# Mathematics (B.A., B.S.)

# Major: Mathematics (B.A., B.S.)

Courses | |
---|---|

MATH 1600 Calculus I | 5 hours |

MATH 1610 Calculus II | 5 hours |

MATH 2200 Introduction to Higher Mathematics | 3 hours |

MATH 2600 Calculus III | 4 hours |

MATH 3200 Linear Algebra | 3 hours |

MATH 3300 Mathematical Statistics I | 3 hours |

MATH 3600 Mathematical Problem Solving | 1 hour |

MATH 3750 Numerical Analysis or MATH 3700 Mathematical Modeling |
3 hours |

MATH 4200 Abstract Algebra I | 3 hours |

MATH 4300 Real Analysis | 3 hours |

Senior Comprehensive: | 3 hours |
---|---|

MATH 4980 Mathematics Seminar | 3 hours |

Students seeking an education field endorsement in mathematics follow the above requirements with the following changes:

- Take MATH 3500 Geometry rather than MATH 4300 Real Analysis.
- Take EDUC 4870 Supervised Teaching in the Secondary School rather than MATH 4980 Mathematics Seminar.
- May use MATH 4300 Real Analysis or MATH 4980 Mathematics Seminar as part of the 3-4 hours of mathematics electives.

See the Nebraska Wesleyan University Department of Education for information regarding education courses required for teaching certification.

An approved supporting program of 20 hours that includes CMPSC 1500 Program Design is also required for all Mathematics majors. Cooperatively designed by the student and advisor, the supporting program may overlap with one or more minors or a second major.

For the mathematics major, the B.A. degree requires a minor from the humanities or arts, or more than 50 percent of the supporting program from these areas, while the B.S. degree requires a minor from the natural or social sciences, or more than 50 percent of the supporting program from these areas. Mathematics majors seeking an education endorsement whose supporting program consists of education courses will receive a B.S. degree.

A disciplined approach to the development of programs to solve problems on a computer. Topics include data types, control structures, abstraction, and software development. A lab component introduces a high-level programming language and software tools.

*Corequisite(s): CMPSC 1000 Introduction to Computational Problem Solving or permission of the instructor.*

(Normally offered each spring semester.)

Students work with one or more regular teachers in a secondary school. They attend the student teaching seminar and conference with their college supervisor as directed.

*Prerequisite(s): Completion of preliminary student teaching requirements or approval of the department chair.*

An introduction to calculus of a single variable. Topics include limits, continuity, differentiation, and beginning integration with applications. Assignments are given that help build proficiency in the use of a computer algebra system.

*Prerequisite(s): Math ACT score of at least 27 or a grade of "C" or better in MATH 1470 Trigonometry or MATH 1400 Pre-Calculus. *

(Normally offered each semester.)

A continuation of MATH 1600 Calculus I. Topics studied include integration techniques and applications, differential equations, numerical approximations, sequences and series, and vectors. Assignments are given that help build proficiency in the use of a computer algebra system.

*Prerequisite(s): Permission of the department chair or grade of "C" or better in MATH 1600 Calculus I. *

(Normally offered each semester.)

A study of mathematical induction and other methods of proof, recursion, formal logic, and set theory.

*Prerequisite(s): Grade of "C" or better in MATH 1610 Calculus II or permission of the instructor. *

(Normally offered each spring semester.)

An introduction to multivariable calculus. Topics include vector-valued functions, functions of several variables, partial differentiation, multiple integrals, and analysis. Assignments are given that help build proficiency in the use of a computer algebra system.

*Prerequisite(s): Permission of department chair or grade of "C" or better in MATH 1610 Calculus II. *

(Normally offered each fall semester.)

See CMPSC-3000.

A study of ordinary differential equations. Topics include first and higher order, and linear and nonlinear differential equations with applications. Additional topics may be chosen from systems of differential equations, transform techniques, and numerical methods. Use will be made of a computer algebra system.

*Prerequisite(s): Grade of "C" or better in MATH 1610 Calculus II. *

(Normally offered each spring semester.)

