Dalton State 2014-15 Catalog

Mathematics

Mathematics Minor

A minor must contain 15 to 18 semester hours of coursework, including at least 9 hours of upper-division courses at the 3000-4000 level. Courses taken to satisfy Core Areas A through E may not be counted toward completion of the minor, but courses taken in Core Area F may be used to fulfill minor requirements.

A minor in Mathematics must include 15 credit hours of mathematics course work, with at least 9 hours at the 3000-level or above.

Two degree-level MATH courses (except 3703, 3803, or 4713)6
Three of the following Upper Electives:9
Intro to Advanced Mathematics
Geometry
Combinatorics
Linear Algebra
Abstract Algebra I
Abstract Algebra II
Number Theory
Graph Theory
Operations Research
Statistics for Process Control
Numerical Analysis I
Numerical Analysis II
Real Analysis I
Real Analysis II
Complex Analysis
Probability and Statistics I
Probability and Statistics II
Topology
Total Hours15

Courses

MATH 0090. Certif Preparatory Mathematics. 3-0-3 Units.

Presents the fundamentals of mathematics: addition, subtraction, multiplication, and division of whole numbers, fractions, decimals and percentages. Prospective students will be required to score at or above 35 on the Pre-Algebra COMPASS exam to be exempt from this course. (Institutional Credit)(F,S,M)
Prerequisites: Must be enrolled in a certificate program.

MATH 0091. Quant Skills/Reason Co-Curricu. 1-0-1 Unit.

Students with learning support mathematics requirements who are enrolled in MATH 1001 are required to take this course concurrently with MATH 1001. It is not intended to supply sufficient algebraic background for students who intend to take Precalculus or the calculus sequences for mathematics and science majors. Together with MATH 1001, this course places quantitative skills and reasoning in the context of experiences that students will be likely to encounter. It emphasizes processing information in context from a variety of representations, understanding of both the information and the processing, and understanding which conclusions can be reasonably determined. Prospective students will be required to score at or above 37 on the COMPASS exam to be exempt from the course.(F,S,M)

MATH 0092. Math Modeling Co-Curricular. 1-0-1 Unit.

Students with learning support requirements in mathematics are required to take this course concurrently with MATH 1101. Together with MATH 1101, it is an option in Area A of the Core Curriculum and is not intended to supply sufficient algebraic background for students who intend to take Precalculus or the calculus sequences for mathematics and science majors. Together with MATH 1101, this course is an introduction to mathematical modeling using graphical, numerical, symbolic, and verbal techniques to describe and explore real-world data and phenomena. Emphasis is on the use of linear, polynomial, exponential, and logarithmic functions to investigate and analyze applied problems and questions, supported by the use of appropriate technology, and on effective communication of quantitative concepts and results.(F,S,M)

MATH 0096. Introductory Algebra. 3-0-3 Units.

Reviews fractions, decimals, and percents. Topics include signed numbers, order of operations, variable expressions, linear equations and inequalities, and polynomials. Prospective students will be required to score at or above 25 on the COMPASS exam to be exempt from this course. (Institutional Credit)(F,S,M)
Prerequisites: Must be enrolled in a degree-level program.

MATH 0098. Intermediate Algebra. 4-0-4 Units.

Continues the development of algebra. Topics include factoring polynomials, rational expressions and equations, linear graphing, simultaneous equations, radicals and quadratic equations. Prospective students will be required to score at or above 37 on the COMPASS exam to be exempt from this course. (Institutional Credit)(F,S,M)
Prerequisites: Must be enrolled in a degree-level program.

MATH 0099. Learning Support Algebra. 6-0-6 Units.

Topics include fractions, geometry, signed numbers, order of operations, variable expressions, linear equations and inequalities, polynomials, factoring polynomials, rational expressions and equations, linear graphing, simultaneous equations, radicals and quadratic equations. Prospective students will be required to score at or above 37 on the COMPASS exam to be exempt for this course. (Institutional Credit).

MATH 1001. Quantitative Skills/Reasoning. 3-0-3 Units.

