Computational algebra and algebraic geometry [The following notes are about Steven Kleiman’s 2010 Undergraduate Seminar in Computational Commutative Algebra and Algebraic Geometry, in which the students give the lectures. The main page for this course is here.] Prerequisites: {18.06, 18,700, or 18.701} plus {18.703 or 18.702} Descriptions of these courses can be found here. Text Book: “Ideals, Varieties, and Algorithms” by Cox, Little, and O’Shea, UTM Springer, third edition, 2007. Google books has most of the book online. You can find it HERE. Grades: – Based equally on classwork, homework, and the term paper; no exams or final. – Written
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[The following notes are from Steven Kleiman’s 2010 Undergraduate Seminar in Computational Commutative Algebra and Algebraic Geometry at MIT.] Another innovation, this spring of 2010, was requiring incremental drafts of the term papers. First, the week after spring break, all ten students handed in a one-page outlines, showing that they done preliminary research of a topic and made a stab at organizing it. The outlines were good, but usually overly ambitious. The next week, the first third of the paper was due. I read each draft, and discussed it individually with its author. The discussions lasted about fifteen minutes and
Read more →[The following notes are about Steven Kleiman’s 2010 Undergraduate Seminar in Computational Commutative Algebra and Algebraic Geometry, in which the students give the lectures.] This spring of 2010, I tried something new: in-class critiques. They worked out very well, far better than I ever expected. When the students arrived for class, I gave them each a standard sheet of blank paper. During each student’s lecture, the others then wrote a critique, describing what was done well and what needed improvement, so as to reinforce good practices and suggest opportunities for growth. The critiques are marvelous — friendly and constructive, addressed
Read more →Computational Commutative Algebra and Algebraic Geometry, An Undergraduate Seminar at M.I.T. Course Description Schedule and Assignments Term Paper Resources for Writing Math Here is a subpage about critiques. Here is a subpage about incremental drafts.
Read more →I’ve saved a copy of the course web page for this undergraduate seminar at MIT. Classwork and homework Additional description of this class is given on the Presentation Assignments page, under “Number of presenters.”
Read more →The aim of this undergraduate seminar at M.I.T. is to expose students with an interest in the modeling of physical systems to recent developments in the literature. Topics will include, but are not restricted to, fluid mechanics, elasticity, fluid-structure interactions, soft matter physics and applications to biological systems. The backbone of the course will be to gain acquaintance with the process of scientific production, namely: reading of recent literature, oral presentation of material, writing of a journal-like paper and refereeing of other’s work. COURSE STRUCTURE Each student will give 4 presentations throughout the semester, with increasing length and depth of
Read more →In this undergraduate seminar at M.I.T., students present and discuss the subject matter taken from current journals or books. Topics vary from year to year. Instruction and practice in written and oral communication are provided. Enrollment is limited to 12. This term’s topic: Kolmogorov complexity and algorithmic randomness Algorithmic Randomness describes what it means for a string of bits to be random using notions from computability theory, information theory, and probability theory. The Kolmogorov Complexity of a string is its intrinsic information and is defined in terms of incompressibility. This seminar will explore these important notions and their applications. Possible
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