18.02A
Calculus
John Bush
Mon-Fri, Jan 4-8, 11-15, 19-22, 25-29, 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
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, 2-108, 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://web.mit.edu/immanuel/www/18.095/
Contact: John Bush, 2-346, x3-4387, bush@math.mit.edu
An Introduction to Dimensional Analysis, Scaling Laws and Similitude
Tristan Gilet
This lecture presents the tools of dimensional analysis frequently used for pilot studies. Which physical variables should we select to model a phenomenon? Is there a simple law that relates them? If so, can we guess it before any further work? How many experiments should we do to check this law? How to build a relevant scale-down? Applications in physics, biology and engineering.
Mon Jan 4, 01-02:30pm, 2-190
When Functions Have No Value(s): Delta Functions and Distributions
Steven Johnson
Wed Jan 6, 01-02:30pm, 2-190
Hex, Politics, and Tug-of-War: A Game Theoretic Approach to Analysis
Scott Sheffield
I will discuss random-turn hex (which students may download and play for free:
http://research.microsoft.com/en-us/um/people/dbwilson/hex/) and a related class of "random-turn" games. These games are fun for mathematicians --- and also useful. Indeed, it turns out that many natural problems in analysis and the geometry of metric spaces are best understood by playing games.
Fri Jan 8, 01-02:30pm, 2-190
Surfaces from a Polygon
Olivier Bernardi
Imagine a square made of an elastic material. Gluing the sides A,B,C,D in pairs give a surface without boundary. For instance, gluing A with B and C with D gives a surface which can be stretched into the sphere; gluing A with C and B with D gives the torus; gluing A with D and B with C gives the sphere. More generally, how many gluings of the
2n-gon give the sphere? the torus?
Mon Jan 11, 01-02:30pm, 2-190
Riemann Sums and Bernoulli Numbers
Daniel Stroock
Wed Jan 13, 01-02:30pm, 2-190
Mathematics As Logic
Hartley Rogers
Chronological history for First-Order Quantifier Logic. Examples: the languages L and P; syntax, semantics, truth, deductive inferences (proofs), and first-order theories. Set theory in L. Arithmetic in P. Newly simplified coding for arithmetization of syntax leading direct to Godel's incompleteness and independence theorems and to Matiyasevich's negative solution to Hilbert's Tenth Problem.
Fri Jan 15, 01-02:30pm, 2-190
Representation Theory By Pictures
Benjamin Brubaker
Wed Jan 20, 01-02:30pm, 2-190
Logistic Map as the Simplest Route to Chaos
Lyubov Chumakova
The world is often nonlinear and chaotic, but we can understand part of it using the theory of dynamical systems. In this course we will talk about one-dimensional maps - a particular example of dynamical systems - and use the logistic map to illustrate how a very simple nonlinear map can produce variety of complex effects and, ultimately, exhibit chaotic behavior.
Fri Jan 22, 01-02:30pm, 2-190
Bernoulli Numbers
Abhinav Kumar
I will talk about the fundamental properties of Bernoulli numbers, and their significance in number theory, as well as their history and connection to other parts of mathematics.
Mon Jan 25, 01-02:30pm, 2-190
Lottery Mathematics and Coin Problems
Tanya Khovanova
We'll analyze the expected return of a lottery game depending on the jackpot and the number of players. We discuss how the probabilities change if you pool money together or buy all ticket combinations. We'll learn about famous scams, as well as some clever, not-so-famous schemes for attempting to beat lotteries. After the break I will discuss recent interesting coin problems that appeared in Russian Math Olympiads.
Wed Jan 27, 01-02:30pm, 2-190
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