# Mathematics

### Bachelor of Arts in Mathematics

Mathematics provides a unique and critical lens for viewing and analyzing the world. In addition to being the international language of the sciences, mathematics facilitates the representation, evaluation and solution of problems in many fields. New England College offers a range of undergraduate courses from introductory mathematics to pure and applied mathematics. The goals of the department are to enable students to develop critical and quantitative thinking that will lead to rational and logical decisions. The mathematics program is designed to prepare students for careers in business, education, and the sciences.

## Requirements to Major in Mathematics

Grades of C- or better are needed in all courses for the mathematics major.

**A. Collegium Requirements**

- NSM 3000 – Careers in Science
*(1cr)* - NSM 4000 – Senior Science Thesis
*(Variable credit)*

**B. Major Requirements**

- CT 1510 – Introduction to Programming Logic and Design
- MT 2110 – Discrete Mathematics
- MT 2310 – Statistics
- MT 2510 – Calculus I
- MT 2520 – Calculus II
- MT 3530 – Calculus III
- MT 4110 – Linear Algebra
- MT 4120 – Abstract Algebra
- MT 4540 – Differential Equations
- PH 2210 – General Physics I
- PH 2220 – General Physics II

**C. Two Electives, from the Following List**

- CT 3560 – Internet Programming
- MT 2610 – Geometry
- MT 3150 – History of Mathematics
- MT 3310 – Mathematical Modeling
- MT 3990 – Topics in Mathematics
- MT 4810 – Directed Study in Math
*(1-4cr)* - MT 4830 – Independent Study in Math
*(1-4cr)*

**D. Distribution Courses and Electives**

## Requirements to Minor in Mathematics

- MT 2110 – Discrete Mathematics
- MT 2310 – Statistics
- MT 2510 – Calculus I
- MT 2520 – Calculus II

One elective selected from the following list:

- MT 3530 – Calculus III
- MT 4110 – Linear Algebra

One elective selected from the following list:

- MT 2610 – Geometry
- MT 3150 – History of Mathematics
- MT 3310 – Mathematical Modeling
- MT 3990 – Topics in Mathematics
- MT 4120 – Abstract Algebra
- MT 4540 – Differential Equations

**Course Descriptions**

***All undergraduate courses are 4 credits unless otherwise noted.*

**MT 0990 Essential Mathematics**

The mathematics of integers and rational numbers, decimals and percent, algebraic expressions, linear equations and geometric formulas. Students may be required to take this course on the basis of their placement test scores. *This course does not satisfy the College’s mathematics requirement. Offered every fall. (2cr)** *

**MT 0995 Essential Mathematics II**

This course will focus on basic algebra topics such as: variable, algebraic expressions, solving equations and inequalities in one variable, translating and solving applied problems, exponents, and polynomials. It is intended for students who need review of basic algebra skills. Students may be required to take this course on the basis of their placement test scores. *This course does not satisfy the College’s mathematics requirement. Offered every semester. (2cr)*** **

**MT 1020 College Algebra**

This course will focus on the application of algebra to real world problems including intermediate algebra topics such as solving linear equations and inequalities, solving quadratic equations, graphing linear, quadratic, and other polynomial functions, rational functions, factoring, and solving systems of equations. Emphasis will be on solving real world problems by incorporating graphical, symbolic, and numeric representations. It is designed primarily for students who require and/or need additional preparation for statistics and pre-calculus. *Prerequisite: MT0995or adequate performance on the mathematics placement test.*** **

**MT 1100 Introduction to Quantitative Reasoning**

The goal of this course is to develop students’ ability to think critically about quantitative statements and information. In this course, students will have opportunities to evaluate the strengths and weaknesses of numerical evidence and logical arguments, to apply mathematical methods in the context of real-world problems, and to study and employ strategies and methods for how to manipulate, understand, analyze, and interpret quantitative information. Students who do not need to take a higher level Algebra course should find this an interesting way of meeting the college-wide mathematics graduation requirement. *Prerequisites: MT0995or adequate performance on the mathematics placement test.*** **

