| | (0-0-3) (Lec-Lab-Credit Hours)
Partial fractions, polynomials, Remainder Theorem, Fundamental Theorem of Algebra, Descartes' Rule, exponential and log functions, trigonometric functions, trigonometry of triangles, right triangles, laws of sines and cosines, and conic sections.
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| | (4-0-4) (Lec-Lab-Credit Hours)
An introduction to differential and integral calculus for functions of one variable. The differential calculus includes limits, continuity, the definition of the derivative, rules for differentiation, and applications to curve sketching, optimization, and elementary initial value problems. The integral calculus includes the definition of the definite integral, the Fundamental Theorem of Calculus, techniques for finding antiderivatives, and applications of the definite integral. Transcendental and inverse functions are included throughout.
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| | (4-0-4) (Lec-Lab-Credit Hours)
Continues from MA 115 with improper integrals, infinite series, Taylor series, and Taylor polynomials. Vectors operations in 3-space, mathematical descriptions of lines and planes, and single-variable calculus for parametric curves. Introduction to calculus for functions of two or more variables including graphical representations, partial derivatives, the gradient vector, directional derivatives, applications to optimization, and double integrals in rectangular and polar coordinates.
Prerequisites:
MA 115 Calculus I
(4-0-4)(Lec-Lab-Credit Hours)
An introduction to differential and integral calculus for functions of one variable. The differential calculus includes limits, continuity, the definition of the derivative, rules for differentiation, and applications to curve sketching, optimization, and elementary initial value problems. The integral calculus includes the definition of the definite integral, the Fundamental Theorem of Calculus, techniques for finding antiderivatives, and applications of the definite integral. Transcendental and inverse functions are included throughout.
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| | (4-0-4) (Lec-Lab-Credit Hours)
This course is designed for undergraduate students in Business and Liberal Arts majors. It includes the following basic topics in calculus: the definition of functions, their graphs, limits and continuity; derivatives and differentiation of functions; applications of derivatives; and definite and indefinite integrals. Properties of some elementary functions, such as the power functions, exponential functions, and logarithmic functions, will be discussed as examples. The course also covers methods of solving the first-order linear differential equations and separable equations, and some basic concepts in multi-variable calculus, such as partial derivatives, double integrals, and optimization of functions.
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| | (3-0-3) (Lec-Lab-Credit Hours)
This course is designed only for undergraduate students in Business and Liberal Arts majors. It introduces basic concepts and methods in probability. Topics includes the definition of sample spaces, events, and their probabilities; elementary combinatorics and counting techniques; and conditional probability, the total probability, and Bayes' Theorem. The course also deals with concepts of discrete and continuous random variables and probability distributions; multi-random variables and their joint distributions; the mean, variance, and covariance of random variables; and the Central Limit Theorem and t-distributions.
Prerequisites:
MA 117 Calculus for Business and Liberal Arts
(4-0-4)(Lec-Lab-Credit Hours)
This course is designed for undergraduate students in Business and Liberal Arts majors. It includes the following basic topics in calculus: the definition of functions, their graphs, limits and continuity; derivatives and differentiation of functions; applications of derivatives; and definite and indefinite integrals. Properties of some elementary functions, such as the power functions, exponential functions, and logarithmic functions, will be discussed as examples. The course also covers methods of solving the first-order linear differential equations and separable equations, and some basic concepts in multi-variable calculus, such as partial derivatives, double integrals, and optimization of functions.
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| | (3-0-3) (Lec-Lab-Credit Hours)
This course provides the background necessary for advanced study of mathematics or computer science. Topics include propositional calculus, predicates and quantifiers, elementary set theory, countability, functions, relations, proof by induction, elementary combinatorics, elements of graph theory, mends, and elements of complexity theory.
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| | (4-0-4) (Lec-Lab-Credit Hours)
Covers the same material as MA 116, but with more breadth and depth. Additional topics discussed. By invitation or permission only.
