North Central’s math faculty involves you in research projects and real-world experience. North Central’s math faculty involves you in research projects and real-world experience. North Central’s math faculty involves you in research projects and real-world experience. North Central’s math faculty involves you in research projects and real-world experience. North Central’s math faculty involves you in research projects and real-world experience.

College of Arts & Sciences

Department of Mathematics

Mathematics

Questions?

Undergraduate Admissions

(630) 637-5800

admissions@noctrl.edu

Why pursue a mathematics degree at North Central College?

You’ll receive all the help, advice and personal attention you need, thanks to our accessible professors and small classes. North Central’s math faculty members are committed to involving you in their research projects, so you’ll also get valuable first hand experiences. Our pure mathematics major is renowned for preparing high school and middle school math teachers and for maintaining an extensive network of school contacts that can lead to valuable field experiences, residency opportunities and career placements. Other math majors go on to graduate school to prepare for a career in higher education, teaching and research.

You can also:

  • Collaborate with your professors on research projects that explore topics like knot theory or mathematical modeling of disease transmission.
  • Attend local, regional and national academic conferences.
  • Participate in campus activities like Math Club and the Pi Day Celebration with alumni.
  • Enroll in a problem-solving seminar that prepares you for competitions including the Putnam Exam.
  • Obtain extra help from a peer tutor—or become one yourself.
  • Join the mathematics honor society Pi Mu Epsilon.

More Department information

Register for the American Mathematics Contest (AMC)

Mathematics, B.A.

For additional programs and courses in this department, see Mathematics.

Major Requirements

At least 40 credit hours in mathematics, including:

  • MTH 141 - Integrated Calculus II: Calculus of Derivatives -or-

    MTH 141 - Integrated Calculus II: Calculus of Derivatives

    3.00 credit hours

    An integrated calculus course which combines the study of exponential, logarithmic and inverse trigonometric functions with a formal development of the derivative. Students may not receive credit for MTH 141 and any of the following: MTH 122, MTH 130 or MTH 151.

    Prerequisite(s)


    MTH 140.

    Core

    Mathematics.

    Schedule Of Classes

  • MTH 151 - Calculus I

    MTH 151 - Calculus I

    3.00 credit hours

    Fundamental concepts of calculus including limits, continuity and differentiation with applications. The Calculus I, II and III sequence is recommended for students in science as well as for students in other divisions desiring a strong preparation in mathematics. Students may not receive credit for MTH 151 and any of the following: MTH 130, MTH 140 or MTH 141.

    Prerequisite(s)


    MTH 121 and MTH 122; or four years high school math including algebra, geometry and trigonometry.

    Core

    Mathematics.
    IAI

    M1 900

    Schedule Of Classes

  • MTH 152 - Calculus II

    MTH 152 - Calculus II

    3.00 credit hours

    Continuation of Calculus I with emphasis on integration and its applications. Required for the B.S. degree in any department.

    Prerequisite(s)


    MTH 141 or MTH 151.

    Core

    Mathematics.
    IAI

    M1 900

    Schedule Of Classes

  • MTH 153 - Calculus III

    MTH 153 - Calculus III

    3.00 credit hours

    Continuation of Calculus II with an emphasis on infinite series.

    Prerequisite(s)


    MTH 152.

    Core

    Mathematics.
    IAI

    M1 900

    Schedule Of Classes

  • MTH 254 - Calculus IV

    MTH 254 - Calculus IV

    3.00 credit hours

    Functions of two or more variables, partial derivatives, multiple integrals and line integrals. Vector analysis, divergence and Stokes's theorems.

    Prerequisite(s)


    MTH 153.

    Core

    Mathematics.

    Schedule Of Classes

  • MTH 280 - The Nature of Proof in Mathematics

    MTH 280 - The Nature of Proof in Mathematics

    3.00 credit hours

    The study of the nature of proof in mathematics. Students learn to find examples and counterexamples of abstractly defined objects and to generalize from those examples to conjecture theorems of their own. Specific proof techniques are taught within the context of subject matter chosen by the instructor.

    Prerequisite(s)


    MTH 152.

