Loyola University Maryland

Department of Mathematics and Statistics

Course Descriptions

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MA 004 Review of Math for College (0 credits)

This course provides a review for students whose mathematical skills are weak and need to improve their abilities prior to taking MA109 (Precalculus) or ST110 (Introduction to Statistical Methods and data Analysis).  Sets, polynomials, algebra of fractions, linear equations, inequalities of one variable, exponents, radicals, complex numbers, graphing equations, inequalities of two variables, systems of equations, and other selected topics.

Note:  No college credit is earned by taking this course.

MA 103 Fundamental Concepts of Mathematics I

This course provides prospective teachers with part of the background needed for teaching the content of elementary mathematics including sets, logic, the development of the whole number system, intuitive geometry, and measurement. The topics are in accordance with the recommendations of the Committee on the Undergraduate Program in Mathematics (CUPM) and the National Council of Teachers of Mathematics (NCTM).

This course is restricted to Elementary Education Majors. It is offered only in the Fall Semester.

MA 104 Fundamental Concepts of Mathematics II

Prereq: MA103. This course provides prospective teachers with part of the background needed for teaching the content of elementary mathematics including rational and real numbers, exponents and decimals, word problems, Cartesian Coordinate System, ratio and proportion, percents, probability, intuitive geometry, and measurement. The topics are in accordance with the recommendations of the Committee on the Undergraduate Program in Mathematics (CUPM) and the National Council of Teachers of Mathematics (NCTM).

This course is restricted to Elementary Education Majors. It is offered only in the Spring Semester.

MA 106 Topics in Modern Math: Ciphers and Codes

Can you figure out the following message? DOO DUH ZHOFRPH? This message is an example of a cipher. There are a wide variety of different schemes for creating ciphers; in fact, one of the earliest known methods was used by Julius Caesar. The course will focus on those schemes that have a mathematical basis. We will begin with Caesar's method and end with a scheme currently used for security on the Internet. The mathematics used will be elementary and will be developed in the course.

MA 107 Mathematics, Numbers and the Real World

"This sentence is false." Does this statement make any sense?
Why is 1 not a prime number?
These questions, and even more interesting ones, will be answered as we examine reasoning and logic (inductive and deductive) in a mathematical setting. We will also look at the nature of numbers, including types of numbers and differences among kinds of numbers. We will examine the uses of numbers in real world applications such as interest, installment buying, amortization, etc. We will also look at the fascinating world of probability. For example, how many people have to be in a room so that the chances of two of them having the same birthday not counting the year are 50-50?

MA107 Mathematics, Numbers and the Real World

The philosopher Proclus described mathematics as "the invisible form of the soul."  In this course, you will experience mathematics in ways that you never thought possible.  We will discover the power and beauty of mathematics by exploring some very intriguing ideas.  Simultaneously, we will learn effective strategies for thinking and making decisions in our everyday lives.  Some of the topics we will examine are: the beauty of numbers (What does the number of spirals on a pineapple have to do with rabbits?), infinity (Are some infinities larger than others?), modular arithmetic (On what day of the week will your birthday fall in 2057?), and financial management (How much do you need to save each month if you want to have $5000 saved up when you graduate?).

Prerequisites:  The only prerequisites for this course are an open and curious mind and the willingness to put aside any preconceived prejudices or dislikes for mathematics.

MA 108 Mathematics and Politics

A mathematical treatment (not involving Calculus or Statistics) of political power, social choice, and international conflict. No previous study of political science is necessary, but some introduction to American or International politics would be relevant.

Topics include:

  • Principles of elementary game theory as applied to such historical
  • Situations as the Cold War, the Cuban Missile Crisis, and the Yom
  • Kippur War
  • Several voting systems and important properties that are preserved under each system; and
  • Methods for determining indices of power of individuals within various types of groups/organizations

MA 109 Precalculus

This is the course for students intending to take Applied Calculus (MA 151) or Calculus I (MA 251), which will allow review of several fundamental elements necessary for Calculus. These reviews include factoring, exponents and radicals; equations and inequalities; functions and relations including algebraic, exponential, logarithmic and trigonometric functions.

Prerequisites: 13 or better on Math Placement Test.

This course does not fulfill the mathematics core requirement. It is offered Fall and Spring Semesters.

