Faculty
Lee Chiang, Associate Professor of Mathematics (Program Chair)
Tasha R. Inniss, Clare Boothe Luce Assistant Professor of Mathematics
Laurie Johnson, Clare Boothe Luce Assistant Professor of Mathematics
Sita Ramamurti, Assistant Professor of Mathematics
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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 analytical 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/statistical software packages
and computer languages. 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.
Women in Math, Science and Engineering (WMSE) is an organization for
students pursuing majors in math, science or in applications of these
areas. The goal of WMSE is to expose students to available career
opportunities, and to inform about summer programs, internships, and
graduate programs. The club sponsors talks with professional scientists
employed in a variety of academic and nonacademic settings and arranges
trips to technical companies and industrial/governmental firms.
The Mathematics Program supports both a major and minor in
mathematics and computer science in the College of Arts and Sciences.
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.
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Major Requirements
To earn the bachelor's degree in mathematics, students must complete
52 credits distributed among required courses, supplemental
requirements, and EITHER Area A OR Area B requirements. MAT 421 Real
Analysis I is strongly recommended for students who plan to attend
graduate school.
Required Courses (32 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
Supplemental Requirements (8 credits)
BOTH of the following physics courses:
PHY 115 General Physics I
PHY 116 General Physics II
Area Requirements (12 credits)
Students must complete the requirements for EITHER Area A OR Area B.
Area A Requirements
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
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
should refer to the B.A./M.A.T. section of
this catalog and confer with an advisor in the School of Education.
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Minor Requirements
Required Courses (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
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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 103/103A. A satisfactory score on the CLEP exam in
calculus will be accepted in lieu of MAT 125.
Cross-listed Courses: Courses
that are cross-listed represent identical courses offered with a
different program prefix. Students may not enroll in or receive credit
for more than one iteration of a cross-listed course even in different
semesters.
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 declare 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 Program Chair.
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Course Descriptions
MAT 100A Beginning Algebra
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.
3 credits
MAT 103A Intermediate Algebra
Provides students with an intensive review of high school algebra.
Topics include a review of basic arithmetic operations, the real number
system, algebraic expression and exponents with basic rules of algebra,
linear equations and inequalities with applications, and graphs of
equations and inequalities. Recommended for students who need a review
of high school algebra before fulfilling the FLC math requirement.
3 credits
MAT 103 College Algebra
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.
3 credits
MAT 108 Elementary Mathematical Modeling
Introduces mathematical modeling based on the use of elementary
functions to describe and explore real-world data and phenomena. Built
on interesting applications of elementary mathematics, students are
taught how to construct useful mathematical models, to analyze them
critically, and to communicate quantitative concepts effectively.
Integrates the use of graphing calculators.
3 credits
Prerequisite: MAT 103a or MAT 103
FLC Area IV, Quantitative Analysis Cluster
Core III
MAT 109 Foundations of Mathematics
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.
3 credits
Prerequisite: MAT 103a or MAT 103
FLC Area IV, Quantitative Analysis Cluster
Core III
MAT 110 Introduction to Statistics
Presents the basic principles of statistics with applications to the
social sciences. Topics include descriptive statistics, probability
theory, normal and binomial distributions, and central limit theorem,
with an introduction to the use of statistical software.
3 credits
Prerequisite: MAT 108 or MAT109
MAT 123 Precalculus Mathematics
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.
4 credits
Prerequisite: MAT103
FLC Area IV, Quantitative Analysis Cluster
Core III
MAT 125 Calculus and Analytic Geometry I
Examines the following topics: functions, limits, continuity,
differentiation and applications, and basic integration.
4 credits
Prerequisite: MAT 123
FLC Area IV, Exploration Cluster
Core III
MAT 126 Calculus and Analytic Geometry II
Examines the following topics: applications of the definite integral,
integration of algebraic and transcendental functions, infinite series,
and topics in analytic geometry.
4 credits
Prerequisite: MAT 125
Core III
MAT 141 Introduction to Programming
Serves as an entry-level programming course recommended for all
students. Objects, arrays, program flow (if-then-else, while, do-while,
for, switch), simple graphical user interfaces and applets, problem
solving techniques, and elementary algorithms are covered. Effective
design, implementation, debugging, and documentation of object-oriented
programs are emphasized.
4 credits
FLC Area IV, Exploration Cluster
MAT 210 Statistical Inference
Applies the principles of inference to the social sciences. Topics
include confidence intervals, inference for distributions, one and
two-sample t-test, z-test, F-test, chi-square test, linear regression
analysis and comparing two proportions. Use of statistical software is
an integral part of the course.
3 credits
Prerequisite: Grade of "C" or better in MAT 110
FLC Area IV, Exploration Cluster
MAT 227 Multi-Variable Calculus
Examines the calculus of functions of several variables. Topics include
partial derivatives, multiple integrals, and the calculus of vector
fields, including Green's Theorem.
4 credits
Prerequisite: Grade of "C" or better in MAT 126
MAT 237 Differential Equations
Examines the basic techniques for solving ordinary differential
equations, which arise in such areas as physics, chemistry, and biology.
3 credits
Prerequisite: MAT 126
MAT 241 Intermediate Programming
Provides a continuation of the development of object-oriented design and
implementation using a current programming language. Inheritance,
polymorphism, error-handling, I/O, advanced graphical user interfaces,
and data representation are covered.