    Schedule Of Classes

  • MTH 300 - Linear Algebra

    MTH 300 - Linear Algebra

    3.00 credit hours

    Vector spaces, linear transformations, inner products, eigenvalues and eigenvectors, Gram-Schmidt process and orthogonal transformations.

    Prerequisite(s)


    MTH 153; MTH 280 recommended.

    Schedule Of Classes

  • MTH 375 - Problem Solving Seminar: Mathematics

    MTH 375 - Problem Solving Seminar: Mathematics

    1.00 credit hours

    An intensive seminar in problem solving, intended to provide participants with the ability to solve non-routine problems similar to those appearing in undergraduate mathematics journals and mathematics competitions such as the AMC 8/10/12, AIME and the William Lowell Putnam competition.

    Prerequisite(s)


    MTH 153 and MTH 280; or instructor consent.

    Schedule Of Classes

  • MTH 421 - Abstract Algebra I

    MTH 421 - Abstract Algebra I

    3.00 credit hours

    Elementary theory of rings, fields and groups, including modular arithmetic, polynomial rings, factorization, ideals and quotient rings, homomorphisms and subgroups.

    Prerequisite(s)


    MTH 280 and at least one 300-level mathematics course.

    Schedule Of Classes

  • MTH 461 - Real Analysis I

    MTH 461 - Real Analysis I

    3.00 credit hours

    Sets, functions, properties and elementary topology of the real number system. Rigorous analysis of limits, sequences, series, continuity, differentiation and integration theory.

    Prerequisite(s)


    MTH 280 and at least one 300-level mathematics course; MTH 290 strongly recommended.

    Schedule Of Classes

  • MTH 490 - Seminar

    MTH 490 - Seminar

    3.00 credit hours

    Exploration of topics not included in other mathematics courses. Specific topics are determined by the interest of the students and faculty. Repeatable with different topic.

    Prerequisite(s)


    MTH 421 or MTH 461 or consent of instructor.

    Schedule Of Classes

Electives

Select one group:

Group One

At least four of the following courses:

  • MTH 305 - College Geometry

    MTH 305 - College Geometry

    3.00 credit hours

    Euclidean and non-Euclidean geometry in two and three dimensions. Axiomatics and the nature of proof. Required for supplemental secondary education majors in mathematics.

    Prerequisite(s)


    MTH 280.

    Schedule Of Classes

  • MTH 310 - History of Mathematics

    MTH 310 - History of Mathematics

    3.00 credit hours

    An examination of the historical origins and genesis of important mathematical concepts from the ancient Greeks to modern times. Emphasis on the methodologies and philosophies of those involved in the creative process. Required for supplemental secondary education majors in mathematics.

    Prerequisite(s)


    MTH 153.

    Schedule Of Classes

  • MTH 315 - Ordinary Differential Equations with Applications

    MTH 315 - Ordinary Differential Equations with Applications

    3.00 credit hours

    First and second order differential equations; algebraic, numerical and graphical solutions; series solutions; Laplace transforms; applications.

    Prerequisite(s)


    MTH 254; MTH 300 strongly recommended.

    Schedule Of Classes

  • MTH 323 - Complex Variables

    MTH 323 - Complex Variables

    3.00 credit hours

    Algebra, geometry and calculus with complex numbers. Transformations of the complex plane, analytic functions, Cauchy theory of integration, power series and residue theory.

    Prerequisite(s)


    MTH 254.

    Schedule Of Classes

  • MTH 341 - Probability and Statistics I

    MTH 341 - Probability and Statistics I

    3.00 credit hours

    Basic laws of probability, discrete distributions, random variables, mathematical expectation, moment generating functions, Chebyshev's inequality and Markov chains.

    Prerequisite(s)


    MTH 254.

    Schedule Of Classes

  • MTH 342 - Probability and Statistics II

    MTH 342 - Probability and Statistics II

    3.00 credit hours

    A continuation of MTH 341 to include continuous distributions, central limit theorem, estimations, hypothesis testing and applications.

    Prerequisite(s)


    MTH 341.

