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Mathematics | Computer Science

Department of Mathematics and Computer Science
Mary Goodloe (chair), Glenn Acree, Stephen Campbell, James Cook, Joyce Blair Crowell, Sharon Crumpton, Delmer DeBoer (professor emeritus), Robert Forrester*, Kay Geving, William Hooper, Keeley Hutchison, Otis McCowan (professor emeritus), Raymond H. Medley (professor emeritus), Andrew Miller, Jeff Moore*, Michael Pinter, Jennifer Rowe, Barbara Ward.
*Part-time.

Vision:

To support the university, college, and school visions through teaching excellence that engages each student in an analytical and personal search for knowledge of mathematics and computer science.

Purpose:

To provide a supportive and challenging intellectual community where students are encouraged to develop independence, creativity, and excellence in mathematics and computer science.

Goals:

To help our students:
1. comprehend the concepts, relationships, and processes of the fundamental material in mathematics and computer science.
2. discover the nature of proof and prove theorems.
3. think independently and creatively.
4. understand applications, formulate and translate problems, and write meaningful algorithms.
5. communicate ideas of mathematics and computer science orally, visually, and in writing using formal notation.
6. solve problems by identifying connections, recognizing patterns, using multiple strategies, and employing appropriate tools.
7. become contributing members of an engaged, responsible community of scholars.

Mathematics (MTH)

Mathematics Placement Test

Placement into Mathematics courses will be determined by the student's Math ACT or Math SAT scores. Alternatively, students may take the Belmont Math placement exam, which is available on-line to all incoming first-year and transfer students during Towering Traditions. Math faculty members will be available to advise students about their Math courses during Towering Traditions, as well.

Questions about which courses taken at other colleges and universities may be substituted for Math requirements at Belmont should be directed to the chairperson of the Department of Mathematics/Computer Science or the associate dean of the School of Sciences.

Mathematics Courses (MTH)

MTH 0900. Basic Algebra* (3). Designed to assist any student whose algebra background is inadequate for College Algebra. Covers basic algebraic properties and operations and emphasizes algebraic skills. Does not satisfy the mathematics requirement for any degree program.

MTH 1020. Basic Concepts of Mathematics* (3). Recommendation: Students with a MTH ACT score greater than or equal to 28, Math SAT score greater than or equal to 630, or Belmont Math Placement Test score greater than or equal to 29, are encouraged to take MTH 1080 instead of MTH 1020. This course is designed to provide some insight into the nature of mathematics by examining various mathematical structures. Topics include some of the following: sets and their properties, symbolic logic, mathematical patterns, inductive reasoning, number systems and their properties, geometry, probability, counting techniques, and descriptive statistics. Unless the student has prior written approval of the Department of Mathematics and Computer Science, credit is not allowed for this course if the student already has credit for MTH 1080.

MTH 1030. Statistical Concepts* (3). Prerequisite: High school algebra or MTH 0900. A basic introduction to descriptive and inferential statistics. Topics include organizing and displaying data, measures of central tendency and variability, elementary probability concepts and distributions, confidence intervals and tests of hypotheses.

MTH 1050, 1060. Mathematics for Elementary Teachers I, II* (3 each). Prerequisite: MTH 1050 is a prerequisite for MTH 1060. Topics include properties of numbers and sets, systems of numeration, arithmetic operations, informal geometry, problem solving, and appropriate applications.

MTH 1080. Mathematical Inquiry* (3). Prerequisite: MTH ACT score greater than or equal to 25, Math SAT score greater than or equal to 570, or Math Placement Test score greater than or equal to 26. This is an inquiry course with topics chosen to develop mathematical thinking, abstract thought, an understanding of proof and the role of mathematics in constructing our world view. Topics will be selected from classical problems and current research, from theoretical proofs and real world applications. There will be related classical problems and current readings and opportunities for writing. Topics include some of the following: symbolic logic, mathematical patterns, inductive and deductive reasoning, counting principles, paradoxes and proofs,Godel's Theorem, Fermat's Last Theorem, graphs and networks, discrete dynamical systems, coding, competitive strategies, recurrence relations, minimax phenomena, and computational complexity.

MTH 1110. College Algebra* (3). Prerequisite: The equivalent of two years of high school algebra and a qualifying score on the Mathematics Placement Test; MTH 0900 or consent of the instructor. Topics include linear, quadratic, polynomial, rational, exponential, and logarithmic functions, equations, inequalities, systems of equations and inequalities, and their applications. Note: Unless the student has prior written approval of the Department of Mathematics and Computer Science, credit is not allowed for this course if the student already has credit for any of the following courses: MTH 1130, MTH 1170, MTH 1210, or MTH 2140.

