| source Northwestern (X) |
level |
department MATH Mathematics (X) |
Recent popular works by prominent scientists and intellectuals have renewed interest in atheism, broadly construed as the absence of belief in deities. In this seminar we will evaluate, compare and contrast four significant contributions in this direction by mathematician John Allen Paulos, biologist Richard Dawkins, neuroscientist Sam Harris and journalist Christopher Hitchens.
Score: 11.6559515 Details | Listing | Web page
Finite Mathematics: Primarily for the behavioral sciences. Topics chosen from elementary linear algebra and its applications, finite probability, and elementary statistics.
Score: 11.6559515 Details | Listing | Web page
Differential calculus in one variable. Review of trigonometric, exponential, logarithmic and inverse functions. Limits, continuity, derivative of a function, product, quotient and chain rule, mean value theorems, Newton's method, linear approximation and differentials, optimization problems. Enrollment is by permission only. This course is intended for students with little or no calculus background. Math 212, 213, and 214 cover the same materials as Math 220 and 224.
Score: 11.6559515 Details | Listing | Web page
Definition of a function, trigonometric, exponential, logarithmic and inverse functions, graphs, limits, continuity, derivative of a function, product, quotient and chain rule, implicit differentiation, linear approximation and differentials, related rates, mean value theorems, curve plotting, optimization problems, Newton's method and anti-derivatives.
Score: 11.6559515 Details | Listing | Web page
Integral Calculus in one variable. Some review of 220-0 (mainly in the Fall Quarter for incoming freshmen). Definite integrals and the Fundamental Theorem of Calculus. Techniques of integration including integration by parts, trigonometric integrals, trigonometric substitutions, partial fractions, numerical integration and improper integrals. Applications of integration: computation of volumes, arc length, average value of functions, the mean value theorem for integration, work and probability. Sequences and Series: the integral and comparison tests, power series, ratio test, introduction to Taylor's formula and Taylor series and using series to solve differential equations.
Score: 11.6559515 Details | Listing | Web page
Vectors, dot and cross products, equations of lines and planes, polar, cylindrical, and spherical coordinates, differentiation of vector functions, velocity and acceleration, arc length, parametric surfaces, functions of several variables, partial derivatives, tangent plane and linear approximations, chain rule for partial derivatives, directional derivative and gradient, max-min problems for functions of several variables, Lagrange multipliers.
Score: 11.6559515 Details | Listing | Web page
Multiple Integration and Vector Calculus. Cylindrical and spherical coordinate systems, double and triple integrals, line and surface integrals. Change of variables in multiple integrals; gradient, divergence, and curl. Theorems of Green, Gauss, and Stokes.
Score: 11.6559515 Details | Listing | Web page
Basic concepts of linear algebra. Solutions of systems of linear equations; vectors and matrices; subspaces, linear independence, and bases; determinants; eigenvalues and eigenvectors; other topics and applications as time permits.
Score: 11.6559515 Details | Listing | Web page
Multivariable differential calculus, multiple integration and vector calculus.
Score: 11.6559515 Details | Listing | Web page
Linear Algebra
Score: 11.6559515 Details | Listing | Web page
An introduction to linear algebra covering computations and applications, but giving primary emphasis to theory. Topics covered in this course include vector spaces, linear independence, dimension, determinants, eigenvalues and eigenvectors. This material provides the foundation for the vector calculus material in Math 290-2 and Math 290-3.
Score: 11.6559515 Details | Listing | Web page
Introduction to fundamental mathematical ideas  such as sets, functions, equivalence relations, and cardinal numbers  and basic techniques of writing proofs.
Score: 11.6559515 Details | Listing | Web page
Discrete probability spaces, random variables, expected value, combinatorial problems. Special distributions, independence, and conditional probability. Weak law and central limit theorem (CLT).
Score: 11.6559515 Details | Listing | Web page
Rigorous analysis in Euclidean space and on metric spaces. Metric space topology, properties of Euclidean spaces, limits and continuity, differentiation and integration, sequences and series, the inverse and implicit function theorems. Lebesgue integration with applications. 321-1,2 differ from 320-1,2 in two respects: they cover more topics in more depth, and aim at intensive development of students ability to analyze and create mathematical proofs. Faster than 320, and at a higher level of abstraction.
Score: 11.6559515 Details | Listing | Web page
Groups and their structure; elementary ring theory; polynomial rings.
Score: 11.6559515 Details | Listing | Web page
An introduction to basic group theory: definition of a group; examples; subgroups; normal subgroups and quotient groups; homomorphisms and automorphisms; Cayley's theorem; permutation groups; Sylow's theorem: direct products; finite abelian groups. Groups and their structure, elementary ring theory; polynomial rings. 331 differs from 330 in two respects: it covers more topics in more depth, and aims at intensive development of students ability to analyze and create mathematical proofs.
Score: 11.6559515 Details | Listing | Web page
A one-quarter introduction to partial differential equations and their solution by the methods of Fourier analysis. Topics include the solution of boundary and initial-value problems for the heat equation, the wave equation and Laplace's equation in both rectangular, cylindrical and spherical coordinates. Special attention will be paid to questions of convergence and asymptotic behavior of the series solutions. Use of the Fourier integral permits an overview of the series solutions obtained.
Score: 11.6559515 Details | Listing | Web page
Ordinary differential equations and partial differential equations with applications to mathematical modeling.
Score: 11.6559515 Details | Listing | Web page
Fourier series and boundary value problems.
Score: 11.6559515 Details | Listing | Web page
Probability theory and its social science applications.
Score: 11.6559515 Details | Listing | Web page
Introduction to classical and schemetheoretic methods of algebraic geometry. Algebraic vector bundles, sheaf cohomology, the Riemann-Roch theorem for curves, and intersection theory.
Score: 11.6559515 Details | Listing | Web page
Set and counting; functions; matrix theory; linear systems; linear programming; introduction to probability and statistics; games and programming; interest and annuities; other topics and applications as time permits.
Score: 11.6559515 Details | Listing | Web page
Cylindrical and spherical coordinate systems, double and triple integrals, line and surface integrals. Change of variables in multiple integrals; gradient, divergence, and curl. Theorems of Green, Gauss, and Stokes.
Score: 11.6559515 Details | Listing | Web page
Complex numbers, analytic functions, contour integrals, Cauchy's Theorem, Laurent series, Residue Theorem, conformal mapping, analytic continuation.
Score: 11.6559515 Details | Listing | Web page
Time series analysis via ARIMA models, analysis of parel data, analysis of discrete data.
Score: 11.6559515 Details | Listing | Web page