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Entrainment of particles during the withdrawal of a fibre from a dilute suspension
- B. M. Dincau, E. Mai, Q. Magdelaine, J. A. Lee, M. Z. Bazant, A. Sauret
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- Journal:
- Journal of Fluid Mechanics / Volume 903 / 25 November 2020
- Published online by Cambridge University Press:
- 30 September 2020, A38
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A fibre withdrawn from a bath of a dilute particulate suspension exhibits different coating regimes depending on the physical properties of the fluid, the withdrawal speed, the particle sizes and the radius of the fibre. Our experiments indicate that only the liquid without particles is entrained for thin coating films. Beyond a threshold capillary number, the fibre is coated by a liquid film with entrained particles. We systematically characterize the role of the capillary number, the particle size and the fibre radius on the threshold speed for particle entrainment. We discuss the boundary between these two regimes and show that the thickness of the liquid film at the stagnation point controls the entrainment process. The radius of the fibre provides a new degree of control in capillary filtering, allowing greater control over the size of the particles entrained in the film.
Contributors
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- By Aakash Agarwala, Linda S. Aglio, Rae M. Allain, Paul D. Allen, Houman Amirfarzan, Yasodananda Kumar Areti, Amit Asopa, Edwin G. Avery, Patricia R. Bachiller, Angela M. Bader, Rana Badr, Sibinka Bajic, David J. Baker, Sheila R. Barnett, Rena Beckerly, Lorenzo Berra, Walter Bethune, Sascha S. Beutler, Tarun Bhalla, Edward A. Bittner, Jonathan D. Bloom, Alina V. Bodas, Lina M. Bolanos-Diaz, Ruma R. Bose, Jan Boublik, John P. Broadnax, Jason C. Brookman, Meredith R. Brooks, Roland Brusseau, Ethan O. Bryson, Linda A. Bulich, Kenji Butterfield, William R. Camann, Denise M. Chan, Theresa S. Chang, Jonathan E. Charnin, Mark Chrostowski, Fred Cobey, Adam B. Collins, Mercedes A. Concepcion, Christopher W. Connor, Bronwyn Cooper, Jeffrey B. Cooper, Martha Cordoba-Amorocho, Stephen B. Corn, Darin J. Correll, Gregory J. Crosby, Lisa J. Crossley, Deborah J. Culley, Tomas Cvrk, Michael N. D'Ambra, Michael Decker, Daniel F. Dedrick, Mark Dershwitz, Francis X. Dillon, Pradeep Dinakar, Alimorad G. Djalali, D. John Doyle, Lambertus Drop, Ian F. Dunn, Theodore E. Dushane, Sunil Eappen, Thomas Edrich, Jesse M. Ehrenfeld, Jason M. Erlich, Lucinda L. Everett, Elliott S. Farber, Khaldoun Faris, Eddy M. Feliz, Massimo Ferrigno, Richard S. Field, Michael G. Fitzsimons, Hugh L. Flanagan Jr., Vladimir Formanek, Amanda A. Fox, John A. Fox, Gyorgy Frendl, Tanja S. Frey, Samuel M. Galvagno Jr., Edward R. Garcia, Jonathan D. Gates, Cosmin Gauran, Brian J. Gelfand, Simon Gelman, Alexander C. Gerhart, Peter Gerner, Omid Ghalambor, Christopher J. Gilligan, Christian D. Gonzalez, Noah E. Gordon, William B. Gormley, Thomas J. Graetz, Wendy L. Gross, Amit Gupta, James P. Hardy, Seetharaman Hariharan, Miriam Harnett, Philip M. Hartigan, Joaquim M. Havens, Bishr Haydar, Stephen O. Heard, James L. Helstrom, David L. Hepner, McCallum R. Hoyt, Robert N. Jamison, Karinne Jervis, Stephanie B. Jones, Swaminathan Karthik, Richard M. Kaufman, Shubjeet Kaur, Lee A. Kearse Jr., John C. Keel, Scott D. Kelley, Albert H. Kim, Amy L. Kim, Grace Y. Kim, Robert J. Klickovich, Robert M. Knapp, Bhavani S. Kodali, Rahul Koka, Alina Lazar, Laura H. Leduc, Stanley Leeson, Lisa R. Leffert, Scott A. LeGrand, Patricio Leyton, J. Lance Lichtor, John Lin, Alvaro A. Macias, Karan Madan, Sohail K. Mahboobi, Devi Mahendran, Christine Mai, Sayeed