Instructor(s):  staff

Required text(s):  Angel, Allen and Dennis Runde. Intermediate Algebra for College Students (packaged with MyMathLab). 8th ed. ISBN-13: 9780321709042. Upper Saddle River, NJ: Pearson-Prentice Hall, 2010. Print.

Textbook notes:  Students are required to have access to MyMathLab for this course. Students buying used textbooks should arrange to purchase MyMathLab separately.

Prerequisites:  None

Course description:  Fundamentals of algebra. Graphs of linear equations, polynomials and factoring, first and second-degree equations and inequalities, radicals and exponents, and systems of equations. Word problems emphasized throughout the course.

Syllabus:  Common

Instructor(s):  Staff

Required text(s):  Consortium for Mathematics and Its Applications (COMAP), S. Garfunkel, ed. For All Practical Purposes: Mathematical Literacy in Today's World. 9th ed. ISBN-13: 978-1429243162. New York: W. H. Freeman, 2011. Print.

Prerequisites:  None

Course description:  An introduction to mathematical modeling. Topics chosen from linear programming, probability theory, Markov chains, scheduling problems, coding theory, social choice, voting theory, geometric concepts, game theory, graph theory, combinatorics, networks. Emphasis placed upon demonstrating the usefulness of mathematical models in other disciplines, especially the social science and business.

Syllabus:  Common

Instructor(s):  staff

Required text(s):  Axler, Sheldon. Algebra and Trigonometry (packaged with WileyPLUS). 1st ed. ISBN-13: 9781118088418. Hoboken, NJ: Wiley, 2012. Print.

Textbook notes:  Students are required to have access to WileyPLUS for this course. Students buying used textbooks should arrange to purchase WileyPLUS separately.

Prerequisites:  MATH 100 or Math Diagnostic Test

Course description:  Inverse functions, quadratic functions, complex numbers. Detailed study of polynomial functions including zeros, factor theorem, and graphs. Rational functions, exponential and logarithmic functions and their applications. Systems of equations, inequalities, partial fractions, linear programming, sequences and series. Word problems are emphasized throughout the course.

Syllabus:  Common

Instructor(s):  Staff

Required text(s):  Axler, Sheldon. Algebra and Trigonometry (packaged with WileyPLUS). 1st ed. ISBN-13: 9781118088418. Hoboken, NJ: Wiley, 2012. Print.

Prerequisites:  MATH 117 or Math Diagnostic Test

Course description:  Functions and change with an emphasis on linear, quadratic, exponential, and logarithmic functions and their graphs. Specific geometric topics include concavity and how transformations affect graphs. Topics in trigonometry include radians, sinusoidal functions, identities, sum/difference formulas, double/half angle formulas, and trigonometric equations. Other topics include polar coordinates.

Syllabus:  Common

Instructor(s):  staff

Required text(s):  Hughes-Hallett, Deborah, et al. Applied & Single Variable Calculus for Loyola University Chicago with WebAssign Custom (packaged with WebAssign). 4th ed. ISBN-13: 9781118762202. Hoboken, NJ: Wiley, 2009. Print.

Textbook notes:  Students are required to have access to WebAssign for this course. Students buying used textbooks should arrange to purchase WebAssign separately. SPECIAL NOTE: this is a change from previous semesters, which required WileyPLUS.

Prerequisites:  MATH 118 or Math Diagnostic Test

Course description:  An introduction to differential and integral calculus, with an emphasis on applications. This course is intended for students in the life and social sciences, computer science, and business. Topics include: modeling change using functions including exponential and trigonometric functions, the concept of the derivative, computing the derivative, applications of the derivative to business and life, social, and computer sciences, and an introduction to integration. This course is not a substitute for MATH 161.

Syllabus:  Common

Instructor(s):  Staff

Required text(s):  Hughes-Hallett, Deborah, et al. Applied Calculus (packaged with WileyPLUS). 4th ed. ISBN-13: 9780470578773. Hoboken, NJ: Wiley, 2009. Print.

