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18.02A
Calculus John Bush Mon-Fri, Jan 5-9, 12-16, 20-23, 26-30, 12-01:00pm, 54-100, Recitation: TR 10am or 2pm Pre-register on WebSIS and attend first class. No listeners Prereq: GIR:CAL1 Level: U 12 units Standard A - F Grading CALC II First half is taught during the last six weeks of the Fall term; covers material in the first half of 18.02 (through double integrals). Second half of 18.02A can be taken either during IAP (daily lectures) or during the second half of the Spring term; it covers the remaining material in 18.02. Contact: Galina Lastovkina, E18-366, x3-4977, galina@math.mit.edu |
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18.031
System Functions and the Laplace Transform Haynes Miller, Jeremy Orloff Mon-Fri, Jan 20-23, 26-30, 11am-12:00pm, Lecture: MTWRF-2-105, Recitation: MTWRF-56-154 Pre-register on WebSIS and attend first class. Prereq: 18.03 Level: U 3 units Graded P/D/F Studies basic continuous control theory as well as representation of functions in the complex frequency domain. Covers generalized functions, unit impulse response, and convolution; and Laplace transform, system (or transfer) function, and the pole diagram. Includes examples from mechanical and electrical engineering. Class meets twice daily. Lecture: 2-105 (11am to 12noon); Recitation: 56-154 (3-4pm). Contact: Haynes Miller, E17-446, x3-7569, hrm@math.mit.edu |
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18.095
Mathematics Lecture Series John Bush Pre-register on WebSIS and attend first class. Listeners welcome at individual sessions (series) Prereq: GIR:CAL1 Level: U 6 units Graded P/D/F Can be repeated for credit Ten lectures by mathematics faculty members on interesting topics from both classical and modern mathematics. All lectures accessible to students with calculus background and an interest in mathematics. At each lecture, reading and exercises are assigned. Students prepare these for discussion in a weekly problem session. Students taking 18.095 for credit are expected to attend regularly and to do problem sets. Recitation Thursday at 10:30 or 1:00. Web: http://math.mit.edu/classes/18.095/ Contact: John Bush, E17-408, x3-4387, bush@math.mit.edu p-adic numbers Andrew Sutherland The real numbers are typically constructed as a "completion" of the rational numbers. But there is more than one way to complete the rational numbers (infinitely many, in fact), and each leads to a new number system that is as useful in its own way as the real numbers. Introduced by Hensel at the beginning of the 20th century, p-adic numbers are now widely used in number theory and arithmetic geometry... Mon Jan 5, 01-02:30pm, 4-270 Convergence of majority dynamics Omer Tamuz What happens when everyone on Facebook tries to have the same opinions as their friends? Does everyone eventually settle on one opinion? It turns out that this depends on the friendship graph. Wed Jan 7, 01-02:30pm, 4-270 A journey into the world of Euler's elastica: when rods, droplets and pendula behave the same Pierre-Thomas Brun Every high school student has encountered the pendulum equation in the course of his or her studies. Surprisingly, the very same equation applies to a broad range of physical systems ranging from pendant drops to the deformations of thin elastic bodies and was thoroughly investigated by Euler in 1744... Fri Jan 9, 01-02:30pm, 4-270 Steven Johnson Mon Jan 12, 01-02:30pm, 4-270 Overdamped dynamics of small objects in fluids. Joern Dunkel The dynamics of small particles in fluids affects a wide spectrum of physical and biological phenomena, ranging from sedimentation processes in the oceans to transport of chemical messenger substances between and within microorganisms. After discussing these and other relevant examples, we will introduce the mathematical equations that describe such particle motions and study their solutions for basic test cases Wed Jan 14, 01-02:30pm, 4-270 Henry Cohn Fri Jan 16, 01-02:30pm, 4-270 Knots and how to detect knotting. Tomasz Mrowka Wed Jan 21, 01-02:30pm, 4-270 On The Convergence of Series. Spencer Hughes Deciding whether or not a given infinite sum of numbers converges (and, when it does, proving that this is so) is perhaps the most fundamental thing an analyst does. And so gaining intuition about questions of convergence is a very important skill. This lecture will be all about this type of problem... Fri Jan 23, 01-02:30pm, 4-270 Chaos in dynamical systems. Semyon Dyatlov We will study several mathematical ways to describe when a given dynamical system exhibits chaotic, or unpredictable, behavior, such as the notions of ergodicity and mixing. These concepts will be illustrated on several examples, both basic (where I will attempt to give a rigorous proof of ergodicity) and more interesting ones, such as chaotic billiards (which will be demonstrated by numerical simulations). Mon Jan 26, 01-02:30pm, 4-270 Postponed-Lie-theoretic Approach to Differential Equations.-New Date-Thurs. Jan. 29 Sigurdur Helgason Wed Jan 28, ??-??:00pm Lie-theoretic Approach to Differential Equations. Sigurdur Helgason Around 1870 Sophus Lie conceived the idea of a theory for differential equations in analogy to Galois theory for algebraic equations. In this lecture we shall explain his methods, show how this led to Lie group theory which has had a pervasive influence of Lie groups on many fields in mathematics, particularly Differential Geometry, Number Theory and Mathematical Physics. Thu Jan 29, 01-02:30pm, E25-111 |
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18.S097
Special Subject in Mathematics Introduction to Proofs Eric Baer Mon-Fri, Jan 5-9, 12-16, 10am-12:00pm, 4-149 Pre-register on WebSIS and attend first class. Limited to 50 participants. Listeners allowed, space permitting Prereq: Permission of instructor Calculus I (GIR) Level: U 3 units Graded P/D/F Can be repeated for credit Opportunity for group study of subjects in mathematics not otherwise included in the curriculum. Offerings are initiated by members of the Mathematics faculty on an ad hoc basis, subject to departmental approval. 18.S097 is graded P/D/F. An introduction to writing mathematical proofs, including discussion of mathematical notation, methods of proof, and strategies for formulating and communicating mathematical arguments. Topics include: introduction to logic and sets, rational numbers and proofs of irrationality, quantifiers, mathematical induction, limits and working with real numbers, countability and uncountability, introduction to the notions of open and closed sets. Additional topics may be discussed according to student interest. There will be some assigned homework problems --there is no textbook. Space may be limited; please email ebaer@math.mit.edu to reserve a spot. Contact: Eric Baer, E18-308, ebaer@math.mit.edu |