MTH 1130. Precalculus Mathematics* (4). Prerequisites: The equivalent of two years of high school algebra, one year of geometry and either MTH ACT score greater than or equal to 25, Math SAT score greater than or equal to 570, a qualifying score on the Belmont Math Placement Test, or consent of the instructor. An intense treatment of elementary functions including exponential, logarithmic, trigonometric, and polynomial functions. Unless the student has prior written approval of the Department of Mathematics and Computer Science, credit is not allowed for this course if the student already has credit for MTH 1170 or MTH 1210.

MTH 1150 - Elementary Statistics* (3 hrs). Prerequisite: MTH ACT score greater than or equal to 22, Math SAT score greater than or equal to 520, a qualifying score on the Belmont Math Placement Test, a grade of C in MTH 1110 or MTH 1130, or consent of the department chair. An introduction to statistical reasoning. Topics include descriptive measures, elementary probability distributions, sampling distributions, one and two sample inferences on means and proportions, simple linear regression, and correlation. Case studies of real data will relate to various fields of interest. Special emphasis will be placed on communication of statistical results through projects using computer software.

MTH 1151 - Elementary Statistics for the Sciences* (3 hrs). Prerequisite: MTH ACT score greater than or equal to 22, Math SAT score greater than or equal to 520, a qualifying score on the Belmont Math Placement Test greater than or equal to 22, or MTH 1110. The study of statistical procedures widely used in the sciences. Topics include, in addition to those taught in MTH 1150, modeling with probability distributions, multiple regression, analysis of variance, chi-square tests, nonparametric statistics, and bootstrapping. Analysis of data using computer software will relate to the sciences. Special emphasis will be placed on the communication of statistical results from scientific research.

MTH 1160. Biostatistics Lab* (1). Co requisite: MTH 1150. Students will collect data from actual biological experiments or surveys and will analyze the data using techniques being studied. Appropriate use of computers and software will be integrated into the laboratory and data analysis experience. May be taken concurrently with MTH 1150.

MTH 1161. Psychology Statistics Lab* (1). Co requisite: MTH 1150. Students will analyze data from psychological experiments or surveys using statistical techniques. Emphasis will be placed on experimental design, ethics in research, and the use of statistical computer software. May be taken concurrently with MTH 1150.

MTH 1170. Calculus I for Business, Economics, and the Social and Life Sciences * (3). Prerequisite: A minimum grade of C in MTH 1110 or MTH 1130, MTH ACT score greater than or equal to 25, Math SAT score greater than or equal to 570, qualifying Belmont Math Placement Test score, or consent of the department chair. A survey of limits, continuity and the differential and integral calculus with applications in business, economics, social and life sciences. Unless the student has prior written approval of the Department of Mathematics and Computer Science, credit is not allowed for this course if the student already has credit for MTH 1210.

MTH 1180. Calculus II for Business, Economics, and the Social and Life Sciences* (3). Prerequisite: A minimum grade of C in MTH 1170. Further studies in limits, derivatives, and definite integrals. Calculus of functions of several variables, logarithms, exponential functions, overview of series, trigonometric functions, techniques of integration, and differential equations with applications.

MTH 1210, 1220, 2210. Calculus I, II, III (4 each). Prerequisite: For Calculus I--A qualifying score on the Math Placement Test, a minimum grade of C on MTH 1130, MTH ACT score greater than or equal to 27, Math SAT score greater than or equal to 610, or consent of the department chair; the equivalent of four years of high school mathematics including Algebra I, II, Geometry, and Trigonometry is expected. Calculus I – an introduction to analytic geometry, limits, integration, differentiation; Calculus II – applications with trigonometric, exponential, logarithmic, and hyperbolic functions, and infinite series; Calculus III-parametric equations, vector calculus and multi-variable calculus. Calculus I cannot be used as part of the 30-hour major in mathematics.

MTH 1990-4990. Special Studies (1-3).

MTH 2020. Intermediate Statistics* (3). Prerequisites: A grade of C in MTH 1150. A continuation of statistical decision making procedures begun in MTH 1150, Elementary Statistics. Topics include Two Sample Tests of Hypotheses, Multiple Regression, Time Series, Analysis of Variance, Nonparametric Statistics, Chi-square, Control Charts, and Decision Analysis.

MTH 2030. Topics in Statistics* (3). Prerequisite: MTH 2020. Topics will be selected from the following: experimental design, sampling, nonparametric methods, time series analysis, categorical analysis, multivariate analysis, and advanced regression analysis. Course offerings and topics will appear in the schedule of classes. This course may be repeated for credit for different topics.

