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Mathematics courses at Carthage help students acquire methods of logical reasoning and deduction, and develop problem-solving skills for a wide variety of applications. Scroll down to read descriptions of the Mathematics courses offered at Carthage, or click on the following links for additional resources.


  • MTH 1030

    Applied Contemporary Mathematics (MTH)

    This is an entry-level course appropriate for most college students that emphasizes mathematical reasoning in everyday experiences. The geometry unit deals with form, growth, size, and patterns found in living populations and created art. The mathematics of social choice studies techniques of decision making, voting, and optimizing alternatives. Operations research discusses algorithms for scheduling, planning, and creating networks. Standard statistical measures also are studied and interpreted. This course is designed for any student who does not need the technical vocabulary of trigonometry or analytic geometry. A student may not receive credit for Applied Mathematics after receiving credit for any course numbered 1120 or above.

  • MTH 1040

    Principles of Modern Mathematics (MTH)

    An introduction to set theory, problem solving, geometry, algebra, probability, and statistics, with selected applications for each. The course satisfies teacher certification requirements.

  • MTH 1050

    Elementary Statistics (MTH)

    Methods of determining averages, variability, and correlation, and of testing the significance of the statistics, prediction, and distribution-free statistics. A student may not receive credit for Elementary Statistics after receiving credit for any other statistics course.

  • MTH 1060

    Finite Mathematics (MTH)

    The main topics covered are Boolean algebra, logic, sets, graph theory, combinatorics, number systems, probability, coding, information theory, recurrence relations, and algorithms. This course cannot be taken for credit after MTH 1240.

  • MTH 1070

    Functions, Graphs, and Analysis (MTH)

    A study of polynomial, rational, trigonometric, and exponential functions and their applications. The nature of functions, equation solving, solution estimation, graphing, and mathematical modeling will be emphasized. A student may not receive credit for this course after receiving credit for any other course numbered 1120 or above.

  • MTH 1120

    Calculus I (MTH)

    This course is a study of coordinate systems, straight lines and conic sections, theory of limits, differentiations of algebraic functions, applications to slopes and curves, and maxima and minima.
    Prerequisite: MTH 1070 or high school preparation

  • MTH 1220

    Calculus II (MTH)

    A study of transcendental functions, infinite series, mean-value theorem, polar coordinates, integration, and application of integration. Students completing this course with a grade of C or better will be awarded credit for MTH 1220.
    Prerequisite: MTH 1120 with C or better or high school preparation

  • MTH 1240

    Discrete Structures (MTH)

    A study of logic, proofs, and sets; graphs, digraphs, trees, colorings, and traversal; permutations and combinations; binomial coefficients; and recurrence relations.
    Prerequisite: MTH 1120, CSC 1100, CSC 1810, or CSC 2030, or departmental approval

  • MTH 2020

    Differential Equations (MTH)

    A study of common types of ordinary differential equations, their solutions and applications, singular solutions, and an introduction to mathematical modeling.
    Prerequisite: MTH 1220

  • MTH 2040

    Linear Algebra (MTH)

    An examination of linear equations, matrices, vector spaces, transformations, and eigensystems.
    Prerequisite: MTH 1220

  • MTH 2080

    Modern Geometry (MTH)

    An introduction to the branches of geometry including plane, solid, higher dimensional, fractal, transformational, non-Euclidean, and combinatorial.
    Prerequisite: MTH 1120

  • MTH 2090

    Mathematical Computing

    This course focuses on three classes of computational tools: structured programming languages, computer algebra systems, and spreadsheets. Students will learn Python, Mathematica, and Excel by solving a wide range of mathematical problems from discrete mathematics, number theory, and applied mathematics; and as importantly, students will learn which tools are appropriate for various problems.
    Prerequisite: MTH 1240 or MTH 1220

  • MTH 2120

    Multivariate Calculus (MTH)

    A study of curvilinear motions, solid analytic geometry, vectors, partial derivatives, and multiple integration. Students completing this course with a grade of C or better will be awarded credit for MTH 1120 and 1220 if not previously taken.
    Prerequisite: MTH 1220 or high school preparation

