Mathematics

Chairperson: Shannon Overbay
Professors: V. Coufal, T. McKenzie, S. Overbay, J. Burke (Emeritus), W. Carsrud (Emeritus), J. Firkins (Emeritus)
Associate Professors: 
L. AxonB. Dichone, G. Nord (Emeritus), R. Ray, J. Vander Beek (Emeritus)
Assistant Professors:
M. Alsaker, R. Cangelosi, M. Ghrist, E. Hogle, M. K. Kearney, D. LarsonJ.Lutz, J.Marks, K. Shultis, J. Stover
Senior Lecturers:
C. Goodwin, F. T. Rux
Lecturers: 
T. Guardia, O. Kozubenko

The Department of Mathematics seeks to train students in both the discipline of mathematics and its application. The curriculum is a blend of pure mathematics, classical applications, and the option of a combination of mathematics and computer science. Majors are well prepared for positions in industry, government, and education, as well as for graduate studies.

The department offers three degrees: Bachelor of Arts in Mathematics, Bachelor of Science in mathematics, and Bachelor of Science in Mathematics and Computer Science. All majors must take the senior comprehensive (MATH 499) in the fall of their final year.

Prospective teachers of mathematics should consult the School of Education for the current state certification requirements.

It is recommended that majors in mathematics take PHYS 103, CHEM 101 or BIOL 105 to satisfy their University Core Scientific Inquiry requirement. The department involves students with activities sponsored by the Mathematical Association of America. Majors may also participate in the annual William Lowell Putnam Mathematical Competition held every December.


B.S. Major in Mathematics: 40 Credits

Lower Division
MATH 157 Calculus and Analytic Geometry I 4 credits
MATH 258 Calculus and Analytic Geometry II 4 credits
MATH 259 Calculus and Analytic Geometry III 4 credits
Upper Division
MATH 301 Fundamentals of Mathematics 3 credits
MATH 339 Linear Algebra 3 credits
MATH 413 Real Analysis I
3 credits
MATH 437 Abstract Algebra I
3 credits
MATH any 400-level, excluding MATH 432 6 credits
MATH Electives,* excluding MATH 432
*One of these courses may be replaced by MATH 260.
9 credits
MATH 499 Senior Comprehensive 1 credit

B.A. Major in Mathematics: 31 Credits

Lower Division
MATH 157 Calculus and Analytic Geometry I 4 credits
MATH 258 Calculus and Analytic Geometry II 4 credits
MATH 259 Calculus and Analytic Geometry III 4 credits
Upper Division
MATH 301 Fundamentals of Mathematics 3 credits
MATH 339 Linear Algebra 3 credits
One of the following two courses:
3 credits
MATH 413 Real Analysis I
 
MATH 437 Abstract Algebra I
 
MATH, any 400-level, excluding MATH 432 3 credits
MATH Electives,* excluding MATH 432
* One of these courses may be replaced by MATH 260.
6 credits
MATH 499 Senior Comprehensive 1 credit

Minor in Mathematics: 24 credits

Lower Division
MATH 157 Calculus and Analytic Geometry I 4 credits
MATH 258 Calculus and Analytic Geometry II 4 credits
MATH 259 Calculus and Analytic Geometry III 4 credits
Upper Division
MATH 301 Fundamentals of Mathematics 3 credits
MATH 339 Linear Algebra 3 credits
MATH any 400-level, excluding MATH 432 3 credits
MATH Electives, excluding MATH 432 3 credits

B.S. Major in Mathematics-Computer Science: 49 Credits

Lower Division
CPSC 121 Computer Science I 3 credits
CPSC 122 Computer Science II 3 credits
CPSC 223 Data Structures 3 credits
CPSC 224 Object-Oriented and Event Driven Programming 3 credits
MATH 157 Calculus and Analytic Geometry I 4 credits
MATH 231 Discrete Structures 3 credits
MATH 258 Calculus and Analytic Geometry II 4 credits
MATH 259 Calculus and Analytic Geometry III 4 credits
Upper Division
CPSC 300-level or above except CPSC 497 6 credits
MATH 301 Fundamentals of Mathematics 3 credits
MATH 339 Linear Algebra 3 credits
MATH, any 400-level, excluding MATH 432 3 credits
MATH Electives, excluding MATH 432 6 credits
MATH 499 Senior Comprehensive 1 credit

