."

67. Math Tools Browse A teaching unit on fractals for students and teachers in grades 4 to 8, Shows the wide spread use of fractals and chaos in science and nature. http://mathforum.org/mathtools/cell/g,10.16.3,ALL,ALL/

Search Catalog Discussions Browse Catalog Discussions All Resource Types Tools Lesson Plans Stories Activities Technology PoWs Support Materials All Technology Types Calculator Texas Instruments Computer Cabri Computer Algebra System Mathematica Fathom Flash Java Applet JavaScript Presentation software PowerPoint Shockwave Sketchpad Spreadsheet Excel PDA Palm OS PocketPC You are not logged in. login register Home About ... Developers Area Submissions Resources Write a Story Newsletter Browsing: All Content in Geometry for Fractals Browse discussions Login to Subscribe / Save Results Resource Name Topic (Course) Technology Type ... A Fractals Unit for Elementary... Fractals (Geometry) Computer Activity A teaching unit on fractals for students and teachers in grades 4 to 8, that adults are free to enjoy, designed to introduce students to fractals and the underlying mathematics. It focuses on fractals... More: lessons, discussions, ratings, reviews,... Aggregation: Growing Fractal S... Fractals (Geometry) Java Applet Activity Students investigate the models by which fractal patterns aggregate. Several questions are posed and different activities are suggested to go along with the Diffusion-Limited Aggregation applet.

68. The Math Forum - Math Library - Articles A site offering the basics of fractals and chaos theory. Games in the Classroom Centre for Innovation in Mathematics Teaching http://mathforum.org/library/resource_types/articles/?keyid=14176893&start_at=60

69. Overview.html This course uses different teaching and learning styles for students who have fractals and chaos Simplified for the Life Sciences Hypertext version of http://www.ccs.fau.edu/~liebovitch/mat1932-05.html

Psychology Undergraduate Students MAT 1932, Spring 2005, Dr. Larry S. Liebovitch The Mathematics and Science of Fractals 15094 M.W.F 11:00 - 11:50 AM (GCS 109 Boca Raton) This course uses different teaching and learning styles for students who have been previously intimidated by mathematics. It can be used as one of the mathematics courses (besides Statistics) needed to fulfill the mathematics requirement for undergraduate Psychology majors. Using CD-ROM electronic curricula materials developed by grants from the National Science Foundation (DUE-9752226 and DUE-9980715). Larry S. Liebovitch, Ph.D. Florida Atlantic University Center for Complex Systems and Brain Sciences 777 Glades Road, Boca Raton, FL 33431 telephone: 561.297.2239, fax: 561.297.2223 http://www.ccs.fau.edu/~liebovitch/larry.html If you want to speak with me please telephone, DO NOT SEND E-MAIL (I am overwhelmed with e-mail which I do not have time to read.) Overview This course emphasize WHAT mathematics is, HOW mathematicians do mathematics, and how mathematics is used in SCIENCE. Different teaching and learning styles including: LECTURE NOTES: HTML, PowerPoint slides, hypertext textbook, videotapes.

70. Schoolofengineering Thematic Lectures on Innovative Teaching Practices, in the 14 th annual Presented a paper in the national seminar on chaos and Fractal held at Rajagiri http://amritapuri.amrita.edu/schoolofengineering/appliedscience/Activities.htm

About the Department Faculty Facilities/Recourses Activities Activities A. Research Publications: 1. Dr .J. Suresh Kumar 1. J. Suresh Kumar, The corona of an odd cycle on a star is Sequential and Harmonious, Published in: Indian J. Pure and Applied Mathematics , August, 1997. 2. S. Arumugam and J. Suresh Kumar, The Tree-t-spanner of a Graph, Accepted for Publication in: Journal of Combinatorics, Information and System Sciences , Louisiana, U.S.A., January, 2000. 3. S. Arumugam and J. Suresh Kumar, Pseudo-complete color critical graphs-I, communicated to Discrete Mathematics , Elsevier Publications, U. S. A., 1998. 4. S. Arumugam and J. Suresh Kumar, Pseudo-complete color critical graphs-II, communicated to Bulletin of Institute of Combinatorics and its applications , Canada, 1999. 5. J. Suresh Kumar, On the degrees of vertices of PAN-critical graphs, communicated to Journal of Graph Theory, U.S.A., 2005. 6. J. Suresh Kumar, On the traversability concepts of PAN-critical graphs, communicated to Journal of Graph Theory, U.S.A., 2005.

