Applications to other branches of mathematics, physics and chemistry will be included. Binary operations and algebras, rings and polynomials, factor rings and ideals, integral domains and fields both finite and infinite , factor theorems, prime, irreducible and unique factorizaton, power series and differential operators, applications including computer algebra techniques, digital communication and encryption. Field theory, splitting fields, Galois groups, fundamental theorem of Galois theory, applications to classical problems of Euclidean constructibility and solvability by radicals, applications of the theory to encryption and digital communication.

This course develops numerical linear algebra and error estimates essential for scientific computing: machine arithmetic, algorithms for solving systems of linear equations, algorithms for computing eigenvalues and singular values LU, QR, Jacobi's and SVD and the theory of error estimates through condition numbers and backward analysis. The course combines numerical linear algebra with numerical differentiation and integration to derive methods of scientific computing: numerical differentiation and integration, existence, uniqueness, stability and numerical approximation of solutions to nonlinear systems and of ordinary or partial differential equations, splines and fast Fourier or wavelet transforms.

The course also includes such applications to engineering and the sciences as the design and analysis of algorithms to compute special functions, computed geometric design, fluid dynamics, heat diffusion or financial Black-Scholes models, image processing or nonlinear regression. This course is an advanced study of ordinary differential equations focusing on linear and nonlinear systems, with analytical, qualitative, and numerical methods of solution including Euler's method, matrix exponential, stability, phase plane analysis, linearization, Lyapunov functions, existence and uniqueness and applications.

This course provides experience with mathematical software. This course is an advanced study of partial differential equations via boundary value problems and Fourier series representations, centered on classical and numerical solutions of the heat equation, wave equation, advection equation and Laplace equation, introductory finite differences, modeling applications and use of technology through mathematical software.

Topics may include Bessel's inequality, energy methods, existence and uniqueness, eigenfunction expansions and integral transforms. The course lays out the foundations for calculus and analytical geometry; the course develops the topology of the n-dimensional real Euclidean space. Topics include the completeness of the real numbers, topological spaces, continuity and properties preserved by continuous functions: compactness and connectedness.

This course applies notions from linear algebra and continuous functions to develop the calculus of functions of several variables. Topics include differentiability, the derivative as a linear transformation, extreme value problems and the implicit and inverse function theorems.

The course includes the study of Euclidean and non-Euclidean isometries. Selected topics in advanced geometry stressing applications to other branches of mathematics, physics, chemistry and biology will be explored. Applications include the solution of Laplace's partial differential equation by Green's functions Cauchy's and Poisson's integral formulae or Fourier Transforms. Detailed proofs of theorems also provide a theoretical foundations for the corresponding theorems from calculus with one or two variables: differentiation and integration of power series and Fourier series, differentiation relative to parameters of integrals along curves and the fundamental theorem of algebra.

This course covers a variety of statistical methods for research in the natural sciences, including analysis of variance, multiple regression, general linear models and nonparametric statistical procedures. One or more additional topics will be selected by the students in consultation with the instructor teaching the course. Use of statistical software will be emphasized. This course covers advanced topics in probability and statistical inference including discrete and continuous multivariate distributions, moment generating functions, proof of the central limit theorem, properties of estimators including efficiency and sufficiency, best linear unbiased estimators BLUE , maximum likelihood estimation, the Neyman-Pearson lemma and likelihood ratio tests.

The course concludes with a practical student-project component in which students apply methods learned to the analysis of a real-world data set. Satisfies: a university graduation requirement—senior capstone. This course provides students with an opportunity to research a mathematical topic and present their findings in writing and orally. The course examines various problem solving strategies and techniques for teaching problem solving at the secondary level such as direct proof, indirect proof, inferences, mathematical representations and the use of technology.

The Senior Seminar course will explore the culture of mathematics through readings and classroom discussions. The students will be required to write a paper on some aspect of mathematics. At the same time, students will review the core mathematics they have studied and comprehensive tests will be administered in order to assess the knowledge they have acquired in their degree programs. Selected topics to be arranged in consultation with the requesting organization. Pre-requisites: graduate standing. Through readings, discussion and a hands-on problem-centered approach, students will develop a profound understanding of the concepts of numeration systems, base ten and place value, operations, fractions, decimals, percents, integers, real numbers and number theory and will deepen their understanding of the research on the teaching and learning of these topics in K—9 mathematics.

