MATHEMATICS (MATH)

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.

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.

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.

Topic to be determined by instructor.

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.

This course contains an introduction to probability and the use of statistics to solve problems in a variety of scientific disciplines. Topics include experimental design, sampling methods, confidence intervals, hypothesis tests, and linear models. The use of statistical software is integral to this course. Fall.

A study of propositional logic, set theory, functions, algorithms, divisibility, introductory number theory, elementary proof techniques, counting techniques, recursive definitions, mathematical induction, and graph theory. Fall and Spring.

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.

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.

Solution methods for first-order equations, second-order linear equations, and linear systems of differential equations, including analytic and qualitative approaches. Topics include mathematical modeling, Laplace transforms, Taylor series solutions, and an introduction to matrix methods. Additional topics may include numerical methods, analyzing nonlinear systems, and techniques for higher-order linear equations. Fall and Spring.

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

A development of the standard techniques of mathematical proof through an examination of logic, set theory, as well as 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.

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.

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.

An applied study of matrices, vector spaces, and linear transformations, with a focus on computations and modeling. Topics include linear systems, dependence and rank, bases, inner product spaces, orthogonal and orthonormal sets, eigenvalues and eigenvectors, matrix factorizations, and singular values. Additional topics may include numerical techniques and applications to static and dynamical physical systems, Markov chains, graph theory, artificial neural networks, image and signal processing. Computer programming will be an integral component of the class. Spring.

A systematic study of the theory of matrices, vector spaces, and linear transformations. Topics include systems of linear equations, determinants, linear independence, bases, dimension, rank, eigenvalues, and eigenvectors. Additional topics may include inner products, orthonormal bases, projections, and quadratic forms. Applications may include geometry, adjacency matrices, calculus, difference equations, least squares, and Markov chains. Some proof-writing expected. Fall and Spring.

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.

An introduction to approximating solutions to problems arising in applied mathematics and science. Topics include solving linear systems, root-finding, interpolations, regression, numerical integration and differentiation, and initial value problems. Computer programming will be an integral component of the class. Fall.

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.

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

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

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

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

This seminar is intended to expose students with a calculus background to a wide variety of interesting topics and applications in mathematics. The goal of this seminar is to help students discover and explore topics in mathematics, not typically covered in a classroom setting. A weekly guest lecturer will present a topic or activity and invite questions and participation from the class. Guest lecturers may be faculty, students who have performed independent research, or guests from the community. Spring

Topic to be determined by faculty.

This proof-based course provides a rigorous treatment of the real number system, the topology of the real line, sequences and series of numbers and functions, continuity of functions, differentiation, and the Riemann integral. Spring and Fall, even years.

Continuation of MATH 413 with topics chosen from Lebesgue theory, metric spaces, function spaces, and multivariable calculus. Spring, odd years.

An introduction to complex numbers and functions of one complex variable. Topics include the geometry and algebra of complex numbers, elementary functions, analytic functions, integration on the complex plane, Taylor and Laurent expansions, and the calculus of residues. Other topics selected from conformal mappings, integral transforms and inversion formulas, harmonic functions, and winding numbers, with applications to physical problems. Spring, even years.

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.

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.

An introduction to random processes and their applications in scientific inquiry, including discrete and continuous time probability models, Markov chains, Poisson processes, random walks, and simulation techniques. Additional topics selected from: queuing theory, branching processes, reliability theory, and Brownian motion. Spring, odd years.

The course covers a wide range of statistical models including simple and multiple linear regression for quantitative and qualitative variables, logistic regression, log-linear models, models for rates (Poisson regression), and non-linear regression models. Inferences and model adequacy checking, model selection, and validation will be covered. The emphasis is on the practical application of these methods using statistical software. Fall, even years.

This course covers ANOVA models without and with interactions, randomized block, Latin square, factorial, confounded factorial, balanced incomplete block, other designs. Working with simple linear regression models, random and mixed-effects models, response surface methodology are covered. The emphasis is on how to plan, design, and conduct experiments efficiently and effectively, and analyze the resulting data using statistical software. Fall, odd years.

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.

Continuation of MATH 437. Spring, even years.

This course introduces advanced foundational techniques used to solve problems arising in applied mathematics, science and engineering. Topics include dimensional analysis and scaling, mathematical modeling, perturbation methods, and asymptotic expansions. Additional topics may include the calculus of variations, similarity methods, integral transforms, Fourier series, special functions, and the derivation of models from conservation laws and constitutive equations; other topics may be selected at the discretion of the instructor. Fall, odd years.

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.

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.

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.

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.

Solutions of boundary value problems with applications to heat flow, wave motion, and potential theory. Topics include derivation of the heat, wave, and Laplace's equations, orthogonal sets of functions, Fourier series, Sturm-Liouville theory, separation of variables, integral transforms, the method of characteristics, and extensions to higher dimensions and non-Cartesian coordinate systems. Additional topics may include numerical methods, inverse methods, and nonlinear equations. Spring.

Introduction to the study of one-dimensional discrete-time nonlinear systems and their potential for chaotic behavior. The course will focus on investigations through computer experiments - numerical and graphical - and the mathematical analysis of the observed behavior. Students are expected to write code in at least one high-level language. Topics include orbit analysis, fixed and periodic points, graphical analysis, bifurcations, symbolic dynamics, chaos, and fractals. Additional topics selected from dynamics in the complex plane, higher dimensional maps, numerical computation of Lyapunov exponents, fractal dimension, Sarkovskii's theorem, and chaos control. Spring, even years.

Elementary number theory topics including modular arithmetic, Diophantine equations, multiplicative functions, factorization techniques, primality testing, and development of the public key code. Additional topics may be included. Fall, even years.

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.

A study of nonlinear ordinary differential equations and systems of such equations, with a focus on approaching problems geometrically. Topics include phase space, equilibrium solutions, bifurcations, stability analysis, limit cycles, chaos, fractals, and strange attractors; other topics may be selected at the discretion of the instructor. Applications to problems in biology, chemistry, physics, engineering and other fields will be explored. Fall, even years.

Selected topics in mathematics.

This course explores the application of mathematics to solving actuarial science problems. Course material is intended to help students prepare for the probability and financial math actuarial exams. Spring upon sufficient demand.

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.

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

A comprehensive survey of mathematics. Students will gain experience with both written and oral communication of mathematics while reviewing 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.