71. Fractals Devaney, Robert L. and Keen, Linda; chaos and fractals The Mathematics Behind the MAA Note Visualization in Teaching and Learning Mathematics, http://www.stolaf.edu/people/cederj/Courses.dir/Geo.dir/bib-356/node14.html

Next: Golden Ratio Up: Index of Topics Previous: Teaching Geometry with Technology Fractals Banchoff, Thomas F. ``Dimension'' in On the Shoulders of Giants , Lynn Arthur Steen, Ed., National Academy Press, Washington DC 1990, 11-59. Bannon, Thomas J. ``Fractals and Transformations.'' Mathematics Teacher 84 (March 1991): 178-85. Barcellos, Anthony ``The Fractal Geometry of Mandelbrot.'' College Mathematics Journal 15 (March 1984): 98-114. Barnsley, Michael Fractals Everywhere. San Diego, CA: Academic Press, 1988. Barton, Ray. ``Chaos and Fractals.'' Mathematics Teacher 83 (October 1990):524-29. Bedford, Crayton; ``The Case for Chaos,'' The Mathematics Teacher , April 1998, p 276-281. Bennett, Dan ``A Fractal Class Activity: The Sierpinski Gasket.'' Discovering Geometry Newsletter 1 (Fall 1989): 3 Berkeley, CA: Key Curriculum Press. Camp, Dane R. ``Benoit Mandelbrot: The Euclid of Fractal Geometry'' Mathematics Teacher. 93:8 (Nov. 2000): 708-712. Camp, Dane R. ``A Fractal Excursion.'' Mathematics Teacher. 84 (April 1991): 265-75.

72. Class Reviews, 1999 chaos theory and fractal geometry are beginning to be taught as units in many high schools. Keywords Connections, Teaching Strategies, activities http://www.stolaf.edu/people/wallace/Courses/MathEd/Reviews/Reviews99/Lisa.html

Return to Index Keywords: Curriculum, , Ref: Author(s): Bedford, Crayton Date: Title: The Case for Chaos Journal or Publisher: Mathematics Teacher Volume, Issue, Pages: 91(4), pp.276-281 Reviewer: Lisa Date of Review: March 28, 1999 Chaos theory and fractal geometry are beginning to be taught as units in many high schools. Crayton Bedford makes a case for offering a semester-long class which incorporates chaos theory with students' knowledge of algebra and trigonometry. Students leave the class with a new way of seeing the world, and it helps them reflect on aspects of order and disorder, searching for patterns, and working with rigorous mathematical techniques. After outlining the basics behind chaos theory, dynamical systems, and fractals, Bedford gives a brief summary for the following 8 units to be used for a high school course: Unit 0: Preliminaries Introduction to dynamical systems, iteration, review of sequences and series, and stresses the use of calculators or computers. Unit 1: Fractals Fractals are defined and explored; the Sierpinski triangle, Koch snowflake, and Cantor set demonstrate self-similarity. Unit 2: Orbit analysis Orbits are analyzed with a graphing calculator, and predictability, cycles, and slopes of curves are explored.

73. K12 Newsletters: 00-02-28: INNOV> [I.T.] Educational Puzzles And Games Update games to teach the nature of Math? John Conway s theory set out to do week; examples of past puzzles include chaos Tiles, Dissecting Convex http://scout.wisc.edu/Projects/PastProjects/K12news/00-02/00-02-28/0010.html

Gleason Sackmann ( gleason@rrnet.com Mon, 28 Feb 2000 12:13:12 -0600 Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Previous message: From: Walter McKenzie [ mailto:mrmck@staffnet.com Sent: Sunday, February 27, 2000 3:43 AM To: innovative-teaching@egroups.com Over 2,500 subscribers strong! INNOVATIVE TEACHING presented by Walter McKenzie - Creative Classroom Consulting Innovative staff development: Technology Applications, Multiple Intelligences, Curriculum Integration and Creative Education. Let's see what we can do for your staff! February 27, 2000 We’re over the 2,500 subscriber mark for the newsletter! Thanks to everyone for their interest and continued support. I’m back from two weeks on the road, finishing up yesterday at Classroom Connect’s New York City Conference, and boy is it good to sit still (well, sort of sit still)!

