# Mathematics

Aaron Clark

CHAIRPERSON

Engleman D 115

(203) 392-5493 – Fax (203) 392-6808

math.chair@SouthernCT.edu

Department Secretary: (203) 392-5576

Braxton Carrigan, Associate Professor

Aaron Clark, Professor

Alain D'Amour, Professor

Joseph Fields, Professor

Ross Gingrich, Associate Professor

Jooyoun Hong, Professor

John Kavanagh, Professor

Klay Kruczek, Associate Professor

Raymond Mugno, Professor

Yulei Pang, Associate Professor

Valeriu Pinciu, Professor

## MAJOR IN MATHEMATICS

The major provides the basic mathematical tools for applications in business and industry, such as actuarial science, computer work, statistics, operations research, teaching mathematics at the secondary school level, or pursuing graduate studies in mathematics, statistics, or related fields.

Additional elective courses in mathematics and the area of application should be chosen in consultation with a departmental adviser and can be selected to further career or graduate school objectives.

### MATHEMATICS COURSES

Entry into 100 level mathematics courses is based on the results of the mathematics placement process used by Southern. Additional information about the placement process is available at SouthernCT.edu/placement

Students may not receive credits toward graduation for both MAT 139 and 150 or both MAT 178 and 250 or both MAT 221 and 320.

Students may not receive more than 3 credits toward graduation from among MAT 100, 100P, 101, and 102 (formerly 119). Students taking both MAT 120 and MAT 122 can receive at most 4 credits toward graduation.

The department offers the following:

Data Science, B.S.

Mathematics, B.A.

Mathematics, B.S - Concentration: Applied

Mathematics 7-12, B.S.

Mathematics 7-12, Post-Baccalaureate Teacher Certification

Minor in Data Science

Minor in Mathematics

## DSC 100 - Data Science IThis course acts as the stepping stone to the realm of data science. Students will learn concepts from data science using python as the programming language. Course contents include: computing and programming, python language fundamentals, basic concepts from linear algebra, statistics, and probability for data science, and topics from various stages of the data science pipeline. Provides the necessary bases for students to develop an understanding of data science from a technical perspective and to move forward to advanced topics. Prerequisite(s): Grade of 'C' or better in MAT 112 or placement in MAT 122 or higher. 3 credit(s). Last Term Offered: Spring 2021 |

## DSC 101 - Data Science IIAn introduction to the data science life cycle. Topics include data extraction, and decision making using machine learning methods including regression, classification, clustering, and anomaly detection. Python language and related tools will be used for solving data science problems. Prerequisite(s): DSC 100 3 credit(s). Last Term Offered: Spring 2021 |

## DSC 490 - Data Science Capstone ProjectCulminating project that revolves around a student-selected data problem. Course activities parallel the various stages of the data science lifecycle. These include project conception, data acquisition, data cleaning and transformation, visualization, model building and evaluation, and presentation of findings. Prerequisite(s): Departmental permission, 6 of 8 Tier 2 complete (Honors Coll.: 15cr. HON or 45 cr. total), and prior or concurrent completion of all Tier 1 (Honors Coll.: T1MC and T1QR only). 3 credit(s). Last Term Offered: not yet offered |

## MAT 001 - Elementary Algebra Emporium0 credit(s). Last Term Offered: Summer 2019 |

## MAT 095 - Elementary AlgebraLinear equations, polynomials, straight lines, graphing, exponents, and word problems. Special Information: Credits count toward GPA calculation, but not toward graduation credit. Approved graphing calculator is required. 3 credit(s). Last Term Offered: Summer 2017 |

## MAT 100 - Intermediate AlgebraTopics include linear, quadratic, polynomial, and basic rational and radical functions with graphing and word problems. Prerequisite(s): 'C-' or better in MAT 095 or appropriate mathematics placement. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 100P - Introductory and Intermediate AlgebraTopics include real numbers and variables, plus linear, quadratic, polynomial, and basic rational and radical functions with graphing, word problems, and linear systems. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 102 - Intermediate Algebra (Extended)Solutions to linear equations and inequalities, polynomials, quadratic equations, exponential equations, graphing, rational and radical expressions, and functions. Special Information: Approved graphing calculator is required. Prerequisite(s): MAT 095 or MAT 101 or appropriate mathematics placement. 3 credit(s). Last Term Offered: Summer 2017 |

