Mathematics

MATH0118 R for Statistics Lab In this course, students will learn R for performing statistical analyses. R is a powerful statistical software which is free and widely available. The workshop will get students familiar with R syntax and to use the software for analyses. Fall and spring semesters. 0 credits Prerequisite: MATH1117

MATH1101 College Algebra

Quantitative Analysis (QA) Quantitative Reasoning (QR)

This course provides a foundation in the skills and concepts of algebra, including linear, quadratic, exponential and logarithmic equations and functions. Applications to real-world problems are emphasized throughout. The course is designed primarily to prepare students for further study in business and the natural and social sciences. Fall and spring semesters. 4 credits

MATH1103 Precalculus Mathematics

Quantitative Analysis (QA) Quantitative Reasoning (QR)

This course is designed to prepare students for calculus (MATH1111). It includes the study of polynomial, exponential, logarithmic and trigonometric functions and their graphs. Fall and spring semesters. 4 credits Prerequisite: Satisfactory score on the math placement exam or MATH1101

MATH1105 Mathematical Reasoning for Modern Society

Quantitative Analysis (QA) Quantitative Reasoning (QR) Social Justice (SJ)

This survey course introduces students to some applications of mathematics and quantitative reasoning with a particular emphasis on how mathematics can be used to spotlight and analyze issues of social justice. The topics chosen will depend on the instructor’s discretion, student interest, and current events; they may include: voting systems and elections, statistics in the news and social media, graph theory and its applications to urban planning, data and algorithmic bias, measuring climate change and social inequalities, and more. This course shows students the usefulness of mathematical thinking and helps them to make sense of, and act on, the abundance of numerical information in modern society. Fall and spring semesters. 4 credits

MATH1111 Calculus I

Quantitative Analysis (QA) Quantitative Reasoning (QR)

This course studies limits and continuity, differential calculus of algebraic, trigonometric and transcendental functions, applications of the derivative, and introduction to integration through the fundamental theorem of calculus. Fall and spring semesters. 4 credits Prerequisite: Satisfactory score on the math placement exam or MATH1103

MATH1112 Calculus II

Quantitative Analysis (QA) Quantitative Reasoning (QR)

This course is a continuation of Calculus I and includes methods of integration, applications of the definite integral, and infinite sequences and series. Fall and spring semesters. 4 credits Prerequisite: MATH1111

MATH1117 Introduction to Statistics

Quantitative Analysis (QA) Quantitative Reasoning (QR)

This is an introductory course in statistics. The objective of this course is to organize, summarize, interpret, and present data using graphical and tabular representations; apply principles of inferential statistics; and assess the validity of statistical conclusions. Students will learn to select and apply

appropriate statistical tests and determine reasonable inferences and predictions from a set of data. Topics include descriptive statistics; introduction to probability; probability distributions including normal and t-distributions; confidence intervals; hypothesis testing; correlation and regression; two-way tables and chisquare test. Course involves regular use of statistical software. Fall and spring semesters. 4 credits Prerequisites: Satisfactory score on the math placement exam or MATH1101

MATH1118 Introduction to Statistics with R

Quantitative Analysis (QA) Quantitative Reasoning (QR)

This is an introductory course in statistics. The objective of this course is to organize, summarize, interpret, and present data using graphical and tabular representations; apply principles of inferential statistics; and assess the validity of statistical conclusions. Students will learn to select and apply appropriate statistical tests and determine reasonable inferences and predictions from a set of data. Topics include descriptive statistics; introduction to probability; probability distributions including normal and t-distributions; confidence intervals; hypothesis testing; correlation and regression; two-way tables and chi-square test. Course includes a 50-minute lab to learn and use R statistical software. Fall and spring semesters. 4 credits Prerequisites: Satisfactory score on the math placement exam or MATH1101

MATH1120 Foundations of Mathematics for Teachers I

Quantitative Analysis (QA) Quantitative Reasoning (QR)