Malek, S. Rao Mallampati, Thomas J. Mancuso, Ramon Martin, Matthew C. Martinez, J. A. Jeevendra Martyn, Kai Matthes, Tommaso Mauri, Mary Ellen McCann, Shannon S. McKenna, Dennis J. McNicholl, Abdel-Kader Mehio, Thor C. Milland, Tonya L. K. Miller, John D. Mitchell, K. Annette Mizuguchi, Naila Moghul, David R. Moss, Ross J. Musumeci, Naveen Nathan, Ju-Mei Ng, Liem C. Nguyen, Ervant Nishanian, Martina Nowak, Ala Nozari, Michael Nurok, Arti Ori, Rafael A. Ortega, Amy J. Ortman, David Oxman, Arvind Palanisamy, Carlo Pancaro, Lisbeth Lopez Pappas, Benjamin Parish, Samuel Park, Deborah S. Pederson, Beverly K. Philip, James H. Philip, Silvia Pivi, Stephen D. Pratt, Douglas E. Raines, Stephen L. Ratcliff, James P. Rathmell, J. Taylor Reed, Elizabeth M. Rickerson, Selwyn O. Rogers Jr., Thomas M. Romanelli, William H. Rosenblatt, Carl E. Rosow, Edgar L. Ross, J. Victor Ryckman, Mônica M. Sá Rêgo, Nicholas Sadovnikoff, Warren S. Sandberg, Annette Y. Schure, B. Scott Segal, Navil F. Sethna, Swapneel K. Shah, Shaheen F. Shaikh, Fred E. Shapiro, Torin D. Shear, Prem S. Shekar, Stanton K. Shernan, Naomi Shimizu, Douglas C. Shook, Kamal K. Sikka, Pankaj K. Sikka, David A. Silver, Jeffrey H. Silverstein, Emily A. Singer, Ken Solt, Spiro G. Spanakis, Wolfgang Steudel, Matthias Stopfkuchen-Evans, Michael P. Storey, Gary R. Strichartz, Balachundhar Subramaniam, Wariya Sukhupragarn, John Summers, Shine Sun, Eswar Sundar, Sugantha Sundar, Neelakantan Sunder, Faraz Syed, Usha B. Tedrow, Nelson L. Thaemert, George P. Topulos, Lawrence C. Tsen, Richard D. Urman, Charles A. Vacanti, Francis X. Vacanti, Joshua C. Vacanti, Assia Valovska, Ivan T. Valovski, Mary Ann Vann, Susan Vassallo, Anasuya Vasudevan, Kamen V. Vlassakov, Gian Paolo Volpato, Essi M. Vulli, J. Matthias Walz, Jingping Wang, James F. Watkins, Maxwell Weinmann, Sharon L. Wetherall, Mallory Williams, Sarah H. Wiser, Zhiling Xiong, Warren M. Zapol, Jie Zhou
- Edited by Charles Vacanti, Scott Segal, Pankaj Sikka, Richard Urman
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- Book:
- Essential Clinical Anesthesia
- Published online:
- 05 January 2012
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- 11 July 2011, pp xv-xxviii
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- By Rose Teteki Abbey, K. C. Abraham, David Tuesday Adamo, LeRoy H. Aden, Efrain Agosto, Victor Aguilan, Gillian T. W. Ahlgren, Charanjit Kaur AjitSingh, Dorothy B E A Akoto, Giuseppe Alberigo, Daniel E. Albrecht, Ruth Albrecht, Daniel O. Aleshire, Urs Altermatt, Anand Amaladass, Michael Amaladoss, James N. Amanze, Lesley G. Anderson, Thomas C. Anderson, Victor Anderson, Hope S. Antone, María Pilar Aquino, Paula Arai, Victorio Araya Guillén, S. Wesley Ariarajah, Ellen T. Armour, Brett Gregory Armstrong, Atsuhiro Asano, Naim Stifan Ateek, Mahmoud Ayoub, John Alembillah Azumah, Mercedes L. García Bachmann, Irena Backus, J. Wayne Baker, Mieke Bal, Lewis V. Baldwin, William Barbieri, António Barbosa da Silva, David Basinger, Bolaji Olukemi Bateye, Oswald Bayer, Daniel H. Bays, Rosalie Beck, Nancy Elizabeth Bedford, Guy-Thomas Bedouelle, Chorbishop Seely Beggiani, Wolfgang Behringer, Christopher M. Bellitto, Byard Bennett, Harold V. Bennett, Teresa Berger, Miguel A. Bernad, Henley Bernard, Alan E. Bernstein, Jon L. Berquist, Johannes Beutler, Ana María Bidegain, Matthew P. Binkewicz, Jennifer Bird, Joseph Blenkinsopp, Dmytro Bondarenko, Paulo Bonfatti, Riet en Pim Bons-Storm, Jessica A. Boon, Marcus J. Borg, Mark Bosco, Peter C. Bouteneff, François Bovon, William D. Bowman, Paul S. Boyer, David Brakke, Richard E. Brantley, Marcus Braybrooke, Ian Breward, Ênio José da Costa Brito, Jewel Spears Brooker, Johannes Brosseder, Nicholas Canfield Read Brown, Robert