Course Descriptions - College of Mount Saint Vincent

Department of Mathematics

Department of Mathematics

Course Descriptions

Data Analytics

DATA 201 FOUNDATIONS OF PYTHON PROGRAMMING
This introduction to computer science, developed by Google and their university partners, emphasizes problem solving and data analysis skills along with computer programming skills. Using Python, you will learn design, implementation, testing, and analysis of algorithms and programs. And within the context of programming, you will learn to formulate problems, think creatively about solutions, and express those solutions clearly and accurately. Problems will be chosen from real-world examples such as graphics, image processing, cryptography, data analysis, astronomy, video games, and environmental simulation. You’ll get instruction from a world-class computer science professor, delivered remotely through video and interactive media. Then you will attend class for collaborative team projects to solve real-life problems, similar to those a team at Google might face. As part of the course, you will also hear from Google engineers about their careers in the tech industry and how you can prepare yourself for a similar career. Prior programming experience is not a requirement for this course (4 credits).

DATA 202 HOW TO THINK LIKE A DATA SCIENTIST
How to Think Like a Data Scientist introduces students to the importance of gathering, cleaning, normalizing, visualizing and analyzing data to drive informed decision-making, no matter the field of study. Students will learn to use a combination of tools and techniques, including spreadsheets, SQL and Python to work on real-world data sets using a combination of procedural and basic machine learning algorithms. They will also learn to ask good, exploratory questions and develop metrics to come up with a well thought-out analysis. Presenting and dis- cussing an analysis of data sets chosen by the students will be an important part of the course. Like DATA 201, this course will be “flipped”, with content learned outside of class and classroom time focused on hands-on, collaborative projects (4 credits).

DATA 210 DIGITAL MEDIA MARKETING
This course examines data through practical applications such as: 1) web analytics, 2) tracking the impact of marketing campaigns and AdWords advertising through specially created Google Analytics and machine learning techniques, 3) understanding the digital measurement landscape and key digital measurement concepts, terminology and analysis techniques, and 4) using web advertisements and predicting mouse clicks (Clickstream analysis). This course will draw on and extend students’ understanding of issues related to digital marketing, “Big Data,”  and quantitative analysis, and interprets ethical and social issues surrounding the use of data sets (3 credits).

DATA 300 APPLIED STATISTICS
This course serves as an introduction to fundamental ideas in multivariate statistics using case studies. It will cover descriptive, exploratory, and graphical techniques in multivariate statistics. Also, it will cover the assumptions, limitations, and uses of basic techniques such as cluster analysis, principal components analysis, factor analysis, multivariate regression, and multivariate analysis of variance, as well as how to implement these methods on available public domain policy and economic data sets, using statistical software such as RPSS and SPSS (3 credits).

DATA 400 DATA MINING
Data mining is the process by which information is extracted from large amounts of data. As organizations stockpile structured and unstructured data, the need for exploring and analyzing these data sets is growing rapidly. This course will provide students with fundamental methodologies, leading to an understanding of how and when they can be used as a problem solving technique. Students will also learn different methods of data mining, how to select the appropriate technique for a specific problem, and how to use available software to examine a prepared set of data and interpret the results (3 credits).

DATA 460 RESEARCH PROJECT
Students will select a topic in one of the areas of concentration and develop it into a major paper including an original research study, presenting their findings in a formal oral presentation (3 credits).

PHIL 355 ETHICS OF DATA AND ARTIFICIAL INTELLIGENCE
Twenty years ago, almost none of our daily activities left a data footprint; twenty years from now, almost all of them will.  Twenty years ago, artificial intelligence existed only in esoteric academic papers; twenty years from now, it will be as ubiquitous as electricity, and even more socially transformative.

As we make these transitions at a blistering pace, it is imperative for us to reflect on how we can use data and A.I. to promote, rather than diminish, human autonomy and human flourishing. To enable such reflection, this course will first investigate the nature of data and A.I. (e.g., what is data, and what is not? Which machine activities can rightly be called ‘intelligent’?). Then the course will consider how both regular citizens and data scientists/A.I. engineers can make ethical decisions about the use of data and A.I. – decisions that not only respect individuals’ digital property and privacy, but also promote their freedom and self-determination (3-credits).