Prerequisites:
MA 115 Calculus I
(4-0-4)(Lec-Lab-Credit Hours)
An introduction to differential and integral calculus for functions of one variable. The differential calculus includes limits, continuity, the definition of the derivative, rules for differentiation, and applications to curve sketching, optimization, and elementary initial value problems. The integral calculus includes the definition of the definite integral, the Fundamental Theorem of Calculus, techniques for finding antiderivatives, and applications of the definite integral. Transcendental and inverse functions are included throughout.
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| | (1-0-1) (Lec-Lab-Credit Hours)
Introduction to the modern applications of mathematics. The applications chosen demonstrate the power, beauty, and effectiveness of mathematics in establishing a rigorous understanding and treatment of scientific phenomena. Typical topics include optimization, chaotic dynamical systems, probability, information theory and coding, and computational mathematics.
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| | (4-0-4) (Lec-Lab-Credit Hours)
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations.
Prerequisites:
MA 116 Calculus II
(4-0-4)(Lec-Lab-Credit Hours)
Continues from MA 115 with improper integrals, infinite series, Taylor series, and Taylor polynomials. Vectors operations in 3-space, mathematical descriptions of lines and planes, and single-variable calculus for parametric curves. Introduction to calculus for functions of two or more variables including graphical representations, partial derivatives, the gradient vector, directional derivatives, applications to optimization, and double integrals in rectangular and polar coordinates.
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| | (3-0-3) (Lec-Lab-Credit Hours)
Introduces the essentials of probability theory and elementary statistics. Lectures and assignments greatly stress the manifold applications of probability and statistics to computer science, production management, quality control, and reliability. A statistical computer package is used throughout the course for teaching and for assignments. Contents include: descriptive statistics, pictorial and tabular methods, and measures of location and of variability; sample space and events, probability axioms, and counting techniques; conditional probability and independence, and Bayes' formula; discrete random variables, distribution functions and moments, and binomial and Poisson distributions; continuous random variables, densities and moments, normal, gamma, and exponential and Weibull distributions unions; distribution of the sum and average of random samples; the Central Limit Theorem; confidence intervals for the mean and the variance; hypothesis testing and p-values, and applications for the mean; simple linear regression, and estimation of and inference about the parameters; and correlation and prediction in a regression model.
Prerequisites:
MA 116 Calculus II
(4-0-4)(Lec-Lab-Credit Hours)
Continues from MA 115 with improper integrals, infinite series, Taylor series, and Taylor polynomials. Vectors operations in 3-space, mathematical descriptions of lines and planes, and single-variable calculus for parametric curves. Introduction to calculus for functions of two or more variables including graphical representations, partial derivatives, the gradient vector, directional derivatives, applications to optimization, and double integrals in rectangular and polar coordinates.
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| | (3-0-3) (Lec-Lab-Credit Hours)
Review of matrix operations, Cramer’s rule, row reduction of matrices; inverse of a matrix, eigenvalues and eigenvectors; systems of linear algebraic equations; matrix methods for linear systems of differential equations, normal form, homogeneous constant coefficient systems, complex eigenvalues, nonhomogeneous systems, the matrix exponential; double and triple integrals; polar, cylindrical and spherical coordinates; surface and line integrals; integral theorems of Green, Gauss and Stokes.
Corequisites:
MA 221 Differential Equations
(4-0-4)(Lec-Lab-Credit Hours)
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations.
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| | (3-0-3) (Lec-Lab-Credit Hours)
Begins with a study of n-dimensional geometry (hyperplanes, hyperspheres, convex hulls, and convex polyhedra), and moves on to study the differential calculus of functions of several variables. In this context, classical optimization theory is studied - that is, the application of calculus to the basic problem of finding the maxima and minima of a continuous function of one or more variables, using Lagrange multipliers, and paying particular attention to convex and concave functions. The final major topic studied is linear programming through the simplex method. Computational methods are stressed throughout. Other topics, such as search techniques, are taken up as time permits.