ST 110 Introduction to Statistical Methods and Data Analysis

An introductory statistics course requiring no calculus. Statistical methods are motivated through real data sets. Topics include graphical summaries of data, measures of central tendency and dispersion, chi-squared tests, regression model fitting, normal distributions, and sampling.

Prerequisite: MA004 or a score of 14 or better on Part I of the Math Placement Test or a math SAT score of 560 or better or a math ACT score of 24 or better or any other MA100-level course.

Offered Fall and Spring semesters.

MA 151 Applied Calculus for Business and Social Sciences

A one semester calculus that stresses applications in business and social sciences. Every concept is considered graphically, numerically, algebraically and verbally. Graphing calculators are used to help students learn to the think mathematically. This is a terminal course so if you plan on taking more mathematics and/or minoring in mathematics or statistics, you should take MA 251 instead.

Prerequisite: MA 109 or a score of 11 or better on Part II of the Math Placement Test.

Offered Fall and Spring semesters.

ST 210 Introduction to Statistics

A non-calculus-based course covering descriptive statistics, regression model fitting, probability, normal, binomial, and sampling distributions, estimation, and hypothesis testing.

ST210 is not open to students who have already taken ST265, ST/EG381, PY292, or EC220.

Prerequisite: MA109 or a score of 12 or better on Part II of the Math Placement Test or one year of high school calculus.

MA 251 Calculus I

Definition, interpretation, and applications of the derivative and definition and interpretation of the integral are studied.

Prerequisite: MA 109 or 13 or better on Part II of the Math Placement Test

Offered Fall and Spring semesters.

MA 252 Calculus II

A continuation of Calculus I.  Techniques and applications of integration, parametric equations, polar coordinates, sequences and series will be studied.

Prerequisite: MA 251

Offered Fall and Spring semesters

ST 265 Biostatistics

A non-calculus-based course covering descriptive statistics, regression model fitting, probability, distributions, estimation, and hypothesis testing. Applications are geared toward research and data analysis in biology and medicine.

ST265 is not open to students who have already taken ST210, ST/EG381, PY292, or EC220.

Prerequisite: MA109 or a score of 12 or better on Part II of the Math Placement Test or one year of high school calculus.

This course is intended mainly for Biology majors. It is offered only in the Spring Semester.

MA 295 Discrete Structures

Boolean algebra, combinatorics, inductive and deductive proofs, graphs, functions and reflections, recurrence.

Prerequisite: MA 251

This course is limited to Computer Science Majors and Minors and is also listed as CS 295. It is offered only in the Fall Semester.

MA 301 Introduction to Linear Algebra

In your video games, what makes Mario jump over the barrel? Linear Algebra! In the airline industry, what technique helps to optimize the scheduling process? Linear Algebra! In the economic world, what technique helps to minimize costs? Linear Algebra! It is the "bread and butter" of mathematics as much as calculus is. In high school, you saw linear algebra. Remember the old "two equations, two unknowns" problems? That was linear algebra. But in the real world, there are 3,000 equations and 5,000 unknowns! That is LINEAR ALGEBRA!!

Prerequisite: MA 252.

This course is required for the major and is usually taken in the sophomore year. It is only offered in the Spring Semester.

MA 304 Ordinary Differential Equations

This is an introductory course in ordinary differential equations (ODEs) and their application in modeling physical phenomena.  In particular, the following topics are covered: first and second order ODEs, separable ODEs, existence and uniqueness of solutions, and numerical solutions (using software such as MATLAB). Modeling plays a crucial role in the course, as do applications to other disciplines.

Prerequisite: MA 351 or MA252 and written permission of the instructor.

This course is only offered in the Spring Semester.

MA 351 Calculus III

This course is a continuation of MA 252 and covers multivariable calculus. Topics covered: vectors and their geometry, parametric curves, functions of several variables, partial derivatives, multiple integrals, and the course climaxes with the big theorems, namely the divergence theorem, Stokes' theorem and Green's theorem.

Prerequisite: MA 252.

This course is required for the major and is usually taken in the sophomore year. It is offered only in the Fall Semester.

ST 365 - Statistical Analysis System (SAS) Laboratory (1.00 cr.)

A laboratory course in the use of the Statistical Analysis System, a statistical software package that is widely used throughout governmental, business, industrial, scientific, and academic sectors. Proficiency in using SAS for data management, analysis, and reporting is developed. The course reviews statistical methodology while focusing on developing computing experience and extensive project work.

