MATHEMATICS MAJOR
39 Credits
The mathematics program provides students with a broad foundation in mathematical knowledge, applications, and aesthetics for the purpose of preparation for careers, graduate school, and personal enrichment.
Students pursuing either a BA or BS in mathematics must complete the common major requirements as well as an area of emphasis chosen from one of the areas below. In addition, it is recommended that students complete PH 330 Critical Thinking, which fulfills a General Education Requirement.
Common Major Requirements (27 Credits):
MA 175 Calculus I 4 cr.
MA 176 Calculus II 4 cr.
MA 277 Calculus III 3 cr.
MA 280 Differential Equations I 3 cr.
MA 330 Modern Geometry 3 cr
MA 331 Linear Algebra and Matrix Theory 3 cr.
MA 332 Introduction to Discrete Mathematics 3 cr.
MA 432 Modern Algebra 3 cr
MA 481 Coordinating Seminar 1 cr.
I. Preprofessional Mathematics Emphasis (39 Credits):
MA 363 Numerical Analysis I 3 cr.
MA 410 Differential Equations II 3 cr.
MA 452 Discrete Structures 3 cr.
Plus one elective 300 level and above
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AREA OF CONCENTRATION IN
MATHEMATICS FOR ADOLESCENT TO
YOUNG ADULT LICENSE (GR. 7-12)
39 Credits
Common Major Requirements plus the following:
MA 221 Statistics I 3 cr.
MA 310 Number Theory 3 cr.
Two upper-biennium math electives 6 cr.
See EDUCATION for Professional Education Requirements.
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AREA OF CONCENTRATION IN
MATHEMATICS FOR MIDDLE
CHILDHOOD LICENSE (GR. 4 - 9)
15 Credits
Requirements:
MA 120 Pre-Calculus 3 cr.
MA 130 Elementary Number Theory 3 cr.
MA 131 Geometry, Probability and Statistics from an elementary point of view 3 cr.
MA 221 Statistics I 3 cr.
MA 330 Geometry 3 cr.
See EDUCATION for Professional Education Requirements.
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MATHEMATICS MINOR
23 Credits
Requirements:
MA 175 Calculus I 4 cr.
MA 176 Calculus II 4 cr.
MA 277 Calculus III 3 cr.
MA 330 Modern Geometry 3 cr.
MA 331 Linear Algebra and Matrix Theory 3 cr.
Plus two electives (one at 200-level and one at 300/400-level) 3 cr.
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MATHEMATICS PLACEMENT TEST
A student who intends to register for any of the following courses is required to have successfully completed the prerequisite for that course within two years prior to registration or to have demonstrated proficiency by taking a mathematics placement test within two years prior to registration.
| MA 100 |
MA 130 |
MA 221 |
| MA 110 |
MA 131 |
MA 330 |
| MA 120 |
MA 175 |
|
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BINARY PROGRAM IN ENGINEERING
Students who are interested in pursuing a career in engineering may enter the Binary Program in Engineering. Students who major in mathematics or science at Notre Dame College can apply for admission to a binary program at Case Western Reserve University. The application should be made during the sophomore year so that course arrangements can be made by the beginning of the junior year. However, a freshman entering Notre Dame College should make known to the academic advisor the intent to enter the binary program.
At the conclusion of the engineering degree requirements, the student will receive a BS degree from Notre Dame College and a BS degree from the School of Engineering, Case Western Reserve University. The program takes a minimum of five years.
Students who wish to pursue engineering after graduation can do this with an undergraduate major in chemistry or mathematics. During the sophomore year the student should know the program requirements of the planned graduate school so that the appropriate course electives can be chosen.
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COURSE OFFERINGS
MA 100 and 110 are developmental courses, do not count toward the 128 credit hours required for graduation, and do not fulfill the General Education Requirement. All courses beyond the developmental series count toward the 128 credit hours required for graduation and fulfill the General Education Requirement.
MA 100 Introductory Algebra 3 cr.
Sets, real numbers, basic algebraic operations and polynomial arithmetic, factoring, linear equations and inequalities, rectangular coordinate systems, solution of linear systems, algebraic fractions, exponents and radicals, solution of quadratic equations and applications. (Placement test required)
MA 110 Intermediate Algebra 3 cr.
Algebraic operations, solving equations and inequalities, lines, inequalities and their graphs, introduction to conic sections, introduction to functions, exponential and logarithmic functions, systems of equations, problem solving techniques and applications. Prerequisite: MA 100 or both of the following: one unit of high school algebra and one unit of high school geometry. (Placement test required)
MA 120 Precalculus Mathematics 3 cr.
Functions, exponential and logarithmic functions, trigonometric functions and their inverses, identities, equations and applications and analytic geometry. Prerequisite: MA 110 or equivalent. (Placement test required)
MA 130 Elementary Number Theory 3 cr.