## MAT 103 - Mathematics for Liberal ArtsIntended for the student whose major field of study requires no specific mathematical preparation. Topics include probability, statistics, and aspects of consumer mathematics. Other topics chosen by the instructor could include critical thinking/problem solving, geometry, graph theory, linear and exponential models, and voting theory. Prerequisite(s): MAT 100 or MAT 100P or MAT 102, or appropriate mathematics placement. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 105 - Mathematics for Elementary Education IProblem solving, mathematical reasoning, sets, whole numbers, numeration systems, number theory and integers. Required of all students in an elementary school certification program. Does not satisfy the Liberal Education Program Quantitative Reasoning requirement. Prerequisite(s): MAT 100 or MAT 100P or MAT 102 or appropriate mathematics placement. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 106 - Mathematics for Elementary Education IIGeometry, measurement, rational numbers, irrational numbers, ratio, proportion, percent, problem solving, mathematical reasoning and connections, probability and statistics. Required of all students in an elementary school certification program. Prerequisite(s): "C-" or better in MAT 105. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 107 - Elementary StatisticsTopics include measures of central tendency and measures of variation; elements of probability; random variables; introduction to estimation and hypothesis testing; linear regression analysis. Special Information: Approved graphing calculator is required. Prerequisite(s): MAT 100 or MAT 100P or MAT 102 or appropriate mathematics placement. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 108 - Mathematics for the Natural SciencesElementary mathematical modeling using linear functions, exponential functions, and power functions. Additional topics include logarithms, curve sketching, and curve fitting. Examples from the natural sciences. Special Information: Approved graphing calculator is required. Prerequisite(s): MAT 100 or MAT 100P or MAT 102 with a grade of 'C-' or better or appropriate mathematics placement. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 112 - Algebra for Business and the SciencesAdvanced Intermediate Algebra course that includes concepts from Precalculus. Topics include multiple perspectives of functions: verbal, numerical, algebraic, and graphical and the various notations used to represent functions. Polynomial, absolute value, rational, and radical families of functions will be covered. Prerequisite(s): 'C-' or better in MAT 100 or MAT 100P, MAT 102 or placement at the appropriate level. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 120 - College AlgebraAlgebraic problem solving and quantitative reasoning skills needed for business and social science majors; equations and inequalities in one variable; linear, quadratic, exponential, and logarithmic functions; systems of linear equations in two variables. Special Information: Approved graphing calculator is required. Students may earn at most 4 credits toward graduation from MAT 120 and MAT 122. Prerequisite(s): C- or better in MAT 112 or appropriate mathematics placement. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 122 - PrecalculusFunctions and their graphs, polynomial functions and their zeros, exponential and logarithmic functions, trigonometric functions and analytic trigonometry. Function modeling of data and problems from the sciences. Special Information: Approved graphing calculator is required. Students may earn at most 4 credits toward graduation from MAT 120 and MAT 122. Prerequisite(s): 'C-' or better in MAT 112 or MAT 120, or appropriate mathematics placement. 4 credit(s). Last Term Offered: Spring 2021 |

## MAT 125 - Applied Business MathematicsTopics include exponential and logarithmic functions, systems of linear equations and matrices, linear inequalities, linear programming, Leontief models, limits, continuity, derivatives, and extrema of functions. interest and annuities, break-even, optimization, and other business applications will be emphasized. Prerequisite(s): 'C-' or better in MAT 112 or MAT 120 or MAT 122 or MAT 124 or appropriate math placement. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 139 - Short Course in CalculusA one-semester course emphasizing techniques and applications in business and social sciences; functions and models, the derivative, exponential and logarithmic functions, integration. Special Information: Approved graphing calculator is required. Students may earn at most 4 credits toward graduation from MAT 139 and MAT 150. Prerequisite(s): 'C-' or better in MAT 120, 122, 124, 125, or appropriate mathematics placement. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 150 - Calculus IFunctions, limits, differentiation of algebraic and trigonometric, exponential, and logarithmic functions with applications, indeterminate forms, elementary integrations, Riemann sums. Special Information: Approved graphing calculator is required. Students may earn at most 4 credits toward graduation from MAT 139 and MAT 150. Prerequisite(s): 'C-' or better in MAT 122 or appropriate mathematics placement. 4 credit(s). Last Term Offered: Spring 2021 |