F. Brown, Pamela K. Brubaker, Walter Brueggemann, Bishop Colin O. Buchanan, Stanley M. Burgess, Amy Nelson Burnett, J. Patout Burns, David B. Burrell, David Buttrick, James P. Byrd, Lavinia Byrne, Gerado Caetano, Marcos Caldas, Alkiviadis Calivas, William J. Callahan, Salvatore Calomino, Euan K. Cameron, William S. Campbell, Marcelo Ayres Camurça, Daniel F. Caner, Paul E. Capetz, Carlos F. Cardoza-Orlandi, Patrick W. Carey, Barbara Carvill, Hal Cauthron, Subhadra Mitra Channa, Mark D. Chapman, James H. Charlesworth, Kenneth R. Chase, Chen Zemin, Luciano Chianeque, Philip Chia Phin Yin, Francisca H. Chimhanda, Daniel Chiquete, John T. Chirban, Soobin Choi, Robert Choquette, Mita Choudhury, Gerald Christianson, John Chryssavgis, Sejong Chun, Esther Chung-Kim, Charles M. A. Clark, Elizabeth A. Clark, Sathianathan Clarke, Fred Cloud, John B. Cobb, W. Owen Cole, John A Coleman, John J. Collins, Sylvia Collins-Mayo, Paul K. Conkin, Beth A. Conklin, Sean Connolly, Demetrios J. Constantelos, Michael A. Conway, Paula M. Cooey, Austin Cooper, Michael L. Cooper-White, Pamela Cooper-White, L. William Countryman, Sérgio Coutinho, Pamela Couture, Shannon Craigo-Snell, James L. Crenshaw, David Crowner, Humberto Horacio Cucchetti, Lawrence S. Cunningham, Elizabeth Mason Currier, Emmanuel Cutrone, Mary L. Daniel, David D. Daniels, Robert Darden, Rolf Darge, Isaiah Dau, Jeffry C. Davis, Jane Dawson, Valentin Dedji, John W. de Gruchy, Paul DeHart, Wendy J. Deichmann Edwards, Miguel A. De La Torre, George E. Demacopoulos, Thomas de Mayo, Leah DeVun, Beatriz de Vasconcellos Dias, Dennis C. Dickerson, John M. Dillon, Luis Miguel Donatello, Igor Dorfmann-Lazarev, Susanna Drake, Jonathan A. Draper, N. Dreher Martin, Otto Dreydoppel, Angelyn Dries, A. J. Droge, Francis X. D'Sa, Marilyn Dunn, Nicole Wilkinson Duran, Rifaat Ebied, Mark J. Edwards, William H. Edwards, Leonard H. Ehrlich, Nancy L. Eiesland, Martin Elbel, J. Harold Ellens, Stephen Ellingson, Marvin M. Ellison, Robert Ellsberg, Jean Bethke Elshtain, Eldon Jay Epp, Peter C. Erb, Tassilo Erhardt, Maria Erling, Noel Leo Erskine, Gillian R. Evans, Virginia Fabella, Michael A. Fahey, Edward Farley, Margaret A. Farley, Wendy Farley, Robert Fastiggi, Seena Fazel, Duncan S. Ferguson, Helwar Figueroa, Paul Corby Finney, Kyriaki Karidoyanes FitzGerald, Thomas E. FitzGerald, John R. Fitzmier, Marie Therese Flanagan, Sabina Flanagan, Claude Flipo, Ronald B. Flowers, Carole Fontaine, David Ford, Mary Ford, Stephanie A. Ford, Jim Forest, William Franke, Robert M. Franklin, Ruth Franzén, Edward H. Friedman, Samuel Frouisou, Lorelei F. Fuchs, Jojo M. Fung, Inger Furseth, Richard R. Gaillardetz, Brandon Gallaher, China Galland, Mark Galli, Ismael García, Tharscisse Gatwa, Jean-Marie Gaudeul, Luis María Gavilanes del Castillo, Pavel L. Gavrilyuk, Volney P. Gay, Metropolitan Athanasios Geevargis, Kondothra M. George, Mary Gerhart, Simon Gikandi, Maurice Gilbert, Michael J. Gillgannon, Verónica Giménez Beliveau, Terryl Givens, Beth Glazier-McDonald, Philip Gleason, Menghun Goh, Brian Golding, Bishop Hilario M. Gomez, Michelle A. Gonzalez, Donald K. Gorrell, Roy Gottfried, Tamara Grdzelidze, Joel B. Green, Niels Henrik Gregersen, Cristina Grenholm, Herbert Griffiths, Eric W. Gritsch, Erich S. Gruen, Christoffer H. Grundmann, Paul H. Gundani, Jon P. Gunnemann, Petre Guran, Vidar L. Haanes, Jeremiah M. Hackett, Getatchew Haile, Douglas John Hall, Nicholas Hammond, Daphne Hampson, Jehu J. Hanciles, Barry Hankins, Jennifer Haraguchi, Stanley S. Harakas, Anthony John Harding, Conrad L. Harkins, J. William Harmless, Marjory Harper, Amir Harrak, Joel F. Harrington, Mark W. Harris, Susan Ashbrook Harvey, Van A. Harvey, R. Chris Hassel, Jione Havea, Daniel Hawk, Diana