Prerequisites:  MATH 131 or MATH 161

Course description:  A continuation of MATH 131. Topics include: properties of the integral, techniques of integration, numerical methods, improper integrals, applications to geometry, physics, economics, and probability theory, introduction to differential equations and mathematical modeling, systems of differential equations, power series. This course is not a substitute for MATH 162.

Syllabus:  Common

Instructor(s):  Staff

Required text(s):  Thomas, George B., Maurice D. Weir, and Joel R. Hass. Thomas' Calculus: Early Transcendentals (Single Variable) (packaged with MyMathLab). 12th ed. ISBN-13: 9780321705402. Boston: Addison-Wesley, 2009. Print.

Textbook notes:  Students are required to have access to MyMathLab for this course. Students buying used textbooks should arrange to purchase MyMathLab separately.

Prerequisites:  MATH 118 or Math Diagnostic Test

Course description:  A traditional introduction to differential and integral calculus. Functions, limits, continuity, differentiation, intermediate and mean-value theorems, curve sketching, optimization problems, related rates, definite and indefinite integrals, fundamental theorem of calculus, logarithmic and exponential functions. Applications to physics and other disciplines.

Syllabus:  Common

Instructor(s):  Staff

Required text(s):  Thomas, George B., Maurice D. Weir, and Joel R. Hass. Thomas' Calculus: Early Transcendentals (Single Variable) (packaged with MyMathLab). 12th ed. ISBN-13: 9780321705402. Boston: Addison-Wesley, 2009. Print.

Textbook notes:  Students are required to have access to MyMathLab for this course. Students buying used textbooks should arrange to purchase MyMathLab separately.

Prerequisites:  MATH 161

Course description:  A continuation of MATH 161. Calculus of logarithmic, exponential, inverse trigonometric, and hyperbolic functions. Techniques of integration. Applications of integration to volume, surface area, arc length, center of mass, and work. Numerical sequences and series. Study of power series and the theory of convergence. Taylor's theorem with remainder.

Syllabus:  Common

Instructor(s):  Dr. Anthony Giaquinto (Section 001) and Dr. Anne Hupert (Section 002)

Required text(s):  Burton, David. Elementary Number Theory, 7th ed. ISBN-13: 978-0073383149. New York: McGraw-Hill, 2011. Print.

Prerequisites:  MATH 161

Course description:  This bridge course to higher level mathematics serves as an introduction both to number theory in particular, and to the art of mathematical argument in general. In exploring fundamental properties of integers and rational numbers, students will learn how to understand and write mathematical proofs. A central role in number theory is played by the prime numbers, whose infinitude was known already to Euclid circa 300 B.C., but whose exact distribution among integers is still so deeply mysterious now in the 21st century as to serve as the basis for secure data transmission.

Topics include: representation of numbers, divisibility, prime numbers, Diophantine equations, congruence of numbers, methods of solving congruences, public-key cryptography, Fermat's Last Theorem.

Instructor(s):  Dr. Joseph Mayne

Required text(s):  Strang, Gilbert. Linear Algebra and its Applications. 4th ed. ISBN-13: 978-0980232714. Belmont, CA: Thomson Brooks/Cole, 2006. Print. .

Prerequisites:  MATH 162 or MATH 132

Course description:  Linear algebra is widely used in mathematics, science, engineering, and the social sciences. For example, statisticians and economists often employ linear models when trying to analyze problems with many variables. And linear algebra is an important tool in many areas of mathematics itself. Much of functional analysis is devoted to the study of functions preserving linearity and field theory uses linear algebra in the proofs of many results.

The course starts with the problem of solving simultaneous linear equations using the Gaussian elimination algorithm. The solution of this important practical problem motivates the definition of many linear algebra concepts: matrices, vectors and vector spaces, linear independence, dimension, and vector subspaces. The emphasis then shifts to general vector spaces and proofs using an axiom system. Most of the results will be for finite dimensional spaces and we will always attempt to visualize theorems in 2 or 3 dimensional Euclidean space.