**MT 1510 Precalculus**

This course will focus on analysis and applications of algebraic and transcendental functions. Topics include: linear and quadratic functions, polynomial functions, rational functions, exponential and logarithmic functions, and trigonometric functions, inequalities, graphical analysis, and an introduction to analytic geometry. Applications of these topics include: rates of change, optimization, logarithmic or exponential modeling, and trigonometric functions. *Prerequisite: C- or better in MT 1020 or adequate performance on the mathematics placement test.*** **

**MT 2110 Discrete Mathematics**

This course is intended to give an introduction to the area of mathematics called “discrete mathematics.” Discrete mathematics is that part of mathematics dealing with finite – but often large – sets of objects. Discrete mathematics is to be contrasted with “continuous” mathematics, for example the classical theory of calculus. Topics include: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, recursion, recurrence relations, and number theory. *Prerequisites: C- or better in MT 2510. Offered every other year.*** **

**MT 2121 (ED 2121) Mathematics Content for Elementary Teachers **

This course will provide prospective or in-service elementary teachers with the opportunity to explore and master concepts involving number systems and operations, data analysis and probability, geometry, measurement, and algebraic thinking. Mathematical reasoning, problem solving, and the use of appropriate manipulatives and technology will be integrated throughout the course. The course will model instructional techniques that can be adapted to elementary curricula. *Prerequisite: Grade of C or better in ED 2110 and MT 1020 or passing score on Math Placement Test. Offered every fall. (2cr)*

**MT 2210 (ED 2210) Curriculum and Methods of Teaching Elementary Mathematics **

This course focuses on current methods in the teaching of mathematics in the K-8 classroom. The material will focus on curriculum and integration of mathematics into the other areas in teaching K-8 children. Mathematics useful for prospective elementary school teachers, including basic arithmetical operations for whole numbers, fractions and decimals, Euclidean and other geometries and other topics will be covered. *Prerequisite: Grade of C or better in ED 2110. Offered every fall. (2cr)*** **

**MT 2310 Statistics**

An introductory course in statistics designed to cover the basic concepts of descriptive statistics: classification and organization of data, graphical displays, measures of central tendency, dispersion and relative position, and correlation and regression. The normal and binomial distributions and the fundamentals of probability theory used in statistical methods will be presented. Basic concepts of estimation (confidence intervals and sample size), tests of significance (*z*, *t*, chi-square, and *F*), multiple regression, and analysis of variance will also be introduced. Real world applications with SPSS, Excel, and/or scientific calculators will be emphasized. *Recommended for second-year students.* *Prerequisite: C- or better in MT 1020 or adequate performance on the mathematics placement test.*** **

**MT 2510 Calculus I**

Elementary set theory and analytic geometry, calculus of one variable covering limits, derivatives of algebraic, trigonometric, exponential, and logarithmic functions; an introduction to integration; applications include curve sketching, max-min problems, and related rates. *Prerequisite: C- or better in MT 1510 or adequate performance on the mathematics placement test. Offered every year.*** **

**MT 2520 Calculus II**

This course is a continuation of the calculus series. The course will investigate differentiation and integration of exponential, logarithmic, trigonometric, hyperbolic functions and their inverses; techniques of integration, L’Hôpital’s rule, improper integrals, and infinite series. *Prerequisite: C- or better in MT 2510. Offered every year.*** **

**MT 2610 Geometry**

Advanced approach to fundamental properties of Euclidean and other geometries. Topics are selected from among projective geometry, finite geometries, convexity, transformational geometry, non-Euclidean geometry, and other areas of elementary geometry within the framework of modern mathematics. Required for mathematics/education majors. *Prerequisite: C- or better in MT 2110. Offered every other year.*** **

**MT 3150 History of Mathematics **

This course analyzes the development of various branches of mathematics (including number theory, geometry, probability, algebra, and analysis) from ancient times through calculus of 17th-century Europe. We will also address the influences of eastern and western cultures and their contributions to the development of mathematics. *Prerequisite: C- or better in MT 2510. Offered every other year.*** **

