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18.02A
Calculus John Bush Mon-Fri, Jan 6-10, 13-17, 21-24, 27-31, 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 first 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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18.095
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 Determinants that Count Homer Reid How many ways can you cover a chessboard with dominoes? How many ways can 4 salesmen visit 17 cities with no overlap? How many ways can a grid of tiny compasses (mis)align? Amazingly, all of these questions can be answered by writing down a simple integer matrix and finding its determinant. We'll learn these powerful methods of counting and see what they tell us about the physics of magnets and molecules. Mon Jan 6, 01-02:30pm, 4-231 Discovering a hidden clique in a random graph Paul Hand An important problem for governments and companies is to determine whether parts of a social graph are unusual. We consider an idealization of this problem. Suppose people know each other randomly, yet there is a large clique -- a large group of people who all know each other. When and how can we find the clique? In some cases, mathematicians do not know whether there is an efficient way to solve this problem. Wed Jan 8, 01-02:30pm, 4-231 Perfect forward secrecy Andrew Sutherland Perfect forward secrecy refers to a cryptographic protocol meant to ensure that the security of a large set of messages (e.g. your entire e-mail history) does not depend on a single private key. As recently implemented by Google, Dropbox, and Facebook (among others), it relies on elliptic curve cryptography. I will explain what elliptic curves are and how they are used in perfect forward secrecy. Fri Jan 10, 01-02:30pm, 4-231 Counting primes David Vogan The prime number theorem says the number of primes less than N is a simple main term plus an error term. The Riemann hypothesis says that the error term grows like the square root of N. I'll explain a formula for counting irreducible polynomials. The main term looks like the main term in the prime number theorem, and the error term grows as the Riemann hypothesis says it should. Mon Jan 13, 01-02:30pm, 4-231 Continued fractions Richard Dudley Continued fractions can be used to approximate some functions, and to find, for a given real number, good rational approximations for it with relatively small integer denominators, such as 22/7 and 355/113 for pi. Such approximations can apply to tuning a piano. Wed Jan 15, 01-02:30pm, 4-231 Overdamped dynamics of small objects in fluids Jorn Dunkel Understanding the dynamics of small particles in fluids is essential for deciphering a wide range of physical and biological processes. The motion of a tiny object in a liquid can be described by a simplified form of Newton's equations. After an extensive discussion of relevant biological and physical examples, we will introduce the underlying mathematical equations and study their solutions for simple test cases. Fri Jan 17, 01-02:30pm, 4-231 Laurent Demanet Wed Jan 22, 01-02:30pm, 4-231 David Spivak Mon Jan 27, 01-02:30pm, 4-231 Surface Tension John Bush Wed Jan 29, 01-02:30pm, 4-231 Tomasz Mrowka Fri Jan 31, 01-02:30pm, 4-231 |
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18.S096
Special Subject in Mathematics Introduction to Julia Computing Alan Edelman Wed Jan 22, Thu Jan 23, Fri Jan 24, 10am-02:00pm, 66-160, Jan. 24: 10am to 12noon Pre-register on WebSIS and attend first class. Limited to 25 participants. Listeners allowed, space permitting Prereq: Permission of instructor Level: U 3 units Standard A - F Grading 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. Julia is an exciting new open source language for numerical computing. It has been gaining traction as a an alternative to Matlab, R and NumPy, especially in performance-critical areas such as machine learning, optimization, linear algebra, big statistics and image analysis. While still relatively new, Julia is already being used in a variety of courses at MIT and elsewhere. (January 22 and 23 includes pizza and a lab) This IAP class provides an introduction to Julia covering topics from loading and analyzing data, to visualization and parallel cluster computation. You will even learn how to build a simple web service in Julia, serving up results from the same process that's generating them. Contact: Alan Edelman, E17-418, x3-7770, edelman@math.mit.edu |
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18.S097
Special Subject in Mathematics A Brief Introduction to Algebraic Topology. James Munkres Mon Jan 6 thru Fri Jan 10, 10:30am-01:00pm, 4-149 Pre-register on WebSIS and attend first class. Listeners allowed, space permitting Prereq: Permission of instructor : 18.901 and 18.701 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. Fundamental group and covering spaces. Applications to basic problems of topology. Proof of the Jordan curve theorem. Class meets 10:30am to 1:00pm, with a break of 20 minutes or so. Three credits if desired. For credit, attendance at each class, participation, and completion of a problem set is required. Text: TOPOLOGY, by James R. Munkres. Contact: James Munkres, E17-338, x3-2948 |