L. Hayes, Leslie Hayes, Priscilla Hayner, S. Mark Heim, Simo Heininen, Richard P. Heitzenrater, Eila Helander, David Hempton, Scott H. Hendrix, Jan-Olav Henriksen, Gina Hens-Piazza, Carter Heyward, Nicholas J. Higham, David Hilliard, Norman A. Hjelm, Peter C. Hodgson, Arthur Holder, M. Jan Holton, Dwight N. Hopkins, Ronnie Po-chia Hsia, Po-Ho Huang, James Hudnut-Beumler, Jennifer S. Hughes, Leonard M. Hummel, Mary E. Hunt, Laennec Hurbon, Mark Hutchinson, Susan E. Hylen, Mary Beth Ingham, H. Larry Ingle, Dale T. Irvin, Jon Isaak, Paul John Isaak, Ada María Isasi-Díaz, Hans Raun Iversen, Margaret C. 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Yee, Viktor Yelensky, Yeo Khiok-Khng, Gustav K. K. Yeung, Angela Yiu, Amos Yong, Yong Ting Jin, You Bin, Youhanna Nessim Youssef, Eliana Yunes, Robert Michael Zaller, Valarie H. Ziegler, Barbara Brown Zikmund, Joyce Ann Zimmerman, Aurora Zlotnik, Zhuo Xinping
- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- The Cambridge Dictionary of Christianity
- Published online:
- 05 August 2012
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- 20 September 2010, pp xi-xliv
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Contributors
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- By Sayeda Abu-Amero, Ivo Brosens, Jan Brosens, Graham J. Burton, Anthony M. Carter, Judith E. Cartwright, Brianna Cloke, Christophe L. Depoix, Sascha Drewlo, Caroline Dunk, Qi Fu, Luca Fusi, David Haig, Myriam C. Hanssens, Frans M. Helmerhorst, Pak Chung Ho, Eric Jauniaux, S. Ananth Karumanchi, Marc J. N. C. Keirse, Eliyahu V. Khankin, T. Yee Khong, Stephen R. Killick, Chong Jai Kim, John C. P. Kingdom, Juan Pedro Kusanovic, Robert H. Lane, Piotr Lesny, Robert D. Martin, Robert A. McKnight, Kari K. Melve, Ashley Moffett, Gudrun E. Moore, Linda Morgan, Ernest Hung Yu Ng, Robert Pijnenborg, Leslie Proctor, Sarosh Rana, Roberto Romero, Rolv Skjaerven, Gordon C. S. Smith, Robert N. Taylor, May Lee Tjoa, Lars J. Vatten, Lisbeth Vercruysse, Guy St. J. Whitley
- Edited by Robert Pijnenborg, Ivo Brosens, Roberto Romero
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- Placental Bed Disorders
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- 06 July 2010
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- 03 June 2010, pp ix-xii
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The Moore Method
- A Pathway to Learner-Centered Instruction
- Charles A. Coppin, W. Ted Mahavier, E. Lee May, G. Edgar Parker
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- Published by:
- Mathematical Association of America
- Published online:
- 26 October 2011
- Print publication:
- 01 August 2009
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The Moore Method: A Pathway to Learner-Centered Instruction offers a practical overview of the method as practiced by the four co-authors, serving as both a 'how to' manual for implementing the method and an answer to the question, 'what is the Moore method?'. Moore is well known as creator of The Moore Method (no textbooks, no lectures, no conferring) in which there is a current and growing revival of interest and modified application under inquiry-based learning projects. Beginning with Moore's Method as practiced by Moore himself, the authors proceed to present their own broader definitions of the method before addressing specific details and mechanics of their individual implementations. Each chapter consists of four essays, one by each author, introduced with the commonality of the authors' writings. Topics include the culture the authors strive to establish in the classroom, their grading methods, the development of materials and typical days in the classroom. Appendices include sample tests, sample notes, and diaries of individual courses. With more than 130 references supporting the themes of the book the work provides ample additional reading supporting the transition to learner-centered methods of instruction.