    Schedule Of Classes

  • MTH 355 - Applied Mathematical Techniques

    MTH 355 - Applied Mathematical Techniques

    3.00 credit hours

    Topics in applied mathematics, including series solutions, systems of linear and nonlinear differential equations, integral transforms (Fourier or Laplace transforms), Fourier series, partial differential equations and a survey of applications from the physical sciences, life sciences and economics.

    Prerequisite(s)


    MTH 254 and MTH 256; or MTH 315.

    Schedule Of Classes

  • MTH 422 - Abstract Algebra II

    MTH 422 - Abstract Algebra II

    3.00 credit hours

    Advanced theory of rings, fields and groups, including symmetric and alternating groups, structure theorems for finite abelian groups, principal ideal domains, unique factorization domains, the field of quotients of an integral domain, vector spaces, extension fields, finite fields and the Galois Theory.

    Prerequisite(s)


    MTH 421.

    Schedule Of Classes

  • MTH 462 - Real Analysis II

    MTH 462 - Real Analysis II

    3.00 credit hours

    A continuation of the topics from MTH 461.

    Prerequisite(s)


    MTH 300 and MTH 461.

    Schedule Of Classes

  • MTH 473 - Topology

    MTH 473 - Topology

    3.00 credit hours

    Set theory, metric spaces, general topological spaces, continuous functions, connectedness, compactness, separation axioms and metrization.

    Prerequisite(s)


    MTH 254, MTH 280 and MTH 300.

    Schedule Of Classes

Group Two

Required for Secondary Education Supplemental majors. Mathematics major (B.A.) with Secondary Education Supplemental major: A typical student will need over 120 total credit hours to complete this degree.

  • MTH 305 - College Geometry

    MTH 305 - College Geometry

    3.00 credit hours

    Euclidean and non-Euclidean geometry in two and three dimensions. Axiomatics and the nature of proof. Required for supplemental secondary education majors in mathematics.

    Prerequisite(s)


    MTH 280.

    Schedule Of Classes

  • MTH 310 - History of Mathematics

    MTH 310 - History of Mathematics

    3.00 credit hours

    An examination of the historical origins and genesis of important mathematical concepts from the ancient Greeks to modern times. Emphasis on the methodologies and philosophies of those involved in the creative process. Required for supplemental secondary education majors in mathematics.

    Prerequisite(s)


    MTH 153.

    Schedule Of Classes

  • MTH 341 - Probability and Statistics I

    MTH 341 - Probability and Statistics I

    3.00 credit hours

    Basic laws of probability, discrete distributions, random variables, mathematical expectation, moment generating functions, Chebyshev's inequality and Markov chains.

    Prerequisite(s)


    MTH 254.

    Schedule Of Classes

  • MTH 342 - Probability and Statistics II

    MTH 342 - Probability and Statistics II

    3.00 credit hours

    A continuation of MTH 341 to include continuous distributions, central limit theorem, estimations, hypothesis testing and applications.

    Prerequisite(s)


    MTH 341.

    Schedule Of Classes

    • Completion of the Supplemental Secondary Education major. 

Recommended

Students intending to go to graduate school in mathematics are strongly encouraged to take MTH 323, MTH 422, MTH 462 and MTH 473.

Typical Course Sequence

Assumes the student has the necessary prerequisites.

  FALL WINTER SPRING
FIRST YEAR:
  • MTH 140 or MTH 151
  • MTH 141 or MTH 152 
  • MTH 152 or MTH 153 
SECOND YEAR:
  • MTH 153 or MTH 254 
  • MTH 280 
  • MTH 254 or MTH 341 
  • MTH 300 
  • MTH 342 
     

 

Mathematics, B.S.

For additional programs and courses in this department, see Mathematics.

Major Requirements

At least 44 credit hours in mathematics, including:

  • MTH 141 - Integrated Calculus II: Calculus of Derivatives -or-

    MTH 141 - Integrated Calculus II: Calculus of Derivatives

    3.00 credit hours

    An integrated calculus course which combines the study of exponential, logarithmic and inverse trigonometric functions with a formal development of the derivative. Students may not receive credit for MTH 141 and any of the following: MTH 122, MTH 130 or MTH 151.