Prerequisite: EC220 or ST/EG381 or ST210 or ST265 or PY292
Corequisite: ST465

This course is required for statistics majors and statistics minors. It is offered only in the Fall Semester of odd numbered years.

ST 366 - Statistical Computing Using R (1.00 cr.)

A laboratory course in the use of R, a free software environment for statistical computing and graphics that is used extensively in academia. Topics include loops, conditional statements, input/output of data, statistical and graphical functions, simulation, bootstrapping, and permutation tests.

Prerequisite: CS201; ST210 or ST265 or written permission of the instructor.

This course will be offered in Fall 2014 for the last time.

ST 381 - Probability and Statistics

Note: This is the same course as EG381.  Random experiments, probability, random variables, probability density functions, expectation, sample statistics, confidence intervals, and hypothesis testing.

Prerequisites: MA252.

Degree credit will not be given for more than one of ST210, ST265, and ST/EG381.  This course is offered only in the Fall semester.

MA 395 Discrete Methods

The logic of compound statements, introduction to proof, mathematical induction, set theory, counting arguments, recurrence relations, permutations and combinations. An introduction to graph theory including Euler and Hamiltonian circuits and trees. Applications may include analysis of algorithms and shortest path problems. Problem solving is stressed.

Prerequisite: MA 252.

This course is required for the major and is usually taken in the sophomore year. It is offered only in the Fall Semester.

MA 302/402 MATLAB Programming on Mathematics

The basics of MATLAB programming are covered through the investigation of various mathematical topics, including functions, conditional statements, loops, and plotting.

Prerequisites: CS201 and MA252.

MA 421 Analysis I

Calculus is an important tool (perhaps the most important) in applied mathematics and in order to apply Calculus successfully it is important that a thorough understanding of Calculus is achieved. In Analysis I we will explore the definitions and rigorously prove many of the results used in differential and integral Calculus, and thus the course will have a theoretical component. The ideas and methods explored play a fundamental role in many applied mathematical areas such as ordinary differential equations, probability theory (and thus statistics), numerical analysis, and complex analysis.

Prerequisites: MA 351, MA 301 or MA 395

This course is required for the major and is usually taken in the junior year. It is offered only in the Fall Semester.

MA 422 Analysis II

This course is a continuation of Analysis I. We will finish off any unfinished business about functions of 1 variable, including sequences and series of functions. We will then talk about functions from Rn to Rm and what differentiation and integration means in the context of different combinations of values for n and m. For example, functions from Rn to R were studied in Calculus III, leading to partial derivatives and multiple integrals. Functions from R to R3 describe curves in space. Functions from Rn to Rm where n and m are both greater than 1 are new and will be discussed.

Prerequisites: MA 421

This course is required for the Pure Mathematics Concentrations; it may be used for the Statistics, Operations Research, Secondary Education and General Program Concentrations. It is offered only in the Spring Semester of even numbered years.

MA 424 Complex Analysis

The subject of Complex Analysis has both pure and applied components. On one hand, one can think of complex functions as natural extensions of real functions. We will study the topology of the complex plane as we define the concepts of complex functions, the derivative and integral. On the other hand, complex functions are often used to solve problems in a wide variety of applied areas such as electrical engineering (e.g., electric circuits) and physics (e.g., air flow around an airplane wing). While applications will be introduced, our main focus will be on understanding the mathematical concepts.

Prerequisites: MA 421

MA 427 Numerical Analysis

This is an introductory course in numerical analysis, the study of methods for obtaining approximate values of mathematically-defined quantities. Since most uses of mathematics in modern day society involve numerical approximation, this course is essential for any student who wishes to work in an area which involves applied mathematics.

Derivation of the methods and analysis of their errors will be presented. Errors (not to be confused with mistakes) are an inevitable part of using finite algorithms in finite-precision arithmetic, and a numerical method is not usually useful unless the errors can be controlled or at least estimated. For this reason the course has an important theoretical component.

At the same time, one of the goals of the course is to give students experience with the practical performance of the algorithms. To this end the software package MATLAB will be used to implement (and test) the algorithms we will study in class.

Topics include: linear systems, interpolation, quadrature, root-finding.  Additional topics may include solutions of differential equations, optimization, and nonlinear systems of equations.

