Loyola University Maryland

# Course Descriptions

### MA 005 Precalculus Lab (1 credit)

Emphasizes problem solving as applied to topics from Precalculus. Class time is spent on computer generated problem sets, workbooks in a question and answer format, and individualized work with the instructor. Topics covered include: Linear equations in one variable, graphing lines, finding equations of lines, functions, function notation, graphing functions, polynomials, exponents, and radicals.  Does not satisfy mathematical sciences core requirement.  (Satisfactory/Unsatisfactory).

### MA 103 Mathematics for Elementary Teachers: Algebraic

Restricted to elementary education majors. Provides an inquiry-based examination of basic concepts, operations and structures occurring in numbers, number sense and algebraic reasoning. Students develop a deeper understanding of the numeric, arithmetic and algebraic concepts required to teach elementary school mathematics. Does not fulfill mathematics and statistics core requirement.

### MA 104 Mathematics for Elementary Teachers: Geometric

Restricted to elementary education majors. Provides an activity-based exploration of informal geometry in two and three dimensions as well as probability and statistics. Emphasis is on visualization skills, fundamental geometric concepts, the analysis of shapes and patterns and analyzing and displaying data. Students develop a deeper understanding of mathematical concepts required to teach mathematics in elementary school. Does not fulfill mathematics and statistics core requirement.

### 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: A score of 56 or better on Part I of the Math Placement Test or a score of 50 or better on ALEKS or a math SAT score of 560 or better or a math ACT score of 24 or better. Students not meeting the prerequisite will take corequisite MA 005 in addition to MA 109.

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.

Offered Fall and Spring Semesters.

### MA 114 Mathematics and Sustainability

Focuses on critical thinking and how to support arguments quantitatively in the context of sustainability. Topics include measurement, flow, connectivity, change, risk, and decision making. How to model sustainability at the local, regional, and global level is studied. Closed to students who have credit for MA/ST 200-level courses.

### MA 115 Introduction to Combinatorics

A basic introduction to counting and its relationship to combinatorial structure. Topics may be chosen from; sets, enumeration, permutations and combinations, probability, graph theory, colorability, planarity, trees. Closed to students who have credit for MA/ST 200-level courses.

### MA 116 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 117 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?

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 118 History of Mathematics

This course surveys the development of mathematical ideas throughout history, with emphasis on critical thinking and problem solving from the historical point of view. Topics include the historical development of numbers, calculations, geometry, algebra, and the concept of infinity in various civilizations with specific emphasis on developments in Europe, Egypt, Mesopotamia, Greece, India, and China. Connections are explored between the history of mathematics and other fields such as natural and applied sciences, social sciences and business.

This course is offered sporadically. (Last offered Fall 2018.)

### 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 48 or better on Part II of the Math Placement Test or a score of 65 or higher on ALEKS or one year of high school calculus.

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.

ST 210 is not open to students who have already taken ST 265, ST/EG 381, PY 292, or EC 220.

Prerequisite: MA 109 or a score of 48 or better on Part II of the Math Placement Test or a score of 65 or higher on ALEKS 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 a score of 56 or better on Part II of the Math Placement Test or a score of 76 or higher on ALEKS or one year of high school calculus..

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: A grade of C- or better in MA 251.

Offered in 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.

ST 265 is not open to students who have already taken ST 210, ST/EG 381, PY 292, or EC 220.

Prerequisite: MA 109 or a score of 48 or better on Part II of the Math Placement Test or a score of 65 or higher on ALEKS 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.

Prerequisites: CS 151; MA 109 or higher or a score of 56 or better on Part I of the Math Placement Test or a score of 50 or higher on ALEKS or one year of high school calculus.

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. In the real world, there are 3,000 equations and 5,000 unknowns! This is LINEAR ALGEBRA!!

Prerequisite: MA 252.

This course is required for both mathematics and statistics majors and is usually taken in the sophomore year.

### MA 302 Programming in Mathematics

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

Prerequisite: CS 151.
Pre/Corequisite: MA 301

### 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.

Prerequisites: MA 351 or MA 252 and written permission of the instructor. Required for mathematics major.

This course is only offered in the Spring Semester.

### ST310 Statistical Computing

The course reviews a number of statistics topics as a vehicle for introducing students to statistical computing and programming using SAS and R for graphical and statistical analysis of data. Statistics topics include graphical and numerical descriptive statistics, probability distributions, one and two sample tests and confidence intervals, simple and multiple linear regression, and chi-square tests. SAS topics include data management, manipulation, cleaning, macros, and matrix computations. Topics in R include data frames, functions, objects, flow control, input and output, matrix computations, and the use of R packages. Lastly, this course also includes an introduction to the resampling and bootstrap approaches to statistical inference.

Prerequisite: ST210 or ST265 or EC220 or written permission of the department chair.

### 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. 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 both mathematics and statistics majors and is usually taken in the sophomore year.

### ST 381 Probability and Statistics

Note: This is the same course as EG 381. Random experiments, probability, random variables, probability density functions, expectation, sample statistics, confidence intervals and hypothesis testing.

Prerequisite: MA 252.

Degree credit will not be given for more than one of ST 210, ST 265, and ST/EG 381. 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 both mathematics and statistics majors and is usually taken in the sophomore year.

### 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.

Prerequisite: 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 351 and MA 421

This course is required for the Pure Mathematics Concentrations; it may be used for the Statistics, Secondary Education and General Program Concentrations. This course is offered 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.

