North Central College - Naperville, IL

Mathematics Courses

NOTE: This page contains all of the regular course descriptions for this discipline or program. Academic credit for each course is noted in parenthesis after the course title. Prerequisites (if any) and the general education requirements, both Core and All-College Requirements (ACRs), which each course fulfills (if any) are noted following each course description. Not all courses are offered every year. Check Merlin, our searchable course schedule, to see which courses are being offered in upcoming terms.

MTH 095 Intermediate Algebra (3.00)
A standard course in intermediate algebra (high school Algebra II) covering equations, exponents and radicals, rational expressions, graphing, and logarithms. It is designed to prepare students for MTH 118 or 121. This course does not count toward a major or minor in mathematics. It does not count toward graduation. It does count toward full-time status.

MTH 106 Elementary Mathematics I - College Algebra (3.00)
College algebra for the prospective elementary teacher, to include linear, quadratic, and absolute value equations and inequalities; graphs and applications of linear, quadratic, rational, exponential and logarithmic functions; conic sections; and use of augmented matrices to solve systems of linear equations. Emphasis on both the procedural and conceptual nature of the material.

MTH 107 Elementary Mathematics II (3.00)
Essentials of mathematics for the prospective elementary teacher to include cognitive reasoning, sets, logic, and structure of arithmetic through the real numbers including numeration systems, percents, proportions, and number theory. Emphasis on problem solving techniques.

MTH 108 Elementary Mathematics III (3.00)
Continuing of MTH 107 to include Euclidean and transformational geometry, measurement and the metric system, basic algebra, probability, and applied statistics. Emphasis on problem solving. Core: Mathematics.

MTH 111 Quantitative Reasoning (3.00)
This course is designed to fulfill the general education core requirement in mathematics for students whose majors do not require specific skills in mathematics. The course focuses on mathematical reasoning and applications in today's world. Some of the following topics are covered in-depth: graph theory including optimal routes, planning and scheduling, statistics ad interpretation of data, and probability. Time permitting, other topics may be chosen at instructor's discretion. Core: Mathematics.

MTH 118 Finite Mathematics (3.00)
An introduction to the elements of finite mathematics for students in management and social sciences. Topics include linear and other functions, matrices, linear programming, probability, and logic. Core: Mathematics.

MTH 121 College Algebra (3.00)
This course covers the algebra skills needed for the study of calculus. Topics include linear, quadratic, and absolute value equations and inequalities; graphs of linear, quadratic, and rational functions; graphs, properties, and applications of exponential and logarithmic functions. Students may not receive credit for both MTH 121 and MTH 140.

MTH 122 College Trigonometry (3.00)
This course covers the topics in trigonometry and the theory of equations needed for the study of calculus. Topics include definitions and graphs of the trigonometric functions, solutions of triangles, conic sections, systems of equations, DeMoivre's theorem, and theory of equations. Students may not receive credit for both MTH 122 and MTH 141.

MTH 130 Calculus for Business and Social Sciences (3.00)
An introductory course in the elements of the differential and integral calculus, including applications in business and social sciences. To include: limits and continuity, differentiation and integration of algebraic functions, max/min theory, exponential functions and their calculus. Students may not receive credit for MTH 130 and either MTH 141 or MTH 151. This course does not prepare students for MTH 152. Core: Mathematics.

MTH 140 Integrated Calculus I: Calculus Limits (3.00)
An integrated calculus course which combines the study of algebraic, trigonometric and inverse trigonometric functions with a formal development of the limit. Credit not awarded for MTH 140 and MTH 121 or MTH

MTH 141 Integrated Calculus II: Calculus of Derivatives (3.00)
An integrated calculus course which combines the study of exponential and logarithmic functions with a formal development of the derivative. Credit not awarded for MTH 141 and MTH 122, MTH

MTH 151 Calculus I (3.00)
Fundamental concepts of calculus including limits, continuity, and differentiation with applications. The Calculus I, II, and III sequence is recommended for students in the Division of Science as well as for students in other divisions desiring a strong preparation in mathematics. MTH 152 is required for the B.S. degree in any department. Students may not receive credit for MTH 151 and MTH 130, MTH 140, or MTH 141. Core: Mathematics.

MTH 152 Calculus II (3.00)
Continuation of Calculus I with emphasis on integration and its applications. Required for the B.S. degree in any department. Core: Mathematics.

MTH 153 Calculus III (3.00)
Continuation of Calculus II with an emphasis on infinite series. Core: Mathematics.