This course is an alternative in Area A of the Core Curriculum and is not intended to supply sufficient algebraic background for students who intend to take precalculus or the calculus sequences for mathematics and science majors. This course places quantitative skills and reasoning in the context of experiences that students will be likely to encounter. It emphasizes processing information in context from a variety of representations, understanding of both the information and the processing, and understanding which conclusions can be reasonably determined.(F,S)
Corequisites: MATH 0091 unless exempt from learning support mathematics.

MATH 1101. Intro to Mathematical Modeling. 3-0-3 Units.

This course is not intended to supply sufficient algebraic background for students who intend to take precalculus or the calculus sequence for mathematics and science majors. This course is an introduction to mathematical modeling using graphical, numerical, symbolic, and verbal techniques to describe and explore real-world data and phenomena. Emphasis is on the use of linear, polynomial, exponential, and logarithmic functions to investigate and analyze applied problems and questions, supported by the use of appropriate technology, and on effective communication of quantitative concepts and results.(F,S,M)
Corequisites: MATH 0092 unless exempt from learning support.

MATH 1102. Medical Mathematics. 3-0-3 Units.

Designed primarily for those students majoring in health professions. Topics covered include a review of computational skills, metric and apothecary systems, and dosage calculations for tablets, solutions, and intravenous fluids. (Career Course)(F,M)
Prerequisites: Satisfactory Mathematics placement score or successfully complete MATH 0090.

MATH 1104. Applied Mathematics. 3-0-3 Units.

Topics include arithmetic, elementary algebra, geometry, measurement, and elementary trigonometry. (Career Course)(F,S,M)
Prerequisites: MATH 0090 unless exempt for learning support mathematics.

MATH 1111. College Algebra. 3-0-3 Units.

Presents topics in algebra, including the number system, polynomials, algebraic functions, exponents, radicals, linear and quadratic equations, inequalities, lines in the plane, linear modeling, conics, algebra of functions, exponential and logarithmic functions and systems of equations and inequalities.(F,S,M)
Prerequisites: MATH 0098 unless exempt.

MATH 1113. Precalculus Mathematics. 3-0-3 Units.

Provides immediate transition from high school algebra into calculus and physics. Material goes beyond that normally covered in Mathematics 1111. Algebra topics include linear, quadratic equations, functions and graphing, exponential and logarithmic functions. Trigonometry topics include trigonometric functions and inverse, law of sines, law of cosines and identities. For students planning to take calculus and/or physics.(F,S,M)
Prerequisites: MATH 1111.

MATH 1401. Introduction to Statistics(eC). 3-0-3 Units.

A course in basic statistics. Topics include descriptive statistics, probability, distributions, hypothesis testing, inferences, correlation, and regression.
Prerequisites: MATH 1101, MATH 1111, MATH 1113 or approved equivalent.

MATH 1501. Calculus I (eCore). 4-0-4 Units.

This course is a four (4) credit hour course and includes material on functions, limits, continuity, the derivative, antidifferentiation, the definite integral, applications of integration and techniques of integration.
Prerequisites: MATH 1113.

MATH 2008. Found of Numbers & Operations. 3-0-3 Units.

This course will emphasize the understanding and use of the major concepts of number and operations. Topics include problem-solving strategies; inductive and deductive reasoning; numeration systems and place value; operations and algorithms; identity elements and inverse operations; rational and irrational numbers; integers and number theory; special sets of numbers; exponents and decimals; ratios, percents, and proportional reasoning.(S,M)
Prerequisites: MATH 1001, MATH 1111, or MATH 1113.

MATH 2181. Applied Calculus. 3-0-3 Units.

Surveys differential and integral calculus of polynomial, rational, exponential and logarithmic functions. Detailed applications to problems and concepts from business, economics and life science are covered.(F,S,M)
Prerequisites: MATH 1111, MATH 1001, or MATH 1113 with a grade of C or better.

MATH 2200. Introduction to Statistics. 3-0-3 Units.

Surveys descriptive and inferential statistics. Topics include organizing and graphing data, measures of central tendency, dispersion, probability, normal distribution, sampling, confidence intervals, hypothesis tests, significance tests, correlation and regression.(F,S,M)
Prerequisites: MATH 1001, MATH 1111, or MATH 1113.

MATH 2253. Calculus and Analytic Geom I. 4-0-4 Units.