Contents
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- Book:
- The Moore Method
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- Mathematical Association of America
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- 26 October 2011
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- 01 August 2009, pp vii-viii
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6 - In the Classroom
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- Book:
- The Moore Method
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- Mathematical Association of America
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- 26 October 2011
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- 01 August 2009, pp 69-98
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Summary
“After stating the axioms and giving motivating examples to illustrate their meaning he would then state definitions and theorems. He simply read them from his book as the students copied them down. He would then instruct the class to find proofs of their own and also to construct examples to show that the hypotheses of the theorems could not be weakened, omitted, or partially omitted. … When a student stated that he could prove Theorem x, he was asked to go to the blackboard and present the proof. Then the other students, especially those who hadn't been able to discover a proof, would make sure that the proof presented was correct and convincing. Moore sternly prevented heckling. This was seldom necessary because the whole atmosphere was one of a serious community effort to understand the argument.”
—F. Burton JonesThis chapter presents snapshots of the day-to-day operations in Moore Method classrooms. Several themes run common to the essays. Each author clearly tailors his instruction to individual students and uses some form of diary to track progress of the class and of individual students. Each stresses the importance of the first day of the course, of “selling” the method to the students, and of active participation by the students. Because of this participation, the unpredictability of what might happen in each class is reflected as well. Each author spends considerable time preparing for class by evaluating what has been accomplished and what might be accomplished if the right seeds are planted during the next class period.
5 - Development and Selection of Materials
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- Book:
- The Moore Method
- Published by:
- Mathematical Association of America
- Published online:
- 26 October 2011
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- 01 August 2009, pp 45-68
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Summary
“That student is taught the best who is told the least.”
R. L. MooreThis chapter addresses the generation of materials to be used to support Moore Method teaching. Development and usage of materials by the prospective user is treated from various perspectives, including
guidelines for writing your own problem sequences,
adapting textbook treatments,
adapting pre-existing Moore Method course notes,
modifying materials to fit the realities of a particular class,
addressing learning-theory issues, and
obtaining support when using another's notes.
These perspectives illustrate principles that may guide the construction of problem sets, resolve the question of authoring notes or adapting pre-existing notes, and provide sources for course notes that have been written for use in Moore Method classes other than your own.