## MAT 151 - Calculus IIContinuation of MAT 150. Calculus of inverse trigonometric functions, techniques, and applications of integration, numerical integration, improper integrals, integration with polar coordinates, parametric curves, infinite sequences and series, power series, Taylor’s formula, vectors in two and three-dimensions. Special Information: Approved graphing calculator is required. Prerequisite(s): 'C-' or better in MAT 150. 4 credit(s). Last Term Offered: Spring 2021 |

## MAT 178 - Elementary Discrete MathematicsSet theory, logic, methods of proof, relations and functions, mathematical induction, recursion, graph theory, and algorithms. Special Information: Students may earn at most 5 credits toward graduation from MAT 178 and MAT 250. Prerequisite(s): MAT 139 or MAT 150 or appropriate mathematics placement; and CSC 152 or DSC 101. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 207 - Mathematics for Middle School TeachersExamines the concepts of functions and patterns, geometry, counting principles, recursion, and statistical analysis while modeling middle school mathematics teaching. Special Information: Approved graphing calculator is required. Prerequisite(s): MAT 106 (or MAT 105 with departmental permission). 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 221 - Intermediate Applied StatisticsA treatment of statistics concentrating on techniques used in science and industry.Topics include probability, sampling distributions, estimation, hypothesis testing, regression analysis, and correlation. Use of appropriate calculator is required. Prerequisite(s): MAT 120 or MAT 122 or appropriate mathematics placement. MAT 139 or MAT 150 recommended. 4 credit(s). Last Term Offered: Spring 2021 |

## MAT 245 - Differential EquationsStudy of ordinary differential equations. Thorough investigation of first order equations. Additionally, second order linear equations with constant coefficients, systems of differential equations, Laplace transforms, and numerical methods. Prerequisite(s): 'C-' or better in MAT 151. 3 credit(s). Last Term Offered: Fall 2020 |

## MAT 250 - Foundations of MathematicsA bridge between the calculus and upper level mathematics courses. Logic, sets, relations, functions, methods of proof. Special Information: Students may earn at most 5 credits toward graduation from MAT 178 and MAT 250. Prerequisite(s): “C-” or better in MAT 151. 4 credit(s). Last Term Offered: Spring 2021 |

## MAT 252 - Calculus IIIContinuation of MAT 151. Vector-valued functions, three-dimensional geometry, functions of several variables, partial differentiation with applications, double and triple integrals with applications, vector calculus. Special Information: Approved graphing calculator is required. Prerequisite(s): 'C-' or better in MAT 151. 4 credit(s). Last Term Offered: Spring 2021 |

## MAT 260 - Geometry and the ArtsThe purpose of the course is to provide students with an adequate geometric background allowing them to understand basic Euclidean geometry. The course will enable students with basic tools for geometric reasoning and proof and will promote their geometric thinking skills. Throughout the course, students will explore and appreciate the use of geometry in the arts. They will identify, analyze, replicate and produce art work using geometric figures and transformations. Prerequisite(s): MAT 103 or higher. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 300 - History of MathematicsHistory of mathematics from earliest days to the discovery of calculus, the proliferation of mathematics in modern times, and the implications of these developments for the present day. Prerequisite(s): MAT 139 or MAT 150. 3 credit(s). Last Term Offered: Fall 2020 |

## MAT 320 - ProbabilityPost-calculus introduction to mathematical probability theory. Topics include Probability Axioms, Conditional Probability, Probability Distributions, Random Variables, Probability Densities, Multivariate Distributions and Densities, Markov Chains, Sampling Distributions, Central Limit Theorem. Prerequisite(s): 'C-' or better in both MAT 250 and MAT 252. 4 credit(s). Last Term Offered: Fall 2019 |

## MAT 321 - Mathematical StatisticsMathematical development of sampling distributions, estimation of parameters, confidence intervals, hypothesis testing, introduction to nonparametric methods. Prerequisite(s): MAT 320. 3 credit(s). Last Term Offered: Spring 2019 |

## MAT 322 - Numerical Analysis ITopics include approximate solutions of equations, polynomial approximations of functions, interpolation, numerical integration and their corresponding techniques of error analysis. Computers and calculators are used. Prerequisite(s): CSC 152 or DSC 101, and “C-” or better in MAT 151. 4 credit(s). Last Term Offered: Fall 2020 |