    Prerequisite(s)


    MTH 140.

    Core

    Mathematics.

    Schedule Of Classes

  • MTH 151 - Calculus I

    MTH 151 - Calculus I

    3.00 credit hours

    Fundamental concepts of calculus including limits, continuity and differentiation with applications. The Calculus I, II and III sequence is recommended for students in science as well as for students in other divisions desiring a strong preparation in mathematics. Students may not receive credit for MTH 151 and any of the following: MTH 130, MTH 140 or MTH 141.

    Prerequisite(s)


    MTH 121 and MTH 122; or four years high school math including algebra, geometry and trigonometry.

    Core

    Mathematics.
    IAI

    M1 900

    Schedule Of Classes

  • MTH 152 - Calculus II

    MTH 152 - Calculus II

    3.00 credit hours

    Continuation of Calculus I with emphasis on integration and its applications. Required for the B.S. degree in any department.

    Prerequisite(s)


    MTH 141 or MTH 151.

    Core

    Mathematics.
    IAI

    M1 900

    Schedule Of Classes

  • MTH 153 - Calculus III

    MTH 153 - Calculus III

    3.00 credit hours

    Continuation of Calculus II with an emphasis on infinite series.

    Prerequisite(s)


    MTH 152.

    Core

    Mathematics.
    IAI

    M1 900

    Schedule Of Classes

  • MTH 254 - Calculus IV

    MTH 254 - Calculus IV

    3.00 credit hours

    Functions of two or more variables, partial derivatives, multiple integrals and line integrals. Vector analysis, divergence and Stokes's theorems.

    Prerequisite(s)


    MTH 153.

    Core

    Mathematics.

    Schedule Of Classes

  • MTH 280 - The Nature of Proof in Mathematics

    MTH 280 - The Nature of Proof in Mathematics

    3.00 credit hours

    The study of the nature of proof in mathematics. Students learn to find examples and counterexamples of abstractly defined objects and to generalize from those examples to conjecture theorems of their own. Specific proof techniques are taught within the context of subject matter chosen by the instructor.

    Prerequisite(s)


    MTH 152.

    Schedule Of Classes

  • MTH 300 - Linear Algebra

    MTH 300 - Linear Algebra

    3.00 credit hours

    Vector spaces, linear transformations, inner products, eigenvalues and eigenvectors, Gram-Schmidt process and orthogonal transformations.

    Prerequisite(s)


    MTH 153; MTH 280 recommended.

    Schedule Of Classes

  • MTH 323 - Complex Variables

    MTH 323 - Complex Variables

    3.00 credit hours

    Algebra, geometry and calculus with complex numbers. Transformations of the complex plane, analytic functions, Cauchy theory of integration, power series and residue theory.

    Prerequisite(s)


    MTH 254.

    Schedule Of Classes

  • MTH 375 - Problem Solving Seminar: Mathematics (must be taken twice)

    MTH 375 - Problem Solving Seminar: Mathematics

    1.00 credit hours

    An intensive seminar in problem solving, intended to provide participants with the ability to solve non-routine problems similar to those appearing in undergraduate mathematics journals and mathematics competitions such as the AMC 8/10/12, AIME and the William Lowell Putnam competition.

    Prerequisite(s)


    MTH 153 and MTH 280; or instructor consent.

    Schedule Of Classes

  • MTH 421 - Abstract Algebra I

    MTH 421 - Abstract Algebra I

    3.00 credit hours

    Elementary theory of rings, fields and groups, including modular arithmetic, polynomial rings, factorization, ideals and quotient rings, homomorphisms and subgroups.

    Prerequisite(s)


    MTH 280 and at least one 300-level mathematics course.

    Schedule Of Classes

  • MTH 461 - Real Analysis I

    MTH 461 - Real Analysis I

    3.00 credit hours

    Sets, functions, properties and elementary topology of the real number system. Rigorous analysis of limits, sequences, series, continuity, differentiation and integration theory.

    Prerequisite(s)


    MTH 280 and at least one 300-level mathematics course; MTH 290 strongly recommended.