Mathematics

MATH 100 PRE-CALCULUS
This course focuses on basic set theory, functions and their graphs, linear and quadratic equations and systems, trigonometry, Cartesian coordinates, congruence transformations in the plane. This course serves as preparation for Calculus (3 credits).

MATH 102 MATHEMATICAL MODELING (C)*
This course centers around communication through graphs, linear, exponential and logarithmic modeling of real data, regression analysis, critical evaluation of appropriateness of a model, quality-of-fit analysis, and unit conversions (3 credits).

MATH 119 – STATISTICS (C)*
This course focuses on communicating with Graphs, data analysis and sample statistics, sampling methods, probability, combinatorics, normal distribution and other probability distributions, hypothesis testing, and optionally, the Monte Carlo Simulation (3 credits).
Prerequisite: Mathematical Modeling

MATH 120 – COMPUTATIONAL MATHEMATICS (C)*
This course focuses on the processing of deterministic and stochastic data structures through spreadsheets. The course also centers around the development of graphic user interfaces for robust processing of a developed hypothesis; processing of experimental data structures by databases; and the emulation of experimental data by mathematical models and generators of random numbers (3 credits).
Prerequisite: Mathematical Modeling 

MATH 131 CALCULUS I (C)* 
This course focuses on real functions of a single real variable: limits, continuity, derivatives, integrals, and the Fundamental Theorem of Calculus (4 credits).
Prerequisite: Pre-Calculus or approval of Department chairperson

MATH 132 CALCULUS II (C)* 
This course focuses on techniques of integration, transcendental functions, optimization, convexity and concavity, introduction to ordinary differential equations, improper integrals, sequences and series, convergence criteria, Taylor series, and applications in physics (4 credits).
Pre-requisite: Calculus I

MATH 212 BIOMEDICAL STATISTICS (C)*
This course is a rigorous introduction to statistics with applications in biological and health sciences using available public domain biomedical data sets. The course also focuses on exploratory data analysis, elements of probability, parametric and nonparametric statistical methods, contingency table analysis and linear regression, as well as hypothesis testing and survival analysis (4 credits).
Prerequisite: Mathematical Modeling

MATH 217 DISCRETE MATHEMATICS
This course is an introduction to a variety of discrete Math topics such as combinatorics, graph theory, linear programming, game theory, voting theory, the Theory of Fair Divisions, fractals. The course also places emphasis on recursion and algorithms with and without computers (3 credits).
Prerequisite: Calculus I

MATH 222 MATHEMATICS FOR ELEMENTARY EDUCATION
This course focuses on the theory and application of arithmetic, algebra, geometry, and probability at the primary school level. This course is exclusively for students pursuing a certification in elementary school education; it is a co-requisite of EDUC 322 (3 credits).

MATH 231 CALCULUS III
This course focuses on vectors, vector operations, dot product, and cross product. The course also centers around multivariate functions and vector valued functions, continuity, partial derivatives, Cartesian, polar, cylindrical and spherical coordinate systems, gradient, tangent plane, total derivative, as well as the classification of quadratic surfaces and multiple integrals (3 credits).
Prerequisite: Calculus II

MATH 241 LINEAR ALGEBRA I
This is the first part of a two-semester sequence, linear equations and matrices, matrix algebra, vector spaces, subspaces, linear independence, bases, dimension, linear transformations, diagonalization of matrices. Gauss-Jordan elimination, L-U factorization, applications of linear algebra in the sciences and business (3 credits).
Prerequisite: Calculus II

MATH 242 LINEAR ALGEBRA II – Elective
This course is the second part of a two-semester sequence. It is a continuation of topics in linear algebra, with emphasis on inner product spaces, orthogonality, eigenvalues and eigenvectors, canonical forms, quadratic forms, numerical methods, least squares analysis, principal component analysis, singular value decomposition (SVD) (3 credits).
Prerequisites: Calculus III and Linear Algebra I 

MATH 255 ORDINARY DIFFERENTIAL EQUATIONS – Elective
This course focuses on ordinary differential equations of first and second order: exact solutions and numerical methods, use of mathematical software, systems of differential equations, Laplace transforms, if time permits. Applications in physics, chemistry, biology (3 credits).
Prerequisite: Calculus III

MATH 261 SYMBOLIC COMPUTING – Elective
This course focuses on concepts and practical use of a computer algebra system such as Maple: Data types and control structures. The course also features two- and three-dimensional plotting, symbolic computing of solutions to selected problems in algebra and analysis, and contrasting exact and numerical solutions (3 credits).