74. ThinkQuest : Library : Math chaos Theory, and fractal generation (Mandelbrot and Julia sets). activities such as 3D tours, crossword puzzles, conversion tables, and calculator http://www.thinkquest.org/library/cat_show.html?cat_id=9

75. Teaching Mathematics With The Internet (7-12) http//www.planemath.com/activities/flightpath/flightpath7w1.html The chaos Game http//math.bu.edu/DYSYS/chaosgame/node1.html. Fractal Pictures http://twi.classroom.com/math/712/

Geometry The Geometry of Visual Perspective The On-Line Visual Literacy Project http://www.pomona.edu/visual-lit/intro/intro.html Solution to the Hallway Problem http://forum.swarthmore.edu/sum95/math_and/perspective/hallway.html The Vault of St. Ignazio http://ananke.advanced.org/3257/data/The.Vault.of.St.Ignazio.jpeg.html Albrecht Durer's engraving St. Jerome dans sa cellule http://sunsite.unc.edu/wm/paint/auth/durer/engravings/st-jerome.jpg Albrecht Durer's engraving Melencolia I sunsite.unc.edu/wm/paint/auth/durer/engravings/melencolia-i.jpg Solution to the RR Track Problem http://forum.swarthmore.edu/sum95/math_and/perspective/RRtracks.html Perspective Drawing http://forum.swarthmore.edu/sum95/math_and/perspective/perspect.html Tessellations and Escher Patterns The Geometry Junkyard http://www.ics.uci.edu/~eppstein/junkyard/penrose.html Penrose Tiling http://www.sover.net/~manx/_001-09.html QuasiTiler 3.0 http://www.geom.umn.edu/apps/quasitiler/#to_do Investigating Tesselations Using Activity Pattern Blocks http://forum.swarthmore.edu/sum95/suzanne/active.html

76. Experience Swami's Teaching At The Summer Lectures On June, 2004 I entwine the scholarship with Swami s Teaching from His books, discourses). The study of fractals and chaos started its history during the 1970s. http://www.saibaba.ws/articles1/experienceswamisteaching.htm

Home Thought for the Day Links News ... Teachings Sri Sathya Sai Baba Articles Experience Swami's Teaching at the Summer lectures on June, 2004 Light and Love Experiences how better to acknowledge and put into practice Swami's Teaching carried out with the group of teachers and specialists during their Summer lectures week on a remote area of wild nature in June 2004. "The world is a great teacher, a constant guide and source of inspiration. That is the reason why man is placed in the world. Every bird, every animal, every tree, mountain and star and each tiny worm has a lesson for man, if he has but the thirst to learn. These make a world a veritable University for man; it is but a Gurukul (a school for spiritual learning) where he is a pupil from birth to death." (Bhagawan Sathya Sai Baba. Thought for the day. 26 June 2004). (To carry out teachers and specialists environmental scholarship is my official job during many years. I entwine the scholarship with Swami's Teaching from His books, discourses).

77. Enrichment - Secondary School activity book includes teaching notes, reproducible student worksheets and problem cards, answers, A lucid introduction to the study of chaos, fractals, http://www.pearsoned.ca/school/math/math/mr/enr/books/enrbooks.html

Titles for Enrichment Seconday Level Reading, Writing, and Doing Mathematical Proofs Daniel Solow (Grades 10-12) SS6-0-86651-148-2, 288 PP, $29.10 The little insights and ideas we all so laboriously discovered for ourselves come together in this carefully-structured, systematic book about mathematical proofs. Once students understand and analyze the structure of proofs, theyll be able to follow the more informal versions in texts and learn to create their own. two workbooks tailored to the high school curriculum short, easy-to-follow lessons followed by exercise sets with solutions Number Treasury Stanley Bezuszka and Margaret Kenney (Grades 7-12) SS6-0-86651-078-8, 208 pp., $29.10 This resource offers an extensive source of information about number patterns, classical and modern. covers prime and composite numbers, plane and figurate numbers, digital patterns, and more solutions included Math Space Mission Regional Math Network Kay Merseth, Director (Grades 7-9) SS6-0-86651-439-2, 256 pp., $33.45 Students explore the outer realms of our solar system and learn estimation, geometry, and problem solving with this four-module, spiral-bound kit. activity book includes teaching notes, reproducible student worksheets and problem cards, answers, and more

