# Course Descriptions

## Mathematics Courses

### ENGR 326 - Energy & the Environment (GD)

3.00 CrCultural Diversity. This three-credit course will look at the role that energy plays in our modern world. Students will learn about the physics of energy so that they can calculate the energy content of a variety of systems, such as: gasoline, other fossil fuels, nuclear, solar, wind, bio mass and so on. Applications of the energy schemes in our lives will then be explored. We will discuss the global use and needs of energy and the environmental problems that have resulted from energy development and how we can improve our community and the world. Three hours of lecture and field trips per week.

### MA 102 - Foundations of College Math

3.00 CrThis course presents fundamental math concepts so students can develop the foundational math skills required for subsequent college math courses. Students will utilize in-class instruction and online learning materials.

### MA 112 - Precalculus: Function & Graphs

3.00 CrA comprehensive study of elementary functions to prepare students for a college course in calculus. Topics include a review of intermediate algebra including the solution of equations and inequalities, and an in-depth look at functions, inverse functions, their graphs, symmetries, asymptotes, intercepts, and transformations. Linear, polynomial, rational, radical, exponential, logarithmic, and trigonometric functions are studied, and graphing calculators are used extensively.

### MA 117 - Diff Equations & Lin Equations

3.00 CrQuantitative Analysis. Difference Equations and Linear Equations. Introductory college mathematics course in finite difference equations and linear algebra. Topics include sequences, differences, linear and nonlinear difference equations, systems of difference equations, numerical solutions of linear and nonlinear equations, and solving systems of linear equations. Applications from many fields are studied and the role of mathematical modeling is a central focus. Formal computer labs are a part of the course each week, with spreadsheets being the primary software employed. This course satisfies a Carroll College Core Curriculum for all students and the mathematics requirement for business majors.

### MA 121 - Differential Calculus

3.00 CrQuantitative Analysis. This is the first of a two-semester, six-credit calculus sequence. We begin the first semester by reviewing functions from several perspectives (symbolic, numeric, and graphic). For most of the course we study differential calculus, emphasizing how we can use calculus to understand real-world problems such as police radar detection, laying an oil pipeline around a swamp, and understanding motion. Specific topics include limits, continuity, derivatives, the mechanics of finding derivatives, instantaneous rate of change, concavity, the extreme value theorem, and optimization. We use technology extensively, and we also focus on learning how to explain mathematics orally and in writing. The sequence MA 121-MA 122 is considered to be equivalent to MA 131.

### MA 122 - Integral Calculus

3.00 CrThis is the second of a two-semester, six-credit calculus sequence. In this course we study topics in integral calculus, emphasizing how we can use calculus to understand real-world problems such as fluid pumping and lifting, how rain catchers are used in city drain systems, and how a compound bow fires an arrow. Specific topics include optimization, related rates, antiderivatives, definite integrals, the fundamental theorems of calculus, integration by substitution, integration by parts, applications of integration, and an introduction to differential equations. We use technology extensively, and we also focus on learning how to explain mathematics orally and in writing. The sequence MA 121-MA 122 is considered to be equivalent to MA 131.

### MA 131 - Calculus Single Variable Funct

4.00 CrQuantitative Analysis. This course covers all aspects of single-variable calculus including derivatives, antiderivatives, definite integrals, and the fundamental theorem of calculus. We highlight how we can use calculus to understand real-world problems such as laying an oil pipeline around a swamp, fluid pumping and lifting, and how rain catchers are used in city drain systems. We use technology extensively, meeting in the computer lab once each week. We also focus on learning how to explain mathematics orally and in writing. This is the same material that is covered in MA 121-122, except this is an accelerated course that does not review precalculus material.

### MA 141 - Intro to Mathematical Modeling

4.00 CrThis course is an introduction to sequences, difference equations, differential calculus, differential equations, and linear algebra. This is the first course in a two semester, eight credit, sequence in differential equations and linear algebra. Specific topics include analytical and numerical solutions to difference equations and first-order and second-order linear differential equations, separation of variables, the method of undetermined coefficients, phase line analysis, stability of equilibrium, systems of equations, matrix equations, determinants, matrix inverses, Gaussian elimination, and eigenvalues and eigenvectors. There is a heavy emphasis on mathematical modeling and applications. We use technology extensively, and we also focus on learning how to explain mathematics orally and in writing. Prerequisite: High school mathematics through pre-calculus. A basic understanding of differential calculus is strongly recommended.

### MA 201 - Math for Elementary Educ I

3.00 CrA course primarily for prospective elementary teachers, designed to build a background in number and operations with a particular focus on visual models for whole numbers, fractions, and early algebraic reasoning. The course focuses on both mathematical content and methods for teaching number and operations. There is a particular focus on current curriculum and children's mathematical thinking at the elementary school level.

### MA 202 - Math for Elementary Educ II

3.00 CrQuantitative Analysis. An extension of MA 201 into geometry, measurement, set theory, and statistics. The course focuses on both mathematical content and methods for teaching geometry and statistics. There is a particular focus on visual models and children's mathematical thinking at the elementary school level.

### MA 207 - Introduction to Statistics

3.00 CrQuantitative Analysis. The basic concepts used in statistics such as measures of central tendency, variation, and probability distributions, and statistical inference are stressed. Applications are made in the social, communication, health, biological, and physical sciences. This course does not count toward a major or minor in mathematics, nor does it count toward the math requirement for biology majors.

