University of Maine at Farmington 2008-2009 Catalog

Mathematics


  MAT 010 - Basic Math
Non-credit math/algebra review leading to MAT 011 or MAT 103M. (Pass/Fail only) Prerequisite(s): Placement test results or permission of instructor. Every semester.

Credit: 0

  MAT 011 - Basic Algebra
Non-credit algebra review leading to MAT 012, MAT 100M, MAT 120M. (Pass/Fail only) Prerequisite(s): Placement test results, MAT 010 or permission of instructor. Every semester.

Credit: 0

  MAT 012 - Intermediate Algebra
Non-credit intermediate algebra review leading to MAT 123M or MAT 132M. Prerequisite(s): Placement test results, MAT 011 or permission of instructor. (Pass/Fail only) Spring semester

Credit: 0

  MAT 100M - Introduction to Mathematics
Introduction to some of the important concepts and ideas of mathematics from the modern point of view. A course not intended for students in business, elementary education, nor those planning to pursue further courses in mathematics or science. Every semester.

Credit: 4

  MAT 103M - Mathematical Content for Elementary School Teachers I
This course is the first in a two-semester sequence which provides students with a deep conceptual understanding of fundamental mathematics.  Coverage of topics follows those outlined by the National Council of Teachers of Mathematics. Prerequisite(s): Two years of high school algebra and high school geometry. Every semester.

Credit: 4

  MAT 104M - Mathematical Content for Elementary Teachers II
This course is the second in a two-semester sequence which provides students with a deep conceptual understanding of fundamental mathematics and it builds on the mathematical concepts covered in MAT 103M. Prerequisite(s): MAT 103M. Every semester.

Credit: 4

  MAT 120M - Introductory Statistics
A general introductory course including descriptive statistics, basic probability, normal distributions, sampling distributions, confidence intervals, hypothesis testing for means and proportions, two-sample t-tests for means, Chi-Squared tests, regression and correlation. Prerequisite(s): Two years of high school algebra. Every semester.

Credit: 4

  MAT 123M - Mathematics for Economics and Business
Mathematical skills useful in business and economics classes are developed:  topics include lines, solving equations and systems of equations, exponential functions including the "Pert" formula, mathematics of finance, derivatives and integrals of polynomial and exponential functions, applications of derivatives and integrals. Prerequisite(s): Two years of high school mathematics or MAT 012; sophomore standing or permission of instructor. Every semester

Credit: 4

  MAT 132M - Precalculus
Rational, quadratic, trigonometric, logarithmic, and exponential functions are presented. Prerequisite(s): Three years of high school mathematics. Every semester

Credit: 4

  MAT 141M - Calculus I
Introduction to the basic concepts of limit, differentiation, and integration; study of their applications to problems in rates of change, extrema, and area between curves. Includes both rational and transcendental functions. Every semester.

Credit: 4

  MAT 142 - Calculus II
Continuation of the investigation of differentiation and integration begun in MAT 141M, examining techniques of integration, indeterminate forms, and infinite series including Taylor series. Applications studied will include volumes of solids of revolution and work. Prerequisite(s): MAT 141M with a grade of C- or better. Every spring.

Credit: 4

  MAT 151M - Foundations of Mathematics
This course considers the basic objects of mathematics and the methods used to elucidate their properties.  Predicate logic and the theory of sets, relations, functions and the natural numbers will be discussed.  The student will learn about proving properties of these objects. Prerequisite(s): At the very least three years of high school mathematics (two years of Algebra and one of Geometry.) Every semester.

Credit: 4

  MAT 197 - Independent Study in Mathematics
An opportunity to pursue selected topics under the supervision of a faculty member. Prerequisite(s): Four credit hours in mathematics and permission of instructor. Variable.

Credit: 1-4

  MAT 220M - Data Analysis

This course is intended for those majoring in mathematics, secondary mathematics education, or computer science. The course is designed to contain the content of AP statistics, but at the deeper level required for pre-service teachers. Topics covered include descriptive statistics, regression and correlation, sampling and experimentation, basic probability, normal distributions, sampling distributions, point estimation confidence intervals, hypothesis testing for means and proportions, two-sample t-tests for means, chi-squared tests, and possible other topics. Appropriate technology will be used. Students may not receive credit for both MAT 120M and MAT 220M. Prerequisite(s): MAT 141M or permission of instructor. Every year.



Credit: 4

  MAT 241 - Calculus III
Multivariable calculus including vectors; analytic geometry of planes, surfaces, and solids; functions of several variables and partial differentiation; multiple integrals; line and surface integrals; and Green's and Stokes' theorems. Prerequisite(s): MAT 142. Every fall.

Credit: 4

  MAT 251 - Linear Algebra
Introduction to linear algebra and its applications. Topics may include matrix operations, systems of linear equations, determinants, vector spaces, linear transformations, orthogonality, eigenvalues, Markov processes, linear programming and the use of mathematical software in modeling and problem solving. Prerequisite(s): MAT 151M or permission of instructor. Every semester

Credit: 4

  MAT 277 - Elementary Topics in Mathematics
Each time this course is offered a mathematical topic will be chosen which requires college mathematical experience. The topics which will be covered will be the ones which are not covered in the regular course offerings of the department. Prerequisite(s): 8 credits in mathematics. Variable.

