Faculty
Sita Ramamurti, Associate Professor of Mathematics (Program Chair)
Lee Chiang, Associate Professor of Mathematics
Emily Gamundi, Clare Boothe Luce Assistant Professor of Mathematics
Laurie Johnson, Clare Boothe Luce 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 a major in
mathematics and minors in mathematics and applied statistics 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. MATH 431 Real
Analysis I is strongly recommended for students who plan to attend
graduate school.
Required Courses (32 credits)
ALL of the following mathematics courses:
MATH 125 Calculus and Analytic Geometry I
MATH 225 Calculus and Analytic Geometry II
MATH 301 Linear Algebra
MATH 325 Multivariable Calculus
MATH 331 Introduction to Abstract Mathematics
MATH 315 Mathematical Probability and Statistics
MATH 403 Abstract Algebra I
MATH 499 Senior Seminar
ONE course in computer science:
CMSC 111 Introduction to Programming
Supplemental Requirements (8 credits)
BOTH of the following physics courses:
PHYS 111 General Physics I
PHYS 112 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:
MATH 431 Real Analysis I
MATH 437 Complex Variables
ONE additional course at the 200-level or above*
TWO additional courses at the 300-level or above*
* Students may substitute courses in computer science (CMSC) with
permission of the Program Chair.
Area B Requirements
ALL of the following courses:
MATH 327 Differential Equations
MATH 371 History of Mathematics
MATH 433 Number Theory
MATH 435 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:
MATH 125 Calculus and Analytic Geometry I
MATH 225 Calculus and Analytic Geometry II
MATH 331 Introduction to Abstract Mathematics
TWO additional courses at the 200-level or above*
TWO additional courses at the 300-level or above*
* Students may substitute courses in computer science (CMSC) with
permission of the Program Chair.
Minor in Applied Statistics
Students minoring in Applied Statistics must complete at least 19
credits of course work that satisfies the following requirements.
Required Courses (13 credits)
ALL of the following courses:
MATH 110
Introduction to Statistics
MATH 125
Calculus and Analytic Geometry I
MATH 210
Statistical Inference
MATH 310
Applied Statistical Methods
TWO more courses (at least 6 credits) chosen from:
CMSC 111
Introduction to Programming
MATH 315
Mathematical Probability and Statistics
MATH 410
Special Topics in Applied Statistics
MATH 345
Operations Research
The descriptions of each of the above courses along with the
prerequisites are included in the Course Descriptions
section below.
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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 MATH 125. Students who score 4 or 5 on the BC calculus exam
may receive credit for MATH 225 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 MATH 103. A satisfactory score on the CLEP exam in
calculus will be accepted in lieu of MATH 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 MATH 125 and MATH 225 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 MATH 499 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
MATH 101 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 or Core math requirement.
Formerly MAT 103A Intermediate Algebra.
3 credits
MATH 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. Recommended for students preparing to take MATH 123 Pre-calculus.
Formerly MAT 103 College Algebra.
3 credits
MATH 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. Recommended for students planning to major in social sciences.
Formerly MAT 108 Elementary Mathematical Modeling.
3 credits
Prerequisites: MATH 101 or placement test proficiency
FLC Area IV, Quantitative Analysis Cluster
Core III
MATH 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. Recommended for students who do not plan to take another math course.
Formerly MAT 109 Foundations of Mathematics.
3 credits
Prerequisites: MATH 101 or placement test proficiency
FLC Area IV, Quantitative Analysis Cluster
Core III
MATH 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.
Formerly MAT 110 Introduction to Statistics.
3 credits
Prerequisites: MATH 108, MATH 109 or higher level mathematics course
MATH 123 Pre-calculus
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.
Formerly MAT 123 Pre-calculus.
4 credits
Prerequisites: MATH 103 or placement test proficiency
FLC Area IV, Quantitative Analysis Cluster
Core III
MATH 125 Calculus and Analytic Geometry I
Examines the following topics: functions, limits, continuity, differentiation and applications, and basic integration.
Formerly MAT 125 Calculus and Analytic Geometry I.
4 credits
Prerequisites: MATH 123 or placement test proficiency
FLC Area IV, Exploration Cluster
Core III
MATH 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.
Formerly MAT 210 Statistical Inference.
3 credits
Prerequisites: MATH 110 with a grade of “C” or better
FLC Area IV, Exploration Cluster
MATH 225 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.
Formerly MAT 126 Calculus and Analytic Geometry II.
4 credits
Prerequisites: MATH 125
MATH 301 Linear Algebra
Develops methods of solutions of systems of linear equations, the theory of matrices, determinants, vector spaces, linear transformations, and
eigenvalues. Formerly MAT 247 Linear Algebra.
4 credits
Prerequisites: MATH 225 (may be taken concurrently)
MATH 310 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.
Formerly MAT 300 Applied Statistical Methods.
3 credits
Prerequisites: MATH 210
MATH 315 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.
Formerly MAT 335 Mathematical Probability and Statistics.
3 credits
Prerequisites: MATH 125
MATH 325 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.
Formerly MAT 227 Multi-Variable Calculus.
4 credits
Prerequisites: MATH 225 with a grade of “C” or better
MATH 327 Differential Equations
Examines the basic techniques for solving ordinary differential equations, which arise in such areas as physics, chemistry, and biology.
Formerly MAT 237 Differential Equations.
3 credits
Prerequisites: MATH 225
MATH 331 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.
Formerly MAT 245 Introduction to Abstract Mathematics.
3 credits
Prerequisites: MATH 225
MATH 341 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.
Formerly MAT 290 Discrete Mathematics and Mathematical Modeling.
3 credits
Prerequisites: MATH 225
MATH 345 Operations Research
Examines selected topics in operations research. Such topics include
linear programming, simplex method, transportation problem, and network
optimization. Formerly MATH 308 Operations Research.
3 credits
Prerequisites: MATH 301
MATH 371 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.
Formerly MAT 340 History of Mathematics.
3 credits
Prerequisites: MATH 125
MATH 403 Abstract Algebra I
Introduces the basic concepts of abstract algebra, including groups, subgroups, factor groups, homomorphism and isomorphism, and rings and fields.
Formerly MAT 301 Abstract Algebra I.
3 credits
Prerequisites: MATH 301 and MATH 331
MATH 410 Special Topics in Applied Statistics
Introduces selected topics in applied statistics such as actuarial mathematics, biostatistics, survival analysis, experimental design, or operations research. Students will be required to read and present information found in journal articles.
Formerly MAT 401 Special Topics in Applied Statistics.
3 credits
Prerequisites: MATH 300
MATH 431 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.
Formerly MAT 421 Real Analysis I.
3 credits
Prerequisites: MATH 331
MATH 433 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.
Formerly MAT 303 Number Theory.
3 credits
Prerequisites: MATH 301 (may be taken concurrently)
MATH 435 Geometry
Examines topics to be selected from Euclidean geometry, non-Euclidean geometry, and projective geometry.
Formerly MAT 450 Geometry.
3 credits
Prerequisites: MATH 301
MATH 437 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.
Formerly MAT 424 Complex Variables.
3 credits
Prerequisites: MATH 331; MATH 431 is recommended
MATH 491 Internship in Mathematics
Provides practical experience in an area of applied mathematics. Students must make special arrangements with the Program Chair.
Credits arranged
Prerequisites: Permission of Program Chair
MATH 498 Independent Study
Provides an opportunity for directed study.
Credits arranged
Prerequisites: Permission of Program Chair
MATH 499 Senior Seminar in Mathematics
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.
Formerly MAT 490 Mathematics Senior Seminar.
3 credits
Prerequisites: Senior Status
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