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Courses:
MATH 0104 PRE-CALCULUS (3) Topics covered include an in-depth investigation of functions; graphing; exponential and logarithmic functions; and trigonometry. Prerequisite: High School Algebra II or MATH 0103.
MATH 0105 CALCULUS I (4) A standard first semester course in calculus. Topics include limits and continuity, the derivative and its properties, applications of differentiation, introduction to anti-differentiation, the definite integrals, and the Fundamental Theorem of Calculus. Prerequisites: Four years of High School Math, including Algebra I and II and Geometry or MATH 0104.
MATH 0106 CALCULUS II (4) A continuation of Calculus I. Topics include techniques of integration, applications of the integral, series and sequences, L'Hôpital's Rule, approximation of functions. Prerequisite: MATH 0105 or equivalent.
MATH 0108 ELEMENTARY STATISTICS (3) An introduction to basic concepts and techniques of statistics for students needing skills for research techniques in education, business, and the physical, life, and social sciences, or simply to understand the mass of statistical information in modern life. Topics include: graphical techniques such as histograms or box plots; measures of location and spread; scatter plots and correlation; sampling and sampling distributions; estimation and statistical inference (confidence intervals and/or hypothesis testing). Prerequisite: High School Algebra II or MATH 0103.
MATH 0110 MATHEMATICAL EXPLORATIONS (3) An introductory course designed to provide the liberal arts major with an opportunity to develop a broader appreciation of mathematics by exploring ways in which the artistic, aesthetic, intellectual, and humanistic aspects of mathematics are as important as its utility. Topics may include: mathematical reasoning, the infinite, topology, chaos and fractals, symmetry, elementary number theory, modern geometry, and the history of mathematics. Prerequisite: High School Algebra II or MATH 0103.
MATH 0111 MATHEMATICAL APPLICATIONS (3) An introductory course designed to provide the liberal arts major with opportunities to investigate ways in which mathematics is used to solve real world problems in a variety of disciplines. Applications may include such topics as voting schemes, fair division, networks, scheduling, finance, probability and statistics. Prerequisite: High School Algebra II or MATH 0103.
MATH 0115 MATHEMATICS FOR BUSINESS AND SOCIAL SCIENCES (3) An introduction to algebraic modeling, with an emphasis on applications in business and the social sciences. Topics include: using algebraic models to describe the relationship between variables, using graphs to visualize models, and choosing and interpreting various models. Calculus is introduced and is used as a tool for studying the structure of algebraic models. Prerequisite: High School Algebra II or MATH 0103.
MATH 0150 FOUNDATIONS: MATHEMATICAL REASONING (3) An introductory course in the foundations of mathematics. Topics will include: finding, analyzing, and describing patterns; sets and classification; functions and relations; inductive and deductive reasoning; problem solving and logic. Students will develop a conceptual understanding of the course material in a learning environment that models the pedagogical foundations of the Massachusetts Curriculum Frameworks for Mathematics and the NCTM Standards. Prerequisite: High School Algebra II or MATH 0103.
MATH 0201 CALCULUS III (4) A continuation of Calculus II. Topics include vector functions and calculus of curves in space, differential calculus of multivariate functions, integral calculus of multivariate functions, polar, spherical and cylindrical coordinates, parametric equations, Cartesian coordinates, line and surface integrals. Prerequisite: MATH 0106 or equivalent.
MATH 0216 STUDIES IN THE LITERATURE OF MATHEMATICS (3) A study of mathematical literature devoted to selected topics from fundamental scientific, philosophical, artistic, cultural, and technological questions, debates, and revolutions. Source material will be taken from the widely varied genres of mathematical literature: fiction, drama, essays, memoirs, exposition for lay audiences, history, and philosophy. Regular class discussions, regular writing assignments, poster projects, and research papers actively will involve students in analyzing and/or creating literature, which reflects both their role in and the understanding of the mathematical experience. Prerequisites: ENGL 0101 and at least one 0100-level mathematics course.
