Course Descriptions - College of Mount Saint Vincent

Department of Mathematics

Department of Mathematics

Course Descriptions

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