General preparation in mathematics for elementary educators. Set theory, problem solving strategies, pattern recognition, numeration systems, number theory, properties of and operations with real numbers Prerequisite: MA 110 or equivalent. (Placement test required)
MA 131 Geometry, Probability and Statistics from an Elementary Point of View 3 cr.
General preparation in mathematics for elementary educators. Geometry with emphasis on shapes and measurement, transformational geometry and symmetry, logic, counting methods, permutations and combinations, an introduction to probability and statistics. Prerequisite: MA 110 or equivalent. (Placement test required)
MA 175 Calculus I 4 cr.
Review of functions and graphs, limits and continuous functions, the derivative, differentiation of algebraic and transcendental functions, applications, anti-derivatives, definite integrals and applications. Prerequisite: MA 120 or equivalent. (Placement test required)
MA 176 Calculus II 4 cr.
Continuation of 175. The definite integral, computation of anti-derivatives, techniques of integration, the Fundamental Theorem of Calculus, applications, plane curves and polar coordinates. Prerequisite: MA 175.
MA 191, 192 Selected Topic 1-3 cr.
MA 220 Applied Finite Mathematics 3 cr.
Introduction to mathematical modeling, usage and arithmetic of matrices, linear programming, counting techniques, probability, Markov processes and the mathematics of finance. Prerequisite: MA 110 or equivalent. (Placement test required)
MA 221 Statistics I 3 cr.
Descriptive statistics, probability, normal and binomial distributions, sampling concepts, sampling distribution, estimation, hypothesis testing, confidence intervals and linear correlation. Prerequisite: MA 110 or equivalent. (Placement test required)
MA 277 Calculus III 3 cr.
Continuation of MA 176. Sequences, series, Taylor series, multivariable calculus, analytic geometry in R3, partial derivatives, applications of the derivative, multiple integrals, applications of multiple integrals, vector functions and their derivatives. Prerequisite: MA 176.
MA 280 Differential Equations I 3 cr.
First-order equations and applications, higher-order linear equations, linear systems, series solution of linear equations, LaPlace transform solution of linear equations and introduction to numerical methods of solution. Prerequisite: MA 277.
MA 300 Statistics II 3 cr.
Continuation of estimation and hypothesis testing, correlation, simple and multiple regression, inferences on variances and proportions, analysis of variance (ANOVA), nonparametric tests, index numbers, time series and introduction to decision theory. Prerequisite: EC/MA/PY 221.
MA 310 Number Theory 3 cr.
Divisibility properties of integers, prime numbers, linear and quadratic congruences, Diophantine equations, special number theory functions and quadratic residue theory. Corequisite: MA 332.
MA 330 Modern Geometry 3 cr.
Axiomatic foundations to Euclidean and non-Euclidean geometries and contemporary approaches to the study of geometry. Prerequisite: MA 120 or equivalent. (Placement test required)
MA 331 Linear Algebra and Matrix Theory 3 cr.
Algebra of matrices, systems of linear equations, Gauss- Jordan reduction, inverses, discriminants, eigen values, linear spaces and subspaces, spanning sets, linear independence, basis, null space, change of basis, orthogonal bases, linear transformations, matrix representation and composition of transformation. Prerequisite: MA 176 or MA 120 with departmental approval, or MA 220 with department approval.
MA 332 Introduction to Discrete Mathematics 3 cr.
Logic and set theory, proof techniques, relations and functions, algorithms, elementary properties of integers, counting techniques and probability. Prerequisite: MA 175 or MA 120 with department approval or MA 220 with department approval.
MA 350 Math History 3 cr.
A study of algebra, number theory, irrational numbers, analytical geometry, the Calculus, non-Euclidean geometries and infinite sets from an historical perspective. Prerequisite: MA 120.
MA 363 Numerical Analysis I 3 cr.
Theory and techniques of numerical computation, interpolation by Lagrange and difference methods, numerical differentiation and integration and numerical solution of differential equations. Prerequisites: MA 176.
MA 391, 392 Selected Topics
MA 410 Differential Equations II 3 cr.
Infinite series, complex variables, vector analysis, Fourier series, curvilinear coordinates and partial differential equations. Prerequisite: MA 280.
MA 432 Modern Algebra 3 cr.
Groups, rings, fields, normal subgroups, congruence, quotient groups, ideals, quotient rings, equivalence relations, abstract algebraic structures. Prerequisite: MA 332 (or corequisite).
MA 452 Discrete Structures 3 cr.
Graph theory, Boolean algebras, logic, networks, structures, morphisms and finite state machines. Prerequisite: MA 332.
MA 463 Numerical Analysis II 3 cr.
Matrix computations and solutions of linear equations, iterative solutions of systems of equations, computer methods of optimization and simulations. Prerequisites: MA 280.
MA 481 Coordinating Seminar 1 cr.
Special topics in mathematics are explored in an interdisciplinary format. Preparation of a research paper for public presentation is required. No prerequisite. Taken in final semester before graduation.
MA 491, 492 Independent Study 1-3 cr.
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