MATH 0218 LINEAR ALGEBRA (3) Study of fundamental concepts of linear algebra over the field of real numbers. Topics include solution of simultaneous linear equations, vector spaces, linear independence an dependence, basis, subspaces, linear transformations and matrices, eigenvalues, eigenvectors. Prerequisite: MATH 0105.
MATH 0220 DISCRETE STRUCTURES (3) An introduction to discrete mathematical structures for Computer Science: discrete algebraic structures, algorithms and applications to structural programming and the analysis of algorithms; graphs, digraphs and applications to electrical and scheduling network; lattices, Boolean algebra and applications to switching theory. Prerequisite: CAIS 0120 and MATH 0118.
MATH 0237 MATHEMATICS TUTOR TRAINING SEMINAR (1) A training seminar for upper-class students involved with the Mathematics Peer Tutoring Program to meet the following three objectives: 1) presenting mathematics with understanding and flexibility; 2) recognizing, diagnosing, and remediating common math misconceptions, 3) becoming more sensitive to some of the affective issues arising both in tutoring relationships and for students struggling with mathematics. Prerequisites: MATH 0106, permission of instructor, and concurrent participation in the mathematics tutoring program. May be elected only once for credit.
MATH 0251 FOUNDATIONS: GEOMETRY (3) The study of the foundations of Geometry and Mensuration. Topics will include topological, projective, and Euclidean properties in 2- and 3- space; the development of the concept of measure in 2- and 3- space; and the introduction of measurement formulas. Students will develop a conceptual understanding of the course material and will work with mathematics manipulatives. Prerequisite: MATH 0150 or equivalent.
MATH 0252 FOUNDATIONS: PROBABILITY AND STATISTICS (3) The study of the foundations of Probability and Statistics. Topics will include techniques for collecting, tabulating, and analyzing data, using probability principles, construction of histograms, hypothesis testing, and the formulation of inferences using principles of statistics. Students will develop a conceptual understanding of the course material and will work with mathematics manipulatives. Prerequisite: MATH 0150 or equivalent.
MATH 0253 FOUNDATIONS: NUMBER SYSTEMS (3) The study of the real number system and its subsets. Topics will include the structure and properties of the whole, integer, rational and real number systems and the application of four-function calculators to problem solving and estimation. Students will develop a conceptual understanding of the course material and will work with mathematics manipulatives. Prerequisite: MATH 0150 or equivalent.
MATH 0301 ABSTRACT ALGEBRA I (3) A study of groups, rings, integral domains and fields, with special emphasis on the real and complex fields. Prerequisite: MATH 0118.
MATH 0304 DIFFERENTIAL EQUATIONS (3) Geometric and physical meaning of differential equations. Theory and solution of first, second and higher order linear and non-linear differential equations. Initial and boundary value problems. Finite difference equations. Prerequisites: MATH 0201 and MATH 0118.
MATH 0306 MODERN GEOMETRIES I (3) An integrated course consisting of intuitive, synthetic, and analytic approaches to Euclidean and other geometries. Topics will include axiomatic foundations, finite geometries, non-Euclidean geometries, and synthetic projective geometry. Prerequisite: MATH 0118.
MATH 0307 MODERN GEOMETRY II (3) Geometric and algebraic invariants, groups of transformations, topological, projective, affine and Euclidean transformations. Prerequisite: MATH 0306.
MATH 0308 REAL ANALYSIS (3) Topology of real numbers, Cauchy sequences, metric completeness, continuity, compactness, connectedness. Sequence and series and uniform convergence of infinite series. Derivatives and definite integrals. Prerequisite: MATH 0106.
MATH 0309 TOPOLOGY (3) A simple, thorough survey of the elementary topics of point-set topology of the real line and plane topological spaces; metric spaces; mappings; connectedness; compactness. Prerequisite: MATH 0201, junior or senior status in the major or permission.
MATH 0311 NUMBER THEORY (3) Properties of integers including congruences, primes and factorization, continued fractions, quadratic residues, linear diophantine equations and number theoretic functions. Prerequisite: junior or senior status in the major or permission.
