# Courses

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 MATH 099 Intermediate Algebra 3.00 credits
Review of basic algebraic operations and concepts for students who need additional preparation before taking other courses involving mathematics. Topics include operations on algebraic expressions, factoring, algebraic functions, linear and quadratic equations, graphing, exponents, radicals, and linear equations in two unknowns. This course does not fulfill the math requirement in the University Core.

 MATH 100 College Algebra 3.00 credits
College algebra for those students who need additional preparation before taking MATH 114, MATH 147, or MATH 148. Topics include equations, polynomials, conics, graphing, algebraic, exponential and logarithmic functions. This course does not fulfill the math requirement in the University Core. Fall and Spring.

 MATH 103 Excursions in Mathematics 3.00 credits
An elementary survey of various mathematical areas such as algebra, geometry, counting (permutations, combinations), probability, and other topics selected by the instructor. This course is intended for the liberal arts student not pursuing business or the sciences. Fall and Spring.

 MATH 104 Elements of Algebra & Stats 3.00 credits
Development and application of concepts from algebra and statistics. Topics include polynomials, solving equations, graphing, functions, modeling, counting (permutations and combinations), data representation, probability, and statistics.

 MATH 114 Mathematical Analysis-Business 3.00 credits
Designed for the student majoring in business. Topics selected from: functions and models, systems of equations, optimization, and introductory calculus. The emphasis will be on examples from business, which may include: cost, revenue, profit, supply, demand, market equilibrium, interest, present-value, future-value, and consumer and producer surplus. Fall and Spring.

 Prerequisite: MATH 100 Minimum Grade: D or MATH 112 Minimum Grade: D
 MATH 121 Introductory Statistics 3.00 credits
An introduction to the basic concepts of descriptive and inferential statistics and their application to the interpretation and analysis of data. Fall and Spring.

 MATH 147 Precalculus 3.00 credits
Topics include advanced equations and inequalities, functions and graphs including composite and inverse functions, logarithmic and exponential functions, trigonometric functions and their graphs, right angle trigonometry, trigonometric identities, systems of equations, and conics. Fall and Spring.

 MATH 148 Survey of Calculus 3.00 credits
A one semester introduction to differential and integral calculus designed to convey the significance, use and application of calculus for liberal arts students, particularly those in the behavioral, biological, and social sciences. Fall and Spring.

 Prerequisite: MATH 100 Minimum Grade: D or MATH 112 Minimum Grade: D
 MATH 157 Calculus-Analytic Geometry I 4.00 credits
An introduction to calculus for engineering, science and mathematics students, with an emphasis on conceptual understanding, problem solving, and modeling. Topics covered include: limits, continuity, derivatives of algebraic, trigonometric, and transcendental functions, applications of the derivative including optimization problems and linear approximations, antiderivatives, introduction to the definite integral, and the Fundamental Theorem of Calculus. Fall and Spring.

 Prerequisite: MATH 147 Minimum Grade: D
 MATH 193 FYS: 3.00 credits
The First-Year Seminar (FYS) introduces new Gonzaga students to the University, the Core Curriculum, and Gonzaga’s Jesuit mission and heritage. While the seminars will be taught by faculty with expertise in particular disciplines, topics will be addressed in a way that illustrates approaches and methods of different academic disciplines. The seminar format of the course highlights the participatory character of university life, emphasizing that learning is an active, collegial process.

 MATH 231 Discrete Structures 3.00 credits
Topics taken from sets, functions, matrices, ordered sets, partially ordered sets, directed graphs, algebraic systems, recursive definitions, and algorithms. Fall and Spring.

 Prerequisite: MATH 157 Minimum Grade: D or MATH 148 Minimum Grade: D or MATH 148 Minimum Grade: D
 MATH 258 Calculus-Analytic Geometry II 4.00 credits
Inverse functions, techniques of integration, applications of integration and series.

 Prerequisite: MATH 157 Minimum Grade: C-
 MATH 259 Calculus-Analytic Geometry III 4.00 credits
Parametric and polar coordinates, vectors, partial derivatives, multiple integrals.

 Prerequisite: MATH 258 Minimum Grade: D
 MATH 260 Ordinary Differential Equation 3.00 credits
Solution methods for first order equations and for second and higher order linear equations. Includes series methods and solution of linear systems of differential equations. Fall and Spring.

