Mathematics Courses (MTH)

Mathematics Courses (MTH)

**MTH 1000. Seminar in Mathematics (1).** *Prerequisite: Seeking a major in Mathematics or Applied Discrete Mathematics.* This course is to be taken during the first fall semester after declaring Mathematics or Applied Discrete Mathematics as a major. The seminar provides an orientation to the field of mathematics and the study of mathematics at Belmont. Students will learn about the mathematics curriculum, mathematics student organizations, research opportunities for faculty and students, careers for mathematics graduates, and graduate study in mathematics.** **

**MTH 1020. Introduction to Mathematical Reasoning* (3).** *This course is intended for students with a Math ACT score less than 25, a Math SAT score less than 570, or a Belmont Math Placement Test score less than 24. Students with higher scores should 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 Chair 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 1050. Mathematics for Elementary Teachers I* (3).** *Prerequisitie: MTH 1020 or MTH 1080.* Topics include the development of the real number system, conventional and unconventional arithmetic algorithms, elementary number theory, and algebraic thinking. Critical thinking and problem solving will be emphasized.

**MTH 1060. Mathematics for Elementary Teachers II* (3).** *Prerequisite: MTH 1050.* Topics include data analysis, probability, geometry, and measurement. Critical thinking and problem solving will be emphasized.

**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 Belmont Math Placement Test score greater than or equal to 24.*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 landmark proofs and and real-world applications spanning ancient times to the 20th century, including some of the following: symbolic logic, Fibonacci numbers, Fermat's Last Theorem, counting principles, infinity, number theory, exotic geometry, iterative processes, chaos, voting, and risk. Unless the student has prior written approval of the Chair of the Department of Mathematics and Computer Science, credit is not allowed for this course if the student already has credit for MTH 1020.

**MTH 1110. College Algebra* (3).** *Prerequisite: Math ACT score greater than or equal to 20, Math SAT score greater than or equal to 480, Belmont Math Placement Test score greater than or equal to 17, or MTH 0900.*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 Chair 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 1140.

**MTH 1130. Precalculus Mathematics* (4).** *Prerequisites: **MTH ACT score greater than or equal to 25, Math SAT score greater than or equal to 570, Belmont Math Placement Test score greater than or equal to 24, or MTH 1110.*An intense treatment of elementary functions including exponential, logarithmic, trigonometric, and polynomial functions. Unless the student has prior written approval of the Chair 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 1140. Quantitative Methods in Business* (3).** *Prerequisites:* *Math ACT score greater than or equal to 24, Math SAT score greater than or equal to 560, Belmont Math Placement Test score greater than or equal to 23, MTH 1110, or MTH 1130.*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 Chair 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 1150 -** **Elementary Statistics* (3 hrs)**. *Prerequisite: MTH ACT score greater than or equal to 22, Math SAT score greater than or equal to 520, Belmont Math Placement Test score greater than or equal to 20, MTH 1110, or MTH 1130.* 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. Credit is not allowed for this course if the student already has credit for MTH 1151.

**MTH 1151 -** **Elementary Statistics for the Sciences (3 hrs)**. *Prerequisite: Math ACT score greater than or equal to 22, Math SAT score greater than or equal to 520, Belmont Math Placement Test score greater than or equal to 20, or MTH 1110, or MTH 1130.*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. Credit is not allowed for this course if the student already has credit for MTH 1150.

**MTH 1160. Biostatistics Lab* (1).** *Prerequisite or corequisite: MTH 1151.* 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. Credit is not allowed for this course if the student already has credit for MTH 1162.

**MTH 1162. Data Analysis Laboratory (1).** *Prerequisite or* co-*requisite: MTH 1151.*Students will analyze data from experiments or surveys using statistical techniques. Emphasis will be placed on experimental design, ethics in research, and the use of statistical computer software. Credit is not allowed for this course if the student already has credit for MTH 1160.

**MTH 1170. Calculus I for Business, Economics, and the Social and Life Sciences * (3).** *Prerequisite: Math ACT score greater than or equal to 25, Math SAT score greater than or equal to 570, Belmont Math Placement Test score greater than or equal to 24, MTH 1110, or MTH 1130.*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 Chair 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 1190. Additional Topics in Calculus* (1).** *Prerequisite: MTH 1170.* A further study of limits, differentiation, and integration, including trigonometric functions. This course is designed as a bridge course for the student who has taken MTH 1170 and would like to be prepared to take MTH 1220. Unless the student has prior written approval of the Chair 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 1210. Calculus I (4).** *Prerequisite: Math ACT score greater than or equal to 27, Math SAT score greater than or equal to 610, Belmont Math Placement Test score greater than or equal to 27, or MTH 1130.* An introduction to analytical geometry, limits, integration, and differentiation.

**MTH 1220. Calculus II (4).** *Prerequisite: MTH 1210; or MTH 1170 and co-requisite MTH 1190.* Further techniques of integration with applications; exponential and logarithmic functions; parametric equations; and sequences and infinite series.