Includes topics limits and continuity, derivatives and their applications and an introduction to the concept of the integral. The first in a four course sequence in Calculus. Prerequisite: MATH 1113 or satisfactory mathematics scores of SAT 600/ACT 26 and one year of high school trigonometry.(F,S,M)
Prerequisites: MATH 1113.

MATH 2254. Calculus and Analytic Geom II. 4-0-4 Units.

Emphasizes the definite integral and its applications, the calculus of trigonometric, exponential, logarithmic, hyperbolic and inverse functions, techniques of integration, improper integrals, L' Hopital's Rule, infinite series and conic sections. The second course in the Calculus sequence.(F,S,M)
Prerequisites: MATH 2253.

MATH 2255. Calculus and Analytic Geom III. 4-0-4 Units.

Emphasizes calculus in three dimensions. Topics include vectors, parametric equations, partial derivatives, multiple integrals and their applications and topics in vector calculus. The third course in the Calculus sequence.(F,S)
Prerequisites: MATH 2254.

MATH 2256. Introduction to Linear Algebra. 3-0-3 Units.

Introduces low-dimensional linear algebra through eigenvalues and eigenvectors. Applications to linear systems, least-square problems, and the calculus, including elementary differential equations.(F,S)
Prerequisites: MATH 2253.
Corequisites: MATH 2254.

MATH 2403. Differential Equations. 3-2-4 Units.

A study of differential equations, including first and higher order equations, linear and nonlinear systems of equations, numerical methods to approximate solutions, using Laplace transforms to determine solutions, and methods that yield infinite series solutions.(F,S)
Prerequisites: MATH 2254 and MATH 2256.

MATH 2602. Linear & Discrete Mathematics. 3-2-4 Units.

Explores topics in linear algebra, induction, combinatorics, difference equations, and multivariate optimization with an emphasis on discrete and recursive methods.(F,S)
Prerequisites: MATH 2255.

MATH 2770. Statistics and Applications. 3-0-3 Units.

Introduces the student to topics in probability, probability distributions, point estimation, confidence intervals hypothesis testing, linear regression and analysis of variance.(F,S,M)
Prerequisites: MATH 2255.

MATH 3101. Intro to Advanced Mathematics. 3-0-3 Units.

Preparation in mathematical reasoning and proof-writing necessary for upper division course work in mathematics. Topics include logic, integers and induction, sets and relations, equivalence relations and partitions, and functions.(S)
Prerequisites: MATH 2255.

MATH 3201. Geometry. 3-0-3 Units.

An introduction to Euclidean and non-Euclidean geometries developed with the study of constructions, transformations, applications, and the rigorous proving of theorems.(F)
Prerequisites: MATH 3101.

MATH 3301. Combinatorics. 3-0-3 Units.

Basic counting principles: permutations, combinations, probability, occupancy problems, and binomial coefficients. More sophisticated methods include generating functions, recurrence relations, inclusion/exclusion principles, and the pigeonhole principle. Additional topics include asymptotic enumeration, Polya counting theory, combinatorial designs, coding theory, and combinatorial optimization.(S)
Prerequisites: MATH 2254.

MATH 3401. Linear Algebra. 3-0-3 Units.

Theory and applications of matrix algebra, vector spaces, and linear transformations; topics include characteristic values, the spectral theorem, and orthogonality.(F)
Prerequisites: MATH 2256.

MATH 3703. Geometry for P-8 Teachers. 3-0-3 Units.

Continues MATH 2008, with emphasis for teachers of grades P-8. Logic; real numbers; basic and transformational geometry; measurement, including the metric system; problem solving; methods and materials for teaching mathematics at the P-8 level.(S,M)
Prerequisites: MATH 2008.

MATH 3803. Algebra for P-8 Teachers. 3-0-3 Units.

Provides special emphasis for teachers of grades P-8 on understanding of the fundamental concepts of algebra with particular attention to specific methods and materials of instruction.(F,S)
Prerequisites: EDUC 2110, EDUC 2130, ISCI 2001, ISCI 2002, MATH 2008, COMM 1110, and PSYC 1101.

MATH 4001. History of Mathematics. 3-0-3 Units.