 Prerequisite: MATH 259 Minimum Grade: D
 MATH 290 Directed Reading 1.00 - 3.00 credits
Readings and reports in selected mathematical topics. On sufficient demand.

 Prerequisite: MATH 157 Minimum Grade: D
 MATH 301 Fundamentals of Mathematics 3.00 credits
A development of standard proof techniques through examination of logic, set theory, topology of the real line, one-to-one, onto, and inverse functions. Additional topics may be chosen from analysis and algebra. Fall and Spring.

 Prerequisite: MATH 259 Minimum Grade: D
 MATH 321 Statistics for Experimentalist 3.00 credits
An applied statistics course for those with calculus preparation. Descriptive statistics, probability theory, discrete and continuous random variables, and methods of inferential statistics including interval estimation, hypothesis testing, and regression. Fall and Spring.

 Prerequisite: MATH 258 Minimum Grade: D
 MATH 328 Operations Research 3.00 credits
Quantitative methods for application to problems from business, engineering, and the social sciences. Topics include linear and dynamic programming, transportation problems, network analysis, PERT, and game theory. Spring, even years.

 Prerequisite: MATH 258 Minimum Grade: D
 MATH 339 Linear Algebra 3.00 credits
A systematic study of matrices, vector spaces, and linear transformations. Topics include systems of linear equations, determinants, dependence, bases, dimension, rank, eigenvalues and eigenvectors. Applications include geometry, calculus, and differential equations. Fall and Spring.

 Prerequisite: MATH 259 Minimum Grade: D
 MATH 341 Modern Geometry 3.00 credits
Axiomatic systems for, and selected topics from, Euclidean geometry, projective geometry, and other non-Euclidean geometries. Special attention will be given to the needs of the individuals preparing to teach at the secondary level. Fall, even years.

 Prerequisite: MATH 259 Minimum Grade: D
 MATH 350 Elementary Numerical Analysis 3.00 credits
An introduction to numerical analysis: root finding, interpolation, numerical integration and differentiation, finite differences, numerical solution to initial value problems, and applications on a digital computer. Spring.

 Prerequisite: MATH 258 Minimum Grade: D
 MATH 351 Combinatorics and Graph Theory 3.00 credits
An introduction to combinatorics and graph theory with topics taken from counting techniques, generating functions, combinatorial designs and codes, matchings, directed graphs, paths, circuits, connectivity, trees, planarity, and colorings. Fall, odd years.

 Prerequisite: MATH 231 Minimum Grade: D or MATH 301 Minimum Grade: D
 MATH 360 Selected Topics 1.00 - 3.00 credits
Various areas of pure and applied mathematics presented at a level accessible to those just completing calculus. On sufficient demand.

 MATH 361 Selected Topics 1.00 - 3.00 credits
Various areas of pure and applied mathematics presented at a level accessible to those just completing calculus. On sufficient demand.

 MATH 362 Selected Topics 1.00 - 3.00 credits
Various areas of pure and applied mathematics presented at a level accessible to those just completing calculus. On sufficient demand.

 MATH 363 Selected Topics 1.00 - 3.00 credits
Various areas of pure and applied mathematics presented at a level accessible to those just completing calculus. On sufficient demand.

 MATH 390 Directed Study 1.00 - 3.00 credits
Topic to be decided by faculty.

 MATH 413 Real Analysis I 3.00 credits
Topics chosen from: the axioms and topology of the real line, sequences and series of numbers and functions, continuity and properties of continuous functions, differentiation, Riemann integrals and generalizations, differential forms, metric spaces, and mappings between Euclidean spaces. Fall, even years.

 Prerequisite: MATH 301 Minimum Grade: D
 MATH 414 Real Analysis II 3.00 credits
Continuation of Math 413 with topics based on instructor and student interest. Spring, odd years.

 Prerequisite: MATH 413 Minimum Grade: D
 MATH 417 Complex Variables 3.00 credits
Complex numbers and functions, analyticity and the Cauchy-Riemann equations, integration, and Cauchy's theorem and formula. Other topics chosen from Taylor and Laurent series, the calculus of residues, conformal mapping, and applications. Spring, odd years.

