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Courses in Mathematics

Our Mathematics Courses can be grouped into Developmental Mathematics, Non-Major courses, and Major Courses.

Developmental Mathematics

MATH 0011 Developmental Mathematics I
Integers, fractions, decimals, ratios, percentage and elementary word problems. 2 credits (institutional).

MATH 0012 Developmental Mathematics II
Simplifying algebraic expressions, exponents, equations, polynomials, graphing, factoring, square roots, algebraic fractions and elementary word problems. Prerequisite: MATH 0011 or appropriate placement. 3 credits (institutional).

Non-Major Courses

MATH 1011 Sabermetrics
Introduces students to the rapidly growing field of sabermetrics, the science of statistics applied to baseball. Demonstrates application of statistical measures to the game. Students gain insight into the interpretation and validity of statistical measures. Prerequisite: MATH 0012 or appropriate placement. 1 credit.

MATH 1014 Intermediate Algebra
The real number system, algebraic manipulations, solving equations and inequalities, exponents and radicals, functions and graphing. Prerequisite: MATH 0012 or appropriate placement. 3 credits.

MATH 1015 Pre-Calculus Mathematics Algebra and Trigonometry
. The real number system, functions, polynomial functions and equations, exponential and logarithmic functions, trigonometric functions (graphs, applications, identities and equations), analytic geometry. Prerequisite: MATH 1014 or appropriate placement. 4 credits.

MATH 1101 Statistical Concepts and Methods (*)
Nature of statistics. Descriptive statistics, graphical methods, measures of central tendency and variability. Probability, correlation and regression, sampling distributions. Inferential statistics, estimation and hypothesis testing, tests of independence and nonparametric statistics. Use of computer statistical packages. Prerequisite: MATH 0012 or appropriate placement. 3 credits.

(*) This course is NOT for students majoring in sociology, political science, social work, social and behavioral sciences, criminal justice, diplomacy, and anthropology.

MATH 1102 Mathematical Perspectives
Introduction to traditional and contemporary mathematical ideas in logic, number theory, geometry, probability and statistics. Historical and cultural development of these topics, as well as connections to other disciplines and various problem-solving strategies are included. Prerequisite: MATH 0012 or appropriate placement. 3 credits.

Math 1112 Mathematical Perspectives II
Selected topics from set theory and number theory. Algebra, Geometry and right triangle Trigonometry. Counting Methods, Probability and Statistics. Prerequisite: Any 1000-level MATH course or appropriate placement, 3 credits

MATH 1202 Mathematical Models in the Social Sciences
For students in the behavioral sciences. Various elementary mathematical techniques (exclusive of statistics) currently used in the field. Computer terminal facilities aid instruction and acquaint students with the employment of subroutines to solve problems. Topics from linear programming, graph theory, matrix algebra, combinatorics, logic and Boolean algebra. Specific and realistic applications to problems illustrate each topic. Prerequisite: MATH 0012 or appropriate placement. 3 credits.

MATH 1203 Statistical Models for the Social Sciences (*)
Applications of statistics in the social sciences. Analysis and interpretation of statistical models. Sampling techniques, common flaws and errors in sampling and in using statistics. Descriptive statistics, levels of measurement, measures of central tendency and dispersion. Contingency tables and measures of association for categorical variables. Correlation and linear regression. Probability and frequency distributions. Parametric and non-parametric inferential statistics. Confidence intervals and hypothesis testing. Prerequisite: MATH 0012 or appropriate placement. 3 credits.

(*) This course is for students majoring in sociology, political science, social work, social and behavioral sciences, criminal justice, diplomacy, and anthropology.

MATH 1303 Quantitative Methods for Business and Economic Students
Functions, limits, continuity, derivatives applications of the derivative, in particular to mathematical economics. Exponential and logarithmic functions. Antiderivatives, area and applications to business models. Probabilities and applications. Matrices and an introduction to linear programming. Prerequisites: MATH 1014 or appropriate placement. 3 credits.

MATH 1311 Calculus for Business and Economic Students II
Implicit differentiation, related rates, differential equations, improper integrals and probability density functions, partial derivatives and applications and multiple integrals. Introduction to matrix theory, solution of systems of linear equations and linear programming. Prerequisite: MATH 1303. 3 credits.

