Skip to main content



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, hypothesis testing, 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 1120.
    Prerequisite: MTH 1120 with C or better

  • 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 1030, 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
    Fall of even-numbered years

  • 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 or instructor approval

  • 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

  • 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 or instructor approval

  • MTH 2190

    Ethics in Data Science

    This course will help students think critically about the complex ethical issues arising in technological fields. Students will learn some of the indicators of bias hidden by technology, analyze recent cases of ethical misconduct involving big data, and will learn to perform a contextual risk-benefit analysis of implementing.

  • MTH 3030

    Probability (MTH)

    A second course on discrete structures including probability, combinations and permutations, recursion, and algorithms.
    Prerequisites: MTH 1220 and MTH 1240
    Fall of odd-numbered years

  • 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

    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.
    Prerequisites: MTH 1050 and MTH 1220 or instructor approval
    Spring of odd-numbered years

  • MTH 3090

    Mathematics of Data Science

    This class dives deeper into the data science process by studying the mathematical foundations of common data science methods and techniques. Methods include linear regression, classification models, and clustering. Techniques include generalized study of functions, best practices for handling data, optimization, and analyzing error measures.
    Prerequisite: CSC 1810

  • 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 gauge 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.
    Prerequisite: MTH 1220

  • MTH 3350

    Data Science Portfolio I

    This is the first course in a two-course sequence in which students develop, propose, and refine their three-course applied sequence in data science; learn about the concept of a data science portfolio; and begin the process of planning and assembling their data science portfolio. Students will also engage in career and professional development activities.
    Prerequisites: CSC 1040 and MTH 1050, MTH 3050, BUS/ECN 2340, or EXS 2330, or instructor approval

  • 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 2020 with a grade of C- or better

  • 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: Mathematics Major and junior standing

  • MTH 4350

    Data Science Portfolio II

    This is the second and final course in the data science portfolio sequence. In this class, students will assemble and present their data science portfolio. In addition, students will reflect upon the learning goals of their three-course sequence and articulate how those learning goals were accomplished. Students will participate in professional and career development activities.
    Prerequisite: MTH 3350 or instructor approval

  • 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.

  • Quick Facts

    • Carthage is named a Best Midwestern College by The Princeton Review (2021), a designation given to only 25 percent of four-year schools.

    • The Tower, Carthage’s newest residence hall, provides some of the best views on campus — if not in the Midwest! In addition to #carthageviews of the lake from seven stories up, residents enjoy suite-style living and two floors of shared campus spaces for gaming, cooking, group meetings, or quiet studying. Learn more about all housing options.

    • You’re going to need brain fuel. Grab a morning coffee and a snack and Starbucks or Einstein Bros. Bagels. Later, meet friends at “The Caf,” where the specials change daily but the staples are constant, or swing through “The Stu” for wings, a burrito, or a sub. A new option, Carthage Cash, even covers some off-campus meals.

    • More than 90% of Carthage alumni report that they have secured a job or are continuing their studies six months after graduation. Visit The Aspire Center.

    • 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.

    • Lots of schools wear the four-year label. Carthage stands behind it. More than 90% of Carthage graduates earn their degrees in four years. Learn more

    • Oscars. Emmys. Tonys. Golden Globes. The playwrights we’ve brought in have them. Each year, the Carthage Theatre Department commissions an original script by a renowned playwright for its New Play Initiative. Carthage students then work with the writer to stage it. 

    • Carthage has ranked as a top Fulbright producer for four of the past five years. Read about Carthage Fulbright winners.

    • Things look new at Carthage because they are. Our science center, student union, athletic and recreation center, and numerous residence halls have all been constructed or newly renovated in the last 15 years.

    • Carthage offers majors, minors, and concentrations in more than 50 areas of study, from marketing to neuroscience, nursing to music theatre.

    • 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 more than 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 students receive financial aid. Carthage awards more than $20 million in scholarship and grant assistance. That includes $5.5 million in competitive scholarships in business, mathematics, science, languages, the fine arts, leadership, and overall academic strength. Learn what’s available.

    • Abraham Lincoln was an early Trustee of the College, and U.S. Secretary of State John Hay was a Carthage alum. The two still have a proud place on our campus. Spend some time with them in our Sesquicentennial Plaza. On warm days you’ll find professors leading their classes here.

    • 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,” recalls biology and neuroscience major Ann O’Leary.

    • Carthage awards up to 35 Presidential Scholarships each year, which range from $22,000 up to full tuition. Learn more.

    • 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 Intellectual Foundations.

    • With a student-faculty ratio of 13:1, 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.

    • There are more than 130 student organizations on campus, from Amnesty International to Fencing to Frisbee, Chem Club to Stand Up Comedy. See how easy it is to get involved.

    • 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.

    • 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 in the Top 5 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 …