The essays will likely offer the greatest benefit if read in the order presented, especially for the reader entertaining thoughts about using the Moore Method for the first time. May's essay is both highly practical and succinct in its outlook. Mahavier deals, in some detail, with making the decision whether to author notes or use a pre-existing problem sequence. He then segues into guidelines for penning materials. Coppin focuses exclusively on authoring one's own notes, addressing issues from learning theory and illustrating how course notes can address these theories directly. Parker writes from the viewpoint of generating course notes, then adapting them consequent to classroom dynamics.
II - Mahavier
- from Appendices
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
-
- Book:
- The Moore Method
- Published by:
- Mathematical Association of America
- Published online:
- 26 October 2011
- Print publication:
- 01 August 2009, pp 201-210
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Summary
Syllabus for Analysis
This is the syllabus that meets the University and Southern Association of Colleges requirements and I pass it out after the first few class meetings.
Course: MATH 3380, Advanced Calculus, Fall 2007, MWF 11:15–12:05, Lucas 114
Requirements: Introduction to Advanced Mathematics or permission of instructor
Instructor: W. Ted Mahavier, Lucas 200E, 409.880.2290 (office), 409.347.1809 (home), 985.381.0292 (cell), wtm@mathnerds.com
Office Hours: MTWRF: 9:00–11:00, 1:30–3:00 or stop by my office anytime.
Course Materials: All materials provided by instructor. See also Honesty Policy.
Course Subject Outline: limit points, sequences, continuity, differentiability, and integration theory for functions of one real variable, culminating in the Fundamental Theorem of Calculus
Student Learning Outcomes: The two primary objectives for students in this course are (1) to master the material listed in the Course Subject Outline and (2) to develop their ability to create mathematics, to make conjectures, to test hypotheses, and to prove theorems. Additionally students will hone their mathematical writing skills, their ability to follow the proofs of other students, their ability to question the work of other students, and their ability to communicate mathematics orally.
Attendance Policy: You are responsible for everything that goes on in class regardless of the reason for an absence. I reserve the right to drop any student for three unexcused absences.
Course Goals and Objectives: To actively involve the students in the process of learning the mathematics provided while developing their appreciation of the subject.
10 - Frequently Asked Questions
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- Book:
- The Moore Method
- Published by:
- Mathematical Association of America
- Published online:
- 26 October 2011
- Print publication:
- 01 August 2009, pp 151-176
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Summary
“The wise man doesn't give the right answers, he poses the right questions.”
—Claude Levi-StraussOver the years, each of us has fielded questions related to the Moore Method from audiences during presentations, from colleagues at conferences, and from friends and relatives. We've compiled here representative questions, along with responses, alphabetized by author.
Does the Moore Method work only for the bright students?
Do Moore Method instructors lecture?
Does the Moore Method cover less material?
Does the Moore Method work best in upper-level and graduate courses?
Does the Moore Method make the students do the work so the teacher doesn't?
Does the Moore Method work with cooperative learning?
Is there a list of features that define the method?
Does the Moore Method foster competition among students?
Are there better ways for students to present than writing on the board?
Does the Moore Method fail to equip those trained via the method, as students and later as professional mathematicians, with the ability to extract information from textbooks?
Are there professional risks associated with teaching a course by the Moore Method?
Are the goals for a Moore Method course the same as for a non-Moore Method course?
How does one prepare to teach a Moore Method course?
Are there lower or upper bounds on the size of a Moore-method class?
4 - On Culture
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- Book:
- The Moore Method
- Published by:
- Mathematical Association of America
- Published online:
- 26 October 2011
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- 01 August 2009, pp 29-44
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Summary
“We have to believe—before students can believe—that hard work pays off, that effort matters, that success depends not on your genes but on your sweat. We must convince students that they can do it when they have teachers who insist on quality work and give them extra remedial help when needed.”
Gene Bottoms, Director, High Schools that WorkWe address the culture in the classroom before addressing the mechanics of the method, for we believe that the mechanics have the best chance for success within a classroom of appropriate culture. As our method of instruction will likely be radically different from that to which our students are accustomed and will likely place more responsibility for active learning on them, part of the established culture is to provide some justification to the students as to how this approach can enhance their intellectual growth. By the same reasoning, we need to provide an environment that has the capacity to maximize the success of each student. The culture should emphasize student responsibility for learning and creating mathematics, while reducing the need for the exercise of authority by the instructor. We strive for a low stress environment and a relaxed atmosphere within the classroom because we are asking students to produce, present, and defend the mathematics of the course. Demonstrating and defending such a personal product can be stressful even in a friendly environment. Who hasn't had butterflies before his or her own research talks at conferences?