3 credits
Prerequisite: MAT 141
MAT 245 Introduction to Abstract Mathematics
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.
3 credits
Prerequisite: MAT 126
MAT 247 Linear Algebra
Develops methods of solutions of systems of linear equations, the theory
of matrices, determinants, vector spaces, linear transformations, and
eigenvalues.
4 credits
Pre-requisite: MAT 126 (may be taken concurrently)
MAT 249 Social Implications of Information Systems
Develops students' awareness of the social, moral, ethical, and
philosophical impact of computers and computer-based systems on current
and future society. Topics include the impact of major computer-based
applications, human-machine relationships, and the major problems of
controlling the use of computers.
3 credits
Prerequisite: MAT 141
MAT 290 Discrete Mathematics and Mathematical Modeling
Introduces discrete mathematics with applications to mathematical
modeling. Possible topics include Markov chains, game theory, group
decision-making, measurement, and utility.
3 credits
Prerequisite: MAT 126
MAT 300 Applied Statistical Methods
Applies statistical techniques to the natural and social sciences.
Topics include: Regression Analysis, Analysis of Variance (ANOVA), Time
Series Analysis, Analysis of Contingency Tables, and Goodness of Fit
Tests. Use of statistical software is an integral part of the course.
3 credits
Prerequisite: MAT 210
MAT 301 Abstract Algebra I
Introduces the basic concepts of abstract algebra, including groups,
subgroups, factor groups, homomorphism and isomorphism, and rings and
fields.
3 credits
Prerequisites: MAT 245 and MAT 247
MAT 303 Number Theory
Examines topics in introductory number theory, including basic concepts
of integers and congruencies, Fermat's and Wilson's theorems,
Diophantine equations, and quadratic reciprocity.
3 credits
Pre-requisite: MAT 247 (may be taken concurrently)
MAT 306 Computer Organization
An introduction to the principles of computer organization and
architecture including register and memory organization, representations
of numbers and data, digital logic, and boolean algebra. Also, an
introduction to assembly language programming including files,
interrupts, and arithmetic and logical operations. Algorithm efficiency
analysis is discussed.
3 credits
Prerequisite: MAT 141
MAT 307 Database Management Systems
An introduction to the design, organization, implementation and
evaluation of database systems. File organization and processing,
hierarchical, network and relational models of database structure,
database languages and queries are studied.
3 credits
Prerequisites: MAT 141
MAT 308 Operations Research
Examines selected topics in operations research. Such topics
include linear programming, simplex method, transportation problem, and
network optimization.
3 credits
Prerequisite: MAT 247
MAT 335 Mathematical Probability and Statistics
Provides a calculus-based analysis of probability and statistics. Topics
include probability, random variables, probability distributions,
sampling distributions, and the central limit theorem.
3 credits
Prerequisite: MAT 125
MAT 340 History of Mathematics
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.
3 credits
Prerequisite: MAT 125 or higher level math course
MAT 343 Computer Networks
Introduces concepts of computer networks, including systems
architecture, system communication and protocols, shared resource
management, and memory management.
3 credits
Prerequisite: MAT 241
MAT 385 Data Structures and Algorithms
Advanced algorithms such as recursion, sorting and searching and data
representation such as lists, linked lists, stacks, queues and hash
tables are discussed. Programming assignments are in a current
programming language.
3 credits
Prerequisite: MAT 241
MAT 401 Special Topics in Applied Statistics
Introduces selected topics in applied statistics such as actuarial
mathematics, biostatistics, survival analysis, design of experiments or
operations research. Students will be required to read and present
information found in journal articles.
3 credits
Prerequisite: MAT 300
MAT 421 Real Analysis I
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.
3 credits
Prerequisite: MAT 245
MAT 424 Complex Variables
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.
3 credits
Prerequisite: MAT 245; recommended: MAT 421
MAT 441 Principles of Programming Languages
Studies the syntax and semantics of computer languages. Topics
include language scope of objects and time of binding, definition
structure, data types and structures, data abstraction, control
structures, run-time considerations, interpretive languages and parsing.
Functional, object-oriented, and logic programming languages will be
covered.
3 credits
Prerequisite: MAT 385
MAT 443 Operating Systems
Covers significant topics in operating systems, including system
structure, process management (scheduling, synchronization, deadlocks),
memory management (allocation, scheduling, swapping), file systems, and
computer security.
3 credits
Prerequisite: MAT 385
MAT 445 Systems Analysis and Design
Introduces principles of software engineering. Topics studied
include requirements analysis, data flow diagrams, software design and
implementation techniques, testing strategies, and project management
techniques. The course includes team development of a large software
project written in a current programming language, utilizing concepts
learned in the course.
3 credits
Prerequisite: MAT 385
MAT 447 Introduction to Artificial Intelligence
Introduces various concepts and applications in artificial
intelligence (AI), the construction of computer programs that act
rationally within an environment to solve problems. Topics include
knowledge representation, searching, heuristic search, reasoning with
uncertainty, and learning.
3 credits
Prerequisite: MAT 385
MAT 450 Geometry
Examines topics to be selected from Euclidean geometry, non-Euclidean
geometry, and projective geometry.
3 credits
Prerequisite: MAT 247
MAT 490 Mathematics Senior Seminar
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.
3 credits
Prerequisite: Senior status
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