    Schedule Of Classes

  • MTH 490 - Seminar

    MTH 490 - Seminar

    3.00 credit hours

    Exploration of topics not included in other mathematics courses. Specific topics are determined by the interest of the students and faculty. Repeatable with different topic.

    Prerequisite(s)


    MTH 421 or MTH 461 or consent of instructor.

    Schedule Of Classes

Electives

At least two of the following:
  • MTH 422 - Abstract Algebra II

    MTH 422 - Abstract Algebra II

    3.00 credit hours

    Advanced theory of rings, fields and groups, including symmetric and alternating groups, structure theorems for finite abelian groups, principal ideal domains, unique factorization domains, the field of quotients of an integral domain, vector spaces, extension fields, finite fields and the Galois Theory.

    Prerequisite(s)


    MTH 421.

    Schedule Of Classes

  • MTH 462 - Real Analysis II

    MTH 462 - Real Analysis II

    3.00 credit hours

    A continuation of the topics from MTH 461.

    Prerequisite(s)


    MTH 300 and MTH 461.

    Schedule Of Classes

  • MTH 473 - Topology

    MTH 473 - Topology

    3.00 credit hours

    Set theory, metric spaces, general topological spaces, continuous functions, connectedness, compactness, separation axioms and metrization.

    Prerequisite(s)


    MTH 254, MTH 280 and MTH 300.

    Schedule Of Classes

At least one pair from the following:
  • MTH 341 - Probability and Statistics I

    MTH 341 - Probability and Statistics I

    3.00 credit hours

    Basic laws of probability, discrete distributions, random variables, mathematical expectation, moment generating functions, Chebyshev's inequality and Markov chains.

    Prerequisite(s)


    MTH 254.

    Schedule Of Classes

  • MTH 342 - Probability and Statistics II

    MTH 342 - Probability and Statistics II

    3.00 credit hours

    A continuation of MTH 341 to include continuous distributions, central limit theorem, estimations, hypothesis testing and applications.

    Prerequisite(s)


    MTH 341.

    Schedule Of Classes

  • -or-

  • MTH 315 - Ordinary Differential Equations with Applications

    MTH 315 - Ordinary Differential Equations with Applications

    3.00 credit hours

    First and second order differential equations; algebraic, numerical and graphical solutions; series solutions; Laplace transforms; applications.

    Prerequisite(s)


    MTH 254; MTH 300 strongly recommended.

    Schedule Of Classes

  • MTH 355 - Applied Mathematical Techniques

    MTH 355 - Applied Mathematical Techniques

    3.00 credit hours

    Topics in applied mathematics, including series solutions, systems of linear and nonlinear differential equations, integral transforms (Fourier or Laplace transforms), Fourier series, partial differential equations and a survey of applications from the physical sciences, life sciences and economics.

    Prerequisite(s)


    MTH 254 and MTH 256; or MTH 315.

    Schedule Of Classes

Required Support for the B.S. Degree

  • At least nine hours in computer science (except CSC 230 and CSC 231)
  • A major/minor from the departments of BiologyChemistry/Physics, Computer Science or Economics, a major/minor in Finance, a major/minor that has been approved by the Chair of the Mathematics Department or completion of the requirements for the Supplemental Secondary Education major

Recommended

Students intending to go to graduate school in mathematics are strongly encouraged to take MTH 422, MTH 462 and MTH 473.

Typical Course Sequence

Assumes the student has the necessary prerequisites.

  FALL WINTER SPRING
FIRST YEAR:
  • MTH 140 or MTH 151
  • MTH 141 or MTH 152 
  • MTH 152 or MTH 153 
SECOND YEAR:
  • MTH 153 or MTH 254 
  • MTH 280 
  • MTH 254 or MTH 341 
  • MTH 300 
  • MTH 342 
     

 

Mathematics Minor

For additional programs and courses in this department, see Mathematics.

Minor Requirements

At least 21 credit hours, including:

  • MTH 141 - Integrated Calculus II: Calculus of Derivatives -or-

    MTH 141 - Integrated Calculus II: Calculus of Derivatives

    3.00 credit hours

    An integrated calculus course which combines the study of exponential, logarithmic and inverse trigonometric functions with a formal development of the derivative. Students may not receive credit for MTH 141 and any of the following: MTH 122, MTH 130 or MTH 151.