## MAT 325 - Design of ExperimentsFundamental concepts in the design of experiments: review of statistical inference, completely randomized designs, randomized block designs, Latin Square designs, factorial experiments, confounding, and fractional replications. Prerequisite(s): MAT 221 or MAT 321. 3 credit(s). Last Term Offered: Spring 2020 |

## MAT 326 - Regression AnalysisModel building and analysis focusing on regression. Topics include method of least squares, ANOVA, model assumptions, interferences about parameters, residual analysis, model adequacy, dummy variables, non-linear terms, pitfalls, and limitations. Prerequisite(s): MAT 221 or MAT 321. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 328 - Time Series AnalysisA continuation of a data science class, which will equip students with various forecasting techniques and knowledge on modern statistical methods for analyzing time series data. Although the course will have a theoretical component it will be practical and exercise-driven. The analyses will be performed using the freely available package ASTSA, which accompanies the book. Both R and RStudio will be required for this class. Prerequisite(s): 'C-' or better in MAT 326 and MAT 372. 3 credit(s). Last Term Offered: not yet offered |

## MAT 329 - Bayesian Analysis and Decision MakingAn introduction to Bayesian analysis and inference. It covers many of the topics covered in a standard frequentist survey course from a Bayesian perspective. Topics include gathering datasets, summarizing datasets, probability, Bayes Theorem, Bayesian inference for discrete random variables, Bayesian inference for continuous random variables, comparing Bayesian and frequentist approaches to inference, Bayesian prediction intervals for single mean and single proportion, Bayesian inference for two means and two proportions, and Bayesian inference for linear regression. Prerequisite(s): MAT 221. 3 credit(s). Last Term Offered: Fall 2020 |

## MAT 342 - Statistical Decision Making in the Twenty-First CenturyMAT 342 is a second course in statistics and focuses on analyzing data, interpreting results and critically analyzing underlying assumptions.The course presumes knowledge of the following concepts in a prio course: probability, descriptive statistics and statistical inference. A software package is required. Prerequisite(s): MAT 107, MAT 221, 6 of 8 Tier 2 complete (Honors Coll.: 15 cr. HON or 45 cr. total), and prior or concurrent completion of all Tier 1 (Honors Coll.: T1MC and T1QR only). 3 credit(s). Last Term Offered: Spring 2019 |

## MAT 360 - Foundations of GeometryIntroduction to the geometries of Bolyai-Lobachevsky and Riemann and their mathematical significance, critique of Euclid, axiomatic approach to geometry with modern standards of rigor, introduction to metamathematics. Prerequisite(s): “C-” or better in MAT 250. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 370 - Number TheoryIntroduction to mathematical reasoning and rigor. Prime numbers, divisibility, the Fundamental Theorem of Arithmetic, congruencies and modular arithmetic, fundamental number theoretic functions, and an introduction to Diophantine equations. Prerequisite(s): MAT 178 or MAT 250. 3 credit(s). Last Term Offered: Fall 2020 |

## MAT 372 - Linear AlgebraCourse emphasizes matrices, systems of linear equations, vector spaces, elementary properties of linear transformation, eigenvalues, and applications. Prerequisite(s): 'C-' or better in MAT 150. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 375 - Abstract Algebra IIntroduction to the study of algebraic structures. Topics include binary operations, abstract groups, cyclic and permutation groups, homomorphisms, isomorphisms, normal subgroups, quotient groups, and a brief introduction to rings and fields. Prerequisite(s): 'C-' or better in both MAT 250 and MAT 372. 3 credit(s). Last Term Offered: Fall 2020 |

## MAT 376 - Abstract Algebra IIStudy of rings, and fields. Topics include rings, ideals, homo-morphisms, polynominal rings, integral domains, divisibility, irreducibility criteria, field extensions, finite fields, geometric constructions and elements of Galois Theory. Prerequisite(s): MAT 375. 3 credit(s). Last Term Offered: Spring 2019 |

## MAT 378 - Discrete MathematicsRigorous introduction to the basic elements of discrete mathematics: recursion, combinatorics, and graph theory. Prerequisite(s): CSC 152 or DSC 101, 'C-' or better in MAT 151, and 'C-' or better in MAT 250 or MAT 178. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 398 - Special Topics in MathematicsExamination of developments, issues and/or creative work in the field of mathematics. Prerequisite(s): Departmental permission 1 to 6 credit(s). Last Term Offered: Spring Break 2018 |

