Mathematics

Faculty

Sita Ramamurti, Assistant Professor of Mathematics (Program Chair)

Lee Chiang, Assistant Professor of Mathematics

Tasha R. Inniss, Assistant Professor of Mathematics

Laurie Johnson, Assistant Professor of Mathematics

Description

The study of mathematics is an integral part of a liberal arts education. All students need to develop critical skills in problem solving and analytic thinking. The Mathematics Program at Trinity serves the community at large and offers mathematics students many opportunities to explore both inside and outside the classroom.

The mathematics major enables students to build a solid theoretical and technical foundation and to develop an appreciation of the nature of mathematics in the liberal arts tradition. Students gain technological expertise through the use of mathematical software packages and the development of their own computer software. As seniors, majors work on individual projects and communicate their work both through speaking and writing.

Mathematics students are involved in many activities outside the classroom such as serving as mentors and tutors to students in introductory courses.

The Mathematics Club, a student chapter of the Mathematical Association of America (MAA), promotes mathematics in the local community. The club sponsors talks with mathematicians employed in a variety of academic and nonacademic settings and arranges trips to places of mathematical interest in the local area. Chapter members attend local and national mathematics meetings and work with students in the local elementary school.

The Mathematics Program supports both a major and minors in mathematics, computer science, and applied statistics in the Weekday Program only. The Program offers two tracks for majors: pure mathematics (Area A) and mathematics education (Area B).

Area A: Pure Mathematics. Prepares students for graduate school and professional positions in government, business, and industry. Majors may adopt a theoretical or applied focus through their selection of electives ranging from number theory and history of mathematics to mathematical modeling and differential equations.

Area B: Mathematics Education. Prepares students for teaching secondary level mathematics. In conjunction with the School of Education, majors may pursue a five-year program. At the end of four years, a mathematics education major has completed the requirements for a Bachelor of Arts degree from Trinity in mathematics. Upon completion of the fifth year, the major is awarded a Master of Arts in Teaching and meets all certification requirements established by the National Association of State Directors of Teacher Education Certification.

Major Requirements

To earn the bachelor's degree, students must complete the required courses, the supplemental requirements, and either additional Area A or Area B requirements. MAT 421 Real Analysis I is strongly recommended for students who plan to attend graduate school.

Required Courses (42 credits)

ALL of the following mathematics courses:

MAT 125 Calculus and Analytic Geometry I

MAT 126 Calculus and Analytic Geometry II

MAT 141 Introduction to Programming

MAT 227 MultiVariable Calculus

MAT 245 Introduction to Abstract Mathematics

MAT 247 Linear Algebra

MAT 301 Abstract Algebra I

MAT 335 Mathematical Probability and Statistics

MAT 490 Senior Seminar

BOTH of the following physics courses:

PHY 115 General Physics I

PHY 116 General Physics II

Area A Requirements (12 credits)

ONE course chosen from between the following:

MAT 421 Real Analysis I

MAT 424 Complex Variables

ONE additional course at the 200-level or above

TWO additional courses at the 300-level or above

 

Area B Requirements (12 credits)

ALL of the following courses:

MAT 237 Differential Equations

MAT 303 Number Theory

MAT 340 History of Mathematics

MAT 450 Geometry

Note: To earn a Master of Arts in Teaching there are additional requirements set forth by the education program. Students must confer with the School of Education.

Mathematics Minor Requirements (23 credits)

ALL of the following courses:

MAT 125 Calculus and Analytic Geometry I

MAT 126 Calculus and Analytic Geometry II

MAT 245 Introduction to Abstract Mathematics

TWO additional courses at the 200-level or above

TWO additional courses at the 300-level or above

Computer Science Minor Requirements (20 credits)

ALL of the following courses:

MAT 141 Introduction to Programming

MAT 241 Intermediate Level Programming

MAT 306 Computer Organization

MAT 385 Data Structures and Algorithms

TWO additional electives chosen from: Systems Analysis and Design, Database Management Systems, Computer Networks, and Operating Systems

Applied Statistics Minor Requirements (20 credits)

ALL of the following courses:

MAT 110 Introduction to Statistics

MAT 125 Calculus I

MAT 210 Statistical Inference

MAT 302 Applied Statistical Methods

TWO additional electives chosen from: Introduction to Programming, Mathematical Probability and Statistics, Special Topics in Applied Statistics, and Operations Research

Program Policies

Advanced Placement: Students who score 4 or 5 on the calculus AB or BC exam will receive credit for MAT 125. Students who score 4 or 5 on the BC calculus exam may receive credit for MAT 126 at the discretion of the program chair.