MTH 230 Discrete Structures I (3.00)
Fundamental topics in mathematics and computer science including formal logic, proof techniques, sets, relations and functions, combinatorics, graphs, logic circuits, and finite state machines. Same as: CSC 230. Core: Mathematics.

MTH 231 Discrete Structures II (3.00)
A second course in discrete mathematics that introduces more advanced topics as well as covering some of the material introduced in CSC 230 in more depth. Topics include growth of functions and complexity of algorithms; number theory; recursive definitions and algorithms, proof techniques; program verification; discrete probability; finite state automata; and formal grammars and language recognizers. Hands-on labs allow students to apply one or more course topics to build practical working systems. Same as: CSC 231.

MTH 254 Calculus IV (3.00)
Functions of two or more variables, partial derivatives, multiple integrals, and line integrals. Vector analysis, divergence, and Stoke's theorems. Core: Mathematics.

MTH 280 The Nature of Proof in Mathematics (3.00)
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.

MTH 290 The Infinite and the Infinitesimal (1.50)
A rigorous investigation of topics from a variety of mathematical settings that involve the infinite and the infinitesimal. Topics include mathematical induction, fractals, limits, and cardinality.

MTH 297 Internship (0.00-9.00)
Instructor consent required.

MTH 299 Independent Study (1.00-9.00)
Instructor consent required.

MTH 300 Linear Algebra (3.00)
Vector spaces, linear transformations, bilinear forms, eigenvalues and eigenvectors, Gram-Schmit process, Jordan canonical form, orthogonal transformations.

MTH 305 College Geometry (3.00)
Euclidean and non-Euclidean geometry in two and three dimensions. Axiomatics and the nature of proof. Required for secondary education majors in mathematics.

MTH 310 History of Mathematics (3.00)
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 secondary education majors in mathematics.

MTH 315 Ordinary Differential Equations With Applications (3.00)
First and second order differential equations; algebraic, numerical, and graphical solutions; series solutions; Laplace transforms; applications. Students may not received credit for both MTH 256 and MTH 315.

MTH 323 Complex Variables (3.00)
Algebra, geometry, and calculus with complex numbers. Transformations of the complex plane, analytic functions, Cauchy theory of integration, power series, and residue theory.

MTH 341 Probability and Statistics I (3.00)
Basic laws of probability, discrete distributions, random variables, mathematical expectation, moment generating functions, Chebyshev's inequality, and Markov chains.

MTH 342 Probability and Statistics II (3.00)
A continuation of MTH 341 to include continuous distributions, central limit theorem, estimations, hypothesis testing, and applications.

MTH 355 Applied Mathematical Techniques (3.00)
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, the life sciences, and economics. Same as: PHY 355.

MTH 365 The Theory of Interest (3.00)
The study of compound interest and annuities; applications to problems in finance and actuarial science. Required for the major in actuarial science. Same as: FIN 365.

MTH 375 Problem Solving Seminar: Mathematics (1.00)
An intensive seminar in problem solving. Intended to provide participants with the ability to solve non-routine problems. Useful preparation for mathematics competitions.

MTH 376 Problem Solving Seminar: Actuarial Science (1.00)
An intensive seminar in problem solving, intended to provide participants with the ability to solve non-routine problems in insurance-related and/or financial/investment mathematics.

MTH 397 Internship (0.00-9.00)
Instructor consent required.

MTH 399 Independent Study (1.00-9.00)
Instructor consent required.

MTH 421 Abstract Algebra I (3.00)
Elementary theory of rings, fields, and groups, including modular arithmetic, polynomial rings, factorization, ideals and quotient rings, homomorphisms, and subgroups.

MTH 422 Abstract Algebra II (3.00)
Advanced theory of rings, fields, and groups, including symmetric and alternating groups, structure theorems for finite abelian groups, principle ideal domains, unique factorization domains, the field of quotients of an integral domain, vector spaces, extension fields, finite fields, and Galois Theory.

MTH 461 Real Analysis I (3.00)
Sets, functions, properties and elementary topology of the real number system. Rigorous analysis of limits, sequences, series, continuity, differentiation, and the Riemann integral.

MTH 462 Real Analysis II (3.00)
A continuation of the topics from MTH 461.

MTH 473 Topology (3.00)
Set theory, metric spaces, general topological spaces, continuous functions, connectedness, compactness, separation axioms, and metrization.

MTH 490 Seminar (3.00)
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.

MTH 497 Internship (0.00-9.00)
Instructor consent required.

MTH 499 Independent Study (1.00-3.00)
Instructor consent required.