Prerequisites:
MA 116 Calculus II
(4-0-4)(Lec-Lab-Credit Hours)
Continues from MA 115 with improper integrals, infinite series, Taylor series, and Taylor polynomials. Vectors operations in 3-space, mathematical descriptions of lines and planes, and single-variable calculus for parametric curves. Introduction to calculus for functions of two or more variables including graphical representations, partial derivatives, the gradient vector, directional derivatives, applications to optimization, and double integrals in rectangular and polar coordinates.
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| | (3-0-3) (Lec-Lab-Credit Hours)
This course introduces basic concepts of linear algebra from a geometric point of view. Topics include the method of Gaussian elimination to solve systems of linear equations; linear spaces and dimension; independent and dependent vectors; norms, inner product, and bases in vector spaces; determinants, eigenvalues and eigenvectors of matrices; symmetric, unitary, and normal matrices; matrix representations of linear transformations and orthogonal projections; the fundamental theorems of linear algebra; and the least-squares method and LU-decomposition. Prerequisites: Sophomore or higher class standing.
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| | (3-0-3) (Lec-Lab-Credit Hours)
An introduction to functions of a complex variable. The topics covered include complex numbers, analytic and harmonic functions, complex integration, Taylor and Laurent series, residue theory, and improper and trigonometric integrals.
Corequisites:
MA 227 Multivariable Calculus
(3-0-3)(Lec-Lab-Credit Hours)
Review of matrix operations, Cramer’s rule, row reduction of matrices; inverse of a matrix, eigenvalues and eigenvectors; systems of linear algebraic equations; matrix methods for linear systems of differential equations, normal form, homogeneous constant coefficient systems, complex eigenvalues, nonhomogeneous systems, the matrix exponential; double and triple integrals; polar, cylindrical and spherical coordinates; surface and line integrals; integral theorems of Green, Gauss and Stokes.
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| | (4-0-4) (Lec-Lab-Credit Hours)
Covers the same material as that dealt with in MA 221, but with more breadth and depth.
Prerequisites:
MA 182 Honors Mathematical Analysis II
(4-0-4)(Lec-Lab-Credit Hours)
Covers the same material as MA 116, but with more breadth and depth. Additional topics discussed. By invitation or permission only.
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| | (4-0-4) (Lec-Lab-Credit Hours)
Covers the same material as that dealt with in MA 227, but with more breadth and depth. By invitation only.
Prerequisites:
MA 281 Honors Mathematical Analysis III
(4-0-4)(Lec-Lab-Credit Hours)
Covers the same material as that dealt with in MA 221, but with more breadth and depth.
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| | (1-0-1) (Lec-Lab-Credit Hours)
This course is designed for the completion of transferring credits for MA 221 Differential Equations. The transfer students, who need to learn some topics of MA 221 not included in the courses taken elsewhere, may enroll in this course only once with permission of an undergraduate adviser in the Math Department, and are required to complete this course under the guidance of the MA 221 course coordinator. The students who pass this course will receive the full transfer credits for MA 221. The students who fail will then be required to enroll in the full course of MA 221 at Stevens. Pass/Fail.
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| | | (1-0-1) (Lec-Lab-Credit Hours)
This course is designed for the completion of transferring credits for MA 227 Multivariable Calculus. The transfer students, who need to learn some topics of MA 227 not included in the courses taken elsewhere, may enroll in this course only once with permission of an undergraduate adviser in the Math Department. The students are required to complete this course under the guidance of the MA 227 course coordinator. The students who pass this course will receive the full transfer credits for MA 227. The students who fail will then be required to enroll in the full course of MA 227 at Stevens. Pass/Fail.
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| | (3-0-3) (Lec-Lab-Credit Hours)
An introduction to statistical inference and to the use of basic statistical tools. Topics include descriptive and inferential statistics; review of point estimation, method of moments, and maximum likelihood; interval estimation and hypothesis testing; simple and multiple linear regression; analysis of variance and design of experiments; and nonparametric methods. Selected topics, such as quality control and time series analysis, may also be included. Statistical software is used throughout the course for exploratory data analysis and statistical inference based in examples and in real data relevant for applications.
