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

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

Courses | |
---|---|

MATH 105 Calculus I | 5 hours |

MATH 106 Calculus II | 5 hours |

MATH 111 Introduction to Higher Mathematics | 3 hours |

MATH 204 Calculus III | 4 hours |

MATH 206 Mathematical Statistics I | 3 hours |

MATH 210 Linear Algebra | 3 hours |

MATH 212 Numerical Analysis or MATH 227 Mathematical Modeling |
3 hours |

MATH 230 Abstract Algebra I | 3 hours |

MATH 235 Mathematical Problem Solving | 1 hour |

MATH 240 Real Analysis | 3 hours |

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

MATH 299 Mathematics Seminar |

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

- Take MATH 221 Geometry rather than MATH 240 Real Analysis.
- Take EDUC 287 Supervised Teaching in the Secondary School rather than MATH 299 Mathematics Seminar.
- May use MATH 240 Real Analysis or MATH 299 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 040 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 and computer science majors, 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 030 Introduction to Computational Problem Solving or permission of the instructor. *

(Normally offered each 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): Appropriate placement score or grade of "C" or better in MATH 050 Pre-Calculus. *

(Normally offered each semester.)

A continuation of Mathematics 105. 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 department or grade of "C" or better in MATH 105 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 105 Calculus I.*

(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 106 Calculus II.*

(Normally offered each fall semester.)

Elementary mathematical theory and applications of basic probability to statistics. Topics studied include random variables, both discrete and continuous, and their probability distributions with applications of a practical nature to numerous fields. Also studied are multivariate probability distributions.

*Prerequisite(s): Grade of "C" or better in MATH 106 Calculus II. *

(Normally offered fall of even-numbered years.)

A continuation of MATH 206 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 206 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 106 Calculus II.*

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 106 Calculus II. *

(Normally offered each spring semester.)

An introduction to the numerical approximation of solutions of various types of problems. Topics include rootfinding, 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 106 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 111 Introduction to Higher Mathematics. *

(Normally offered fall of even-numbered years.)

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 106 Calculus II. *

(Normally offered each spring 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.

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

*Prerequisite(s): Grades of "C" or better in MATH 111 Introduction to Higher Mathematics and any 200-level mathematics course.*

(Normally offered fall of even-numbered years.)

A continuation of MATH 230 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 230 Abstract Algebra I.*

A seminar on problem solving skills and their application to nontrivial problems. Students will be required to take the Putnam Exam. May be repeated.

*Prerequisite(s): Grade of "C" or better in MATH-111 or permission of the instructor. *

(Normally offered each fall semester.)

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 111 Introduction to Higher Mathematics and MATH 204 Calculus III.*

(Normally offered spring of even-numbered years.)

Further study of a topic selected by the department, the selection based partially upon student demand. The title, content, and credit hours will be determined by current mutual interests of faculty and students. Possible topics include complex analysis, measure theory, topology, logic and set theory, advanced modeling, algebraic number theory, group theory and ring theory.

A study of special interest topics in mathematics. The student will study independently under the supervision of a faculty member and present their work in oral and written form. As a culmination of the course, the student will write an in-depth paper of a research or expository nature.

*Prerequisite(s): Major in mathematics, senior standing, grade of "C" or better in either MATH 230 Abstract Algebra I or MATH 240 Real Analysis, and permission of the instructor.*

(Normally offered each spring semester.)

If you do not find the information you need, please contact the Registrar’s Office:

402.465.2243

The online version of the Nebraska Wesleyan University catalog supersedes any printed catalog or PDF version as the official catalog of NWU. NWU reserves the right to make changes in the regulations and offerings announced in this official online version, as circumstances require. It is expected that the only changes will be the correction of errors and the inclusion of new courses and programs approved during the academic year.