We will disucss the theory of Differentiable Manifolds
This course introduces students to single variable calculus. Topics covered include: functions, limits, continuity, derivative, mean value theorem for derivative, indefinite integral, definite integral, fundamental theorem of calculus, applications of derivatives, maximum and minimum, rate of change, mean value theorem for integrals, approximations of the integrals, applications of integrals, area, volume, transcendental functions, techniques of integration, improper integrals, first order differential equations.
This course introduces methods of discrete mathematics to students.
Topics covered include: logic, arguments, sets, functions, matrices, number theory, counting techniques, pigeonhole principle, permutations and combinations, relations, graphs, Euler paths, Hamiltonian paths, trees, spanning trees, Boolean algebra.
This course introduces methods of discrete mathematics to students.
Topics covered include: logic, arguments, sets, functions, matrices, number theory, counting techniques, pigeonhole principle, permutations and combinations, relations, graphs, Euler paths, Hamiltonian paths, trees, spanning trees and Boolean algebras.
This course introduces methods of discrete mathematics to students.
Topics covered include: logic, arguments, algorithms, well-ordering principle, recursion, counting techniques, pigeonhole principle, permutations and combinations, divide-and-conquer algorithms, generating functions, inclusion-exclusion, equivalence relation, partial orderings.
model, Black-Scholes formula, Black-Scholes-Merton formula, market making, delta-hedging, exotic options, lognormal distribution, Monte
Carlo valuations, Brownian motion and Itô’s lemma, volatility.
This course introduces students to multivariable calculus. Topics covered include three-dimensional geometry, conics, quadric surfaces, polar coordinates, cylindrical coordinates, spherical coordinates, partial derivatives, gradient, maximum and minimum, double integrals, triple integrals, divergence, curl, line integrals, surface integrals, Green’s Theorem, Gauss’s Divergence Theorem, Stokes’s Theorem.
Building on the calculus learned in the first year, this course provides students a rigorous foundation of single variable calculus.
This course introduces students to curves and surfaces in the three dimensional Euclidean Space.
This course is an introductory course in mathematics that introduces students to some fundamental concepts and methods of algebra and analytic geometry. Topics covered include: number systems, polynomials, sequences and series, partial fractions, complex numbers, polar coordinates, parametric curves, conics, geometry of three space, vectors, lines and planes in three space.
This course introduces students to single variable calculus. Topics covered include: functions, limits, continuity, derivative, mean value theorem for derivative, indefinite integral, definite integral, fundamental theorem of calculus, applications of derivatives, maximum and minimum, rate of change, mean value theorem for integrals, approximations of the integrals, applications of integrals, area, volume, transcendental functions, techniques of integration, improper integrals, first order differential equations.
Topics covered include: analytic functions, power series, Goursat’s theorem, Cauchy integral formula, Morera’s theorem, Schwarz reflection principle, Runge’s approximation theorem, analytic continuation, zeros and poles, residue formula, meromorphic functions, argument principle, complex logarithm, harmonic functions, Jensen’s formula, functions of finite order, infinite products, Hadamard’s factorization theorem, Schwarz lemma, Riemann mapping theorem, gamma function, Riemann zeta function, elliptic functions, theta function.