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.

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.

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.

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.

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

An introduction to the basic concepts of descriptive and inferential statistics and their application to the interpretation and analysis of data. Fall and Spring.

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.

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

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: C

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.
This course does not meet major or minor requirements.

Topics taken from sets, functions, matrices, ordered sets, partially ordered sets, directed graphs, algebraic systems, recursive definitions, and algorithms. Fall and Spring.

Prerequisite:

MATH 148 Minimum Grade: D
or MATH 157 Minimum Grade: D

A continuation of MATH 157. Topics covered are: techniques of integration, applications of the integral, improper integrals, sequences and infinite series with an introduction to convergence tests, parametric equations, and polar coordinates.

Prerequisite:

MATH 157 Minimum Grade: C-

A treatment of multivariable calculus and the calculus of vector fields. Topics include: vectors and vector-valued functions, partial derivatives, multiple integration, curl and divergence, line integrals, Green’s theorem, Stokes’ theorem, and the Divergence theorem.

Prerequisite:

MATH 258 Minimum Grade: C-

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

Readings and reports in selected mathematical topics. Upon sufficient demand.

Prerequisite:

MATH 157 Minimum Grade: D

A development of standard proof techniques through examination of logic, set theory, one-to-one, onto, and inverse functions. Additional topics may be chosen from the topology of the real line, the cardinality of sets, basic number theory, and basic group theory. Fall and Spring.

Prerequisite:

MATH 259 Minimum Grade: D

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

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, odd years.

Prerequisite:

MATH 258 Minimum Grade: D

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

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

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. Fall.

Prerequisite:

MATH 258 Minimum Grade: D

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

Various areas of pure and applied mathematics presented at a level accessible to those just completing calculus. Upon sufficient demand.

Topic to be determined by faculty.

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. Spring and Fall, even years.

Prerequisite:

MATH 301 Minimum Grade: D

Continuation of MATH 413 with topics based on instructor and student interest. Spring, odd years.

Prerequisite:

MATH 413 Minimum Grade: D

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, even years.

Prerequisite:

MATH 301 Minimum Grade: D

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.

Prerequisite:

MATH 301 Minimum Grade: D

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

An undergraduate course in stochastic processes. This course covers a variety of random processes and their applications. Topics include convergence of random variables, conditional expectation, Markov chains, Poisson processes, and simulation techniques. Additional topics
may be chosen from random walks, queuing theory, branching processes, reliability theory, and Brownian motion. Spring, odd years.

Prerequisite:

MATH 421 Minimum Grade: D

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.
This course does not meet major or minor requirements.

A detailed examination of topics chosen from groups, rings, integral domains, Euclidean domains, unique factorization, fields, Galois theory, and solvability by radicals. Spring and Fall, odd years.

Prerequisite:

MATH 301 Minimum Grade: D

Continuation of MATH 437. Spring, even years.

Prerequisite:

MATH 437 Minimum Grade: D

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. Upon sufficient demand.

Prerequisite:

MATH 301 Minimum Grade: D

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

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. Upon sufficient demand.

Prerequisite:

MATH 301 Minimum Grade: D

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. Upon sufficient demand.

Prerequisite:

MATH 301 Minimum Grade: D

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.

Prerequisite:

MATH 260 Minimum Grade: C-

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

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. Spring, odd years.

Prerequisite:

MATH 301 Minimum Grade: D

This course provides an introduction to nonlinear dynamics and chaos theory. We examine concepts related to geometric and global ways of analyzing nonlinear evolution equations. These concepts include: phase space analysis, dissipative versus conservative systems, attractors, basins of attraction, elementary bifurcation theory, linear stability theory, Poincare sections and maps, strange attractors, Lyapunov exponents, fractals and fractal dimension. Fall, even years.

Prerequisite:

MATH 260 Minimum Grade: C-

Selected topics in mathematics.

A comprehensive survey of applied mathematics and its connections with various technical disciplines. Students will gain experience with both written and oral communication while reviewing a breadth of mathematical topics and exploring interdisciplinary applications. Students will be required to take the Educational Testing Service’s Major Field Test in Mathematics. Required of all Applied Mathematics majors in their final year. Fall.

Special program for Mathematics majors.

This course provides the motivated student with the opportunity to conduct an independent research project under the direction of a Mathematics Department faculty member. Rigorous research and study of advanced material with a significant technical writing component. Contingent on the student finding a faculty member in the Department of Mathematics who is willing to serve as a mentor. Fall and Spring.

Prerequisite:

MATH 301 Minimum Grade: C

Continuation of MATH 498A, culminating in a written thesis. Students are expected to present their work at a conference. Fall and Spring.

Prerequisite:

MATH 498A Minimum Grade: B

A comprehensive survey of mathematics. Students will gain experience with both written and oral communication of a breadth of mathematical topics. Students will be required to take the Educational Testing Service’s Major Field Test in mathematics. Required of all Mathematics majors in their final year. Fall.