Minor in Mathematics-Computer Science is not available



Lower Division
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
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
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. This course does not meet major or minor requirements.
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 148 Minimum Grade: D or MATH 157 Minimum Grade: D
MATH 258 Calculus-Analytic Geometry II
4.00 credits
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-
MATH 259 Calculus-Analytic Geometry III
4.00 credits
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: 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
Upper Division
MATH 301 Fundamentals of Mathematics
3.00 credits
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.
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. Spring and 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. This course does not meet major or minor requirements.
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. Spring and 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
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.
 

In addition to their major and minor areas of study, all undergraduate students follow a common program designed to complete their education in those areas that the University considers essential for a Catholic, Jesuit, liberal, and humanistic education. The University Core Curriculum consists of forty-five credits of course work, with additional designation requirements that can be met through core, major, or elective courses.

The University Core Curriculum is a four-year program, organized around one overarching question, which is progressively addressed through yearly themes and questions. Hence, core courses are best taken within the year for which they are designated. First year core courses encourage intellectual engagement and provide a broad foundation of fundamental skills. Second and third year courses examine central issues and questions in philosophy and religious studies. The fourth year course, the Core Integration Seminar, offers a culminating core experience. Taken at any time throughout the four years, broadening courses intersect with the core themes and extend students’ appreciation for the humanities, arts, and social and behavioral sciences. Finally, the designation requirements (writing enriched, global studies, and social justice) reflect important values and reinforce students’ knowledge and competencies.

Overarching Core Question: As students of a Catholic, Jesuit, and Humanistic University, how do we educate ourselves to become women and men for a more just and humane global community?
Year 1 Theme and Question: Understanding and Creating: How do we pursue knowledge and cultivate understanding?

  • The First-Year Seminar (DEPT 193, 3 credits): The First-Year Seminar (FYS), taken in the fall or spring of the first year, is designed to promote an intellectual shift in students as they transition to college academic life. Each small seminar is organized around an engaging topic, which students explore from multiple perspectives. The FYS is offered by many departments across the University (click here [PDF] for list of FYS courses).  
  • Writing (ENGL 101, 3 credits) and Reasoning (PHIL 101, 3 credits): The Writing and Reasoning courses are designed to help students develop the foundational skills of critical reading, thinking, analysis, and writing. They may be taken as linked sections. Writing (ENGL 101) carries one of the three required writing-enriched designations (see below).
  • Communication & Speech (COMM 100, 3 credits): This course introduces students to interpersonal and small group communication and requires the application of critical thinking, reasoning, and research skills necessary to organize, write, and present several speeches.
  • Scientific Inquiry (BIOL 104/104L, CHEM 104/104L, or PHYS 104/104L, 3 credits): This course explores the scientific process in the natural world through evidence-based logic and includes significant laboratory experience. Students pursuing majors that require science courses will satisfy this requirement through their major.
  • Mathematics (above Math 100, 3 credits): Mathematics courses promote thinking according to the modes of the discipline—abstractly, symbolically, logically, and computationally. One course in mathematics, above Math 100, including any math course required for a major or minor, will fulfill this requirement. MATH 100 (College Algebra) and courses without the MATH prefix do not fulfill this requirement.

Year 2 Theme and Question: Being and Becoming: Who are we and what does it mean to be human?