MATH1120 is the first course in a threesemester mathematics content sequence designed to develop fundamental computation skills and a comprehensive, in-depth understanding of K-8 mathematics among elementary education majors. This course focuses on numeration systems and properties of numbers. Different numeration systems will be studied, followed by operations on whole numbers, integers and rational numbers. Problem solving will be emphasized throughout the course. Spring semester. 4 credits

MATH1121 Applied Mathematics for Management

Quantitative Analysis (QA) Quantitative Reasoning (QR)

This course introduces students to a variety of useful mathematical principles and techniques, and develops their skills in problem-solving and utilizing technological resources, e.g. Microsoft Excel. Particular topics will be chosen by the instructor to emphasize applications in business and economics and may include: linear functions and models, systems of linear equations, exponential and logarithmic functions, linear programming and the Simplex Method, and formulas for financial mathematics. Fall and spring semesters. 4 credits Prerequisite: Satisfactory score on the math placement exam or MATH1101

MATH1122 Foundations of Mathematics for Teachers II

Quantitative Analysis (QA) Quantitative Reasoning (QR)

MATH1122 is the second course in a three-semester mathematics content sequence designed to develop fundamental computation skills and a comprehensive, in-depth understanding of K-8 mathematics among elementary education majors. This course begins with a study of patterns and functions, followed by a study of twodimensional geometry, and concludes with a study of measurement. Problem solving will be emphasized throughout the course. Fall semester. 4 credits Prerequisite: MATH1120

MATH2101 Linear Algebra

Quantitative Analysis (QA) Quantitative Reasoning (QR)

This course serves as a transition from computational mathematics to more theoretical approaches. Topics include systems of linear equations and their solutions; matrices and matrix algebra; inverse matrices; determinants; vector spaces and their axioms; linear transformations; and eigenvalues and eigenvectors. Some applications of linear algebra will also be discussed. Fall semester. 4 credits Prerequisite: MATH1111 or MATH1121 or placement by department

MATH2103 Calculus III

Quantitative Analysis (QA) Quantitative Reasoning (QR)

This course extends the study of calculus to functions of several variables. Topics covered include vectors, partial derivatives, multivariable optimization, multiple integrals, and vector calculus. Applications to the natural sciences are emphasized. Fall semester. 4 credits Prerequisite: MATH1112

MATH2104 College Geometry

Quantitative Analysis (QA) Quantitative Reasoning (QR)

Euclidean geometry has long been held as an essential part of mathematics. Its results and methods of deduction have been valued and found application in architecture, law, engineering, and many other fields. This class is a deeper look into Euclidean geometry and the underlying axioms. Particular emphasis will be placed on the development of mathematical reasoning through critical analysis and construction of formal proof. In addition, we will explore changes in the underlying axioms of Euclidean geometry and several different types of non-Euclidean geometry created by these changes. Geometric software will be used as a tool to construct geometric figures and for analytic proofs. Fall semester odd years. 4 credits Prerequisite: MATH1111

MATH2107 Differential Equations

Quantitative Analysis (QA) Quantitative Reasoning (QR)

Many of the principles governing the behavior of the real world can be described mathematically by differential equations. This course studies the theory and applications of ordinary differential equations. Topics covered include first-order and higher-order differential equations, systems of differential equations, Laplace transforms, numerical methods, phase plane methods, and modeling using differential equations. Applications will be drawn from science and engineering. Spring semester, even years. 4 credits Prerequisite: MATH1112

MATH2109 Introduction to Proofs

Quantitative Analysis (QA) Quantitative Reasoning (QR)

In this course, students are introduced to methods for reading and writing formal mathematical proofs, including proofs by contradiction, by induction, and by contrapositive. More advanced courses in mathematics will assume familiarity with such methods. Particular topics are chosen at the instructor’s discretion and may include set theory, number theory, algebraic structures, combinatorics, or graph theory. Spring semester. 4 credits Prerequisite: MATH1111

MATH2111 Mathematical Modeling for Social Justice

Quantitative Analysis (QA) Quantitative Reasoning (QR) Social Justice (SJ)