Prerequisites: MA 301, MA 302, and MA351, or written permission of the instructor.

This course is required for the Computer Science and Actuarial Sciences Concentrations. It is offered only in the Spring Semester of even numbered years.

MA 431 Geometry

A review of Euclidean geometry and an introduction to non-Euclidean geometry.  Rigorous deduction and axiom systems are emphasized.  Possible techniques include the use of coordinate geometry, linear algebra, and computer geometry systems.

Prerequisite: MA 252.

This course is offered only in the Spring Semester of even numbered years.

MA 441 Algebraic Structures I

Abstract algebra searches for patterns common to mathematical systems, explores these common threads, and returns to the particular for its applications. Groups, rings, and fields form the topics of study. Applications may include symmetries of geometrical objects, arithmetic with large integers, and combinatorial problem solving.

Prerequisites: MA 301, MA 395

This course is required for the Pure Mathematics, Computer Science, Secondary Education and General Program Concentrations. It is offered only in the Fall Semester.

MA 442 Algebraic Structures II

Further study of groups, rings, and fields with particular emphasis on finite fields and their uses ---- methods of constructing them and implementing their arithmetic.
As an extended application, the course will contain an introduction to so-called "error-correcting codes."
These are mathematical constructions useful in the transmission of electronic data. They are endowed with the ability to "reconstruct" data that has been "corrupted" by a noisy channel. Extensive use is made of them, for example, in compact disc and cellular phone technology.
The prerequisite is Algebraic Structures I taken at any time.

Prerequisites: MA 441

This course is required for the Pure Mathematics Concentration; it may be used for the Secondary Education and General Program Concentrations. It is offered only in the Spring Semester of odd numbered years.

MA 445 Advanced Linear Algebra

A deeper study of matrices - their properties and uses. Topics include eigenvalues and eigenvectors, special factorizations of matrices, and computational algorithms involving matrices. This looks to be a nice blend of theory and applications.

Prerequisites: MA 301

This course may be used for the Statistics and the Operations Research Concentrations. It is offered only in the Fall Semester of even numbered years.

MA 447 Number Theory

Number Theory deals with properties of whole numbers and is one of the oldest and most fascinating branches of mathematics. Topics include prime numbers and the mystique surrounding them, modular arithmetic and its uses, and equations, solutions of which must be integers. Public-key cryptography and integer arithmetic on computers provide some applications. A nice blend of theory and practice.

Prerequisite: MA 301 or MA 395.

ST 461 -  Elements of Statistical Theory I: Distributions

This course is the first in the two semester sequence of probability and mathematical statistics.  Probability, discrete and continuous distributions, moment generating functions, multivariate distributions, transformations of variables, and  order statistics.

Prerequisites: ST 210 or ST265 or ST/EG381 or EC220 or PY292; MA 351.
 
It is offered only in the Fall Semester of even numbered years

ST 462 - Elements of Statistical Theory II: Inference

A continuation of ST461. Theory of estimation and hypothesis testing, the central limit theorem, maximum likelihood estimation, Bayesian estimation, and the likelihood ratio test.

Prerequisite: ST 461.
 
It is offered only in the Spring Semester of odd numbered years.

ST 465 Experimental Research Methods

Concepts and techniques for experimental research including simple, logistic,  and multiple regression, analysis of variance, analysis of categorical data.

Prerequisites: ST 210, or ST 265, or ST/EG381 or EC 220 or PY292
Corequisite: ST 365 (for statistics majors and statistics minors)

It is offered only in the Fall Semester of odd numbered years.

ST 466 Experimental Design

A continuation of ST465. The theory of linear models and its relationship to regression, analysis of variance and covariance. Coverage of interaction, blocking, replication, and experimental designs: split-plot, nested, and Latin squares.

Prerequisites: MA 301; ST 365; ST 465.
 
It is offered only in the Spring Semester of even numbered years.

ST 471 - Statistical Quality Control

Quality has become an integral part of the lives of both the consumer and the producer. Covered topics include the ideas of W. Edwards Deming; six sigma; Shewhart concepts of process control; control charts for attributes and variables; CUSUM, EWMA, and MA charts; and factorial experimental designs.

Prerequisites: ST 210 or ST265 or ST/EG381 or EC 220 or PY292.