MATH 1401 Calculus I
Real numbers, functions, elements of plane analytic geometry, limits, continuity, derivatives, differentiation of algebraic functions, applications of the derivative, antiderivatives, definite integral and Fundamental Theorem of Calculus. Applications using computer software packages. Prerequisite: MATH 1015 or appropriate placement. 4 credits.

MATH 1411 Calculus II
Applications of integration. Differentiation of trigonometric and exponential functions and their inverses. Techniques of integration. Improper integrals, indeterminate forms, polar coordinates and vectors. Applications using computer software packages. Prerequisite: MATH 1401. 4 credits.

MATH 2411 Calculus III
Elements of solid analytic geometry, parametric equations, vector-valued functions, partial differentiation, multiple integrals, line integrals and surface integrals. Applications using computer software packages. Prerequisite: MATH 1411. 4 credits.

MATH 2111 Statistics for Science Majors
Oriented toward direct application to research problems in the sciences. Collecting and organizing data, design of experiments, statistical tests and procedures used in accepting or rejecting a given hypothesis. A discursive treatment of the probability theory necessary to understand statistical tests is included but minimized. Emphasis on statistical inference and developing an awareness of statistical methods in a given situation. Prerequisite: MATH 1411. 4 credits.

Major Courses

MATH 1501 Honors Calculus I
Real numbers, proof by induction, functions, definition by recursion, limits, continuity, derivatives and applications, definite integral, Fundamental Theorem of Calculus and inverse functions. Applications using computer software packages. Emphasis on theory. Prerequisite: MATH 1015 or appropriate placement. 4 credits.

MATH 1511 Honors Calculus II
Applications of integration, polar coordinates, techniques of integration, infinite series, conics, two-dimensional vectors and differential equations. Applications using computer software packages. Emphasis on theory. Prerequisite: MATH 1501. 4 credits.

MATH 1611 Introductory Discrete Mathematics
Basic counting rules, permutations, combinations, Pigeonhole principle, inclusion-exclusion, generating functions, recurrence relations, graphs, digraphs, trees and algorithms. Corequisite: MATH 1511. 3 credits.

MATH 2511 Honors Calculus III
Vectors in space, vector-valued functions, partial differentiation, multiple integrals, vector analysis, and line and surface integrals. Applications using computer software packages. Emphasis on theory. Prerequisite: MATH 1511. 4 credits.

MATH 2611 Foundations of Higher Mathematics
The logical and set-theoretic foundations of mathematics and computer science. Introduction to mathematical logic and proof techniques. Elementary set theory, including numbers, sets, relations, functions, equivalence classes, partial orders, Boolean algebras and cardinality. Prerequisites: MATH 1511 and MATH 1611. 3 credits.

Math 2812 Mathematical Computing (proposed only)
Numerical methods and numerical analysis; error analysis. Topics from series representation, zeroes of functions, numerical integration, linear algebra (primarily matrix theory) and linear programming. Advanced topics such as Fast Fourier Transformation and Multivariate Polynomical techniques. Prerequisites: Math 1411/1511 and CSAS 2121. 4 credits

MATH 2813 Linear Algebra
Matrix algebra, determinants, solutions of systems of linear equations, Rn, abstract vector spaces, linear transformations, inner product spaces and eigenvectors. Prerequisites: MATH 2611. 4 credits.

MATH 3094, 3095, 3096 Math Co-op I, II, III
(See Co-op Adviser). 3 credits each.

Math 3111 History of Mathematics
The development of mathematical ideas in various cultures, civilizations, and eras including Ancient Greece, Medieval China, the Renaissance, Era of Descartes and Fermat, Era of Newton and Leibniz, Modern Mathematics. Prerequisites: Math 2511 and Math 2611. 3 Credits

MATH 3513 Introduction to Numerical Analysis
Direct and iterative methods for solving equations and systems of equations. Numerical methods, including interpolation, polynomial approximations, numerical differentiation and integration. Numerical solution to differential equations. Knowledge of computer programming helpful. Prerequisite: MATH 2512. 3 credits.

MATH 3514 Differential Equations
Existence theorems, graphical methods, phase plane analysis, boundary value problems and selected topics. Prerequisite: MATH 2511, MATH 2813. 3 credits.