    Prerequisite(s)


    MTH 140.

    Core

    Mathematics.

    Schedule Of Classes

  • MTH 151 - Calculus I

    MTH 151 - Calculus I

    3.00 credit hours

    Fundamental concepts of calculus including limits, continuity and differentiation with applications. The Calculus I, II and III sequence is recommended for students in science as well as for students in other divisions desiring a strong preparation in mathematics. Students may not receive credit for MTH 151 and any of the following: MTH 130, MTH 140 or MTH 141.

    Prerequisite(s)


    MTH 121 and MTH 122; or four years high school math including algebra, geometry and trigonometry.

    Core

    Mathematics.
    IAI

    M1 900

    Schedule Of Classes

  • MTH 152 - Calculus II

    MTH 152 - Calculus II

    3.00 credit hours

    Continuation of Calculus I with emphasis on integration and its applications. Required for the B.S. degree in any department.

    Prerequisite(s)


    MTH 141 or MTH 151.

    Core

    Mathematics.
    IAI

    M1 900

    Schedule Of Classes

  • MTH 153 - Calculus III

    MTH 153 - Calculus III

    3.00 credit hours

    Continuation of Calculus II with an emphasis on infinite series.

    Prerequisite(s)


    MTH 152.

    Core

    Mathematics.
    IAI

    M1 900

    Schedule Of Classes

  • MTH 254 - Calculus IV

    MTH 254 - Calculus IV

    3.00 credit hours

    Functions of two or more variables, partial derivatives, multiple integrals and line integrals. Vector analysis, divergence and Stokes's theorems.

    Prerequisite(s)


    MTH 153.

    Core

    Mathematics.

    Schedule Of Classes

  • MTH 300 - Linear Algebra

    MTH 300 - Linear Algebra

    3.00 credit hours

    Vector spaces, linear transformations, inner products, eigenvalues and eigenvectors, Gram-Schmidt process and orthogonal transformations.

    Prerequisite(s)


    MTH 153; MTH 280 recommended.

    Schedule Of Classes

  • MTH 315 - Ordinary Differential Equations with Applications

    MTH 315 - Ordinary Differential Equations with Applications

    3.00 credit hours

    First and second order differential equations; algebraic, numerical and graphical solutions; series solutions; Laplace transforms; applications.

    Prerequisite(s)


    MTH 254; MTH 300 strongly recommended.

    Schedule Of Classes

Elective

Three credit hours from one of the following:

  • 300-level or higher mathematics course
  • 400-level course or independent study project in another discipline*

*This course or independent study project must involve significant applications of mathematics (such as ECN 440, ECN 445PHY 441); other options must be approved by the chair of the mathematics department before the end of the junior year.

Mathematics Internships and Jobs

A North Central education integrates career preparation with rich academic study. Our faculty encourages you to refine and apply your knowledge in an interconnected world. Here you'll learn to think independently and work globally to solve problems and lead.

Internships

  • Intern, Reinhart & Associates, Naperville
  • Mathematics in business intern, All Information Services, Countryside, IL
  • Program intern, Navistar Inc., Downers Grove, IL
  • Software tester, BondWave LLC, Wheaton, IL
  • Billing management intern, AMC Accounting Solutions, Naperville

Graduate Schools

Recent graduates in mathematics have been accepted at:

  • University of Wisconsin-Madison
  • University of Wisconsin-Milwaukee
  • Purdue University
  • University of Notre Dame
  • University of Illinois-Chicago
  • University of Texas-Arlington
  • University of Iowa
  • Purdue University

Careers

Math majors frequently find teaching positions in districts within a 30-mile radius of North Central, like:

  • Aurora school districts
  • Chicago Public Schools
  • East Aurora School District 131
  • Naperville School District 203
  • Indian Prairie School District 204
  • Plainfield School District 202

Recent graduates in mathematics also include:

  • Algorithm analyst
  • Software engineer
  • Computer scientist
  • Financial consultant
  • Commercial loan officer
     

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