This course will be offered in the Fall of 2014 and next in Fall 2017.

ST 472 - Applied Multivariate Analysis

Applications of multivariate statistical methods including: principal components, factor analysis, cluster analysis, discriminant analysis, Hotelling's t-square, and multivariate analysis of variance. An applied journal article is read and summarized verbally, in written form, and rewritten form. A final course project, based on an original study, is presented verbally, in written form, and rewritten form.

Prerequisites: ST 210 or ST265 or ST/EG381 or EC 220 or PY292 or written permission of the instructor.

This course is offered in the Spring Semester of even numbered years.

MA 481 Operations Research

This course will investigate mathematical techniques for determining optimal courses of action for decision problems under restrictions of limited resources. These techniques include the simplex algorithm, the traveling salesman algorithm, branch and bound algorithm, shortest route algorithm.

Prerequisite: MA 301

This course is required for the Operations Research Concentration. It is offered only in the Fall Semester of odd numbered years.

MA/ST 485 Stochastic Processes

The fundamental concepts of random phenomena including: Bernoulli processes, Markov chains, Poisson processes, queuing theory, inventory theory, and birth-death processes. Applied and theoretical assignments computer simulation.

Prerequisites:  ST 210, or ST 265, or ST/EG381 or EC 220 or PY292; MA 301.
 
It is offered only in the Spring Semester of odd numbered years.

MA 490 - Special Topics in Mathematics: Introduction to Cryptology

This course will cover methods of encryption (making codes) and cryptanalysis (attacking and breaking codes).  It will include classical methods that don’t require a computer, as well as algorithms that need computers for practical use (although we will not cover practical issues of computer security and implementation).  Methods will include most of the following: Vigenere ciphers, Hill ciphers, RSA public key, DES standard, AES standard,  Rabin encryption, Diffie-Hellman key exchange.  We will use computers, but only as calculational aids,  not for full implementation of each algorithm.

Prerequisites: Any 300 level MA course.

MA 490 - Special Topics in Mathematics: Introduction to Non-Linear Programming

Nonlinear programming deals with the problem of optimizing an objective function in the presence of equality and inequality constraints. If all the functions are linear, we have a linear program. Otherwise, the problem is called a nonlinear program. In this course, we will study Unconstrained Optimization, Convex Sets and Convex Functions, Convex Programming and the Karush-Kuhn-Tucker Conditions.
Note: this course is the foundation of nonlinear programming, computer skill is not required.  Students may be asked to do one final project using MATLAB.

Prerequisite: MA 301(Linear Algebra) and MA 351 (Multivariable Calculus).

MA 490 - Special Topics in Mathematics: Topology

An introduction to topology. Topics include metric spaces, general topological spaces, open and closed sets, bases of topologies, continuity, connectedness, compactness, product and quotient spaces and Urysohn's metrization theorem.

Prerequisite: MA 395 or permission of instructor.

MA 490 - Special Topics in Mathematics: Pricing Derivative Securities

This course will build on mathematical models of stock and bond prices to cover two major areas of mathematical finance that have an enormous impact on the way that modern financial markets operate:

  1. The Black-Scholes arbitrage pricing model of options and other derivative securities;
  2. Financial Portfolio Optimization Theory due to Tobin and Markowitz, and the Capital Asset Pricing Model.

Prerequisite: A very basic familiarity with probability, statistics, and calculus (MA252 and ST210).

MA 490 - Special Topics in Mathematics: The Art of Counting

Remember when you first learned 1, 2, 3,...  Now, years later, you have powerful mathematical tools at your command that will allow you to count more than apples: permutations, partitions, (mathematical) trees, strings, and uncountably more.  We will also look at graphs, cliques, probability, existence and external problems as time permits.  The course will focus on problem solving.  Some of the tools we will study are the pigeon-hole principle, inclusion-exclusion, generating functions, and recursion.  The material learned in this course and more importantly the thought processes can be useful in any mathematical field from the most basic to the graduate level.  Combinatorics has applications to Computer Science, Statistics, and much more.

Prerequisite: MA 395 or permission of instructor.

MA 490 - Special Topics in Mathematics: Partial Differential Equations

We will study a variety of types of partial differential equation and learn techniques to solve them.  The emphasis will be on exact techniques but some discussion of numerical techniques will be included.  Applications will be emphasized.