MATH 3515 Analysis I
Structure of R1 and Rn; compactness and connectedness; continuity, differentiability and integrability in Rn. Prerequisites: MATH 2411 or 2511; MATH 2813. 4 credits.

MATH 3611 Introduction to Operations Research
Construction and use of mathematical models in operations research. Classical techniques for optimization of functions of one and several variables. Linear programming problem and simplex method for its solution. Applications to practical problems. Prerequisite: MATH 2511, MATH 2813. 3 credits.

MATH 3612-3613 Discrete Mathematics I and II
Explores problem-formulation and solution strategies in widely varying domain. Allows mathematics majors familiarity with area range and techniques in computer science structures and analysis, and modeling in other fields. Underlying construction and models used in various disciplines and the modeling process. Prerequisites: MATH 2511, MATH 2813. 3 credits each.

MATH 3711-3712 Statistical Analysis I and II
Probability spaces, random variables, sampling, the law of large numbers, central limit theorem, confidence intervals and tests of hypotheses, regression, statistical decision theory, sampling from a normal population, testing hypotheses, experimental design and analysis of variance. Other sampling methods. Prerequisites: MATH 1611, MATH 2511. 3 credits each.

MATH 3813 Number Theory
Unique factorization and its applications, congruency, quadratic reciprocity and diophantine equations. Other topics as time permits. Prerequisite: MATH 2611. 3 credits.

MATH 3814 Linear Algebra and Matrix Theory
Vector spaces and algebras, unitary and orthogonal transformations, characteristic equation of a matrix, the Jordan canonical form. Bilinear, quadratic and Hermitian forms. Spectral theorem. Prerequisite: MATH 2813. 3 credits.

MATH 3815 Algebra I
Introduction to algebraic structures: monoids, groups, rings and fields. Examples are given, and the elementary theory of these structures is described. Prerequisite: MATH 2813. 4 credits.

MATH 3911 Geometry
Possible topics include Euclidean geometry, non-Euclidean geometry, projective geometry, transformation geometry, complex geometry. Prerequisite: MATH 2511, MATH 2611. 3 credits.

MATH 3912 Junior Seminar
Seminars and discussions designed to integrate readings of mathematical literature with both oral and written presentations. Prerequisites: MATH 3515 or 3815. 2 credits.

MATH 4091-4092 Topics in Applied Mathematics I and II
Topics chosen from among operations research, optimization, including an introduction to the calculus of variations, combinatorics, discrete mathematics, Fourier analysis, integral equations, partial differential equations. Students acquire some experience at constructing mathematical models. Prerequisite: MATH 2511, MATH 2813. 3 credits each.

MATH 4093-4098 Independent Study in Mathematics
Prerequisite: permission of department chair. 2-3 credits each.

MATH 4511 Introduction to Real Analysis
Sets, equivalence, countability, infinite series, metric spaces; complete, compact, connected spaces, sequences and series of functions and uniform convergence. Prerequisite: MATH 3512. 3 credits.

MATH 4512 Introduction to Complex Analysis
Analytic functions, elementary functions and mappings, integrals, Cauchy?s integral theorem and formula, power series, residues and poles. Prerequisite: MATH 2511. 3 credits.

MATH 4515 Analysis II
Consequences of continuity, differentiability and integrability in Rn; uniform convergence; introduction to metric spaces. Prerequisite: MATH 3515. 3 credits.

MATH 4815 Algebra II
This course continues MATH 3815. Further properties of groups and fields, with a section on the applications of finite fields. Concentrates on Galois theory, the theory of the solution of algebraic equations. Prerequisite: MATH 3815. 3 credits.

MATH 4911 Introduction to Topology
Topological spaces, subspaces, product spaces, identification spaces. General convergence. Connected and compact spaces. Separation and countability. Compactifications. Prerequisite: MATH 3515. 3 credits.

MATH 4912 Senior Project
Individual research project applying skills developed in Junior Seminar (MATH 3912) under the guidance of faculty adviser. Grade is ordinarily based on oral and written presentations. Prerequisites: MATH 3912 and permission of department chair. 3 credits.

Last Modified: Apr 2004
Maintained by: Math/CS @ SHU.edu (bgw)