  • Philosophy of Human Nature (PHIL 201, 3 credits): This course provides students with a philosophical study of key figures, theories, and intellectual traditions that contribute to understanding the human condition; the meaning and dignity of human life; and the human relationship to ultimate reality.
  • Christianity and Catholic Traditions (RELI, 3 credits). Religious Studies core courses approved for this requirement explore diverse topics including Christian scriptures, history, theology, and practices as well as major contributions from the Catholic intellectual and theological traditions (click here [PDF] for a list of approved courses) .

Year 3 Theme and Question: Caring and Doing: What principles characterize a well lived life?

  • Ethics (PHIL 301 or RELI, 3 credits): The Ethics courses are designed to help students develop their moral imagination by exploring and explaining the reasons humans should care about the needs and interests of others. This requirement is satisfied by an approved ethics course in either Philosophy (PHIL 301) or Religious Studies (click here [PDF] for a list of approved courses).
  • World/Comparative Religion (RELI, 3 credits): Religious Studies courses approved for this core requirement draw attention to the diversity that exists within and among traditions and encourage students to bring critical, analytical thinking to bear on the traditions and questions considered. These courses carries one of the required two global-studies designations (see below) (click here [PDF] for a list of approved courses).

Year 4 Theme and Question: Imagining the Possible: What is our role in the world?” 

  • Core Integration Seminar (DEPT 432, 3 credits). The Core Integration Seminar (CIS) offers students a culminating core experience in which they integrate the principles of Jesuit education, prior components of the core, and their disciplinary expertise. Some CIS courses may also count toward a student’s major or minor. The CIS is offered by several departments across the University (click here [PDF] for list of CIS courses).

The Broadening Courses

  • Fine Arts & Design (VART, MUSC, THEA, 3 credits): Arts courses explore multiple ways the human experience can be expressed through creativity, including across different cultures and societies. One approved course in fine arts, music, theatre, or dance will fulfill this requirement (click here [PDF] for a list of approved courses).
  • History (HIST, 3 credits): History courses are intended to develop students’ awareness of the historical context of both the individual and the collective human experience. One course in History (HIST 101, HIST 102, HIST 112, HIST 201, HIST 202) will fulfill this requirement.
  • Literature (3 credits): Literature courses foster reflection on how literature engages with a range of human experience. One approved course in Literature (offered by English, Classics, or Modern Languages) will fulfill this requirement (click here [PDF] for a list of approved courses).
  • Social & Behavioral Sciences (3 credits): Courses in the social and behavioral sciences engage students in studying human behavior, social systems, and social issues. One approved course offered by Criminal Justice, Economics, Political Science, Psychology, Sociology, or Women and Gender Studies will fulfill this requirement (click here [PDF] for a list of approved courses).

The Designations
Designations are embedded within already existing core, major, minor, and elective courses. Students are encouraged to meet designation requirements within elective courses as their schedule allows; however, with careful planning students should be able to complete most of the designation requirements within other core, major, or minor courses.

  • Writing Enriched (WE; 3 courses meeting this designation): Courses carrying the WE designation are designed to promote the humanistic and Jesuit pedagogical ideal of clear, effective communication. In addition to the required core course, Writing (ENGL 101), which carries one of the WE designations, students must take two other WE-designated courses (click here [PDF] for a list of approved courses).
  • Global-Studies (GS; 2 courses meeting this designation): Courses carrying the GS designation are designed to challenge students to perceive and understand human diversity by exploring diversity within a context of constantly changing global systems. In addition to the required core course, World/Comparative Religion (RELI 300-level), which carries one of the GS designations, students must take one other GS-designated course (click here [PDF] for a list of approved courses).
  • Social-Justice (SJ; 1 course meeting this designation): Courses carrying the SJ designation are designed to introduce students to one or more social justice concerns. Students must take one course that meets the SJ designation (click here [PDF] for a list of approved courses).

Major-specific adaptations to the University Core Curriculum

All Gonzaga students, regardless of their major, will complete the University Core Curriculum requirements. However some Gonzaga students will satisfy certain core requirements through major-specific programs or courses. Any major-specific adaptations to the core are described with the requirements for the majors to which they apply.