**MT 3310 Mathematical Modeling**

An introduction to the mathematical techniques used to explore, model, and analyze phenomena in business, engineering, and the social, biological and earth sciences. Topics include probability theory, exponential growth and decay, stochastic modeling, regression and Markov models, optimization, periodic functions, rates of change, graphical analyses, and asymptotic behavior of functions. In many instances, real data drawn from the biological and earth sciences will be used to develop, implement and analyze the models. *Prerequisites: CT 1510 and C- or better in MT 2510. Offered every other year.*

**MT 3530 Calculus III**

This course covers the topics of conic sections, polar coordinates, parametric equations, vector algebra; vector functions, partial derivatives, and multiple integrals. *Prerequisite: C- or better in MT 2520. Offered every other year*.** **

**MT 3990 Topics in Mathematics**

Different topics in mathematics at the introductory level. Topics may include: real and complex analysis, topology, number theory, dynamical systems, numerical analysis, etc. *May be repeated for credit on different topics.* *Prerequisite: varies by topic. Offered upon sufficient demand.*** **

**MT 4110 Linear Algebra**

Basic concepts of linear algebra including: linear systems and matrices, determinants, eigenvalues and eigenvectors, vector spaces, subspaces, linear independence, basis, dimension, linear transformations, and diagonalization. Applications may include linear programming, the simplex method, graph theory, least squares approximations, and quadratic forms. *Prerequisite: C- or better in MT 2110. Offered every other year.*** **

**MT 4120 Abstract Algebra**

Presents basic concepts and techniques of group theory: axiomatic definition of groups, important classes of groups (abelian groups, cyclic groups, additive groups of residues, and permutation groups), quotient groups, and direct products. This course also introduces basic concepts of rings, such as ideals, integral domains, polynomial rings, and factor rings, the basic concepts of fields, and the theory of extension fields. Emphasis will be placed on structural properties of groups, rings, and fields. *Prerequisite:* C*- or better in MT 2110. Offered every other year.*** **

**MT 4540 Differential Equations**

First order differential equations, including existence and uniqueness theorems, separation of variables, and their applications, linear systems of differential equations, Laplace transforms and their use in solving linear systems. Applications include population models, ecological models, mechanical systems, forced oscillation, and resonance. Additional topics that will be covered may include dynamical systems and chaos, series, matrix, and numerical methods. *Prerequisite: C- or better in MT 3530. Offered every other year.*

**MT 4810 Directed Study in Mathematics **

Course of study to be arranged between faculty and student in the field of mathematics. *May be repeated for credit. Variable credit (1-4), depending on contract.*** **

**MT 4830 Independent Study in Mathematics**

Advanced, independent study of a specific topic arranged with a faculty member. *Variable credit (1-4), depending on contract.*** **

**MT 4910 Internship in Mathematics**

Qualified juniors or seniors apply knowledge and theories gained in class to real situations. Students may work with cooperating employers on either a full or part-time basis to achieve predefined objectives that have been developed and accepted by the student, the employer and a faculty supervisor. The student’s internship is developed under the guidance of the director of the mathematics program. *Variable credit (1-15).*** **

**NSM 3000 Careers in Science**

This one-credit course is designed to give junior science majors the opportunity to hone the practical skills needed to have a successful career in the fields under the NSM Collegium. There will be activities addressing: self-assessment of personal attributes, potential career paths, resume and cover letter writing, job searching and interviewing, and graduate school options. *Offered every spring*. *(1cr)*

**NSM 4000 Senior Science Thesis**

As a two-semester capstone experience, students will develop and implement a thesis that utilizes skills and knowledge gained from their NSM major. During the fall semester students will form a faculty committee and develop a thesis proposal in a topic associated with their major. During the spring semester students will implement and report on the thesis. The thesis will emphasize application of skills such as: literature review, critical thinking, data collection and analysis, written communication, oral communication, and project management. *Offered every year.* *(2 credits fall and 2 credits spring)*