Mathematics (B.S.)
Faculty
Dr. Lee Chiang, Associate Professor of Mathematics (program chair)
Dr. Kerry Luse, Clare Boothe Luce 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 exposure to the use of mathematical and 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. Students are exposed to available career opportunities, summer programs and internships, and graduate programs through the department and Trinity’s student-led math and science club (Ladies FIRST). The mathematics department also sponsors and co-sponsors visits by a variety of academic and nonacademic professionals in STEM fields.
The mathematics program supports a major as well as a minor in the College of Arts and Sciences. The major prepares students for graduate school and professional positions in government, business, education 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. Students interested in secondary education can major in mathematics and minor in education.
Major Requirements
To earn the bachelor’s degree in mathematics, students must complete 52 credits distributed among required courses and supplemental requirements.
Please note:
- Strongly recommended for students who plan to attend graduate school: 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
- Strongly recommended for students interested in secondary education: MATH 435 GeometryExamines topics to be selected from Euclidean geometry, non-Euclidean geometry, and projective geometry. Formerly MAT 450 Geometry.
3 credits
Prerequisites: MATH 331
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.
3 credits
Prerequisite: MATH 125
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: Knowledge 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 435 GeometryExamines topics to be selected from Euclidean geometry, non-Euclidean geometry, and projective geometry. Formerly MAT 450 Geometry.
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.
3 credits
Prerequisite: MATH 331
ONE additional mathematics course at the 200-level or above
TWO additional mathematics 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 mathematics courses at the 200-level or above
TWO additional mathematics courses at the 300-level or above
Individualized Minor
Students interested in further studies in the area of statistics may pursue an individualized minor in applied statistics in consultation with the program chair.
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 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:
To declare the mathematics major, a student must successfully complete MATH 125 and MATH 225 with either a “B” (3.0) or better or the approval of the program chair. Majors and minors are required to earn a grade of “C” (2.0) or better in all other courses counted to fulfill requirements.
Pass/No Pass:
No major or minor courses may be taken pass/no pass.
Senior Assessment:
Every mathematics major must successfully complete MATH 499.
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.
Course Descriptions
MATH 102 College AlgebraThis is a quantitative literacy course intended for mathematics, science (STEM), business, and economics majors. Topics covered include exponents, factoring, polynomials, quadratic equations, and rational and radical equations. Additional topics include functions, graphs, and systems of equations and inequalities. Unit conversions and dimensional analysis is also covered. Real-world applications will be emphasized throughout the course. Formerly MATH 102 Intermediate Algebra.
4 credits
Prerequisites: None
General Education: Foundational Skills
MATH 108 Finite MathematicsThis is a quantitative literacy and reasoning course designed for education majors and those students intending to study nursing and other allied health fields. Topics include: problem solving, set theory, logic, algebra, and measurement; including unit conversions and dimensional analysis. Additional topics include functions, graphs, systems of equations and inequalities, as well as probability and statistics. Real-world applications will be emphasized throughout the course. Formerly MATH 108 and MAT 108 Elementary Mathematical Modeling.
4 credits
Prerequisites: None
General Education Area: Foundational Skills
MATH 109 Foundations of MathematicsThis quantitative literacy course is intended for social science and humanities majors. The course is designed to teach quantitative reasoning by emphasizing topics, both useful and relevant to a liberal-arts program, that enable students to become quantitatively literate. Topics include financial literacy, unit conversions, an introduction to linear and exponential functions and mathematical modeling, probability and statistics as well as math in politics.Formerly MAT 109 Foundations of Mathematics. This course may not be taken pass/fail by School of Professional Studies students.
4 credits
Prerequisites: None
General Education Area: Foundational Skills
MATH 110 Introduction to StatisticsThis course presents the basic principles of statistics with applications to the social sciences. Topics include descriptive statistics, graphical representations of data, normal probability distributions and the Central Limit Theorem, linear correlation and regression and probability theory. This course also offers an introduction to the use of statistical software. Formerly MAT 110 Introduction to Statistics.
3 credits
Prerequisites: MATH 102, MATH 108, MATH 109 or higher level mathematics course.
MATH 123 Pre-CalculusPrepares 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 102 with C or better or proficiency test with permission of instructor
General Education: Knowledge and Inquiry Area
FLC Area IV: Quantitative Analysis Cluster
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 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 299H Math Across Cultures: Ethnomathematics - HONORSCourse Description: Ethnomathematics is the study of mathematical ideas expressed and embedded in various traditional cultures of indigenous people from around the world. The different cultures introduced will include the Maya, Marshall Islanders, Tongans, Trobriand Islanders, Borano, Malagasy, Basque, Tamil, Balinese, and Kodi. This capstone Honors course will explore the mathematical concepts of numeration systems, graph theory, probability, geometry and logic. The seminar will focus on how culture gives rise to and influences each of these mathematical ideas. This course is limited to Honors Program students or with permission of instructor only.
Credits: 3
Prerequisites: status as an Honors Program student or with permission of instructor only
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 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.
3 credits
Prerequisite: MATH 125
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 327 Differential EquationsExamines 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 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 341 Discrete Mathematics and Mathematical ModelingIntroduces 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 371 History of MathematicsSurveys 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 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 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 433 Number TheoryExamines 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 GeometryExamines topics to be selected from Euclidean geometry, non-Euclidean geometry, and projective geometry. Formerly MAT 450 Geometry.
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.
3 credits
Prerequisite: MATH 331
MATH 491 Internship in MathematicsProvides 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 StudyProvides an opportunity for directed study. Credits arranged by Program Chair.
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