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Mathematics

Courses

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)

    4cr
    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.
    Prerequisite: Placement via high school performance
    Fall/Spring/J-Term

  • MTH 1040

    Principles of Modern Mathematics (MTH)

    4cr
    An introduction to set theory, problem solving, geometry, algebra, probability, and statistics, with selected applications for each. The course satisfies teacher certification requirements.
    Prerequisite: Placement via high school performance
    Fall/Spring/J-Term

  • MTH 1050

    Elementary Statistics (MTH)

    4cr
    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.
    Prerequisite: Placement via high school performance
    Spring

  • MTH 1060

    Finite Mathematics (MTH)

    4cr
    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.
    Prerequisite: Placement via high school performance
    Spring

  • MTH 1070

    Functions, Graphs, and Analysis (MTH)

    4cr
    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.
    Prerequisite: Placement via high school performance
    Fall/Spring

  • MTH 1120

    Calculus I (MTH)

    4cr
    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: Placement via high school performance or MTH 1070
    Fall/Spring

  • MTH 1220

    Calculus II (MTH)

    4cr
    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 departmental approval
    Fall/Spring

  • MTH 1240

    Discrete Structures (MTH)

    4cr
    A study of logic, proofs, and sets; graphs, digraphs, trees, colorings, and traversal; permutations and combinations; binomial coefficients; and recurrence relations.
    Prerequisite: MTH 1120 or CSC 1110, or departmental approval
    Fall/J-Term/Spring

  • MTH 2020

    Differential Equations (MTH)

    4cr
    A study of common types of ordinary differential equations, their solutions and applications, singular solutions, and an introduction to mathematical modeling.
    Prerequisite: MTH 1220
    Fall/Spring

  • MTH 2040

    Linear Algebra (MTH)

    4cr
    An examination of linear equations, matrices, vector spaces, transformations, and eigensystems.
    Prerequisite: MTH 1220
    Fall/Spring

  • MTH 2080

    Modern Geometry (MTH)

    4cr
    An introduction to the branches of geometry including plane, solid, higher dimensional, fractal, transformational, non-Euclidean, and combinatorial.
    Prerequisite: MTH 1120
    Fall

  • MTH 2120

    Multivariate Calculus (MTH)

    4cr
    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 departmental approval
    Spring

  • MTH 2130

    Mathematics of Actuarial Science (MTH)

    4cr
    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
    Fall

  • MTH 3030

    Discrete Structures II (MTH)

    4cr
    A second course on discrete structures including probability, combinations and permutations, recursion, and algorithms.
    Prerequisites: MTH 1220 and MTH 1240
    Fall

  • MTH 3040

    Abstract Algebra I (MTH)

    4cr
    A study of groups, Lagrange's theorem, normal subgroups, fields, rings, integral domains, subrings, ideals, and vector spaces.
    Prerequisites: MTH 1240 and MTH 2040
    Fall/Spring

  • MTH 3050

    Theory of Statistics (MTH)

    4cr
    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
    Spring

  • MTH 3120

    Real Analysis (MTH)

    4cr
    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
    Spring

  • MTH 3140

    Abstract Algebra II (MTH)

    4cr
    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)

    4cr
    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)

    4cr
    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)

    4cr
    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
    Spring

  • MTH 4200

    Methods and Materials in Teaching Mathematics

    4cr
    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
    Spring

  • MTH 4300

    Senior Research

    4cr
    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
    Fall

  • MTH 4500

    Independent Study in Mathematics

    2-4cr
    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

    4cr
    An opportunity to conduct research in mathematics, culminating in a research paper.
    Prerequisites: MTH 1220 and instructor approval

  • MTH 4990

    Senior Thesis Completion

    0cr
    Students should register for MTH 4990 during the semester in which they plan to complete their senior thesis.

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    • 91% of employers say critical thinking, communication, and problem-solving skills matter more than your major when it comes to career success. Learn more about how the liberal arts prepare you for a successful career.

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    • Our Summer Undergraduate Research Experience offers select students a research budget, one-on-one mentoring with a professor, and 10 weeks of analyzing, deciphering — and getting paid.

    • So the lake is kind of a focal point, but there’s a lot more to love about our campus — like the fact that our 80-acre campus is also an arboretum and wildlife sanctuary. Focused on keeping campus lush forever, we plant between 50 and 75 new trees every year from a variety of species.

    • Carthage was founded in 1847. That’s more than 170 years of leaders, makers, and go-getters going out and going forth. Read more about Carthage’s rich history.

    • More than 90 percent of our students receive financial aid, a hefty chunk of which is scholarships and grants — including $1.25 million annually from the Presidential Scholarship Competition and numerous Merit Scholarships. Learn what’s available.

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    • Come to Carthage; hear yourself think — think … think …
      Legend has it that Sesquicentennial Plaza holds a perfect echo. Just stand with both your feet on the “1847,” face Straz, and start talking. “You’re the only one who can hear you, but you’ll be crystal clear,” promises English and theatre alumna Mikaley Osley.

    • Our Great Lake provides Carthage students with some amazing views. Think classes on the beach, lake views from the lab, and sunrises from your dorm room. “I love waking up in the morning with the sun shining off the lake. Nothing compares to the view in the morning,” says biology and neuroscience major Ann O’Leary.

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    • For a full decade, NASA has selected Carthage students to conduct research aboard its zero-gravity aircraft. Lately, the stakes have risen. A team of underclassmen is grinding to prepare a tiny but powerful Earth-imaging satellite for launch to the International Space Station. Learn more about the space sciences at Carthage

    • Carthage is the only college or university in the Midwest where every freshman takes a full-year sequence of foundational texts of the Western intellectual tradition. Learn about the Carthage core.

    • With a student-faculty ratio of 12:1, your professors will know who you are. They will also know who you want to be — and how to get you there. Meet our faculty.

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    • True story: There are more than 27 art galleries, a dozen museums, and nine theatres within 25 miles of Carthage. Some highlights: The nationally recognized Racine Art Museum, the world-renowned Art Institute of Chicago, and the Milwaukee Art Museum. Learn more about our location.

    • What’s better than one professor? Two professors. What’s better than two professors? Two professors from totally different fields teaching a single class. There’s debate. Discussion. Differing perspectives. This is where the magic happens. That’s why every student takes a Carthage Symposium.

    • Imagine presenting your original research at an international conference — as an undergraduate. Carthage is dedicated to undergraduate research. Learn more about current opportunities.

    • You can’t hide here — not with only 17 other students in the classroom with you. That’s going to be rough some mornings. But later, when you’re able to argue your point of view thoughtfully, express your opinions succinctly, and meet challenges head-on, without fear … Yep, you’ll thank us.

    • Carthage is ranked No. 11 in the country for student participation in short-term study abroad. Every J-Term, hundreds of students travel all over the world on faculty-led study tours. Imagine a month in Sweden, Rome, Cuba, Senegal, India, Japan …

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