Mathematics

Faculty
Description
Major Requirements
Minor Requirements
Program Policies
Course Descriptions

Faculty

Lee Chiang, Associate Professor of Mathematics (Program Chair)
Sita Ramamurti, Associate Professor of Mathematics 
Nermine El-Sissi, 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 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.

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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 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
CMSC 111 Introduction to Programming

Supplemental Requirements (20 credits)

BOTH of the following physics courses: 

PHYS 111 General Physics I 
PHYS 112 General Physics II

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

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Minor Requirements

Minor in Mathematics:

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

Minor in Applied Statistics:

Required Courses (19 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

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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-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 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 101S Supplemental Instruction Introductory Algebra
Constitutes the supplemental instruction portion of MATH 101.  Strengthens mathematical skills through a variety of theoretical and practical exercises whose purpose is to reinforce students' success in MATH 101.
1 credit
Corequisite MATH 101
 

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 103S Supplemental Instruction College Algebra
Constitutes the supplemental instruction portion of MATH 103.  Strengthens mathematical skills through a variety of theoretical and practical exercises whose purpose is to reinforce students' success in MATH 103.
1 credit
Corequisite MATH 103

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
General Education  Curriculum: Foundational Skills Area
FLC Area IV, Quantitative Analysis Cluster

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
General Education Curriculum: Foundational Skills Area
FLC Area IV, Quantitative Analysis Cluster

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
General Education Curriculum: Knowledge and Inquiry Area
Prerequisites: MATH 108, MATH 109 or higher level mathematics course

CMSC 111 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. Formerly MAT 141 Introduction to Programming.
4 credits
FLC Area IV: Exploration Cluster

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
General Education Curriculum: Knowledge and Inquiry Area
FLC Area IV: Quantitative Analysis Cluster

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
General Education Curriculum: Knowledge and Inquiry Area
FLC Area IV: Exploration Cluster

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

CMSC 211 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. Formerly MAT 241 Intermediate Programming.
3 credits
Prerequisites: CMSC 111
Cross-tallied with ISYS 241 Intermediate Programming

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
Prerequisite: 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

CMSC 311 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. Formerly MAT 385 Data Structures and Algorithms.
3 credits
Prerequisites: CMSC 111
Cross-tallied with ISYS 341 Data Structures and Algorithms

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 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

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 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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