300
Teaching Mathematics Content and Methods for Middle Grades This course is intended to build deep conceptual understanding of mathematics as well as the understanding and implementation of teaching methods for 5th - 8th grade mathematics. Specific topics include the teaching and learning of algebraic reasoning, proportional relationships, and functions. There is a particular focus on current middle grades mathematics curriculum and children's mathematical thinking at the middle grades level (5th through 8th grade). This course is intended for either elementary education majors or secondary mathematics education majors.
Why does calculus work? In this course, we study real numbers, sequences, and functions, in order to develop the logical foundations for calculus. What does it mean to say that a function has a particular limit? What does it mean for a function to be continuous? We learn to create the mathematical proofs that make up the logical structure behind the limits, derivatives, infinite series, and integrals of calculus.
This course is a calculus-based introduction to the topics in probability and statistics that are necessary in engineering. Topics to be covered include the normal, binomial, and Poisson distributions, hypothesis tests, and confidence intervals. Particular attention will be given to applications in the sciences and engineering. This course includes an introduction to the R statistics language. Note: this course is identical to the first 10 weeks of
MA 315. Students may not receive credit for both
MA 314 and
MA 315.
This course provides a calculus-based introduction to probability and statistics. After a brief introduction to probability, this course will focus on statistics with a strong emphasis on experimental design. Topics to be covered include the normal, binomial, and Poisson distributions, hypothesis tests, confidence intervals, ANOVA, design of experiments, and least squares regression. Particular attention will be given to applications in the sciences and engineering. This course includes an introduction to the R statistics language.
Math in the Mountains is an interdisciplinary course in which students engage in a hands-on learning experience using mathematical modeling to understand current major societal issues of local and national interest. The course is run in collaboration with local businesses, research centers, non-profits, and government organizations that provide data so that teams of students can act as consultants throughout the course thus creating strong connections between Carroll College and the greater Helena community, while engaging in a learning and discovery process. This one-semester upper-level course is open to mathematics and non-mathematics majors at the sophomore level and above.
Modern Applications of Discrete Mathematics. A look at some applications of discrete mathematics that emphasize such unifying themes as mathematical reasoning, proof, algorithmic thinking, modeling, combinatorial analysis, graph theory, and the use of technology. Possible topics include proof techniques, cryptography, primes and factoring, computer passwords, networking problems, shortest paths, scheduling problems, building circuits, and modeling computation.
Advanced Differential Equations and Linear Algebra. This is the second course (after
MA 141) in a two course sequence in differential equations and linear algebra. 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, orthogonality, vector spaces, inner product spaces and the eigenvalue/eigenvector problem. 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. Students will have the opportunity to explore topics beyond the textbook on group projects throughout the semester.
Intermediate Writing.
This course is an introduction to numerical methods and MATLAB programming. We focus not just on how numerical methods work, but when they are appropriate, where they fail, and how to interpret their results. Specific topics vary by instructor but will be chosen from roundoff and truncation errors, root-finding methods, numerical methods for linear algebra, least squares regression methods, interpolation, numerical integration and differentiation, and numerical algorithms for solving ordinary and partial differential equations. Students will learn to write functions in MATLAB using looping and control statements. This is a writing intensive course and students will complete several coding and writing intensive projects throughout the semester.
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).
Special Topics courses include ad-hoc courses on various selected topics that are not part of the regular curriculum, however they may still fulfill certain curricular requirements. Special topics courses are offered at the discretion of each department and will be published as part of the semester course schedule - view available sections for more information. Questions about special topics classes can be directed to the instructor or department chair.