Through readings, discussion and a hands-on problem-centered approach, students will develop a profound understanding of the concepts of ratio and proportion and deepen their understanding of the research on the teaching and learning of ratio and proportion in K—9 mathematics.

## A Level Maths P3 Vector Notes

Through readings, discussion and a hands-on problem-centered approach, students will develop a profound understanding of geometry concepts and deepen their understanding of the research on the teaching and learning of geometry concepts in K—9 mathematics. Through readings, discussion and a hands-on problem-centered approach, students will develop a profound understanding of concepts of data analysis and probability and deepen their understanding of the research on the teaching and learning of data analysis and probability in K—9 mathematics.

Through readings, discussion and a hands-on problem-centered approach, students will develop a profound understanding of algebraic reasoning and deepen their understanding of the research on the teaching and learning of algebraic reasoning in K—9 mathematics. Through readings, discussion and a hands-on problem-centered approach, students will develop a profound understanding of measurement concepts and deepen their understanding of the research on the teaching and learning of measurement in K—9 mathematics.

This course is intended for middle school teachers and focuses on conceptual and procedural understandings of limit, continuity, differentiation and integration. It also addresses the historical development of calculus and the contributions to its development from many cultures. This course explores how to create classroom environments where rich tasks form the basis for mathematical learning. Special emphasis will be placed on task construction, selection and problem-posing. Participants will engage in a series of non-routine problem-solving activities. They will also be expected to develop non-routine problem-solving activities addressing specific mathematical ideas.

These activities will serve as a basis for examining and reflecting on the research about and the implications of such an approach to the teaching and learning of mathematics. Pre-requisites: acceptance into the graduate program. This course provides theory and practice with vector spaces, Hilbert spaces, and continuous processes making use of finite elements, the Fourier, Laplace, and Wavelet transforms.

Methods may include solutions of integral equations with applications to computer assisted tomography and magnetic resonance imaging. Pre-requisites: admission to graduate program. This course uses the structure of group theory to analyze real problems. Topics may include: tesselations and crystal structure, molecular symmetries, electronic structures, representation of vibrations, spin and double groups, virology.

This course provides theory and practice with discrete mathematical modeling. Topics may include chaos theory and fractals, linear programming, graph theory, computational complexity. This course is an introduction to Cryptography. Topics may include; public key encryption, digital signatures, identification protocols, key agreement protocols, DES and AES blockciphers, RSA and ElGamal public-key encryption, cryptographic hash functions, information-theoretic and complexity-theoretic security.

This course provides theory and practice with machine arithmetic, propagation, analysis, and alleviation of rounding errors and other perturbations. Typical applications are Google PageRank, Kalman filtering, data compression and image processing with wavelets. This course requires the use of computers and software available at EWU. To this end the course introduces the computational toolset necessary to investigate numerical solutions to differential equations and linear systems and method of optimization, including iterative methods, with analysis of stability and error.

A course in dynamical systems theory. We discuss characterizations of stability, flows on stable, unstable, and center manifolds, and invariant sets. Other topics may include planar dynamics, Lyapunov functions, conservative systems, and the Hartman-Grobman theorem. This course provides advanced theory and practice with analytical and computational studies of biological systems.

The course contains sophisticated mathematical models from physiological systems, ranging from single cell models to dynamics of coupled cells to behavior of systems or networks.

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This course provides theory and practice with continuous optimization for instance, general, non-necessarily linear least-squares, with non-necessarily linear constraints, or convex analysis , with such applications as geodetic coordinates, non-linear curve and surface fitting, or machine learning. Notes: may be repeated for credit provided the topic is different. The course focuses on the mathematics of applications, depending on the interests of the class and the instructor. Topics will be specified in the section subtitle. This course provides theory and practice with complex analysis and its applications, for instance, linear and non-linear initial-boundary-value problems in electrostatics, electrodynamics, fluid dynamics, as well as Fourier and Radon Transforms in inverse problems of geologic, medical, oceanographic, and radar imaging.