9 - Evaluation and Assessment: Effectiveness of the Method
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- Book:
- The Moore Method
- Published by:
- Mathematical Association of America
- Published online:
- 26 October 2011
- Print publication:
- 01 August 2009, pp 139-150
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Summary
“All the instruments have been tried save one, the only one precisely that can succeed: well-regulated freedom.”
—Jean-Jacques RousseauIn this chapter, we discuss the results of educational research that has been conducted evaluating the impact of the Moore Method and describe the results of educational research on similar teaching approaches, draw parallels to the Moore Method, and make suggestions for further assessment of the effectiveness of the Moore Method for interested readers.
Introduction
Whenever an innovation emerges in teaching, there are important questions to be asked. Does the innovation actually work? That is, does it truly improve students' learning, or does it just give the appearance of doing so? Is it feasible that the innovation can be implemented by other instructors in other educational settings, or does it rely upon the talent of a few gifted instructors in a particular context? Is the innovation appropriate for all learners, or just for a particular subgroup? Though the proponents of such innovations are often quite enthusiastic in their efforts to describe and promote the innovation, they are often only able to provide anecdotal evidence for its success. While important and frequently convincing, such evidence is not sufficient to answer the questions posed above. Rather, careful, systematic research should be done to establish the effectiveness of the innovation.
III - May
- from Appendices
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- Book:
- The Moore Method
- Published by:
- Mathematical Association of America
- Published online:
- 26 October 2011
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- 01 August 2009, pp 211-216
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Summary
Syllabus for Introduction to Abstract Mathematics
SALISBURY UNIVERSITY
DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE
SYLLABUS (Tentative)
MATH 300 Introduction to Abstract Mathematics
Intended Audience: Students minoring in mathematics, particularly prospective teachers, will find this a good capstone to their undergraduate mathematical experience. Students majoring in mathematics who have not already completed a 400-level mathematics course will find this a valuable course to help them develop a better understanding of the connection between computational and theoretical mathematics.
Objective: To provide students with an opportunity to develop the foundations of abstract mathematics in a manner similar to that employed by professional mathematicians.
Prerequisite: Discrete Mathematics, completed with a grade of C or better.
Text: Notes distributed by the instructor.
Foundations, I: The Theory of Sets (2 weeks)
Points and sets. Axioms on sets. Subsets. Operations on sets.
Foundations, II: Functions (3–4 weeks)
Ordered pairs. Relations, functions, and operations. Injections, surjections, and bijections. Binary operations and their properties.
A Deeper Look at the Real Numbers (3–4 weeks)
The integers. Algebraic and order properties. Completeness. Supremum Property. Intervals, decimals, and rational and irrational numbers. Mathematical induction. The Archimedean Property. Recursion. Primes. Finiteness and infinity. Countability and uncountability.
Equivalence Relations (2 weeks)
Reflexivity, symmetry, and transitivity. The Equivalence-Relation Theorem. Elementary functions.
Index
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- Book:
- The Moore Method
- Published by:
- Mathematical Association of America
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- 26 October 2011
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- 01 August 2009, pp 243-245
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About the Authors
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- The Moore Method
- Published by:
- Mathematical Association of America
- Published online:
- 26 October 2011
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- 01 August 2009, pp 229-234
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2 - Moore's Moore Method
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- Book:
- The Moore Method
- Published by:
- Mathematical Association of America
- Published online:
- 26 October 2011
- Print publication:
- 01 August 2009, pp 7-12
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Summary
“The greatest sign of success for a teacher…is to be able to say, ‘The children are now working as if I did not exist.’”
—Maria Montessori“Education is what remains after one has forgotten everything one learned in school.”
—Albert Einstein(Coppin) Herein is an attempt to give the reader a snapshot of what an R. L. Moore class was like by examining a particular course of his I took in 1964 and 1965. Contemporaneous classmates will have an account that may vary somewhat from my own but I believe those differences are not of a different species.
