David Rittenhouse Laboratories
209 S. 33rd Street
Philadelphia, PA 19104
Links: CV
This class is about incidence geometry and projective geometry: how lines and planes intersect, and how to add points to euclidean spaces (the familiar R^2, R^3, etc.) to obtain a space that include points and lines at infinity. It's also about art, and how classical artists used projective geometry, sometimes without knowling they were doing so, to create perspective drawings that render three-dimensional space on a canvas in a way our eyes intuitively understand. The projective geometry content will be at times pretty mathy. We use axiom systems, figure out what's true about them, prove theorems, and construct abstract spaces that are models for the axioms. The applications to art will be very hands-on. Expect to sketch a lot, to draw lines on existing pieces of art or sample drawings, and to look at physical objects and attempt to capture them in perspective drawings. If you think of yourself as a bad artist (as I do) it shouldn't matter: we're all going to take a major step forward in one technical aspect of art, namely how to get the lines right in perspective drawings. If you have no real math background, or are even a bit math-phobic, that shouldn't matter either. No math background beyond algebra and trigonometry is necessary. All that is required is willingness to try your hand at logic, to learn the structure of mathematical argument, and to harness your geometric intuition.
MATH0025001
The required background is (1) enough math background to understand proof techniques in real analysis (closed sets, uniform covergence, fourier series, etc.) and (2) some exposure to probability theory at an intuitive level (a course at the level of Ross's probability text or some exposure to probability in a statistics class).
Independent Study allows students to pursue academic interests not available in regularly offered courses. Students must consult with their academic advisor to formulate a project directly related to the student’s research interests. All independent study courses are subject to the approval of the AMCS Graduate Group Chair.
Study under the direction of a faculty member.
Graduate Arts and Sciences doctoral students may register for GAS 6010 as an introduction to the methods of graduate study and research. To be conducted by individual graduate group faculty.
This class is about incidence geometry and projective geometry: how lines and planes intersect, and how to add points to euclidean spaces (the familiar R^2, R^3, etc.) to obtain a space that include points and lines at infinity. It's also about art, and how classical artists used projective geometry, sometimes without knowling they were doing so, to create perspective drawings that render three-dimensional space on a canvas in a way our eyes intuitively understand. The projective geometry content will be at times pretty mathy. We use axiom systems, figure out what's true about them, prove theorems, and construct abstract spaces that are models for the axioms. The applications to art will be very hands-on. Expect to sketch a lot, to draw lines on existing pieces of art or sample drawings, and to look at physical objects and attempt to capture them in perspective drawings. If you think of yourself as a bad artist (as I do) it shouldn't matter: we're all going to take a major step forward in one technical aspect of art, namely how to get the lines right in perspective drawings. If you have no real math background, or are even a bit math-phobic, that shouldn't matter either. No math background beyond algebra and trigonometry is necessary. All that is required is willingness to try your hand at logic, to learn the structure of mathematical argument, and to harness your geometric intuition.
Limits, orders of magnitude, differential and integral calculus; Taylor polynomials; estimating and bounding; probability densities. Mathematical modeling and applications to the social, economic and information sciences.
Multivariate calculus; optimization; multivariate probability densities. Introduction to linear algebra; introduction to differential equations. Mathematical modeling and applications to the social, economic and information sciences.
Differential calculus, integral calculus, series, differential equations and elements of multivariable calculus, with an emphasis on applications.
Study under the direction of a faculty member. Intended for a limited number ofmathematics majors.
The required background is (1) enough math background to understand proof techniques in real analysis (closed sets, uniform covergence, fourier series, etc.) and (2) some exposure to probability theory at an intuitive level (a course at the level of Ross's probability text or some exposure to probability in a statistics class).
Variable topics connected to current research in combinatorial theory. Recent topics include algebraic combinatorics and symmetric functions, analytic combinatorics and discrete probability.
Study under the direction of a faculty member. Hours to be arranged.
Measure theoretic foundations, laws of large numbers, large deviations, distributional limit theorems, Poisson processes, random walks, stopping times.
Continuation of MATH 6480/STAT 9300, the 2nd part of Probability Theory for PhD students in the math or statistics department. The main topics include Brownian motion, martingales, Ito's formula, and their applications to random walk and PDE.
Seminar on current and recent literature in logic.
Seminar on current and recent literature in probability and algorithms.
Seminar on current and recent literature in combinatorics.
Measure theoretic foundations, laws of large numbers, large deviations, distributional limit theorems, Poisson processes, random walks, stopping times.
Continuation of MATH 6480/STAT 9300, the 2nd part of Probability Theory for PhD students in the math or statistics department. The main topics include Brownian motion, martingales, Ito's formula, and their applications to random walk and PDE.
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