This course introduces the methods of mathematical modeling, focusing on applications to problems of social justice. Students will learn to formulate models appropriate for intended applications

in social justice, and investigate them mathematically and computationally. Topics are chosen by instructor. Modeling techniques may include discrete dynamical systems, differential equations, Markov chains, and game theory. Applications may include measures of social welfare, dynamics of inequality, redlining, climate change, voting, and social choice. The course will culminate in an independent modeling project on a social justice topic of the student’s choice. Spring semester, odd years. 4 credits Prerequisite: MATH1112

MATH2113 Statistics with R

Quantitative Analysis (QA) Quantitative Reasoning (QR)

This course is a calculus-based introduction to statistics. Topics covered include descriptive statistics, elements of probability, binomial and normal probability distributions, estimation, hypotheses testing, and simple linear regression. R statistical software is used to summarize data and perform statistical tests. Fall semester. 4 credits Corequisite: MATH1112

MATH2115 Introduction to Programming with MATLAB

Quantitative Analysis (QA) Quantitative Reasoning (QR)

MATLAB is a programming language that is used extensively by mathematicians and scientists in both academia and industry. This course, which does not assume any prior experience with programming, will introduce students to general concepts in computer science and programming as they formulate, solve, and visualize quantitative problems. Applications will be drawn from mathematics and science. The course will culminate in a project in which students develop a MATLAB program to study a problem of their choosing. Fall semester, even years. 4 credits Prerequisite: MATH1111 MATH2122 Foundations of Mathematics for Teachers III

Quantitative Analysis (QA) Quantitative Reasoning (QR)

MATH2122 is the third course in a threesemester mathematics content sequence designed to develop fundamental computation skills and a comprehensive, in-depth understanding of K-8 mathematics among elementary education majors. The course will focus on topics in linear programming, analytic geometry, probability, and statistics. This course, like Foundations I and II, will deepen students’ knowledge of mathematics and provide a solid foundation for learning about the methods for teaching elementary school mathematics. Spring semester. 4 credits Prerequisite: MATH1122 Corequisite: MATH2122L

MATH2122L Preparatory Lab for Math Subtest MTEL The audience for this laboratory is teacher candidates intending to become licensed to teach at the elementary level in grades 1–6. This is a preparatory lab designed to familiarize teacher candidates with the content and structure of the mathematics subtest of the General Curriculum Massachusetts Test for Educator Licensure (03). Teacher candidates will examine the mathematical content of the MTEL (03) test objectives as they practice multiple-choice and open-response problems both during and outside of class. Teacher candidates enrolled in MATH 2122 who have not successfully completed the math subtest of the General Curriculum MTEL (03) by the start of the MATH 2122 course must concurrently enroll in this preparatory lab. Teacher candidates enrolled in the lab are also required to register for a late spring MTEL (03) test date within the first two weeks of beginning the preparatory lab. This lab does NOT satisfy the college-wide QA requirement and does not contribute to the credits for graduation. Any teacher

candidate enrolled in MATH 2122 who has successfully completed the math subtest of the (03) MTEL is exempt from taking this preparatory lab. Spring semester. 0 credits

MATH3101 Real Analysis In this course, students investigate the theoretical foundations of calculus and deepen their conceptual knowledge by reading and writing formal proofs about sequences, limits, functions, and derivatives. This also serves as an introduction to fundamental principles and techniques of mathematical analysis. Other topics – such as integration or sequences of functions –may be explored, at the instructor’s discretion. Spring semester, even years. 4 credits Prerequisites: MATH2103, MATH2109

MATH3103 Probability This course is an introduction to the theory of probability and its applications. Topics include combinatorial analysis, probability laws, discrete and continuous random variables, joint distributions, the Law of Large Numbers, and the Central Limit Theorem. Spring semester, odd years. 4 credits Prerequisite: MATH2103 and MATH2113

MATH3105 Advanced Statistics This course is a continuation of MATH 2113 Statistics with R. More advanced topics in statistics will be covered, including contingency tables, exact tests, single and multiple linear regression, one-way and two way analyses of variance, logistic regression and nonparametric methods. Students will learn both the theory behind these statistical procedures and practical applications using a statistical software. At the end of the course, students will perform data analyses on their own data sets, write a paper summarizing the statistical methods they used, the data they worked on, the results they received, and give a short presentation. Fall semester, odd years. 4 credits Prerequisites: MATH2101, MATH2113

