# Mathematics (MATH)

Major Courses

MATH A110 Concepts in College Algebra, 3 crs.

This course introduces the topics of college algebra focusing on a conceptual understanding and application algebra. Following a contemporary approach to mathematics education, this course includes exploration of real-world problems, group discussion of problems, and technological exploration of concepts with an emphasis on mathematical reasoning and communication. Course replaces MATH A117. Placement into MATH A110 is determined by ACT/SAT scores.

Co-requisite: MATH A111

MATH A111 College Math Enrichment, 1 cr.

Required accompaniment to MATH A110.

Co-requisite: MATH A110

# MATH A115 Introduction to Finite Mathematics, 3 crs.

This course is designed to give social science, psychology, and business students an introduction to the necessary analytic and quantitative tools in mathematics. Topics include elementary matrix theory and linear programming, life science models, and an introduction to probability.

Prerequisite: MATH A110 & A111 or Math Placement

MATH A116 Survey of Calculus, 3 crs.

This course includes techniques in the calculus of algebraic, exponential, and logarithmic functions of one and two variables as met in the application fields of business, political science, and other social science disciplines.

Prerequisite: MATH A115 or Math Placement

MATH A118 Pre-calculus Mathematics, 3 crs.

This course offers preparation for students who plan to take calculus, but need to build their proficiency in algebra and trigonometry.  Topics include exponential, logarithmic, and trigonometric functions.

Prerequisite: Grade of C- or higher in MATH A110, or Math Placement

MATH A200 Introduction to Linear Algebra, 3 crs.

This course introduces topics in matrix algebra for applications that are basic to future coursework in mathematics. Topics include vector spaces, determinants, matrices, linear transformations, and eigenvectors.

Prerequisite: MATH A115, A117, A118, or A257

MATH A204 Discrete Math Structures, 3 crs.

This course bridges infinitesimal calculus and the world of sets, relations, digraphs, lattices, logic, etc. Topics include algebraic flow chart language, syntax and semantics, isomorphisms and invariants, directed graphs, Boolean algebra, permutations and cyclic groups, polish expressions, etc.

Prerequisite: MATH A115A117A118, or A257

MATH A241 Introduction to Probability and Statistics I, 3 crs.

This course introduces statistical concepts and applications in the natural and social sciences that are related to environmental issues.  Emphasis is placed on methods of data analysis, normal distributions, statistical inference, special distributions, regression, and analysis of variance.

MATH A257 Calculus I, 4 crs.

This is a beginning course in the calculus of one variable and analytic geometry. The concept of limits and their use in differential and integral calculus, max and min values of functions, and solving for areas and volumes are treated.

Prerequisite: Grade of C- or higher in MATH A118, or permission from the Chair of the Department of Mathematics and Computer Science, or Math Placement

MATH A258 Calculus II, 4 crs.

Topics include the Mean Value Theorem and its applications, applications of the integral, transcendental functions, techniques of integration, sequences and series, and conic sections.

Prerequisite: MATH A257

MATH A259 Calculus III, 3 crs.

This course addresses the calculus of several variables and vector analysis. Topics include differentiation of vector valued functions, extreme values, Lagrange multipliers, multiple integration, line and surface integrals, and an introduction to vector fields.

Prerequisites: MATH A200 and MATH A258

MATH A260 Statistical Inference for Scientists, 3 crs.

This is a course in statistical methods for science students. Emphasis centers on the practical application of statistical inference and estimation in the quest for scientific knowledge. Topics include exploratory data analysis, techniques for data collection, summarization, and presentation, graphical techniques and numerical measures, the role of the Normal distribution, regression and correlation analysis, confidence intervals, hypothesis testing, the analysis of variance, and distribution-free methods.

Prerequisite: MATH A115MATH A117MATH 118, or MATH A257, or Math Placement

MATH A261 Statistical Inference for Scientists, Lab 1 cr.

Optional lab accompaniment for Math A260.

Prerequisite: MATH A115 or MATH A117 or MATH 118

MATH A271 Applied Scientific Computing, 3 crs

This course introduces students to techniques and methods commonly used by scientists to analyze, build models, visualize and make decisions based on data collected in laboratory and field experiments. It emphasizes the interdisciplinary nature of scientific computing by applying the mathematical tools of statistics and numerical computations to hands on experiments from diverse areas of science.

Prerequisite: COSC A211MATH A257 or permission of instructor

MATH A310 Introduction to Differential Equations, 3 crs.

This course examines the fundamental methods of solving elementary differential equations. Topics include exact solutions, series solutions, numerical solutions and solutions using Laplace transforms.

Prerequisite: MATH A258

MATH A320 Linear Algebra, 3 crs.

In Linear Algebra expands on topics introducted in MATH A200 such as vector spaces, matrices, determinants, eigenvalues, linear functionals, bilinear forms, vector geometry, and their applications.

Prerequisite: MATH A200

MATH A340 Math Probability, 3 crs.

This course introduces the theory of probability. Topics include combinatorial analysis, axioms of probability, discrete and continuous random variables, expectation, multivariate probability distributions, function of random variables, and basic limit theorems.

