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  • MA 232: Differential Equations & Linear Algebra I

    4.00 Credits
    The University of Montana

    This course is an introduction to difference equations, differential equations, and linear algebra. Specific topics include analytical and numerical solutions to difference equations and first-order linear differential equations, phase line analysis, stability of equilibrium, matrix equations and eigenvalues. We emphasize how this mathematics can be used on many real-world problems such as how to predict the spread of a disease, how a home mortgage works, and how to understand the growth of animal populations. We use computers and calculators extensively, meeting in the computer lab once each week. We also focus on learning how to explain mathematics verbally and in writing. Prerequisite: A grade of C or better in MA 131 or in MA 122. Spring semester.
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  • MA 233: Multivariable Calculus

    4.00 Credits
    The University of Montana

    In this course we study multivariable and vector calculus including vectors, parametric equations, surfaces, partial differentiation, multiple integrals, and vector calculus. The big spotlight in this course is using these ideas to understand things like force fields, the flow of water, and magnetic fields. Once a week we meet in the computer lab to use the power of computers to focus on the visual aspects of these concepts to gain insight into more complex situations. We also focus on learning how to explain mathematics verbally and in writing. Prerequisite: A grade of C or better in MA 131 or in MA 122. Fall semester.
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  • MA 301: Foundations of Mathematics

    3.00 Credits
    The University of Montana

    An examination of logic, sets, functions, and methods of proof as a foundation for the study of mathematics. Other topics covered include mathematical induction, recursive definitions, relations (equivalence relations), elementary number theory, transformational geometry, and some history of mathematics. Prerequisite: Grade of "C" or better in MA 233. Spring semester.
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  • MA 328: Modern Applications of Discrete Mathematics

    3.00 Credits
    The University of Montana

    A look at some actual applications of discrete mathematics that emphasize such unifying themes as mathematical reasoning, alagorithmic thinking, modeling, combinatorial analysis, the kinds of structures used in discrete mathematics, and the use of technology. Possible topics include cryptography, primes and factoring, computer passwords, networking problems, shortest paths, scheduling problems, building circuits, modeling computation, and correctness of algorithms. Three one-hour class periods with a substantial computing component illustrating the technology and the ideas studied. Prerequisite: Grades of "C" of better in MA 131 or MA 121-122. Fall semester.
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  • MA 334: Differential Equations & Linear Algebra II

    4.00 Credits
    The University of Montana

    In this course, we focus on both systems of differential equations, with special attention given to modeling, linearization, and equilibrium analysis; as well as the mathematical language of systems - linear algebra, especially transformations and vector spaces. We will motivate the material through applications such as population models, structural, and electrical systems, and linear algebra applications such as 3-D imaging, Markov processes, and Leslie matrices. Technology will again play a major role in this course, as we will have frequent computer demonstrations in class and weekly computer labs to explore the quantitative aspects of these topics. You will have the opportunity to explore topics beyond the textbook on a series of group projects throughout the semester. Prerequisite: A grade of C or better in MA 232. Spring semester.
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  • MA 336: Probability and Statistics I

    2.00 Credits
    The University of Montana

    This course is a calculus-based introduction to basic concepts in probability and statistics. Topics in probability include: probability of simple and compound events; an introduction to discrete and continuous random variables including the uniform, binomial, and normal distributions, and random event simulation. Topics in statistics include statistical measures and graphs and simple linear regression. We begin to learn how to perform statistical analysis on data sets and draw appropriate conclusions based on their analysis. Prerequisite: A grade of C or better in MA 131 or in MA 122. Spring semester.
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  • MA 341: Probability and Statistics II

    3.00 Credits
    The University of Montana

    A calculus-based course in applied probability and statistics. Many types of univariate and multivariate probability distributions are derived and applications are studied. Exposes the student to various decision-making techniques when working with statistical information. Students also gain experience with statistical computing software. Prerequisite: A grade of "C" or better in MA 336. Fall semester. Fulfills writing intensiverequirement.
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  • MA 342: Numerical Computing and Visualization

    3.00 Credits
    The University of Montana

    In this course we study the basic numerical methods used by computers to solve a wide variety of problems, emphasizing how we can use graphics to understand how things work. We focus not just on how these methods work, but when they are appropriate, where they fail, and how to interpret their results. This course is designed around a series of open-ended projects based on real-world problems, such as how to predict the price of heating oil, testing rocket orbital trajectories, and studying the flow of heat throughout a building. The topics we study include least squares regression methods, interpolation, curve fitting, and the numerical solution of a wide range of differential equations (both ODEs and PDEs). Prerequisite: A grade of "C"or better in MA 334, or taken concurrently with MA 334. Spring semester. Fulfills Writing Intensive requirement.
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  • MA 366: Junior Seminar

    1.00 Credits
    The University of Montana

    This is a one-credit, pass/fail, seminar-style course. There will be three main segments: select a faculty director for either an honors thesis or a senior project and write a research proposal, write a resume and research job opportunities, and write a graduate school essay and research graduate school opportunities. The overall goal of this course is to prepare students for their senior year and beyond. This course should be taken in the spring of the year before intended graduation (typically in the spring of the junior year). Spring semester annually.
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  • MA 401: Modern Algebra and Applied Geometry

    3.00 Credits
    The University of Montana

    This course covers the traditional topics from abstract algebra, including groups, rings, integral domains, fields, and homomorphic and isomorphic relationships, as well as standard topics from geometry, including axiomatic systems in both Euclidean and Non-Euclidean geometrics and transformational geometry with vectors and matrices. The focus for the class is the contemporary applications of the concepts presented, together with the weaving together of geometric and algebraic themes. Linear algebra is the integrating theme. Prerequisites: Grade of "C" or better in MA 301.
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