If time permits, may include application to Algebraic Geometry, Number Theory and Coding or extensions to several complex variables, for example. This course provides theory and practice with linear statistical models. Topics include: multiple regression, analysis of variance, non-parametric models. The course will include both a theoretical component as well as a practical component in the form of a student project. This course provides theory and practice with advanced topics in statistics chosen based on faculty expertise and student interests.

Topics may include: generalized linear models, time series analysis, survival analysis. A research thesis under the direction of a graduate committee. A research study in lieu of a bound thesis conducted as partial fulfillment of a master's degree in K—9 mathematics education or applied mathematics under the direction of a graduate committee. Pre-requisites: an approved internship. This course will consist of an internship with an approved business or research facility.

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Not for math majors. Focuses on the theory and application of numerical techniques including error analysis. Also discusses solution of linear, nonlinear and differential equations, interpolation, numerical integration, and curve fitting. Computer solutions are emphasized. Computer analysis of data derived from research conducted in physical, social, and life sciences. Data preparation. Data modification, file manipulation, and descriptive statistics using SPSS.

Programming ability is not required. Student works with an advisor to develop a proposal for a senior project that will be carried out as part of MATH. Generally taken during the spring of the junior year. Prerequisite: Permission of instructor. Intended for students having completed 2 full years of physics and math, this course is designed to develop competency in the applied mathematical skills required of junior and senior level physics majors.

Covering topics involving infinite series, power series, complex numbers, and linear algebra along with vector and Fourier analysis, students will be trained with the rigor required to solve a wide range of applications in the physical sciences. Physics majors only. Introduction to experimental design, data analysis and formal statistical procedures from an applied point of view. Provides a one-semester course in probability and statistics with applications in the engineering sciences. Probability of events, discrete and continuous random variables cumulative distribution, moment generatory functions, chi-square distribution, density functions, distributions.

Introduction to estimation, hypothesis testing, regression and correlation. No credit for both MATH. The real numbers, completeness, sequences of real numbers, functions, continuity, uniform continuity, differentiability, the Riemann integral, series or real numbers, sequences and series of functions, uniform convergence, power series. Addresses the topics of probability, random variables, discrete and continuous densities, expectation and variance, special distributions binomial, Poisson, normal, etc.

This course explores the roles of mainframes, PC's and hand calculators in instruction, examine some of the available software and consider their use in a variety of areas of secondary mathematics, such as algebra, geometry Euclidean and analytic , probability and statistics and introductory calculus.

A first course in theory of analytic functions of one complex variable: complex differentiability and the Cauchy-Riemann equations, Cauchy Integral Theorem and Cauchy Integral Formula, Taylor and Laurent series, zeroes of analytic functions and uniqueness, the maximum modulus principle, isolated singularities and residues. Studies congruencies and the Chinese Remainder Theorem, Primitive roots, quadratic reciprocity, approximation properties of continued fractions, Pell's equation.

Recent application of number theory such as primality testing, cryptology, and random number generation will also be covered. A project -based course starting with an introduction to the basic features of Mathematica. A project that allows the student to focus on certain features in more detail is required and occupies the second half of the course. Focuses on: mathematical resources, ability to use heuristics, the student's beliefs about the use of mathematics to solve problems, and the student's self-confidence as a problem solver. Effective strategies for incorporating problem solving in the curriculum will also be discussed.

Elementary group theory, groups, cosets, normal subgroups, quotient groups, isomorphisms, homomorphisms, applications. Metric spaces, topological spaces, connectedness, compactness, the fundamental group, classifications of surfaces, Brouwer's fixed point theorem. This course is designed for current and prospective geometry teachers. In addition to the development of Euclidean geometry, students will become familiar with geometry applications in Geometer's Sketchpad software, and to a lesser degree with other geometry software applications including Geogebra, and Cabri.