Some background may be in order so that the reader may have a backdrop against which to judge a class like this. I went to graduate school during the social revolution of the 1960s that included civil rights marches, demonstrations in the streets and the assassinations of John F. Kennedy, Martin Luther King and Robert F. Kennedy. My contemporaries were products of the decades containing World War II, the Korean Conflict, the Vietnam War and, of course, the Cold War. This was a time colored by a potential worldwide nuclear conflagration. We were Sputnik's children. We thought our country was behind in the space race. Many of my generation decided to go into mathematics and science because we wanted to contribute to our nation's defense and its existence. This was the milieu in which my classmates and I found ourselves doing mathematics.
I - Coppin
- from Appendices
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
-
- Book:
- The Moore Method
- Published by:
- Mathematical Association of America
- Published online:
- 26 October 2011
- Print publication:
- 01 August 2009, pp 177-200
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Summary
I.A Syllabus for Linear Point Set Theory
Math 3321
Fall, 2011
SYLLABUS
Instructor: Charles Coppin
Office: SB 50 (lower level)
Office Hours: 2:00–3:00 MW; 2:00–3:30 F or by appointment
Text: Notes
Content: An axiomatic development of the numbers. A study of limit points, convergent sequences, compact sets, connected sets, dense sets, nowhere dense sets, separable sets
Objectives and Issues: The primary objective of Math 3321 is to begin to inculcate in you those mental processes that characterize mathematical thought. This course will develop your powers of deduction and imagination. You will learn to use language precisely and concisely. Settling conjectures, creating counterexamples and conceptualizing an abstract definition will stretch your imagination.
I have taught this course twenty-seven years at the University of Dallas. We will attempt to run this course in the spirit of R. L. Moore, the father of the American school of point set topology. In his prime, he was considered to be one of the top ten mathematicians in the world. He was considered to be one of the most effective teachers in collegiate mathematics in the first half of this century.
The format is not lecture. There are no surprises about the way people learn. Vince Lombardi, the coach of the Green Bay Packers in their heyday, said that football is nothing more than blocking, tackling, and running—the fundamentals. We will also stress the fundamentals of mathematics—logic and imagination.
Dedication
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- Book:
- The Moore Method
- Published by:
- Mathematical Association of America
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- 26 October 2011
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- 01 August 2009, pp ix-x
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Frontmatter
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- The Moore Method
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- Mathematical Association of America
- Published online:
- 26 October 2011
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- 01 August 2009, pp i-vi
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IV - Parker
- from Appendices
- Charles A. Coppin, Lamar University, W. Ted Mahavier, Lamar University, E. Lee May, Salisbury University, G. Edgar Parker, James Madison University
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- Book:
- The Moore Method
- Published by:
- Mathematical Association of America
- Published online:
- 26 October 2011
- Print publication:
- 01 August 2009, pp 217-228
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Summary
Syllabus for Real Analysis
Following is an excerpt from the syllabus and introduction to the notes from a course in real analysis.
COURSE: Mathematics 410 Advanced Calculus I (An Introduction to Analysis)
INSTRUCTOR: Ed Parker
OFFICE: Burruss 001, JMU6938, parkerge@jmu.edu
OFFICE HOURS: MF 8–9, W 2:30–3:30, Tu 9–10, Th 10–11 (student priority, MF 2:30–3:30, W 8–9, Tu 10–11, Th 9–10 (advisee priority), or by appointment
TEXTBOOK: There will be no formal textbook. Classes will be conducted from problem sets distributed by the instructor; solutions to those problems should effectively allow the student to write his/her own text.
COURSE CONTENT: Number functions and continuity, intermediate and extreme values, derivatives, and (time permitting) integrals.
POLICIES: This course is concerned with the creation and application of the theory that supports elementary calculus. Its conduct will be studentoriented in the sense that you will be asked to create solutions to problems, present your solutions for the scrutiny of the class, and to “criticize” the work of others when presented. You may earn credit during the semester by presenting your solutions in written or oral form. Oral presentation carries twice as much credit as written presentations. A final examination covering the entire course will be given at the end of the semester. The final grade will be determined from the problems solved during the semester (both quantity and quality are factors) and from the final examination.