Topics to be covered include: linear transformations, change of basis, determinants, eigenvalues and eigenvectors, and diagonalization. Students will learn much linear algebra and will be encouraged to improve their skills at constructing mathematical proofs.

Instructor(s):  Dr. Christine Haught

Required text(s):  Miller, Bradley N. and David L. Ranum. Python Programming in Context. 2nd ed. ISBN-13: 978-1449699390. Burlington, MA: Jones and Bartlett Learning, 2014. Print.

Prerequisites:  MATH 162

Course description:  Math 215 is an introductory programming course for students interested in mathematics and scientific applications. No previous programming experience is required. This course can be used to satisfy the Comp 170 requirement in the math major. Students will learn object-oriented programming using the programming language Python. Python is easy to learn and we will quickly be able to solve interesting problems with it. Programming examples will come from mathematics, bioinformatics and other scientific computing applications. In particular we will work with examples from calculus, number theory, statistics, geometry, fractals and linear algebra.

The course is programming intensive. There will be weekly programming assignments as well as frequent in-class exercises. There will be approximately 10 quizzes during the term, a final project and a final exam.

Instructor(s):  Dr. Alan Saleski (Section 001 - MoWeFr 9:20AM - 11:15AM)
Dr. Loretta Bartolini (Section 002 - MoWeFr 12:35PM - 2:30PM)
Dr. Adam Spiegler (Section 003 - MoWeFr 1:40PM - 3:35PM)

Required text(s):  Thomas, George B., Maurice D. Weir, and Joel R. Hass. Thomas' Calculus, Multivariable (packaged with MyMathLab), 12th ed. ISBN-13: 9780321651952. New York: Pearson, 2009. Print.

Textbook notes:  Students are required to have access to MyMathLab for this course. Students buying used textbooks should arrange to purchase MyMathLab separately.

Prerequisites:  MATH 162

Course description:  Vectors and vector algebra, curves and surfaces in space, functions of several variables, partial derivatives, the chain rule, the gradient vector, LaGrange multipliers, multiple integrals, volume, surface area, the Change of Variables theorem, line integrals, surface integrals, Green's theorem, the Divergence Theorem, and Stokes' Theorem.

Instructor(s):  Dr. Steven L. Jordan

Required text(s):  Katz, Victor J. A History of Mathematics, An Introduction. 3rd ed. ISBN-13: 978-0321387004. New York: Pearson, 2009. Print.

Textbook notes:  I will provide a library of materials to supplement the text. We will compile an annotated bibliography of web sites

Prerequisites:  MATH 132 or MATH 162. MATH 201 is recommended

Course description: 

In this course students will study some of the most influential and insightful mathematics from the time of Babylonian cuneiform tablets, through the invention of calculus and beyond.

This course is designed to give prospective math teachers, math majors, philosophy majors and others an appreciation of the universal appeal and the triumphs of mathematics in all cultures and times.

The approach will emphasize historical scholarship and mathematical problem-solving. We will study in depth representative documents. We will use original source materials – which are surprisingly accessible. These “documents” demonstrate the thinking behind great mathematics through the centuries, in diverse cultures, and in different subjects: geometry, analysis, number theory, etc.

Main topics: Plimpton 322, Rhind Papyrus, Euclid’s Elements, Archimedes’ The Sand Reckoner, Ptolemy’s Table of Chords, Diophantus, Sun-Tsu, al-Khowarizmi, Brahmagupta and Indian mathematics, Mayan mathematics, Robert Recorde, Isaac Newton and Leibnitz, Fermat and Descartes, solution to cubics, Gauss’ contributions, species of numbers, mathematical tables and machines, unsolved problems and contests. Additional or alternate topics may be included depending on the interest of students.

Teachers in this course will prepare lessons and materials appropriate for classroom use. We will prepare a collection of biographies of women and other mathematicians who serve as models for students.