There will be an introduction to spherical and hyperbolic geometry and triangle measurements will be computed for each. Calculus based derivations of area and volume for surfaces and solids will be generated and related to Euclidean geometry topics. Examines ancient numeral systems, Babylonian and Egyptian mathematics, Pythagorean mathematics, duplication, trisection, and quadrature, Euclid's elements and Greek mathematics after Euclid, Hindu and Arabian mathematics, European mathematics from to , origins of modern mathematics, analytic geometry, the history of calculus.

Also covers the transition to the twentieth century and contemporary perspectives. Linear and quasilinear first order PDE. The method of characteristics. Conservation laws and propagation of shocks. Initial value problems - solution formulas. Fundamental solutions. Green's functions. Eigenfunction expansion method for initial-boundary and boundary value problems. Representation of Signals: Fourier analysis, fast Fourier transforms, orthogonal expansions. Transformation of signals: linear filters, modulation. Band-limited signals.

Uncertainty principle.

Windows and extrapolation. Applications to medical imaging and array processing. Applications of mathematics to real life problems. Topics include dimensional analysis, population dynamics wave and heat propagation, traffic flow. An introduction to creation and manipulation of databases and statistical analysis using SAS software.

SAS is widely used in the pharmaceutical industry, medical research and other areas. Cannot be used as a Math Elective. Undergraduate seminar on advanced mathematical topics. Students are required to develop an understanding of an advanced subject beyond the scope of an existing course or synthesize two or more different areas form their curriculum.

Students are required to participate in the seminar, present their results to the Department and write a substantial thesis in their topic area. Essential course elements include library research, original research, and both verbal and written exposition. The first semester is a graduation requirement for majors in mathematics. An optional second semester seminar to allow for continuation of study initiated in Senior Seminar I.

Point estimation, confidence intervals, hypothesis testing. Two-sample t-test. Correlation and linear regression. The bivariate normal distribution. Analysis of variance for one-and two-way designs. F tests. Nonparametric methods. Chi-squared tests for contingency tables. Generalized likelihood ratio. Individual study for the student desiring more advanced or more specialized work.

Course may not be substituted for scheduled offerings. Prerequisite: Permission of Department Chair. Individual study for the student desiring more advanced or more specialized work in algebra. May be repeated for a total of six semester credits. Individual study for the student desiring more advanced or more specialized work in Statistics. Unpaid internship in the Department of Mathematical Sciences. This allows students to receive up to 3 free elective credits while working on an approved project.

Students who have a position and who wish to take advantage of this Practicum should see the department Internship Coordinator. Mathematical Sciences. Academic Catalog. Freshman Seminar in Mathematics Formerly Prerequisites Pre-req: Math Majors Only. Elementary Math for Teaching: Algebra and Data Analysis Description This course seeks to support students in furthering their understanding of elementary mathematics concepts.

Quantitative Reasoning Formerly Prerequisites Co-Req: Fundamentals of Algebra Formerly Management Precalculus Formerly Management Calculus Supplemental Instruction Formerly Calculus IA Formerly Calculus IB Formerly Calculus I Formerly Calculus II Formerly Calculus for the Life Sciences I Formerly Honors Calculus I Formerly Honors Calculus II Formerly Explorations in Mathematics Formerly Functions and Modeling Formerly Linear Algebra I Formerly Linear Algebra II Formerly Calculus III Formerly Math Lab I Formerly Differential Equations Formerly Engineering Differential Equations Formerly Introduction to Statistics Formerly Introduction to Applied Mathematics I Formerly Discrete Structures II Formerly Symbolic Logic Formerly Mathematic Structure for Computer Engineers Formerly Numerical Analysis I Formerly Intro to Data Analysis Formerly Senior Seminar I Formerly Mathematical Physics Formerly Applied Statistics Formerly Probability and Statistics I Formerly Mathematical Analysis Formerly Probability and Mathematical Statistics I Formerly Computers and Calculators in the Classroom Formerly Complex Variables I Formerly Number Theory Formerly Mathematica Description A project -based course starting with an introduction to the basic features of Mathematica.

Mathematical Problem Solving Formerly Abstract Algebra I Formerly Topology Formerly History of Mathematics Formerly Partial Differential Equations Formerly Mathematics of Signal Processing Formerly