Examines major developments, central themes, and important issues in mathematics throughout history. Undertakes an overview of the historical development of the discipline by focusing on specific theories, problems, and results.(F)
Prerequisites: MATH 3101.

MATH 4101. Abstract Algebra I. 3-0-3 Units.

An axiomatic approach to algebraic structures. Topics include groups, permutations, homomorphisms, and factor groups.(F)
Prerequisites: MATH 3101.

MATH 4102. Abstract Algebra II. 3-0-3 Units.

Examines the central concepts of ring theory and field theory. Topics include modules, Galois theory, integral domains, and advanced linear algebra. Strongly recommended for students intending to complete a graduate degree in mathematics.(S)
Prerequisites: MATH 4101.

MATH 4201. Number Theory. 3-0-3 Units.

A study of elementary problems in number theory with topics from divisibility, congruences, residues, special functions, Diophantine equations, and continued fractions.(S)
Prerequisites: MATH 3101.

MATH 4301. Graph Theory. 3-0-3 Units.

Elementary theory of graphs and digraphs. Topics include connectivity, reconstructions, trees, Euler's problem, hamiltonicity, network flows, planarity, node and edge colorings, tournaments, matchings, and extremal graphs. A number of algorithms and applications are included.(F)
Prerequisites: MATH 3101.

MATH 4401. Operations Research. 3-0-3 Units.

Linear programming, the simplex method, network theory, game theory, Markov analysis, and other topics such as inventory analysis, queuing theory, integer programming.(S)
Prerequisites: MATH 3401.

MATH 4502. Statistics for Process Control. 3-0-3 Units.

Introduces application techniques used in quality/process control with particular application to area industries. Topics include probability, sampling distributions, control charts for variables and attributes, lot-by-lot sampling plans, acceptance sampling for variables, elementary reliability calculations, and an introduction to the concept of quality costs. Offered as needed.
Prerequisites: MATH 2181 and MATH 2200.

MATH 4511. Numerical Analysis I. 3-0-3 Units.

Numerical solution of equations, polynomial approximation, numerical differentiation and integration, numerical solutions of ordinary differential equations, error analysis. Written programs using algorithms.(F)
Prerequisites: MATH 2403 and CMPS 1301.

MATH 4512. Numerical Analysis II. 3-0-3 Units.

Numerical solutions of systems of linear equations, numerical computations of eigenvalues and eigenvectors, error analysis. Written programs using the algorithms.(S)
Prerequisites: MATH 2256 or CMPS 1301.

MATH 4601. Real Analysis I. 3-2-4 Units.

Develops a rigorous approach to functions of a real variable. Topics include limits, continuous functions, differentiation, and Riemann integration.(F)
Prerequisites: MATH 3101.

MATH 4602. Real Analysis II. 3-0-3 Units.

Continuous and rigorous approach to functions with an emphasis on functions in higher dimensions, including derivatives and intergrals in n-dimensional Euclidean space.(S)
Prerequisites: MATH 4601.

MATH 4611. Complex Analysis. 3-0-3 Units.

Complex numbers, analytic functions, complex series, Cauchy theory, residue calculus, conformal mapping.
Prerequisites: MATH 4601.

MATH 4701. Probability and Statistics I. 3-0-3 Units.

Sampling distributions, Normal, t, chi-square and F distributions. Moment generating function methods, Bayesian estimation and introduction to hypothesis testing.(F)
Prerequisites: MATH 2255.

MATH 4702. Probability and Statistics II. 3-0-3 Units.

Hypothesis testing, likelihood ration tests, nonparametric tests, bivariate and multivariate normal distributions.(S)
Prerequisites: MATH 4701.

MATH 4713. Prob & Stat for P-8 Teachers. 3-0-3 Units.

Provides special emphasis for teachers of grades P-8 on the fundamental concepts of probability and statistics with particular attention to specific methods and materials of instruction.(F,S,M)
Prerequisites: MATH 2008.

MATH 4800. Topology. 3-0-3 Units.

This course develops the concepts of open and closed sets, topological spaces, bases, subspaces, continuous functions, homeomorphisms, connected spaces and compact spaces.(F)
Prerequisites: MATH 3101.

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