Prerequisite: MATH A310

MATH A341 Statistics Theory and Methods, 3 crs.

This course shows how statistics makes inferences about a population based on information from samples. Topics include estimation, hypothesis testing, linear models, and estimation by least squares. Experimental design, analysis of variance, analysis of enumerative data, and nonparametric statistics.

Prerequisites: MATH A340; permission of instructor

MATH A345 Topics in Geometry, 3 crs.

The course includes foundations of geometry, congruences, parallelism, similarities, measures, coordinate systems, axiom systems for the Euclidean, and projective planes.

Prerequisite: MATH A258

MATH A350 Differential Equations, 3 crs.

This course reviews and continues the introduction to ordinary differential equations covered in MATH A310. Selected topics in partial differential equations and include applications to various fields.

Prerequisites: MATH A259, MATH A310

MATH A360 Biomathematics, 3 crs.

This course is an introduction to the development and analysis of mathematical models with biological applications.  Topics include difference equations, stability and bifurcation analysis, population growth, predator-prey models, and models of infectious disease.  This course will also provide an introduction to the software package MATLAB.

Prerequisites: MATH A259 or MATH A310

MATH A375 Computational Mathematics, 3 crs

This course develops the computational procedures fundamental to numeric applications. Topics include, but are not limited to, error analysis, numerical solutions of non-linear equations, systems of linear equations using direct and iterative methods, polynomial interpolation, quadrature, least squares curve fitting, and numerical solutions of ordinary differential equations. This course does not count as a mathematics elective for the Mathematics major. It is a requirement for the Computational Mathematics major and the Computational Science minor.

Prerequisites: COSC A211, MATH A258 or permission of instructor

MATH A400 Abstract Algebra I, 3 crs.

This is a general survey course in the concepts of algebra treating number systems, groups, rings, domains, fields, matrices over a field, elements of Galois theory, and canonical forms.

Prerequisite: MATH A200

MATH A401 Abstract Algebra II, 3 crs.

This course is a continuation of MATH A400.

Prerequisite: MATH A400

MATH A410 Advanced Calculus I, 3 crs.

This course offers a deeper look at analysis with special attention to linear methods as applied to the calculus of several variables. Topics include extrema, Jacobians, uniform continuity, line and surface integrals, differentials, integration theory, and series.

Prerequisites: MATH A259, MATH A310

MATH A411 Advanced Calculus II, 3 crs.

This course is a continuation of MATH A410.

Prerequisite: MATH A410

MATH A415 Complex Variables, 3 crs.

This course studies the theory of analytic functions. Topics include Cauchy's integration theory, series representation, analytic continuation and conformal mappings.

Prerequisites: MATH A259, MATH A310

MATH A425 General Topology, 3 crs.

This course studies basic concepts from the topics of topological spaces, Hausdorff spaces, connectedness, metric spaces, continuous mappings, separability, compactness, and product spaces.

Prerequisite: Permission of instructor

MATH A430 Applied Math I, 3 crs.

This course illustrates the application of mathematics to one or more fields by considering the aspects of model building, and further developes theory and techniques relevant to the needs of the field. Topics include partial differential equations, Eigen functions, Green’s functions, perturbation, and approximation methods.

Prerequisites: MATH A259, MATH A310

MATH A493 Directed Readings, 3 crs.

Course content varies and is keyed to the participants' interests in relevant professional topics.

MATH A495 Special Project, credits vary

This course focuses on the creative or productive efforts of one or more students. A special project is distinguished from a research project in its lack of the historical or experimental method and perspective characteristics of research.

MATH A496 Math Seminar, 1 cr.

Topics from various branches of mathematics will be presented, discussed, and argued by the students. By invitation only.

MATH A498 Research Project, credits vary

The research project focuses on empirical or historical investigation, culminating in a written report.

MATH A499 Independent Study, credits vary

Independent work done under professorial supervision.

MATH H295 Honors Seminar, 3 crs.

This seminar course overs a variety of topics in the mathematical sciences determined by the instructor.

Loyola Core

MATH T121 First-Year Seminar, 3 crs

Foundation Courses: First-Year Seminar

The gateway course to the Loyola Core is the First-Year Seminar (FYS). This issues-based, interdisciplinary seminar introduces students to college-level thinking and learning as well as Jesuit values at the core of a Loyola education. A full list of currently offered FYS courses can be found on the Loyola Online Records Access (LORA) system.

MATH T122 Math Models, 3 crs.

Foundation Courses: Math

This course provides an introduction to a variety of topics in mathematics for non-science majors.  The course develops students understanding of basic concepts in statistics, geometry and scientific modeling.  The course serves as a foundation for Loyola Core natural and social science courses.

Prerequisite: Math Placement

Math Y135 Mathematics, Logic, and Language, 3 crs.

Knowledge-Values Courses: Natural Science in Context

This course develops the connections between language and mathematics.  These subjects seem quite disparate but are actually quite closely connected.  Students use language-based techniques to develop algorithms to solve various mathematical problems.  In particular, students learn that different mathematical problems, although equally simple in concept, require quite different resources for their solutions.