Prerequisites:
MA 222
(3-0-3)(Lec-Lab-Credit Hours)
Introduces the essentials of probability theory and elementary statistics. Lectures and assignments greatly stress the manifold applications of probability and statistics to computer science, production management, quality control, and reliability. A statistical computer package is used throughout the course for teaching and for assignments. Contents include: descriptive statistics, pictorial and tabular methods, and measures of location and of variability; sample space and events, probability axioms, and counting techniques; conditional probability and independence, and Bayes' formula; discrete random variables, distribution functions and moments, and binomial and Poisson distributions; continuous random variables, densities and moments, normal, gamma, and exponential and Weibull distributions unions; distribution of the sum and average of random samples; the Central Limit Theorem; confidence intervals for the mean and the variance; hypothesis testing and p-values, and applications for the mean; simple linear regression, and estimation of and inference about the parameters; and correlation and prediction in a regression model.
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| | (3-0-3) (Lec-Lab-Credit Hours)
This is an introductory course to number theory. Topics include divisibility, prime numbers and modular arithmetic, arithmetic functions, the sum of divisors and the number of divisors, rational approximation, linear Diophantine equations, congruences, the Chinese Remainder Theorem, quadratic residues, and continued fractions.
Prerequisites:
MA 232
(3-0-3)(Lec-Lab-Credit Hours)
This course introduces basic concepts of linear algebra from a geometric point of view. Topics include the method of Gaussian elimination to solve systems of linear equations; linear spaces and dimension; independent and dependent vectors; norms, inner product, and bases in vector spaces; determinants, eigenvalues and eigenvectors of matrices; symmetric, unitary, and normal matrices; matrix representations of linear transformations and orthogonal projections; the fundamental theorems of linear algebra; and the least-squares method and LU-decomposition. Prerequisites: Sophomore or higher class standing.
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| | (3-0-3) (Lec-Lab-Credit Hours)
A rigorous introduction to group theory and related areas with applications as time permits. Topics include proof by induction, greatest common divisor, and prime factorization; sets, functions, and relations; definition of groups and examples of other algebraic structures; and permutation groups, Lagrange's Theorem, and Sylow's Theorems. Typical application: error correcting group codes. Sample text: Numbers Groups and Codes, Humphries and Prest, Cambridge U.P.
Prerequisites:
MA 232
(3-0-3)(Lec-Lab-Credit Hours)
This course introduces basic concepts of linear algebra from a geometric point of view. Topics include the method of Gaussian elimination to solve systems of linear equations; linear spaces and dimension; independent and dependent vectors; norms, inner product, and bases in vector spaces; determinants, eigenvalues and eigenvectors of matrices; symmetric, unitary, and normal matrices; matrix representations of linear transformations and orthogonal projections; the fundamental theorems of linear algebra; and the least-squares method and LU-decomposition. Prerequisites: Sophomore or higher class standing.
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| | (3-0-3) (Lec-Lab-Credit Hours)
This course begins with a brief introduction to writing programs in a higher level language, such as Matlab. Students are taught fundamental principles regarding machine representation of numbers, types of computational errors, and propagation of errors. The numerical methods include finding zeros of functions, solving systems of linear equations, interpolation and approximation of functions, numerical integration and differentiation, and solving initial value problems of ordinary differential equations.
Corequisites:
MA 221 Differential Equations
(4-0-4)(Lec-Lab-Credit Hours)
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations.
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Prerequisites:
MA 116
(4-0-4)(Lec-Lab-Credit Hours)
Continues from MA 115 with improper integrals, infinite series, Taylor series, and Taylor polynomials. Vectors operations in 3-space, mathematical descriptions of lines and planes, and single-variable calculus for parametric curves. Introduction to calculus for functions of two or more variables including graphical representations, partial derivatives, the gradient vector, directional derivatives, applications to optimization, and double integrals in rectangular and polar coordinates.
