Math 006: Colliding Balls & Springs The Microstructure of How Materials Behave Class meets Mo,We,Fr, 1:00-1:50 PM in Graham Memorial 212 Instructor: Sorin Mitran, Office hours: Mo,We,Th, 2:00-3:00 PM, Phillips 307 [Motivation] [Syllabus] [Grading] [Homework] [Computer work] [Final] [Texts] [Debates] Motivation and objectives Why are some materials soft and others hard? Why are some substances solid while others are fluid? How do we know that ice, water and steam are really the same substance? The answers to these questions have fascinated inquisitive minds before history started. Imagine the awe and wonder of one our ancestors in some forgotten place hundreds of thousands of years ago when it was discovered that flint can be chipped to give a sharp edge - so useful in scraping the meat of hides and ensuring a warm summer. The similar wonder when part of the stones left in the overnight fire were found in strange new shapes the following morning. Someone followed through and found that these shiny parts of some rocks flowed when heated just like water flows. When cooled it became as solid as rock and could be made into useful new shapes. This journey started so long ago is with us still - indeed you are embarking upon a new phase of it in starting your higher education. We will try to recapture what our ancestors have accomplished before us and set the stage for what is being done today in studying the material world around us. While paying homage to history we will introduce how contemporary computational technology is introducing a promising new way of actually designing the materials that we need. Indeed progress is fast apace in the understanding not only of inanimate matter but of the molecular functioning of biological systems. Syllabus Historical overview of humanity's understanding of the structure of matter The evolution of modeling the structure of matter Social implications of theories and technologies of matter Computational modeling Grading Policy Grading is based upon the following course work: Preparation and defense of one of the debates on atomic theory at various historical stages of the development (20 points) A report on historical consequences (both scientific and cultural) of atomic theory (20 points) Working through and presenting conclusions on 3 of 6 computer lab experiments (30 points) A report on possible future directions in various contemporary fields (10 points) Final examination (20 points) Grade points are translated to letter grades according to the following table: B+ 86-90 C+ 71-75 D+ 56-60 A 96-100 B 81-85 C 66-70 D 50-55 A- 91-95 B- 76-80 C- 61-65 F 0-49 Homework Homework assignments will cover both basic aspects of modeling material structure and the historical evolution of the subject and its implications. There are 6 homework assignments: prepare a debate on atomic theory along with an opponent respecting the historical climate of a certain period prepare a report on the consequences for human society of different stages in the development of atomic theory fully work through 3 of the 6 computer labs done during the course prepare a vision into the future report on what breakthroughs in modeling atomic structure might mean both scientifically and socially Homework assignments will be given out individually in response to student interests. Computer work We will build simple computer models of the internal structure of materials and see how they behave. This will serve as an introduction to the Matlab computing environment. Matlab basics AFS basics Lab no. Date Title Lab starter program 1 9/1-9/15 Billiard balls Preview of final result Starter program Lab objectives 2 9/15-9/29 Slinky springs Starter program Lab objectives 3 9/29-10/13 Super balls Collision theory Starter program Lab objectives 4 10/20-11/3 Magic balls Collision theory Starter program Lab objectives 5 11/3-11/17 Lattice world Starter programs: - lattice.m - init.m - timestep.m - translate.m - collisionrule.m Lab objectives 6 11/17-12/1 Multi-color lattices Starter programs: - lattice2.m - init2.m - timestep2.m Lab objectives Final examination We'll have a final examination to test basic understanding of the physical and mathematical concepts discussed in the course. I'll also ask an essay question on the societal implications of such knowledge and simulation capabilties. The final examination is scheduled for Monday, December 13, 12:00 PM in our regular Course Texts and Media There is no fixed course text. Students are encouraged to peruse and perhaps actively read from the following bibliography. The bibliography will grow as the course proceeds. Lecture notes will be available online after each class starting 8/27 The Feynman Lectures on Physics. (Addison-Wesley, 1970). The Greeks - Crucible of Civilization - Paul Cartledge and associated PBS DVD (PBS website) Infinite Secrets - A PBS Nova documentary on Archimedes (website) Alexandria - website dedicated to the ancient city; Library of Alexandria Hypatia of Alexandria Mendeleev's periodic table of the elements Discovery of electron Atom models Lecture notes Lecture Date Topic Notes Lecture Date Topic Notes 1, 8/27 Prehistoric times Sem01.doc   2, 8/30 Earliest civilizations Sem02.doc  3, 9/1 Ancient Greeks sem03.doc Greeks.pdf 4, 9/3   5, 9/8   6, 9/10   7, 9/13   8, 9/15       9, 9/17   10, 9/20   11, 9/22   12, 9/24     13, 9/27   14, 9/29   15, 10/1       Debates We shall try to recreate in the classroom the intellectual climate of various key historical times in the development of atomic theory. The technique we shall use is the time-honored method of two proponents of opposing viewpoints having a debate on a question relating to physical theories on the structure of matter. The students playing the role of proponents are expected to carry out extensive background research, i.e. conscientiously prepare for the debate. Debate preparation shall serve as a way to build good scholarly habits of library research. The rest of the class is expected to actively participate and signal when the debate is off topic. A significant aspect is that debates are supposed to occur in their proper historical time so anachronisms are to be avoided. Plato vs. Aristotle The first debate shall be held on Friday, Sep. 25 and shall feature proponents of Aristotle and Plato arguing the question: "What is substance?". The entire class is expected to read a short overview of the relevant topic: Encarta article on Greek philosophers - text that everybody should read and understand prior to our first debate. A depiction of Plato and Aristotle debating by Raphael - everybody should try to identify the persons in this painting.