Prerequisite: MA 351

### MA 427 Numerical Analysis

This course, along with MA 428, will emphasize the development of numerical algorithms to provide stable and efficient solutions to common problems in science and engineering. MA 427 topics include direct and iterative methods appearing in linear algebra, root finding methods and interpolation. 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.

Prerequisites: MA 301, MA 302, or written permission from the instructor.

### MA 428 Computational Mathematics

This course, along with MA 427, will emphasize the development of numerical algorithms to provide stable and efficient solutions to common problems in science and engineering. MA 428 topics include numerical differentiation, initial value problems, two point boundary value problems and partial differential equations.

Prerequisites: MA 302, MA 304, or written permission from the instructor.

### 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 395.

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

### MA 441 Ring Theory

An investigation of the fundamental algebraic systems of integers, rings, polynomials and fields. Topics drawn from homomorphisms, cosets and quotient structures.

Prerequisites: MA 301, MA 395

### MA 442 Group Theory

An investigation of the fundamental algebraic system of groups. Topics include homomorphism, cosets and quotient structures. May include applications, Sylow theory, combinatorics, coding theory, Galois theory, etc.

Prerequisites: MA 301, MA 395

This course is offered 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.

Prerequisite: MA 301

This course may be used for the Statistics Concentration. It is frequently offered.

### 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 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 ST 265 or ST/EG 381 or EC 220 or PY 292; MA 351.

This course is offered in the Fall Semester of even numbered years

### ST 462 Elements of Statistical Theory II: Inference

A continuation of ST 461. Theory of estimation and hypothesis testing, the central limit theorem, maximum likelihood estimation, Bayesian estimation and the likelihood ratio test.

Prerequisite: ST 461.

This course is offered 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.

Prerequisite: ST 210 or ST 265 or ST/EG 381 or EC 220 or PY 292
Corequisite: ST 365 (for statistics majors and statistics minors)

This course is offered in the Fall Semester of odd numbered years.

### ST 466 Experimental Design

A continuation of ST 465. 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.

This course is offered 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 ST 265 or ST/EG 381 or EC 220 or PY 292.

This course is offered in the Fall Semester of odd numbered years.

### 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: Sophomore standing; ST 210 or ST 265 or ST/EG 381 or EC 220 or PY 292 or written permission of the instructor.

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

### ST 473 Statistical Learning and Big Data

Covers foundations and recent advances in statistical learning for complex and massive data. Topics include nonlinear regression, smoothing splines, linear/quadratic discriminant analysis, k-nearest neighbors, regression trees, bagging, random forests, boosting, and support vector machines. Some unsupervised learning methods are discussed: principal components and clustering (k-means and hierarchical). Those methods are performed using statistical software - R and SAS.

Prerequisite: (may be taken concurrently): ST 310.

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

### ST 475 Survival Analysis & Generalized Linear Models

The course consists of two parts. The first part provides a survey of the theory and application of survival analysis. Topics include time-to-event data, types of censoring, hazard functions, survival functions, Kaplan-Meier estimators, Nelson-Aalen estimators, and Cox proportional hazards models. Parametric methods and various nonparametric alternatives are discussed. The second part introduces the concepts and background of generalized linear models (GLMs). Topics include exponential family distributions, likelihood functions, link functions, simple and multiple linear regression, logistic regression for binary data, and Poisson regression for count data. Those methods are performed using statistical software - R and SAS.

Prerequisite: ST 310

This course is offered in the Fall 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

### 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/EG 381 or EC 220 or PY 292; MA 301.

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

### MA 490 Special Topics in Mathematics: Graph Theory

The fundamentals of graphs will be discussed. Topics may include graphs, trees, connectivity, Eulerian circuits, Hamiltonian cycles, vertex and edge colorings, planar graphs and extremal problems.

Prerequisite: MA 395 or permission of the instructor.

### MA 490 Special Topics in Mathematics: Cryptology

This course will provide an introduction to classical and modern cryptology. We will study methods to encrypt messages to keep the contents secret, methods to attack these encryption schemes and the mathematics underlying these methods.

Prerequisite: MA 301

### 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.

Prerequisites: 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:

The Black-Scholes arbitrage pricing model of options and other derivative securities; 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 (MA 252 and ST 210).

### 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.

### MA 499 Mathematics Internship

Students gain a better understanding of mathematics through work experience. Interns are required to work in a business or professional environment under the guidance of an on-site supervisor for a minimum of 100 hours. The work conducted during the internship must in some way relate to mathematics or the application of the discipline to the business or professional environment. The location may be in- or out-of-state, on a paid or unpaid basis. Course requirements include a weekly work log, a scheduled performance evaluation signed by the on-site supervisor, and an updated résumé and cover letter.

Offered in Fall Semesters.

Prerequisite: Permission of the instructor or department chair.

### ST 499 Statistics Internship

Students gain a better understanding of statistics through work experience. Interns are required to work in a business or professional environment under the guidance of an on-site supervisor for a minimum of 100 hours. The work conducted during the internship must in some way relate to statistics or the application of the discipline to the business or professional environment. The location may be in- or out-of-state, on a paid or unpaid basis. Course requirements include a weekly work log, a scheduled performance evaluation signed by the on-site supervisor, and an updated résumé and cover letter.

Offered in Fall Semesters.

Prerequisite: Permission of the instructor or department chair.

Faculty

## Lisa Oberbroeckling

As class dean for the Class of 2022, Dr. Oberbroeckling hopes to lead and mentor Loyola students

Mathematics and Statistics