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| | (3-0-3) (Lec-Lab-Credit Hours)
This course offers more in-depth coverage of differential equations. Topics include ordinary differential equations as finite-dimensional dynamical systems; vector fields and flows in phase space; existence/uniqueness theorems; invariant manifolds; stability of equilibrium points; bifurcation theory; Poincaré-Bendixson Theorem and chaos in both continuous and discrete dynamical systems; and applications to physics, biology, economics, and engineering.
Prerequisites:
MA 221
(4-0-4)(Lec-Lab-Credit Hours)
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations.
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(3-0-3)(Lec-Lab-Credit Hours)
This course introduces basic concepts of linear algebra from a geometric point of view. Topics include the method of Gaussian elimination to solve systems of linear equations; linear spaces and dimension; independent and dependent vectors; norms, inner product, and bases in vector spaces; determinants, eigenvalues and eigenvectors of matrices; symmetric, unitary, and normal matrices; matrix representations of linear transformations and orthogonal projections; the fundamental theorems of linear algebra; and the least-squares method and LU-decomposition. Prerequisites: Sophomore or higher class standing.
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| | (3-0-3) (Lec-Lab-Credit Hours)
This course offers a rigorous approach to classical partial differential equations. It begins with definitions, properties, and derivations of some basic equations of mathematical physics followed by the topics: solving of first order equations with the method of characteristics; classification of second order equations; the heat equation and wave equation; Fourier series and separation of variables; Green's functions and elliptic theory; examples of the first and second order nonlinear partial differential equations.
Prerequisites:
MA 221
(4-0-4)(Lec-Lab-Credit Hours)
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations.
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(3-0-3)(Lec-Lab-Credit Hours)
Review of matrix operations, Cramer’s rule, row reduction of matrices; inverse of a matrix, eigenvalues and eigenvectors; systems of linear algebraic equations; matrix methods for linear systems of differential equations, normal form, homogeneous constant coefficient systems, complex eigenvalues, nonhomogeneous systems, the matrix exponential; double and triple integrals; polar, cylindrical and spherical coordinates; surface and line integrals; integral theorems of Green, Gauss and Stokes.
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| | (3-0-3) (Lec-Lab-Credit Hours)
This course is an introduction to the geometry of curves and surfaces. Topics include tangent vectors, tangent bundles, directional derivatives, differential forms, Euclidean geometry and calculus on surfaces, Gaussian curvatures, Riemannian geometry, and geodesics.
Prerequisites:
MA 227
(3-0-3)(Lec-Lab-Credit Hours)
Review of matrix operations, Cramer’s rule, row reduction of matrices; inverse of a matrix, eigenvalues and eigenvectors; systems of linear algebraic equations; matrix methods for linear systems of differential equations, normal form, homogeneous constant coefficient systems, complex eigenvalues, nonhomogeneous systems, the matrix exponential; double and triple integrals; polar, cylindrical and spherical coordinates; surface and line integrals; integral theorems of Green, Gauss and Stokes.
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| | (3-0-3) (Lec-Lab-Credit Hours)
This course introduces students to the fundamentals of mathematical analysis at an adequate level of rigor. Topics include fundamental mathematical logic and set theory, the real number systems, sequences, limits and completeness, elements of topology, continuity, derivatives and related theorems, Taylor expansions, the Riemann integral, and the Fundamental Theorem of Calculus.
Prerequisites:
MA 227
(3-0-3)(Lec-Lab-Credit Hours)
Review of matrix operations, Cramer’s rule, row reduction of matrices; inverse of a matrix, eigenvalues and eigenvectors; systems of linear algebraic equations; matrix methods for linear systems of differential equations, normal form, homogeneous constant coefficient systems, complex eigenvalues, nonhomogeneous systems, the matrix exponential; double and triple integrals; polar, cylindrical and spherical coordinates; surface and line integrals; integral theorems of Green, Gauss and Stokes.