MTH 2140. Quantitative Methods in Business* (3). Prerequisites: A minimum grade of C in MTH 1110 or MTH 1130, MTH ACT score greater than or equal to 25, Math SAT score greater than or equal to 570, qualifying Belmont Math Placement Test score, or consent of the department chair. Topics covered in the first half of the course include linear, polynomial, logarithmic, and exponential functions, and applications of each type function, linear programming and matrices. Second half topics include limits and differential calculus, including maximization and minimization of functions. Applications to business and economics are emphasized. . Unless the student has prior written approval of the Department of Mathematics and computer Science, credit is not allowed for this course if the student already has credit for the following courses, MTH 1170 or MTH 1210.

MTH 2170. Mathematical Modeling for the Environmental Sciences* (3). Prerequisites: MTH 1210 or co requisite 1180. This course introduces the concept of modeling as a means of both understanding systems and of the making predictions about their future behaviors. It will present concepts in environmental science from a problem solving perspective and will develop the student's ability to transform realistic, qualitatively described problems into quantifiably solvable form and then to arrive at approximate solutions. Computer software will be used, but primarily emphasis will be placed on achieving a mental understanding of the relationship described within the models.

MTH 2240. Differential Equations (3). Prerequisite: MTH 2210. An introduction to ordinary differential equations. Topics include equations of order one and degree one, orthogonal trajectories, linear differential equations, Laplace transforms, variations of parameters and applications.

MTH 2250. Discrete Mathematics (3). Prerequisites: CSC 1110, MTH 1220. An introduction to discrete mathematics with an emphasis on mathematical reasoning. Topics include sets, relations, propositional logic, basic proof structures, algorithms, functions and computability, introductory graph theory and introductory combinatorics.

MTH 2260. Linear Algebra (3). Prerequisite: MTH 2210. Topics include matrices, vectors and vector spaces, and linear transformations.

MTH 3210. Probability (3). Prerequisite: MTH 1180 or MTH 1220. An introduction to the laws of probability, mathematical expectation, probabilistic model building, random variables, and probability distributions.

MTH 3220. Mathematical Statistics (3). Prerequisite: MTH 3210. A development of the mathematical basis for measures of central tendency and variation, sampling distributions, statistical inference, hypothesis testing, and decision theory.

MTH 3260. Graph Theory (3). Prerequisite: MTH 2250. A continuation of the introduction to graph theory begun in MTH 2250. Topics include trees, planar graphs, Hamilton cycles, Euler tours, matchings, coverings, and colorings.

MTH 3270. Combinatorics (3). Prerequisite: MTH 2250. A continuation of the introduction to combinatorics begun in MTH 2250. Topics include the principles of counting patterns by means of generating functions, recurrence relations, and Polya's Theory; the existence of patterns by means of the pigeonhole principle and its generalizations; and the optimization of patterns by means of the minimax principle.

MTH 4110. Modern Geometry (3). Prerequisite: 11 hours toward the major or consent of the instructor. An axiomatic approach to the study of elementary geometry. Euclidean geometry, non-Euclidean geometries, and finite geometries are examined.

MTH 4120. Introduction to Analysis (3). Prerequisite: 11 hours toward the major or consent of the instructor. A theoretical study of properties of the real numbers, functions, metric sets, limits, continuity, differentiation, and integration.

MTH 4130. History of Mathematics (3). Prerequisites: 11 hours toward the major or consent of the instructor. An overview of the historical development of elementary mathematics including arithmetic, geometry, algebra, trigonometry, and calculus. Biographical and historical content will be reinforced with studies of procedures and techniques of earlier mathematical cultures. Required for all students seeking to meet secondary licensing standards in mathematics.

MTH 4140. Abstract Algebra (3). Prerequisite: MTH 2260. Topics include sets, number theory, functions and mappings, rings, groups, and fields.

MTH 4150. Numerical Methods (3). Prerequisites: CSC 1120; MTH 2210 or MTH 2250. A problem-oriented course emphasizing the solution of linear systems and nonlinear equations, curve fitting, interpolation and approximation, error analysis, and numerical integration and differentiation.

MTH 4170. Modeling and Simulation (3). Prerequisites: MTH 2210, MTH 3210. An introduction to modeling and simulation which will include experience in modeling and simulating actual systems.

MTH 4610. Advanced Topics in Mathematics (3). Prerequisite: See the instructor or the department chair prior to registration regarding prerequisites. Course offerings and topics will be scheduled based on student needs and interest. Topics will appear in the schedule of classes. This course may be repeated for credit for different topics.

MTH 4710. Senior Seminar (2). Prerequisite: Consent of instructor. This capstone course will provide opportunities to assess student achievement of the department learning goals. Course content will include “topic days” using problems from the student’s portfolios related primarily to the core calculus, probability/statistics, discrete mathematics, and computer programming courses. There will be a reading and presentation component.