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Course Criteria
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3.00 Credits
This course covers basic ideas of matrix theory and linear algebra, including applications in mathematics and other disciplines. The course begins with systems of linear equations, then explores matrices and their relation to systems of linear equations. This includes elementary row operations, the arithmetic of matrices, inverting a matrix, special types of matrices, and the determinant of a matrix. Other topics covered are linear transformations, eigenvalues and eigenvectors. (Prerequisite: Math. 117 and sophomore standing, or permission of instructor.) Every fall.
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3.00 Credits
A study of the concepts from Calculus I and II in the multivariable case. This includes partial derivatives, multiple integrals, and vector calculus. The course makes extensive use of computer explorations and cooperative learning. (Prerequisite: Math. 118.) Every spring.
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3.00 Credits
An exploration of fundamental concepts involving natural numbers, integers, rational numbers, real numbers, and complex numbers, and their operations. We will examine field properties, cardinality issues, and ordering properties, with other topics as time allows. The course will emphasize conjecture and proof. Students will develop, write and present their proofs. (Prerequisite: Math. 118 and 120.) Every spring.
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3.00 Credits
The objective of the course is to introduce applications and solution methods for equations which include derivatives. Maple software will be used extensively. The following topics will be covered: basic definitions and terminology; direction fields, phase portraits; first-order differential equations; modeling with first-order differential equations; higher-order differential equations; modeling with initial-value problems and boundary-value problems; the Laplace transform; the Dirac delta function; systems of first-order differential equations; numerical solution of ordinary differential equations. (Prerequisite: Math. 118.) Fall, odd years.
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3.00 Credits
A survey of topics in advanced geometry from three historical perspectives: synthetic, analytic, and transformational. Topics include advanced results in Euclidean geometry, axiomatics of Euclidean geometry, axioms and results in non-Euclidean geometry, an introduction to projective geometry, the use of coordinates, and insights gained from transformations. (Prerequisite: Math. 215 or permission of the instructor.) Every spring.
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3.00 Credits
This class is an introduction to topology and as such includes both general and point-set topology. General topology topics may include Euler characteristic, classification of orientable 2-manifolds, and knot theory. Point-set topology topics may include different topological structures on the real line and plane making use of bases and subbases as an avenue for a study of connectedness, compactness, separation properties, and continuity. (Prerequisite: Math. 231 or permission of the instructor.) Spring, even years
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3.00 Credits
These courses will focus on the probability theory needed in mathematical statistics while helping to prepare students for the Actuarial Exams. Topics covered include combinatorics, the basic probability axioms and theorems, conditional probability, random variables and their probability distributions, expectation, conditional expectation, moments, moment generating functions, functions of random variables, and the Central Limit Theorem. Some special attention will be given to the connection between the various standard probability distributions so that they fit together as a whole. (Prerequisite for Math 118.) Every fall.
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3.00 Credits
This course will build on the probability theory from Math 314 to develop understanding of mathematical statistics. Topics covered include derivation and properties of point estimators through various techniques including method of moments and maximum likelihood, confidence intervals, general hypothesis testing, including tests for means and proportions and linear regression. Some time will also be spent on basic descriptive statistics. (Prerequisites: Math 314 and Math 216.) Every spring.
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3.00 Credits
Topics in graph theory, including circuits, coloring, trees and searching. Enumeration methods, including permutations and combinations, the inclusion-exclusion principle, generating functions and recurrence relations. (Prerequisite: Math. 118, 120, 215.) Fall, odd years.
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3.00 Credits
An examination of addition and multiplication, and how their properties resemble other operations in other settings. With a single operation the notion of group is available; adding a second operation extends this to rings and fields. Basic properties of groups, rings, and fields will be examined, including the Fundamental Theorem of Homomorphisms. Applications will be included as time allows. (Prerequisite: Math. 215 and 231.) Fall, even years.
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