Mathematics has been called “the queen and servant of the sciences.” It is an apt description, for it is the one indispensable discipline without which scientific inquiry itself would be impossible. As such, mathematics serves every other science while reigning over all of them. It is quintessentially versatile. Graduates of the Mathematical Sciences program are given a foundation in both pure and practical mathematics, enabling them to pursue careers in applied sciences or a wide-range of related fields.
Course Name
Course #
Credits
Topics include, limits and continuity, differentiation of algebraic and transcendental functions, mean value theorem, applications of differentiation, anti-derivatives, indefinite integrals, inverse trigonometric functions, substitutions, definite integrals, the Fundamental Theorem of Calculus, applications of integration. Applications will be emphasized. In addition to regular class meetings, all students are required to participate in calculus lab sessions. The schedule, frequency, and modality of these labs may vary by section. Refer to the class schedule and course syllabus for details.
MCS 1414
4
Hyperbolic functions, L’Hospital’s rule, techniques of integration, application to arc length and surface area, polar coordinates, infinite series, Taylor Series. In addition to regular class meetings, all students are required to participate in calculus lab sessions. The schedule, frequency, and modality of these labs may vary by section. Refer to the class schedule and course syllabus for details.
MCS 1424
4
Laboratory experiments to complement the material presented in PHY3653. 1 Credit hours. Lab 3 hrs. The following course can be taken concurrently with this course: PHY 3653.
MCS 2414
4
The Minor in Mathematics consists of 5 courses from the following three lists. A minimum of 15 credit hours must be taken beyond the prerequisite courses:
Course Name
Course #
Credits
Topics include, but are not limited to, solving first and second-order differential equations and first-order linear systems of differential equations by various techniques such as separation of variables, integrating factors, substitution methods, variation of parameters, and Laplace Transforms. Emphasis will be placed on applications of differential equations arising from engineering applications and the natural sciences.
MCS 2423
3
Number Theory, review of induction and recursion, advanced counting, equivalence, partial ordering, graphs, trees.
MCS 2523
3
This course covers descriptive statistics, probability, and probability distributions with an emphasis on statistical inference such as confidence intervals, hypothesis testing, correlation and regression, chi-square tests, t-and F-distributions, and selected nonparametric tests.
MCS 2124
4
Representation of data, probability, random variables, discrete and continuous distributions, sampling theory, central limit theorem, confidence intervals, tests of statistical hypotheses, regression analysis. Lecture 3 hrs.
MCS 3403
3
Line and surface integrals, Green’s theorem, Stokes’ theorem, Divergence Theorem. Topics from differential and integral calculus theory. Power series solution of differential equations. Bessel functions, Leg endre’s equation. Lecture 3 hrs.
MCS 3723
3
Systems of linear equations, matrices, determinants, eigenvalues, eigenvectors, Finite-dimensional vector spaces, linear transformations and their matrices, Gram-Schmidt orthogonalization, inner product spaces. Lecture 3 hrs.
MCS 3863
3
The Data Science course delivers the fundamentals of data sets analysis arising in various disciplines, like banking, finance, health care, bioinformatics, security, education, and social services. The content of this course introduces theories and practices of data science concepts based on mathematical and statistical concepts. This course offers a multitude of topics relevant to the analysis of complex data sets accompanying programming and code algorithms in R that underpinning data science. This course is ideal for students and practitioners without a strong background in data science. The students will also learn analyses of foundational theoretical subjects, including the history of data science, matrix algebra, and random vectors, and multivariate analysis; a comprehensive examination of time series forecasting, including the different components of time series and transformations to achieve stationarity; introductions to the R programming languages, including basic data types and sample manipulations; an exploration of algorithms, including how to write one and how to perform an asymptotic analysis; and, a comprehensive discussion of several techniques for analyzing and predicting complex data sets. Towards the end of the class, students will develop a case study by gathering data to apply and practice the learned concepts in a large-scale project.
MCS 2403
3
Laplace transforms of continuous and piecewise continous functions, inverse Laplace transforms, applications to ordinary differential equations. Complex variables, analytic functions, Laurent expansions, residue theory with applications, complex inversion integral and convolution integral. Lecture 3 hrs.
MCS 3413
3
This course is designed to provide students with an understanding of mathematical modeling and the link between Mathematics and Engineering, Science and Nature. This course will introduce modeling techniques and dynamical systems analysis using examples from Engineering, Physics, and Biology. Coverage includes both the analysis, including bifurcation theory, and computation. Matlab will be used extensively in this class.
MCS 3523
3
Orthogonality, orthonormal bases, Fourier series, Fourier integral. Solution techniques for first and second order equations. Solutions of homogeneous and non-homogeneous boundary value problems. Sturm-Liouville theory. Lecture 3 hrs.
MCS 3733
3
Complex numbers. DeMoivre’s Theorem. Complex variables, analytic functions, Cauchy-Riemann equations, Laurent expansions, contour integration, residue theory. Lecture 3 hrs.
MCS 3743
3
Approximation and error. Roots of equations approximation of algebraic and transcendental functions, differentiation, indefinite and definite integration. Quadrature, interpolation. Lecture 3 hrs.
MCS 4813
3
Course not found.
MCS 4823
3
Introduction to algebraic systems. Groups, homomorphisms, isomorphisms, subgroups, normal subgroups, factor groups, Rings and ideals, integral domains, fields. The real number system. Lecture 3 hrs.
MCS 4863
3
Topics of current interest in mathematics and computer science. (May be taken more than once if the topic is different.)
MCS 4993
3
Students who are transferring in credit must take the last three courses at LTU.
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