MATH 262 NUMERICAL COMPUTING – Elective
This course focuses on programming constructs and data structures for a programming language suitable for compute intensive applications, such as C++. Development, implementation, and debugging of algorithms for selected computational problems on workstations and clusters (3 credits).
Pre-requisite: Computing or permission of the Department chairperson

MATH 263 COMPUTING I
This course focuses on introductory to basic computer programming: control structures, data types, data structures, formatting, input/output control, debugging, documenting applied to simple algorithms. Implementing algorithms in various software systems such as Basic, Visual Basic, Maple, Matlab, Mathematica (3 credits).

MATH 311 PROBABILITY DISTRIBUTIONS & STATISTICAL INFERENCE
This course centers around random variables, discrete and continuous probability distributions (Binomial, Poisson, Normal, T), statistical moments, point estimation, interval estimation, hypothesis testing, optionally, analysis of variance and covariance, simulation, and the introduction to experimental design (3 credits).
Prerequisite: Calculus I 

MATH 321 INTRODUCTION TO HIGHER GEOMETRY
This course focuses on Euclidean, Non-Euclidean, axiomatic geometry, and formal proofs. Optionally, the course may cover on analytic geometry of conic sections. Projective Geometry (3 credits).
Prerequisite: Calculus III

MATH 331 REAL ANALYSIS
This course centers around the calculus of a single real variable, with emphasis on proofs. The course also focuses on the axiomatic foundation of real number system, the rigorous development of the Riemann integration. Optionally, the course may cover the Introduction to theory of Measure and the Fourier analysis (3 credits).
Prerequisites: Calculus III and Linear Algebra I

MATH 341 ABSTRACT ALGEBRA I
This course is the first part of a two-semester sequence. It is an introduction to algebraic structures with an emphasis on groups, normal subgroups, co-sets, Lagrange’s Theorem, and the fundamental homomorphism theorems (3 credits).
Prerequisite: Linear Algebra I

MATH 342 ABSTRACT ALGEBRA II – Elective
This course is the second part of a two-semester sequence. It furthers the study of algebraic structures, such as rings, integral domains, fields, and includes the homomorphism theorem and its applications (3 credits).
Prerequisite: Abstract Algebra I

MATH 431 VECTOR CALCULUS – Elective
This course focuses on calculus for vector functions, line and surface integrals, the theorems of Gauss, Green, and Stokes, and applications in electrostatics, electrodynamics, fluid dynamics (3 credits).
Prerequisite: Calculus III

MATH 450 CAPSTONE I
This is a special topic course chosen by the faculty of the Department to allow students to complement their study of mathematics by delving deeply into a specific area requiring application and synthesis of knowledge and understanding developed throughout the mathematics curriculum (3 credits).
To be taken during senior year 

MATH 451 CAPSTONE II
This course is the continuation of the special topic studied in Capstone I, with emphasis on student undergraduate research and presentation.
Prerequisite: MATH 450 Capstone I

MATH 453 COMPLEX FUNCTIONS – Elective
This course centers around complex plane and elementary complex functions, analytic functions, Cauchy-Riemann equations, and Cauchy integral theorem. The course also covers Taylor series, Laurent series, singularities, zeroes, and calculus of residues, as well as conformal mapping and its applications (3 credits).
Prerequisite: MATH 331 Real Analysis

MATH 455 LINEAR PARTIAL DIFFERENTIAL EQUATIONS – Elective
This course focuses on the classification of second-order linear partial differential equations, the method of separation of variables, and the methods of Fourier series and Taylor series. The course also covers the method of Laplace transforms, if time permits. Additionally, the course focuses on general solutions, initial problems, boundary problems, and initial-boundary value problems (3 credits).
Prerequisite: Ordinary Differential equations

MATH 465 TOPICS IN MATHEMATICS – Elective
This is a special topic course offered when demand warrants. Registration requires permission by Department Chair (3 credits).

MATH 469 INDEPENDENT STUDY – Elective
This is an independent study and/or research under faculty guidance. Registration requires approval of the Chair (3 credits).

(C)* May be taken to meet Core Requirements