**MTH 1920. Peer Tutoring in Mathematics (1-3). ***Prerequisite: Consent of Instructor. *By invitation of a professor, a student may serve as a peer tutor for a course. Each peer tutor works with the professor to define the specific role in the class, which may include helping conduct classes, leading study or discussion sessions, and helping students master the course material. The peer tutor does not grade or keep other records for the class. The peer tutor will submit a paper of reflection on the work and the student's learning. This reflection paper will be expected to appear in the student's portfolio required in MTH 4710 (Senior Seminar). This course will be pass-fall and will fulfill the Internship, Clinicals, and Practica category of Experiential Learning of the BELL Core.**MTH 1950-4950. Studies Abroad (3-18). ** This course provides an opportunity to study mathematics in another country. Individual titles will be assigned to each course taken, indicating place of study and subject matter. Courses, if equivalent to Belmont requirements, may count toward major, minor, general education or elective credit. Students must consult with their advisor prior to enrollment to determine credit within their program of study.

**MTH 1990-4990. Independent Studies (1-3).** Courses designed with a professor for independent study purposes.

**MTH 1895-4895. Special Studies (1-3). **Special Topics or pilot courses.**MTH 2030. Topics in Statistics* (3).** *Prerequisite: MTH 1151 and MTH 1162.*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.

Gen. Ed. Designation: EL (R – Undergraduate Research).

**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 primary emphasis will be placed on achieving a mental understanding of the relationship described within the models.

**MTH 2210. Calculus III (4).** *Prerequisite: MTH 1220.* Vectors and the geometry of space, vector functions, partial derivatives, multiple integrals, surface integrals, Green's Theorem, Stokes' Theorem, and the Divergence Theorem, and, if time permits, second-order differential equations.

**MTH 2240. Differential Equations (3).** *Prerequisite: MTH 1220. *An introduction to ordinary differential equations. Topics may include equations of order one, linear differential equations, Laplace transforms, variation of parameters, power series solutions, systems of differential equations, and applications.

**MTH 2250. Discrete Mathematics (3).** *Prerequisites: CSC 1110 or MTH 1080. *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 or (MTH 1220 and MTH 2250).* Topics include matrices, vectors and vector spaces, and linear transformations.

**MTH 3000. Research in Mathematics (1-3).** *Prerequisite: 15 hours completed toward the major.*Students will conduct a research project and present their findings at the School of Sciences Undergraduate Research Symposium (SURS), the Belmont Undergraduate Research Symposium (BURS), or a regional or national conference. All aspects of designing and carrying out the study will be the responsibility of the student: posing the original research question, presenting supporting mathematical proofs, calculations, or simulations, literature review, abstract, and final paper (possibly submitted for publication). The course is open to all interested students who have satisfied the prerequisites and wish to design and conduct a research project in mathematics.

**MTH 3050. Internship in Mathematics (0-1).** *Prerequisite: 12 hours of Mathematics Courses.* Students who are doing mathematical related work can apply to have one semester or summer of such work designated as an internship. The student will be required to convince the instructor that he/she will be working in a mathematics related job and will use principles, practices, and skills learned in mathematics classes in order to enroll. To get credit, the student will submit a paper of reflection on the work and the student's learning. This reflection paper will be expected to appear in the student's portfolio required in MTH 4710 Senior Seminar course. This course will be pass/fail and will fulfill the internship category of Experiential Learning of the BELL core.

**MTH 3210. Probability (3).** *Prerequisite: 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 3230. Actuarial Studies (1).** *Prerequisite or corequisite: MTH 2210 and MTH 3210.* Topics from calculus and probability necessary for successful completion of the first Actuarial Exam P/1 will be reviewed and expanded. Solving problems of the types found on Actuarial Exam P/1 will be emphasized. This course may be repeated once for credit.

**MTH 3260. Graph Theory (3).** *Prerequisite: MTH 2250 or CSC 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 or CSC 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: 10 hours toward the major.* 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: 10 hours toward the major.* A theoretical study of properties of the real numbers, functions, metric sets, limits, continuity, differentiation, and integration.

**MTH 4130. History of Mathematics (3).** *Prerequisites: 10 hours toward the major.* 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.

Gen. Ed. Designation: GS (G – Global Studies).

**MTH 4140. Abstract Algebra (3).** *Prerequisite: MTH 2260.* An introduction to mathematical structures that generalize a variety of concepts from elementary mathematics, including numbers, permutations, symmetry, and polynomials. Topics include sets, number theory, functions and mappings, rings, groups, and fields.

**MTH 4150. Numerical Methods (3).** *Prerequisites: CSC 1120 and MTH 1220.* 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).** *Prerequisite: MTH 1220 and CSC 1110.* Emphasizes experiences in the development of mathematical models and computer simulations of phenomena which are of interest across a wide variety of disciplines. Models may be based on: difference equations, dynamical systems, statistics, probability, discrete optimization methods, graphs, and differential equations.

**MTH 4610. Advanced Topics in Mathematics (3).** *Prerequisite: Consent of instructor.* 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 (1).** *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.

**NOTE:** Courses with an asterisk (*) following the title will not count toward either a major or a minor in mathematics.