78. MED 307 MED 307 Uses of Technology in the Teaching of Mathematics Devaney, Robert L. chaos, fractals, and Dynamics Computer Experiments in Mathematics, http://136.183.135.100/~math/courses/undergraduate/MED307.html

STATE UNIVERSITY COLLEGE AT BUFFALO Department of Mathematics Request for Course I. Number and Title of Course MED 307 Uses of Technology in the Teaching of Mathematics II. Reasons for Revision We have updated the bibliography and topical outline to better address and reflect the current work in this area. We have also redefined the major objectives of the course in terms of student outcomes. The course continues to serve the following purposes in our program: A. This course instructs pre-service teachers in the use of calculators, computers, software, and other current technical aids available for the teaching of mathematics. The focus is on the effective use of technology to teach the concepts of mathematics. B. This course addresses the growing need for teachers with technical experience, particularly in the use of computers and calculators in mathematics classrooms. This course is intended to meet the recommendations from national organizations that mathematics teachers use technology appropriately and effectively as problem-solving tools. C. This course addresses the current interest of elementary and secondary education students who want experience with mathematics software and with lesson development involving computers and calculators.

79. Focus On Mathematics :: Teacher Handbook The openended approach a new proposal for teaching mathematics. A thorough resource for your students who are curious about fractals and chaos. http://www.focusonmath.org/FOM/resources/learning/teacherhandbook/Resources/Reso

Resources Math Problems Lesson Study Teacher Handbook Publications ... Calendar Teacher Handbook Resources Teachers and students engaged in research need ready access to mathematics resources. An investigation may take us into areas of mathematics that are not entirely familiar. When it does, we need to read up on the topic and learn enough to determine if the ideas might be of use in our work. For example, a student in a mathematics research seminar investigated peg solitaire games. He found several journal articles about these games that used methods based on group theory. In order to understand and apply the ideas from the published literature, he needed to find out how groups were defined and what their basic properties were. He was then able to adapt the methods of earlier researchers to his particular problems. As the above example suggests, it is neither possible nor advisable for students to have to rediscover, and make sense of, all mathematics on their own. They do need to recognize when learning new content might be helpful and how to obtain and use the resources that are available (see Getting Information ). As students apply the results that they encounter in their readings or that their peers produce, they come to recognize the cumulative and communal nature of mathematics. Interesting mathematics is almost always the product of building on the work of others.

80. Teaching.htm Introduction to the Fractal Structures and Dynamical Systems (30 hours). PreGraduate teaching activities. I teach at the Dpt. of Applied Mathematics http://personales.unican.es/iglesias/Teaching.htm

Teaching activities Post-Graduate teaching courses Ph. D. Courses Master Courses Specialization Courses Other Courses ... Pre-Graduate Courses Post-Graduate teaching activities Ph. D. Courses Nonlinear Dynamics and the Fractal Geometry (30 hours). Contribution: 15 hours. Dpt. of Applied Mathematics and Computational Sciences. University of Cantabria (Spain). Computer-Aided Geometric Design (CAGD) (40 hours). Contribution: 10 hours. Dpt. of Applied Mathematics and Computational Sciences. University of Cantabria (Spain). Computer Graphics. Applications to Industry (30 hours). Contribution: 20 hours. Dpt. of Applied Mathematics and Computational Sciences. University of Cantabria (Spain). Computer-Aided Geometric Design (CAGD) (40 hours). Contribution: 10 hours. Dpt. of Applied Mathematics and Computational Sciences. University of Cantabria (Spain). Introduction to the Fractal Structures and Dynamical Systems (30 hours). Contribution: 15 hours. Dpt. of Applied Mathematics and Computational Sciences. University of Cantabria (Spain). Introduction to the Fractal Structures and Dynamical Systems (30 hours). Contribution: 15 hours. Dpt. of Applied Mathematics and Computational Sciences. University of Cantabria (Spain).

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