MATH3107 Abstract Algebra This course studies abstract algebraic systems such as groups, examples of which are abundant throughout mathematics. It attempts to understand the process of mathematical abstraction, the formulation of algebraic axiom systems, and the development of an abstract theory from these axiom systems. Topics may include groups, rings, fields, and homomorphisms. Spring semester, odd years. 4 credits Prerequisites: MATH2101, MATH2109

MATH3113 Special Topics in Mathematics This course is on a special topic in Mathematics not listed among the current course offerings. Fall semester, even years. 4 credits Prerequisites: MATH1112 and (MATH 2101 or MATH 2109)

MATH4101 Programming in SAS SAS is a powerful statistical software package used by statisticians worldwide in a diverse range of fields, from sociology to business to medicine. In this course, students will be introduced to SAS, and learn to develop templates, scripts and routines they can use to analyze data. Statistical concepts will come from MATH 2113 Statistics with R and MATH 3105 Advanced Statistics. At the end of the course, students will use SAS to perform data analyses on their own data sets, write a paper summarizing the statistical methods they used, the data they worked on, the results they received, and give a short presentation. Spring semester, even years. 4 credits Prerequisite: MATH3105

MATH4157 Senior Seminar This seminar serves as the culminating experience for mathematics majors.

Students will research and present on advanced topics in mathematics, as chosen by the students and/or the instructor. In addition, as part of the capstone experience, each student will compile and present a portfolio of their work as a mathematics major. Spring semester. 4 credits Prerequisite: Senior mathematics major status

MATH4178 Directed Study The course is available for junior or senior mathematics majors. This is an independent study of material not covered in offered courses. Offered as needed. 4 credits Prerequisite: Consent of department chair

MATH 4194/4195 Research Internships I and II Qualified students may undertake senior year research projects under the supervision of Emmanuel mathematics faculty or with faculty at other departments or institutions. With their research supervisor, students plan and carry out original research projects in mathematics and/or statistics that reflect their interests and goals. If the research supervisor is not a member of the Emmanuel mathematics faculty, a faculty coordinator from the department will be assigned to the project. A proposal for the internship must be submitted by April 1 of their junior year for committee review. The proposal describes the project, the name and commitment from the research supervisor (and faculty coordinator if applicable), and the expectations and significance of the project. Students devote a minimum of 15 hours per week to the project. Students meet weekly with their research supervisor, and also with the faculty coordinator, if applicable. An undergraduate thesis and presentation, including a defense, are required. MATH4194 and MATH4195 together represent a two-semester course. Students are not permitted to register for only one semester. Upon successful completion of the sequence, only MATH4194 may count as a mathematics elective. Both MATH 4194 and MATH4195 are required for distinction in the fields of mathematics or biostatistics. Offered as needed. 4 credits Prerequisite: Senior status, at least 3.3 grade point average in courses toward Mathematics or Biostatistics major, and permission of the department.

INT3211 Experiential Internship in the Natural Sciences/Mathematics Biology, biostatistics, chemistry and mathematics majors may apply to do an internship in a research or non-research setting. The internship site and project must be appropriate for the disciplines above and it is the student’s responsibility to obtain an internship. The options for sites could include venues that would allow for career exploration. A complete proposal form for the internship must be submitted to the faculty teaching the course and to the Career Center by the first day of class. The proposal must describe the project, the name and commitment from the onsite supervisor and the expectations and significance of the internship. The proposal must be approved by the student’s academic advisor and signed by the site supervisor. Students meet for a minimum of 15 hours per week at the internship site. Students meet weekly with a faculty coordinator and are evaluated by the site supervisor and faculty coordinator. A comprehensive portfolio and formal presentation are required. This one-semester internship course counts as an Emmanuel College elective, but not as an elective toward the biology, biostatistics, chemistry or mathematics major. Arts and Sciences Course Descriptions for