CLEP Policy: A satisfactory score on the CLEP exam in college algebra will be accepted in lieu of MAT 103. A satisfactory score on the CLEP exam in calculus will be accepted in lieu of MAT 125. Only MAT 125 satisfies the FLC, Area V.

Grades in Major and Minor Courses: Students are required to earn a grade of "C" (2.0) or better in all courses counted to fulfill requirements for the major or the minor. To become a mathematics major, a student must receive a "B" or better in MAT 125 and MAT 126 or the approval of the program chair.

Pass/No Pass: No major or minor courses may be taken pass/no pass.

Senior Assessment: Every mathematics major must successfully complete MAT 490 Senior Seminar.

TELL Policy: TELL credits are accepted toward the Trinity degree based on the approval of program faculty. TELL credits do not count toward the major in mathematics.

Transfer Credits: Students wishing to transfer credits must consult the chair of the program.

Course Descriptions

MAT 100A Beginning Algebra 3 cr

Prepares students for college math courses. Students enroll in this course based on their placement scores. Topics in this course include a review of the operations on real numbers, decimals, percentages, fractions, exponents, linear equations and inequalities, with applications, polynomials, rational expressions, factoring, quadratic equations with applications, and graphs of equations and inequalities. Recommended for students who require a review of high school algebra.

MAT 103 College Algebra 3 cr

Provides students with a solid foundation in basic algebra with an emphasis on problem solving skills. Topics include linear, quadratic, polynomial, and rational equations and inequalities with applications; functions and graphs; polynomial, rational, exponential, and logarithmic functions; systems of linear equations; and linear inequalities.

Prerequisite: MAT 100A or approval of instructor

MAT 104 Introduction to Computer Science 3 cr

Provides a foundation for using computers in other courses and curricula for research, communication, and writing. Students are introduced to the fundamental ideas in the science of computing and how computers work. Hands-on experience using a variety of professional software tools including word processing, databases, spreadsheets, graphics packages, and scientific packages such as Matlab and Minitab will be provided. The Internet, the World Wide Web, and future trends will be discussed in detail. Social and ethical issues that impact the information age such as privacy, encryption policy, reliability of socially critical systems, and the role of simulations in decision-making will be studied. This is the first course for the study of computer information. Recommended for all students.

MAT 109 Foundations of Mathematics 3 cr

Introduces the fundamental principles of various areas of mathematics as they relate to the other liberal arts. Topics may include symbolic logic, sets and combinatorics, probability, introductory descriptive statistics, geometric structures, and finance.

FLC, Area I, Level 1

Core, III

MAT 110 Introduction to Statistics 3 cr

Presents the basic principles of statistics with applications to the social sciences. Topics include descriptive statistics, correlation, regression, experimental design, probability theory, normal and binomial distributions, central limit theorem, and control charts, with an introduction to the use of statistical software (SPSS).

Prerequisite: MAT 109 or higher level math course

FLC, Area V, Level 1

MAT 123 PreCalculus Mathematics 4 cr

Prepares students for calculus. Subjects include the concept of a function, exponential and logarithmic functions, trigonometric functions and coordinate geometry. A student who already has a good grasp of these topics should elect MAT 125 instead of this course.

Prerequisite: High school algebra

FLC, Area V, Level 1

Core, III

MAT 125 Calculus and Analytic Geometry I 4 cr

Examines the following topics: functions, limits, continuity, differentiation and applications, and basic integration.

Prerequisite: High school algebra and trigonometry

FLC, Area V, Level 1

Core, III

MAT 126 Calculus and Analytic Geometry II 4 cr

Examines the following topics: applications of the definite integral, integration of algebraic and transcendental functions, infinite series, and topics in analytic geometry.

Prerequisite: MAT 125

FLC, Area V, Level 1

Core, III

MAT 141 Introduction to Programming 3 cr

Introduces students to programming and graphical user interfaces. Basic principles of programming including object-oriented design will be covered.

Prerequisite: MAT 104 or by permission of the instructor

MAT 210 Statistical Inference 3 cr

Applies the principles of inference to the social sciences. Topics include confidence intervals, inference for distributions, one and two sample ttest, ztest, Ftest, comparing two proportions, chi square test, simple and multiple linear regression, and analysis of variance. Use of statistical software is an integral part of the course.

Prerequisite: Grade of "C" or better in MAT 110

FLC, Area V, Level 2

MAT 212 Statistics for Teachers of Advanced Placement Statistics 3 cr

Recommended for the high school teachers who teach advanced placement statistics courses. Topics include descriptive statistics, estimation of one population mean, chi-square test, goodness of fit test, and simple regression. Hands-on activities accompanying the theories will be provided.

MAT 227 MultiVariable Calculus 4 cr

Examines the calculus of functions of several variables. Topics include partial derivatives, multiple integrals, and the calculus of vector fields, including Green's Theorem.

