Please note:  Non-NYU students who wish to register for summer session graduate mathematics courses will apply as summer non-degree students through the Graduate School of Arts and Science (GSAS) at http://gsas.nyu.edu/object/grad.app.summer. Applicants must pay close attention to the prerequisite(s) for the course(s) of their choice and make a decision about their eligibility to apply for summer graduate mathematics courses.  When in doubt, please contact the course instructor .

Please also note that meeting the prerequisites does not, in itself, guarantee that an offer of admission will be made by the Department.



Course Descriptions: Summer session 2012

Course Schedule

Undergraduate

Graduate


G63.2110.001  LINEAR ALGEBRA I
May 21 - June 29
Monday, Wednesday, 6:00-8:20 p.m.
Credits: 3 points
Instructor: Jorge Arvesu (jac965@cims.nyu.edu)

Prerequisites: undergraduate linear algebra (some knowledge of matrix operations; determinants; eigenvalues; vector spaces and subspaces; algebraic and geometric properties of single variable functions).

Linear Spaces, Subspaces Linear Dependence, Linear Independence; Span, Basis, Dimension Isomorphism, Quotient Spaces, Linear Functionals, Dual Spaces, Linear Mappings, Null Space, Range, Fundamental Theorem of Linear Algebra, Underdetermined Systems of Linear Equations, Composition, Inverse, Transpose of Linear Maps, Algebra of Linear Maps, Similarity Transformations, Matrices, Matrix Multiplication, Matrix Inverse, Matrix Representation of Linear Maps, Determinant, D Function, Laplace Expansion, Cramer's Rule, Eigenvalue Problem, Eigenvalues & Eigenvectors, Characteristic Polynomial, Cayley-Hamilton Theorem, Diagonalization.

Text: Linear Algebra, Friedbert, Insel & Spence

G63.2120.001   LINEAR ALGEBRA II

July 2 - August 10
Monday, Wednesday, 6:00-8:20 p.m.
Credits: 3 points
Instructor: Tom LaGatta (lagatta@cims.nyu.edu)

Prerequisite: G63.2110 Linear Algebra I or permission of the instructor.

Eigenvalue Problem, Eigenvalues & Eigenvectors, Characteristic Polynomial, Cayley-Hamilton Theorem, Diagonalization. Spectral Theorem; Generalized Eigenvetors, Eigenspace Decomposition, Minimal Polynomial, Similar Matrices, Jordan Canonical Form Euclidean Spaces, Scalar Product, Norm, Distance, Orthonormal Basis Orthgonality, Orthogonal Complement and Projection. Adjoint, Norm of a Linear Map (Matrix), Isometry Spectral Theory of Selfadjoint Maps; Symmetric, Hermitian, Orthogonal, Unitary and Positive Selfadjoint Matrices Quadratic Forms, Min-Max Principle.

Text: Linear Algebra and Its Applications, Peter D. Lax

G63.2901.001  BASIC PROBABILITY

May 21 - June 29
Tuesday, Thursday 6:00–8:20 p.m.
Credits: 3 points
Instructor: Rob Thompson (robert.thompson@hunter.cuny.edu)

Prerequisites: calculus through partial derivatives and multiple integrals; no previous knowledge of probability is required.

We will cover the first five chapters and portions of the sixth and thirteenth chapter of the text. Topics will include probability spaces, random variables, probability distributions, generating functions, law of large numbers and the central limit theorem, random walks, discrete and continous Markov processes, Brownian motion.  Homework will be due once a week (and will be put up on the board in class and posted on the instructor's website).

Exams: We will have a one hour midterm exam, announced a week in advance. There will be NO MAKEUPS. The final exam will be cumulative, but skewed toward the last half of the term.

Text:  Probability and Random Processes, G. Grimmett & D. Stirzaker, Oxford Universtiy Press, 3rd Ed.

For more information about the Basic Probabilty course, please visit the website: http://math.hunter.cuny.edu/thompson/NYUprobability

G63.2902.001 STOCHASTIC CALCULUS

May 21 - August 10
Tuesday, 6:00-8:20 p.m.
Credits: 3 points
Instructor:  Alexey Kuptsov (kuptsov@cims.nyu.edu)

Prerequisite: G63.2901 Basic Probability or equivalent.

Review of basic probability and useful tools. Bernoulli trials and random walk.  Law of large numbers and central limit theorem. Conditional expectation and martingales. Brownian motion and its simplest properties.  Diffusion in general: forward and backward Kolmogorov equations, stochastic differential equations and the Ito calculus. Feynman-Kac and Cameron-Martin Formulas. Applications as time permits.

G63.1002.001  MULTIVARIABLE CALCULUS

July 2 - August 10
Tuesday, Thursday, 6:00-8:20 p.m.
Credits: 3 points
Instructor:  Jani Virtanen (virtanen@cims.nyu.edu)

Prerequisites: calculus I, Calculus II and some linear algebra.

The course will cover the following topics: he Calculus of several variables: vector algebra in 3-space, partial derivatives, multiple integrals of various types, integral theorems and applications, Taylor’s theorem, Implicit function theorem, Maxima and minima and Lagrange multiplier method, Green’s Theorem, Gauss’ Theorem, Stoke’s Theorem. 

Exams: There will be one quiz at the end of the second week, a midterm exam at the beginning of the fourth week, and a final exam at the end of the term.



Revised February 2012