Mathematics
Faculty
Dr. Kerry Luse, Clare Boothe Luce Assistant Professor of Mathematics (program chair)
Dr. Lee Chiang, Associate Professor of Mathematics
Dr. Sita Ramamurti, Professor of Mathematics
The mathematics program is also supported by a dedicated team of Instructional Specialists.
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.
The Women in Math and Science (TWMS) is an organization for students pursuing majors in math, science or in applications of these areas. The goal of TWMS 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 and a minor in mathematics in the College of Arts and Sciences. The major 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.
Major Requirements
To earn the bachelor’s degree in mathematics, students must complete 52 credits distributed among required courses and supplemental requirements. MATH 431 Real Analysis IPresents 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 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 IExamines 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
General Education: Knowledge and Inquiry Area
FLC Area IV: Exploration Cluster
MATH 225 Calculus and Analytic Geometry IIExamines 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
Prerequisite: MATH 125
MATH 301 Linear AlgebraDevelops 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 325 Multi-Variable CalculusExamines 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 331 Introduction to Abstract MathematicsProvides 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 315 Mathematical Probability and StatisticsProvides 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.
MATH 403 Abstract Algebra IIntroduces 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 499 Senior Seminar in MathematicsProvides 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
CMSC 111 Introduction to ProgrammingServes 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. Formerly MAT 141 Introduction to Programming.
Supplemental Requirements (20 credits)
BOTH of the following physics courses:
PHYS 111 General Physics ICovers mechanics in a calculus-based course in fundamental physics. Topics include Newton's laws, work and energy, rotational dynamics, conservation of energy, and momentum. Intended primarily for students in math and science but open to all qualified students. The course consists of three hours of lecture, three of laboratory, and a one-hour problem session per week. There is an additional laboratory fee for this course. Formerly PHY 115 General Physics I.
4 credits
Prerequisite: MATH 125
General Education Requirement: Kniowledge and Inquiry Area
FLC Area IV, Laboratory Science Cluster
PHYS 112 General Physics IICovers electricity, magnetism, and electro-magnetic propagation in a calculus-based course in fundamental physics. Topics include electric fields, Maxwell's equations, electrical circuits, magnetic fields, and light. Intended primarily for students in math and science but open to all qualified students. The course consists of three hours of lecture, three of laboratory, and a one-hour problem session per week. There is an additional laboratory fee for this course. Formerly PHY 116 General Physics II.
4 credits
Prerequisites: MATH 125 and PHYS 111
ONE course chosen from between the following:
MATH 431 Real Analysis IPresents 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 437 Complex VariablesExamines 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.
ONE additional course at the 200-level or above
TWO additional courses at the 300-level or above
Minor Requirements
Minor in Mathematics:
Required Courses (23 credits)
ALL of the following courses:
MATH 125 Calculus and Analytic Geometry IExamines 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
General Education: Knowledge and Inquiry Area
FLC Area IV: Exploration Cluster
MATH 225 Calculus and Analytic Geometry IIExamines 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
Prerequisite: MATH 125
MATH 331 Introduction to Abstract MathematicsProvides 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
TWO additional courses at the 200-level or above
TWO additional courses at the 300-level or above
Minor in Applied Statistics:
Required Courses (19 credits)
ALL of the following courses:
MATH 110 Introduction to StatisticsPresents 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
General Education: Knowledge and Inquiry Area
Prerequisites: MATH 108, MATH 109 or higher level mathematics course
MATH 125 Calculus and Analytic Geometry IExamines 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
General Education: Knowledge and Inquiry Area
FLC Area IV: Exploration Cluster
MATH 210 Statistical InferenceApplies 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 310 Applied Statistical MethodsApplies 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
TWO more courses (at least 6 credits) chosen from:
CMSC 111 Introduction to ProgrammingServes 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. Formerly MAT 141 Introduction to Programming.
MATH 315 Mathematical Probability and StatisticsProvides 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.
MATH 410 Special Topics in Applied StatisticsIntroduces 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
MATH 345 Operations ResearchExamines selected topics in operations research. Such topics include linear programming, simplex method, transportation problem, and network optimization. Formerly MAT 308 Operations Research.
Program Policies
Advanced Placement:
Students who score 4 or 5 on the calculus AB or BC exam will receive credit for MATH 125 Calculus and Analytic Geometry IExamines 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
General Education: Knowledge and Inquiry Area
FLC Area IV: Exploration Cluster. Students who score 4 or 5 on the BC calculus exam may receive credit for MATH 225 Calculus and Analytic Geometry IIExamines 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
Prerequisite: MATH 125 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 Calculus and Analytic Geometry IExamines 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
General Education: Knowledge and Inquiry Area
FLC Area IV: Exploration Cluster.
Cross-tallied Courses:
Courses that are cross-tallied 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-tallied 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 the mathematics major, a student must receive a “B” or better in MATH 125 Calculus and Analytic Geometry IExamines 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
General Education: Knowledge and Inquiry Area
FLC Area IV: Exploration Cluster and MATH 225 Calculus and Analytic Geometry IIExamines 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
Prerequisite: MATH 125 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 in MathematicsProvides 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.
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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