## MAT 405 - Elementary Mathematics from an Advanced StandpointAn examination of the theoretical bases for fundamental mathematics topics which are normally taught in secondary school. Prerequisite(s): 'C-' or better in MAT 250, junior status and mathematics major. 3 credit(s). Last Term Offered: Fall 2020 |

## MAT 408 - Technology for Teaching Secondary Math EducationMathematics-specific technology tools for the secondary mathematics teacher for lesson preparation and presentations. Techniques for integrating dynamic computer software, the graphing calculator and its applications in teaching. Designing technology-based activities for mathematics instruction. Special Information: Field work component included. Graphing calculator required. Prerequisite(s): Departmental permission. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 428 - Mathematical Foundations in Machine LearningA broad introduction to machine learning by using the tools of basic knowledge of programming and probability theory, including classification; support vector machines; neural networks; clustering; feature selection; ensemble learning and reinforcement learning. The course will also discuss recent applications of machine learning, such as to computer science, data mining, bioinformatics and so on. Prerequisite(s): 'C-' or better in MAT 221 and MAT 372. 3 credit(s). Last Term Offered: not yet offered |

## MAT 429 - Modern Nonparametric StatisticsCovers nonparametric statistical analysis and inference. Topics include empirical distribution functions, inference using bootstrapping, permutation tests, density estimation and nonparametric linear regression. Prerequisite(s): 'C-' or better in MAT 221 and MAT 372. 3 credit(s). Last Term Offered: not yet offered |

## MAT 450 - AnalysisTheoretical foundations of functions of one real variable: limits, continuity, differentiability, Riemann integral. Prerequisite(s): “C-” or better in both MAT 250 and MAT 252. 3 credit(s). Last Term Offered: Spring 2020 |

## MAT 480 - TopologyMetric spaces and fundamental concepts, topological spaces, subspaces and product spaces, countability properties, separation properties, compactness and connectedness. Prerequisite(s): “C-” or better in both MAT 250 and 372. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 488 - Seminar in Mathematical ModelingThe process of constructing and using mathematical models. Investigations focus on deterministic, probabilistic, and axiomatic models in the physical, social, and life sciences. Emphasis on independent work and on student written and oral presentations. Prerequisite(s): MAT 221 or MAT 321, and CSC 152 or DSC 101, and 'C-' or better in MAT 252 and MAT 372. 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 490 - Teaching Mathematics in the Secondary SchoolMethods of teaching mathematics grades 7-12. Lesson and unit planning, classroom management, learning styles, tasks, assessment, incorporating technology, state and national standards. This course has a required field experience component. For secondary certification candidates only. Prerequisite(s): Departmental permission. 3 credit(s). Last Term Offered: Fall 2020 |

## MAT 494 - Student Teaching — MathematicsGuided observation and supervised student teaching in grades 7–12 in cooperating schools. Twelve-week course. Prerequisite(s): MAT 490. 9 credit(s). Last Term Offered: Spring 2021 |

## MAT 496 - Service Learning for Mathematics EducationStudent teachers design, analyze, and reflect on teaching techniques to be used in the field. Student teachers also perform case studies that encompass and address various issues and demonstrate positive impact on the learning of their secondary students. This course is taken concurrently with MAT 494, Student Teaching (Mathematics). Prerequisite(s): Departmental permission, 6 of 8 Tier 2 complete (Honors Coll.: 15 cr. HON or 45 cr. total), and prior or concurrent completion of all Tier 1 (Honors Coll.: T1MC and T1QR only). 3 credit(s). Last Term Offered: Spring 2021 |

## MAT 497 - InternshipA supervised internship offering practical business, industry or government experience which relates to the student’s specialization. Special Information: 10 to 20 hours per week. Prerequisite (s): Senior status in the B.S. degree program in Applicati ons of Mathematics, mathematics GPA of 2.7, overall GPA of 2.5 and departmental permission. 3 or 6 credit(s). Last Term Offered: Spring 2020 |

## MAT 499 - Independent StudyProvides properly qualified students with an opportunity for independent study and careful discussion from an advanced standpoint of selected topics in undergraduate mathematics. Prerequisite(s): Departmental permission. 1 to 4 credit(s). Last Term Offered: Spring 2020 |