  • MTH 2130

    Mathematics of Actuarial Science (MTH)

    This course is designed to help students prepare for a career in the actuarial sciences, and to help students learn material covered on the first actuarial examination. Topics will include limits, series, sequences, derivatives of single and multivariate functions, integrals of single and multivariate functions, general probability, Bayes' Theorem, univariate probability distributions, and multivariate probability distributions.
    Prerequisites: MTH 1220 and MTH 1240

  • MTH 3030

    Probability (MTH)

    A second course on discrete structures including probability, combinations and permutations, recursion, and algorithms.
    Prerequisites: MTH 1220 and MTH 1240

  • MTH 3040

    Abstract Algebra I (MTH)

    A study of groups, Lagrange's theorem, normal subgroups, fields, rings, integral domains, subrings, ideals, and vector spaces.
    Prerequisites: MTH 1240 and MTH 2040

  • MTH 3050

    Theory of Statistics (MTH)

    Data collection and analysis; continuous and discrete distributions, Central Limit Theorem, sampling theory, confidence intervals and estimation theory, regression analysis and correlation including multiple linear regression models and hypothesis testing and confidence intervals in regression models, chi-square test of independence and other nonparametric statistical tests, time series models and forecasting, linear time series models, moving average and autoregressive models, estimation, data analysis, index numbers, forecasting with time series models, forecasting errors and confidence intervals, and application of statistics to significant real-world data.
    Prerequisite: MTH 1220

  • MTH 3120

    Real Analysis (MTH)

    Fundamental concepts of analysis, limits, continuity, differentiation, and integration. Major topics include the real number system, sequences, series, the Riemann integral, and the generalized Riemann integral.
    Prerequisites: MTH 1240 and MTH 2040

  • MTH 3140

    Abstract Algebra II (MTH)

    A continuation of Abstract Algebra I, concentrating on topics in ring theory and field theory, including applications. Specially arranged, odd-numbered years.
    Prerequisite: MTH 3040

  • MTH 3180

    Introduction to Topology (MTH)

    This course will serve as an introduction to the topology of Euclidean spaces and manifolds, with an emphasis on basic sets (disks, spheres, annuli, Cantor sets) in lower dimensional space. Continuous maps, homeomorphisms, and embeddings will be studied in conjunction with connectedness and paths, convergence and compactness, manifolds, homotopy, contractible sets, the Brouwer fixed-point theorem, and covering spaces. At the end of the course, each student will complete an individual project based on a research article that examines one of the major areas (e.g., physical knot theory) in the modern study of topology.
    Prerequisites: MTH 1220 and MTH 1240

  • MTH 3220

    Complex Variables (MTH)

    This course is an introduction to complex analysis, including the Cauchy-Riemann Equations, Cauchy's Theorem, residue theory, and conformal mapping.
    Prerequisites: MTH 1220 and MTH 2040

  • MTH 3470

    Mathematics for Scientists and Engineers (MTH)

    A study of differential equations, partial differential equations, multiple integration, Laplace transforms, Fourier transforms, and vector analysis. Most spring semesters.
    Prerequisite: MTH 1220 with a grade of C- or better, or departmental approval

  • MTH 4200

    Methods and Materials in Teaching Mathematics

    A study of teaching methods and instructional materials in mathematics. Special attention is given to the selection and organization of subject matter and learning activities. Fieldwork required.
    Prerequisites: Admission to the Teacher Education Program and to be nearly completed with the major

  • MTH 4300

    Senior Research

    Students will engage in mathematics research. Technical oral and written communication skills will be emphasized. Students will produce a high-quality Senior Thesis as part of this course.
    Prerequisites: MTH 1220 and junior standing

  • MTH 4500

    Independent Study in Mathematics

    Independent study in a topic of interest in mathematics that does not duplicate any other course in the regular course offerings.
    Prerequisites: MTH 1220 and instructor approval

  • MTH 4900

    Research in Mathematics

    An opportunity to conduct research in mathematics, culminating in a research paper.
    Prerequisites: MTH 1220 and instructor approval

  • MTH 4990

    Senior Thesis Completion

    Students should register for MTH 4990 during the semester in which they plan to complete their senior thesis.

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