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| | (3-0-3) (Lec-Lab-Credit Hours)
This course introduces principles of real analysis and the modern treatment of functions of one and several variables. Topics include metric spaces, the Heine-Borel theorem in R-n, Lebesgue measure, measurable functions, Lebesgue and Stieltjes integrals, Fubini's theorem, abstract integration, L-p classes, metric and Banach space properties, and Hilbert space.
Prerequisites:
MA 232
(3-0-3)(Lec-Lab-Credit Hours)
This course introduces basic concepts of linear algebra from a geometric point of view. Topics include the method of Gaussian elimination to solve systems of linear equations; linear spaces and dimension; independent and dependent vectors; norms, inner product, and bases in vector spaces; determinants, eigenvalues and eigenvectors of matrices; symmetric, unitary, and normal matrices; matrix representations of linear transformations and orthogonal projections; the fundamental theorems of linear algebra; and the least-squares method and LU-decomposition. Prerequisites: Sophomore or higher class standing.
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(3-0-3)(Lec-Lab-Credit Hours)
This course introduces students to the fundamentals of mathematical analysis at an adequate level of rigor. Topics include fundamental mathematical logic and set theory, the real number systems, sequences, limits and completeness, elements of topology, continuity, derivatives and related theorems, Taylor expansions, the Riemann integral, and the Fundamental Theorem of Calculus.
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| | (3-0-3) (Lec-Lab-Credit Hours)
This course introduces students to the concepts behind the modern theory of dynamical systems, particularly chaotic systems. Although the course is mathematical in nature, the emphasis is on the underpinning ideas and applications, rather than a systematic exposition of results. Topics include: standard examples and definitions, solutions of ODEs as dynamical systems, flows, and maps; fixed points of linear maps, periodic orbits, limit cycles, and asymptotic stability; rudiments of hyperbolicity; and symbolic dynamics and the Horse Shoe. Further topics may include: fundamentals of topological dynamics, fundamentals of ergodic theory, attractors, and fractals. A good part of the assigned work involves computer experimentation and computations.
Prerequisites:
MA 221
(4-0-4)(Lec-Lab-Credit Hours)
Ordinary differential equations of first and second order, homogeneous and non-homogeneous equations; improper integrals, Laplace transforms; review of infinite series, series solutions of ordinary differential equations near an ordinary point; boundary-value problems; orthogonal functions; Fourier series; separation of variables for partial differential equations.
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(3-0-3)(Lec-Lab-Credit Hours)
This course introduces basic concepts of linear algebra from a geometric point of view. Topics include the method of Gaussian elimination to solve systems of linear equations; linear spaces and dimension; independent and dependent vectors; norms, inner product, and bases in vector spaces; determinants, eigenvalues and eigenvectors of matrices; symmetric, unitary, and normal matrices; matrix representations of linear transformations and orthogonal projections; the fundamental theorems of linear algebra; and the least-squares method and LU-decomposition. Prerequisites: Sophomore or higher class standing.
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| | (0-3-2) (Lec-Lab-Credit Hours)
Individual projects in pure and applied mathematics.
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| | (0-3-2) (Lec-Lab-Credit Hours)
Individual projects in pure and applied mathematics.
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| | (3-0-3) (Lec-Lab-Credit Hours)
Seminar in selected topics, such as: combinatorial topology, differential geometry, finite groups, number theory, or statistical techniques.
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| | (3-0-3) (Lec-Lab-Credit Hours)
Seminar in selected topics such as: combinatorial topology, differential geometry, finite groups, number theory, or statistical techniques.
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| | (0-8-3) (Lec-Lab-Credit Hours)
Students will do a research project under the guidance of a faculty advisor. Senior standing and prior approval are required. Topics may be selected from any area of mathematics with the instructor's approval. Each student will be required to present results in both a written and oral report. The written report may be in the form of a senior thesis.
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| | (0-8-3) (Lec-Lab-Credit Hours)
Students will do a research project under the guidance of a faculty advisor. Senior standing and prior approval are required. Topics may be selected from any area of mathematics with the instructor's approval. Each student will be required to present results in both a written and oral report. The written report may be in the form of a senior thesis.
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