 Prerequisite: MATH 301 Minimum Grade: D
 MATH 421 Probability Theory 3.00 credits
A mathematical treatment of the laws of probability with emphasis on those properties fundamental to mathematical statistics. General probability spaces, combinatorial analysis, random variables, conditional probability, moment generating functions, Bayes' law, distribution theory, and law of large numbers. Fall, odd years.

 Prerequisite: MATH 301 Minimum Grade: D
 MATH 422 Mathematical Statistics 3.00 credits
An examination of the mathematical principles underlying the basic statistical inference techniques of estimation, hypothesis testing, regression and correlation, nonparametric statistics, analysis of variance. Spring, even years.

 Prerequisite: MATH 421 Minimum Grade: D
 MATH 432 CIS: 3.00 credits
The Core Integration Seminar (CIS) engages the Year Four Question: “Imagining the possible: What is our role in the world?” by offering students a culminating seminar experience in which students integrate the principles of Jesuit education, prior components of the Core, and their disciplinary expertise. Each section of the course will focus on a problem or issue raised by the contemporary world that encourages integration, collaboration, and problem solving. The topic for each section of the course will be proposed and developed by each faculty member in a way that clearly connects to the Jesuit Mission, to multiple disciplinary perspectives, and to our students’ future role in the world.

 MATH 437 Abstract Algebra I 3.00 credits
A detailed examination of topics chosen from groups, rings, integral domains, Euclidean domains, unique factorization, fields, Galois theory, and solvability by radicals. Fall, odd years.

 Prerequisite: MATH 301 Minimum Grade: D
 MATH 438 Abstract Algebra II 3.00 credits
Continuation of MATH 437. Spring, even years.

 Prerequisite: MATH 437 Minimum Grade: D
 MATH 450 Selected Topics 1.00 - 3.00 credits
Possible topics include combinatorics, topology, number theory, advanced numerical analysis, advanced linear algebra, theory of computation and complexity, and history of mathematics. Credit by arrangement. On sufficient demand.

 Prerequisite: MATH 301 Minimum Grade: D
 MATH 451 Special Topics 1.00 - 3.00 credits
Possible topics include combinatorics, topology, number theory, advanced numerical analysis, advanced linear algebra, theory of computation and complexity, and history of mathematics. Credit by arrangement. On sufficient demand.

 Prerequisite: MATH 301 Minimum Grade: D
 MATH 452 Selected Topics 1.00 - 3.00 credits
Possible topics include combinatorics, topology, number theory, advanced numerical analysis, advanced linear algebra, theory of computation and complexity, and history of mathematics. Credit by arrangement. On sufficient demand.

 Prerequisite: MATH 301 Minimum Grade: D
 MATH 453 Selected Topic 1.00 - 3.00 credits
Possible topics include combinatorics, topology, number theory, advanced numerical analysis, advanced linear algebra, theory of computation and complexity, and history of mathematics. Credit by arrangement. On sufficient demand.

 Prerequisite: MATH 301 Minimum Grade: D
 MATH 454 Partial Differential Equations 3.00 credits
Derivation of the wave, heat, and Laplace's equations, separation of variables, Sturm-Liouville problems, sets of orthogonal functions, Fourier series, solutions of boundary value problems, Laplace transforms, and numerical methods. Spring, even years.

 Prerequisite: MATH 260 Minimum Grade: D
 MATH 457 Number Theory & Cryptography 3.00 credits
Elementary number theory topics including modular arithmetic, Diophantine equations, multiplicative functions, factorization techniques, primality testing, and development of the public key code. Fall, even years.

 Prerequisite: MATH 301 Minimum Grade: D
 MATH 459 Topology 3.00 credits
Topics selected from the following: Metric spaces, manifolds, general topological spaces. Sequences, continuous functions, homeomorphisms. The separation axioms, connectedness, compactness. The theory of surfaces. Knot theory. Topics from combinatorial topology, algebraic topology, differential topology. Other topics to be determined by the instructor. Fall, even years.

 Prerequisite: MATH 301 Minimum Grade: D
 MATH 490 Directed Reading .00 - 4.00 credits
Selected topics in mathematics.

 MATH 497 Mathematics Internship .00 - 6.00 credits
Special program for Mathematics majors.

 MATH 499 Comprehensive 1.00 credit
Preparation for and writing of the Educational Testing Service's Major Field Test in mathematics. Required of all Mathematics and Mathematics-Computer Science majors in their final year. Fall.