A study of vector spaces, determinants, linear transformations, matrices, and matrix equations, and their applications in the natural and social sciences.

*Prerequisite(s): Grade of "C" or better in MATH 1610 Calculus II. *

(Normally offered each spring semester.)

An introduction to basic probability and statistics concepts with an emphasis on applications. Topics include descriptive statistics, axioms and calculations of probabilities, Bayes' Theorem, discrete and continuous probability distributions, joint probability distributions, estimation and hypothesis testing.

*Prerequisite(s): Grade of "C" or better in MATH 1610 Calculus II.*

(Normally offered fall of even-numbered years.)

A continuation of MATH 3300 Mathematical Statistics I, with further applications of probability theory to statistical problems of estimation and hypothesis testing, including least squares estimation and correlation. Also studied is analysis of variance with numerous applications of this technique.

*Prerequisite(s): Grade of "C" or better in MATH 3300 Mathematical Statistics I.*

A study of fundamental concepts in number theory, including divisibility and factorization of integers, linear and quadratic congruences, the quadratic reciprocity theorem, Diophantine equations, number-theoretic functions, and continued fractions. Additional topics may include Euler's theorem and cryptography, perfect numbers and Mersenne primes, Pythagorean triples, and Fermat's Last Theorem.

*Prerequisite(s): Grade of "C" or better in MATH 1610 Calculus II.*

Selected topics from Euclidean and non-Euclidean geometry, geometry as a mathematical structure, and geometry as a study of invariants of set transformations.

*Prerequisite(s): Grade of "C" or better in MATH 2200 Introduction to Higher Mathematics. *

(Normally offered fall of odd-numbered years.)

A seminar on problem solving skills and their application to nontrivial problems. May be repeated.

*Prerequisite(s): Grade of "C" or better in MATH 2200 Introduction to Higher Mathematics or permission of the instructor. *

(Normally offered each fall semester.)

A course that explores applications of mathematics to real-world problems. One or more topics may be chosen from the non-inclusive list: dynamical systems, linear programming, queueing theory, game theory, numerical analysis, wavelets, coding theory, and partial differential equations. Computer-based exercises will be a component of the course.

An introduction to the numerical approximation of solutions of various types of problems. Topics include root-finding, interpolation and numerical differentiation, and integration. Additional topics may be drawn from numerical solutions of ordinary differential equations and linear systems.

*Prerequisite(s): Grade of "C" or better in MATH 1610 Calculus II.*

(Normally offered fall of odd-numbered years.)

A topical course designed to investigate relevant subject matter not included in any standard courses. The title and the content will be determined by current mutual interests of students and faculty. This course may be offered to meet a requirement for a major only by approval of the department chair.

A study of various algebraic systems arising in modern mathematics, such as groups and rings.

*Prerequisite(s): Grades of "C" or better in MATH 2200 Introduction to Higher Mathematics and any 3000-level or 4000-level mathematics course. *

(Normally offered fall of even-numbered years.)

A continuation of MATH 4200 Abstract Algebra I. More study of groups, rings, and fields. Additional topics may be drawn from modules and finite fields.

*Prerequisite(s): Grade of "C" or better in MATH 4200 Abstract Algebra I.*

A formal approach to limits, continuity, differentiation, and integration with emphasis on the proofs of theorems. Additional topics may include topology, uniform continuity, and uniform convergence.

*Prerequisite(s): Grade of "C" or better in MATH 2200 Introduction to Higher Mathematics and MATH 2600 Calculus III. *

(Normally offered spring of even-numbered years.)

A topical course designed to investigate relevant subject matter not included in any standard courses. The title and the content will be determined by current mutual interests of students and faculty. This course may be offered to meet a requirement for a major only by approval of the department chair.

A study of topics of special interest in mathematics. Students will be required to make at least three presentations including individual study of a specific mathematics topic under the supervision of the faculty.

*Prerequisite(s): Major in mathematics, senior standing, grade of "C" or better in either MATH 4200 Abstract Algebra I or MATH 4300 Real Analysis, and permission of the instructor. *

(Normally offered each spring semester.)

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