Prerequisite: Grade of "C" or better in MAT 126

FLC, Area V, Level 1

MAT 237 Differential Equations 3 cr

Examines the basic techniques for solving ordinary differential equations, which arise in such areas as physics, chemistry, and biology.

Prerequisite: MAT 126

 

MAT 241 Intermediate Level Programming 3 cr

Builds on the material from MAT 141, Introduction to Programming. Students will build larger programs with an emphasis on problem solving and algorithm development. Abstract data structures such as arrays, linked lists, queues, graphs, and trees and the design analysis of efficient algorithms will be studied. Applications from business and science will be covered.

Prerequisite: MAT 141

MAT 240 Advanced Programming 3 cr

Examines topics in computer science requiring programming expertise. Topics include recursion, dynamic data structures, sorting, searching, and elements of numerical analysis and computer graphics. Programming done in the Pascal language.

Prerequisite: MAT 241

MAT 245 Introduction to Abstract Mathematics 3 cr

Provides a transition from the skills courses in mathematics to the more abstract courses for the mathematics major. Students will be exposed to the research tools in mathematics. Proof as a concept and a process will be examined in light of previous content in calculus, geometry, and algebra.

Prerequisite: MAT 126

MAT 247 Linear Algebra 4 cr

Develops methods of solutions of systems of linear equations, the theory of matrices, determinants, vector spaces, linear transformations, and eigenvalues.

Pre or co-requisite: MAT 126

MAT 290 Discrete Mathematics and Mathematical Modeling 3 cr

Introduces discrete mathematics with applications to mathematical modeling. Possible topics include Markov chains, game theory, group decision-making, measurement, and utility.

Prerequisite: MAT 126

MAT 300 Statistical Methods 3 cr

Reviews two types of statistical study: observational and experimental study. Using either MINTAB or SPSS, exploring data, assessing random sampling, and interpreting computer output will be disussed. Topics also include estimation, hypothesis testing, correlation analysis, and experimental design. Students will work on a semester project that combines all materials that they learn through this course.

Prerequisite: MAT 210

MAT 301 Abstract Algebra I 3 cr

Introduces the basic concepts of abstract algebra, including groups, subgroups, factor groups, homomorphism and isomorphism, and rings and fields.

Prerequisites: MAT 245 and MAT 247

MAT 303 Number Theory 3 cr

Examines topics in introductory number theory, including basic concepts of integers and congruencies, Fermat's and Wilson's theorems, Diophantine equations, and quadratic reciprocity.

Pre or co-requisite: MAT 247

MAT 305 Computer Applications to Statistics 3 cr

Students will learn how to use statistical software such as MINITAB, SPSS, and SAS. Topics include basic statistical analysis and understanding programming languages using MINITAB, SPSS and SAS.

Prerequisite: MAT 210

MAT 335 Mathematical Probability and Statistics 3 cr

Provides a calculusbased analysis of probability and statistics. Topics include probability, random variables, probability distributions, sampling distributions, and the central limit theorem.

Prerequisite: MAT 126

 

MAT 340 History of Mathematics 3 cr

Surveys the development of mathematics from ancient civilizations to modern times. The student sees that mathematics is a human endeavor developed through experimentation and the need to solve real world problems.

Prerequisite: MAT 125 or higherlevel math course

FLC, Area V, Level 2

MAT 401 Special Topics in Statistics 3 cr

Offers the opportunity to study selected topics in-depth. Topics include sampling theory, regression analysis, multivariate statistical methods, experimental design, and nonparametric statistics. Students may repeat this course with different topics.

Prerequisite: MAT 300

MAT 421 Real Analysis I 3 cr

Presents the basic concepts of analysis, including sets and functions, the real numbers, the topology of Euclidean spaces, compact and connected sets, continuity and uniform continuity, convergence and uniform convergence, and the Riemann integral.

Prerequisite: MAT 245

MAT 424 Complex Variables 3 cr

Examines the theory of functions of a complex variable. The course includes the complex number system and the theory of differentiation and integration of complex functions through the residue theorem.

Prerequisite: MAT 245; recommended: MAT 421

MAT 450 Geometry 3 cr

Examines topics to be selected from Euclidean geometry, nonEuclidean geometry, and projective geometry.

Prerequisite: MAT 247

MAT 490 Mathematics Senior Seminar 3 cr

Provides a capstone experience required of all senior mathematics majors. Each student completes a comprehensive project that involves researching an area of mathematics not studied in formal course work. Through the project the student must demonstrate the ability to read and write mathematics, and as a culmination of the experience, students present their work in a formal lecture.

Prerequisite: Senior status