MATH 0323 COMPLEX ANALYSIS (3) Algebra of complex numbers, analytic functions, Cauchy Riemann conditions, conformal mapping, line integrals, Cauchy integral formula, residue integration, Taylor and Laurent series. Prerequisite: MATH 0201.
MATH 0334 OPERATIONS RESEARCH AND MODELING (3) A study of mathematical modeling and of the models of interest in operations research, which may include distribution problems, linear programming, the simplex method and applications. CPM, network problems, non-linear programming problems, Markov chains, queuing models, and simulation. Prerequisites: MATH 0118, MATH 0108, and knowledge of at least one programming language.
MATH 0335 NUMERICAL ANALYSIS (3) Intended for majors in mathematics or computer science. Uses the FORTRAN language for numerical computation but no previous knowledge of FORTRAN is assumed. Standard algorithms of numerical analysis will be chosen from: systems of linear equations, differential equations, integration, interpolation, non-linear equations. Prerequisites: MATH 0118, MATH 0106 and knowledge of at least one programming language.
MATH 0337 FOUNDATIONS OF SECONDARY AND MIDDLE SCHOOL MATHEMATICS (3) Designed to build upon student's mathematics background, relating students' mathematical knowledge to understanding and teaching the middle or secondary school mathematics curriculum. Topics to be considered are: geometry, algebra, basic skills, number theory, probability and statistics and the use of calculators and computers in the classroom. A thirty (30) hour field experience is a course requirement. Prerequisites: Junior or senior status in the major or permission.
MATH 0340 MATHEMATICAL STATISTICS I (3) Covers mathematical probability theory including: review of set theory, principles of counting, sample spaces and probability functions, random variables, joint probability functions, discrete distributions and continuous distributions. Prerequisite: MATH 0106.
MATH 0351 FOUNDATION OF TEACHING MATHEMATICS: PreK-6 (2) Designed to introduce the prospective early childhood, elementary, and special education school teacher to the teahing of mathematics. An activity-based format will be used to create a learning environment that fosters an exploration of the processes of mathematics. Emphasis will be placed on the role and use of manipulatives in a laboratory setting that encourages the development of fundamental concepts in mathematics. Topics may include: the inductive and deductive processes, measurement, graphing, cognitive development theory, the learning cycle, discussion of innovative projects, state and national frameworks, techniques for assessment, number and arithmetic operations, patterns, variables, modeling and geometry. Three contact hours per week, including substantial laboratory/activity time.
Prerequisites: Mathematics and science courses required for early childhood, elementary, and special education licensure, or permission of instructor.
MATH 0360 CURRENT TRENDS IN MATHEMATICS AND MATHEMATICS EDUCATION (1-3) Students will work individually with a professor on a project or activity relating to current innovations in mathematics or mathematics education. Potential sources for study include: evaluation of innovative textual materials, trends in media and technology development, evaluation of software, development of laboratory materials, attendance at professional conferences, review and analysis of journal articles, and the presentation of reports on individual and institutional research activities. Course may be taken up to two times with the permission of the department chair. Prerequisite: Permission of instructor.
MATH 0390 SENIOR SEMINAR IN MATHEMATICS (3) A capstone experience for senior mathematics majors which unifies many areas of the undergraduate curriculum and serves as a right of passage into the community of mathematicians. The curriculum is topical in nature and varies by course offering. Topics that are studied are of contemporary importance and are considered from their historical genesis through their current role in the ongoing development of the field of mathematics. Prerequisite: Senior standing in mathematics or permission of instructor.
MATH 0398 INTERNSHIP IN MATHEMATICS (3-15) Internship in mathematics for full-time, upper level mathematics majors. Prerequisites: Junior/senior standing and dept. permission.
MATH 0399 INDEPENDENT STUDY (1-6) Independent study of topics in mathematics under careful faculty supervision. Intended for capable students to broaden their mathematics program or to gain depth in a particular area of interest. Prerequisite: permission of instructor and Department Chair.
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