The study of abstract algebra grew out of an interest in knowing how attributes of sets of mathematical objects behave when one or more properties we associate with real numbers are restricted. The student will begin this course by reviewing basic set theory, integers, and functions in order to understand how algebraic operations arise and are used. The student then will proceed to the heart of the course, which is an exploration of the fundamentals of groups, rings, and fields. Upon successful completion of this course, the student will be able to: Describe and generate groups, rings, and fields; Relate abstract algebraic constructs to more familiar number sets and operations and see from where the constructs derive; Identify examples of specific constructs; Identify and differentiate between different structures and understand how changing properties give rise to new structures; Explain the theory behind relations and functions and identify domains and images of functions, based on the structures given; Explain how functions may relate seemingly dissimilar structures to each other and how knowing properties of one structure allows us to know the same properties in the related structure, if certain functions exist between them. (Mathematics 231)

This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. The student will also take a look at ring factorization, general lattices, and vector spaces. Later this course presents more advanced topics, such as Galois theory - one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand. Upon successful completion of this course, students will be able to: Compute the sizes of finite groups when certain properties are known about those groups; Identify and manipulate solvable and nilpotent groups; Determine whether a polynomial ring is divisible or not and divide the polynomial (if it is divisible); Determine the basis of a vector space, change bases, and manipulate linear transformations; Define and use the Fundamental Theorem of Invertible Matrices; Use Galois theory to find general solutions of a polynomial over a field. (Mathematics 232)

An introduction to the principles of array signal processing and to our project.

Discusses the basics of beamforming concerning our project.

Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. The textbook is also available in printed form from Qoop.com.

Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. This custom textbook collection has been modified by R. Bloom for her classes at De Anza College; the homework content for the custom collection is now contained in a separate homework collection.

This is a custom collection (by R. Bloom) of homework and review problems to accompany Collaborative Statistics textbook custom collection by R. Bloom. Content is derived from Collaborative Statistics written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook by S. Dean and B. Illowsky was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. This custom version of their collection has been modified by R. Bloom for her classes at De Anza College.

Introduces students to the basic tools in using data to make informed management decisions. Covers introductory probability, decision analysis, basic statistics, regression, simulation, and linear and nonlinear optimization. Computer spreadsheet exercises and examples drawn from marketing, finance, operations management, and other management functions. Restricted to Sloan Fellows.

This module discusses the concept of modeling data with linear functions in Algebra.

A discussion of the ULA, its properties, the array that we used for our project, and an introduction to beamforming.

Average stock price as an example of discrete-time filtering.

Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.

Elementary Algebra: An introduction to solving linear equations in one variable.

Examples with the use of matched filters.

Investigation of different aspects of filtering in the frequency domain, particularly the use of discrete Fourier transforms.

Correlates the unit response with the frequency and time domains.

This lesson is designed for students to gather and analyze data about baseball figures. The student will use the Internet or other resources to collect statistical data on the top five home run hitters for the current season as well as their career home run totals. The students will graph the data and determine if it is linear or non-linear.

This module provides examples of the elementary circuit elements; the resistor, the capacitor, and the inductor, which provide linear relationships between voltage and current.

Partial differential equations (PDEs) describe the relationships among the derivatives of an unknown function with respect to different independent variables, such as time and position. Experiment and observation provide information about the connections between rates of change of an important quantity, such as heat, with respect to different variables. Upon successful completion of this course, the student will be able to: State the heat, wave, Laplace, and Poisson equations and explain their physical origins; Define harmonic functions; State and justify the maximum principle for harmonic functions; State the mean value property for harmonic functions; Define linear operators and identify linear operations; Identify and classify linear PDEs; Identify homogeneous PDEs and evolution equations; Relate solving homogeneous linear PDEs to finding kernels of linear operators; Define boundary value problem and identify boundary conditions as periodic, Dirichlet, Neumann, or Robin (mixed); Explain physical significance of boundary conditions; Show uniqueness of solutions to the heat, wave, Laplace and Poisson equations with various boundary conditions; Define well-posedness; Define, characterize, and use inner products; Define the space of L2 functions, state its key properties, and identify L2 functions; Define orthogonality and orthonormal basis and show the orthogonality of certain trigonometric functions; Distinguish between pointwise, uniform, and L2 convergence and show convergence of Fourier series; Define Fourier series on [0,pi] and [0,L] and identify sufficient conditions for their convergence and uniqueness; Compute Fourier coefficients and construct Fourier series; Use the method of characteristics to solve linear and nonlinear first-order wave equations; Solve the one-dimensional wave equation using d'Alembert's formula; Use similarity methods to solve PDEs; Solve the heat, wave, Laplace, and Poisson equations using separation of variables and apply boundary conditions; Define the delta function and apply ideas from calculus and Fourier series to generalized functions; Derive Green's representation formula; Use Green's functions to solve the Poisson equation on the unit disk; Define the Fourier transform; Derive basic properties of the Fourier transform of a function, such as its relationship to the Fourier transform of the derivative; Show that the inverse Fourier transform of a product is a convolution; Compute Fourier transforms of functions; Use the Fourier transform to solve the heat and wave equations on unbounded domains. (Mathematics 222)