### MA 233 - Multivariable Calculus

4.00 CrIn 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.

### MA 301 - Teaching Math Content & Methds

3.00 CrTeaching 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.

### MA 306 - Real Analysis

3.00 CrWhy 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.

### MA 314 - Prob & Stats for Engineers

2.00 CrThis 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.

### MA 315 - Probability and Statistics

3.00 CrThis 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.

### MA 321 - Math in the Mountains

3.00 CrMath 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.

### MA 328 - Modern Apps of Discrete Math

3.00 CrModern 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.

### MA 334 - Adv Diff Equa & Linear Algebra

4.00 CrAdvanced 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.

### MA 342 - Numerical Methods (WI)

3.00 CrThis 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.

### MA 366 - Junior Seminar

1.00 CrThis 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).

### MA 401 - Abstract Algebra & Modern Geom

3.00 CrThis 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.

### MA 406 - Complex Analysis

3.00 CrThis course covers the calculus of functions of a single complex variable. We will follow the traditional development of calculus of a single real variable, but we will discover the beauty that naturally arises when allowing the domains and ranges of functions to be subsets of the complex numbers. The topics covered are: complex numbers, limits, differentiation, Cauchy-Riemann equations, harmonic functions, elementary functions, conformal mapping, contour integrals, Cauchy integral representation, power series, and residues. Attention will be given to theoretical, computational, geometric, and applied problems. As such, students will be expected to prove theorems and to use a variety of tools to solve problems.

### MA 421 - Math Optimztn, Apps & Analys

3.00 CrThis course is a project-based exploration of topics in optimization and simulation. Topics vary by instructor but typically include linear, integer, binary, and nonlinear programming, stochastic processes, some network optimization, and the Analytic Hierarchy Process. We explore the modeling, algorithmic and heuristic solution approaches to, and sensitivity analysis of problems such as the simplex method, scheduling problems, resource allocation problems, the Knapsack problem, Traveling Salesman problem, and ranking problems. Computers and technology will again play an important role as we investigate both the implementation and the theoretical basis of solution techniques. This course will bring together topics from single and multivariable calculus, linear algebra, and probability.

### MA 422 - Senior Project

3.00 CrAdvanced Writing. In this course, each student will complete an independent research project in mathematics under the direction of a faculty member who will serve as the project director. The student and the project director will work together to select a topic that is of interest to the student, and at the end of the project the student will complete a written report and an illustrated presentation of the work involved.

### MA 425 - Internship

1.00 CrInternship Experiences recognize that learning can take place outside the classroom. Carroll College allows its students to participate in opportunities that relate to their area of study. This opportunity must relate directly a student's program of study in order to qualify for an internship. Close cooperation among Carroll and the participating organizations ensures an experience that contributes significantly to the student's overall growth and professional development. Juniors and seniors in any major area may participate with the approval of faculty internship advisor and/or department chair, Career Services, and a site supervisor. Students will receive academic credit and may or may not receive monetary compensation for an internship. A student may apply a maximum of 12 semester hours to degree requirements; academic departments will determine the number of credits that may count toward the major (most majors accept 6 hours total). Enrollment in the course must be during the same semester in which the experience takes place. Interested students should contact their academic advisor and Career Services prior to the start of an experience.

### MA 471 - History Seminar in Mathematics

1.00 CrThis course in the history of mathematics is intended to give students an insight into some of the great masterpieces of mathematics, as seen in their historical contexts. Developing an understanding of the individuals who were the creators of mathematics helps one better appreciate their creations.

### MA 485 - Independent Study

1.00 CrIndependent study is open to junior and senior students only. At the time of application, a student must have earned a 3.0 cumulative grade point average. A student may register for no more than three (3) semester hours of independent study in any one term. In all cases, registration for independent study must be approved by the appropriate department chairperson and the Vice President for Academic Affairs.

### MA 499 - Senior Thesis

1.00 CrAdvanced Writing. The senior thesis is designed to encourage creative thinking and to stimulate individual research. A student may undertake a thesis in an area in which s/he has the necessary background. Ordinarily a thesis topic is chosen in the student's major or minor. It is also possible to choose an interdisciplinary topic. Interested students should decide upon a thesis topic as early as possible in the junior year so that adequate attention may be given to the project. In order to be eligible to apply to write a thesis, a student must have achieved a cumulative grade point average of at least 3.25 based upon all courses attempted at Carroll College. The thesis committee consists of a director and two readers. The thesis director is a full-time Carroll College faculty member from the student's major discipline or approved by the department chair of the student's major. At least one reader must be from outside the student's major. The thesis director and the appropriate department chair must approve all readers. The thesis committee should assist and mentor the student during the entire project. For any projects involving human participants, each student and his or her director must follow the guidelines published by the Institutional Review Board (IRB). Students must submit a copy of their IRB approval letter with their thesis application. As part of the IRB approval process, each student and his or her director must also complete training by the National Cancer Institute Protection of Human Participants. The thesis is typically to be completed for three (3) credits in the discipline that best matches the content of the thesis. Departments with a designated thesis research/writing course may award credits differently with approval of the Curriculum Committee. If the thesis credits exceed the full-time tuition credit limit for students, the charge for additional credits will be waived. Applications and further information are available in the Registrar's Office.