Credit: 1-4

  MAT 304 - College Geometry
This course examines Euclidean geometry of the plane in comparison with geometry on the sphere and other surfaces, examines the structure of Euclidean geometry as an axiomatic system, and looks at isometries and tiling as well as other topics in geometry such as other dimensions and trigonometry on the sphere.  The historical context of geometry, the nature of geometric proof and writing to explain geometric ideas are included. Prerequisite(s): 10 credits of mathematics including MAT 141M and MAT 151M. Every year.

Credit: 4

  MAT 313 - Introduction to Abstraction
This class is intended to introduce future elementary teachers to processes of abstract mathematical reasoning, using logic and group theory as models. Prerequisite(s): 12 credits of mathematics including MAT 141M. Every year.

Credit: 4

  MAT 320 - History of Mathematics
The history of mathematics from antiquity to the twentieth century, with emphasis placed on the major developments of arithmetic, algebra, and geometry. Problems will be solved in the historical context. The cultures in which mathematics developed will also be discussed.Prerequisite(s): 12 hours of mathematics including MAT 141M. Every year. CCP

Credit: 4

  MAT 333 - Graph Theory and Combinatorics

The two areas of Mathematics considered in this course highlight the interplay between different parts of Mathematics. The elementary and sophisticated counting methods of Combinatorics elucidate properties of Graphs while the Theory of Graphs stimulates and provides insights into counting methods. Applications to the understanding of problems are an integral part of the course. Prerequisite(s): MAT 151M. Every two years.



Credit: 4

  MAT 352 - Abstract Algebra
An introduction to the algebraic structure of groups, rings and fields. Prerequisite(s): 12 credits in mathematics, MAT 151M and 8 credits of other mathematics courses numbered MAT 141M or higher. Every year.

Credit: 4

  MAT 363 - Mathematical Problem Solving
A seminar course to integrate the mathematics the students have learned and to foster the improvement of their problem solving skills through work on group and individual research problems. Prerequisite(s): 32 credits in mathematics. Every year.

Credit: 4

  MAT 367 - Intermediate Statistics

The focus of this course is determining and conducting the appropriate analysis for different types of data and various applications.  Topics covered include experimental design, power, confidence intervals and hypothesis testing for two populations, contingency tables, one-way and two-way ANOVA, multiple regression, logistic regression, and non-parametric statistics.  A statistical computer package will be used. Prerequisite(s): MAT 120M or MAT 220M. Every year.



Credit: 4

  MAT 371 - Mathematical Probability
An introduction to Probability using the tools learned in courses through Calculus.  Combinatorial and integral methods will be used to calculate probabilities and expectations of functions of random variables.  There will be discussion of Discrete and Continuous Probability Distributions including Binomial, Poisson, Normal, Gamma and Multivariate Distributions. Prerequisite(s): MAT 142. Every year.

Credit: 4

  MAT 372 - Mathematical Statistics
An introduction to statistical methods using the tools learned in Linear Algebra and the study of Probability.  There will be discussion of sampling distributions, estimation, hypothesis tests, linear and multi-linear regression, and analysis of variance.  Prerequisite(s): MAT 251, MAT 371. Every 2 Years.

Credit: 4

  MAT 377 - Intermediate Topics in Mathematics
Each time this course is offered a mathematical topic will be chosen which requires college mathematical experience. The topics which will be offered will be ones which are not covered in the regular course offerings of the department. Prerequisite(s): 12 credits in mathematics. Variable

Credit: 1-4

  MAT 400 - Topology and Real Analysis
The topologies of the real line and real n-space give a foundation for more general concepts of topology:  metric spaces, closed and open sets, closure, boundary, the separation axioms, continuity, compactness and other topics. Prerequisite(s): MAT 241, MAT 151M. At least once in a three year cycle.

Credit: 4

  MAT 401 - Ring, Field and Number Theory
The theory of rings, integral domains and fields is examined in detail, with applications to number theory. Prerequisite(s): MAT 352 At least once in a three-year cycle.

Credit: 4

  MAT 402 - Complex Analysis
This course introduces function theory of a single complex  variable. Topics include the field of complex numbers, complex analytic fuctions, complex integration, linear fractional transformations, series representations for analytic functions, classification of singularities, and residues. Prerequisite(s): MAT 241. At last once every 3 years.

Credit: 4

  MAT 403 - Numerical Analysis and Differential Equations
We will consider Ordinary Differential Equations and their applications.  The topics will include first order equations, Linear equations, and systems of equations.  We will examine the formulation of equations, exact solutions, and numerical approximation of solutions. Prerequisite(s): MAT 241, MAT 251. At least once in a three-year cycle.

Credit: 4

  MAT 477 - Advanced Topics in Mathematics
Each time this course is offered, an advanced mathematical topic will be chosen which requires extensive college mathematics experience.  The topics which will be covered will be ones which are not covered in the regular course offerings of the department. Prerequisite(s): 16 credits in mathematics including MAT 141M. Variable.

Credit: 1-4

  MAT 497 - Independent Study in Mathematics
An opportunity to pursue independent study in a selected mathematics topics under the direction of a faculty member. Prerequisite(s): 20 hours of mathematics and permission of instructor. Variable.

Credit: 1-4