Syllabus:  Grading System: Two presentations to the class a) Biography (25%). b) Additional topic (e.g., medieval Islamic astronomy) (25%). Several short presentations and homework (25%). Test emphasizing doing mathematics with historical methods (25%).

Instructor(s):  Dr. John G. Del Greco

Required text(s):  Larson, Richard J., and Morris L. Marx. An Introduction to Mathematical Statistics and Its Applications. 5th ed. ISBN-13: 978-0321693945. Boston: Prentice Hall, 2012. Print.

Prerequisites:  Statistics majors: MATH 263, STAT 203
Mathematics majors: MATH 263

Course description:  This course will be a rigorous treatment of mathematical probability with an eye toward statistics which will be the subject of the follow-up course, STAT 305.

In STAT 304 we will cover axiomatic probability, combinatorial probability, conditional probability and Bayes Theorem, and independence. We will then turn to a study of random variables, both discrete and continuous, and their various distributions. Joint distributions, marginal distributions, and conditional distributions of two or more random variables will also be discussed.

Advanced topics will include order statistics, moment-generating functions, and the Central Limit Theorem. Time permitting, a discussion of the Bayesian approach to probability and statistics will be included as well.

There will be two midterm exams, a final exam, and multiple written homework assignments during the semester which may include computer exercises using R or Minitab.

Instructor(s):  Dr. Peter Tingley

Required text(s):  Pinter, Charles C. A Book of Abstract Algebra. Dover ed. ISBN-13: 978-0486474175. New York: McGraw-Hill, 1990. Print.

Prerequisites:  MATH 201 and MATH 212

Course description:  This course provides a rigorous introduction to abstract algebra. We will consider various algebraic structures including groups, rings, and fields, but will mainly focus on groups. We will cover the basic structure theory: homomorphisms, subgroups, cosets, factor groups, and isomorphism theorems. Various examples and special types of groups (Abelian groups, permutation groups, symmetry groups...) will be discussed in detail. We will also consider some applications of abstract algebra, but for the most part this class will be concerned with "pure" mathematics questions about the algebraic structures themselves.

Instructor(s):  Dr. W. Cary Huffman

Required text(s):  Friedbreg, Stephen H., Arnold J. Insel, and Lawrence E. Spence. Linear Algebra. 4th ed. ISBN-13: 978-0130084514. Upper Saddle River, NJ: Pearson Education, 2003. Print.

Prerequisites:  MATH 313, or the equivalent, or permission of the instructor.

Course description:  Many problems in applied mathematics, physics, and engineering involve systems of equations that may be very difficult to solve. Sometimes the first approximation to solving such systems is to linearize them and solve these linearized systems using various theoretical and applied techniques. This class will be a second course in linear algebra, where advanced topics will be considered. These topics will be chosen from inner product spaces, Gram-Schmidt orthogonalization, normal and self-adjoint operators, unitary and orthogonal operators, bilinear and quadratic forms, and Jordan and rational canonical forms. There will be applications of these ideas to least squares problems and regression, orthogonal polynomials, exponential functions with matrix exponents, time contraction in Einstein's Theory of relativity, and others. The course will begin with a review of some necessary material from MATH 212 and MATH 313.

This course is a combined undergraduate/graduate course. The requirements of the course for the graduate students will be different from the requirements for the undergraduates.

Instructor(s):  Dr. Stephen Doty

Required text(s):  Paar, Christof and Jan Pelzl. Understanding Cryptography: A Textbook for Students and Practitioners. ISBN-13: 978-3642041006 (Print). ASIN: B00475ARKM (Kindle). Heidelberg: Springer, 2010. Print and Kindle.

Prerequisites:  Mathematics (one of COMP 163, MATH 313 or MATH 201) and Programming (COMP 125, COMP 170, COMP 215, or equivalent).

Course description:  This interdisciplinary course applies number theory from mathematics in order to construct modern "asymmetric" cryptosystems for use in public-key cryptography. Some mathematical maturity along with a prior exposure to computer programming is required (see specific prerequisites above). The course will look at both the underlying mathematical concepts as well as issues of implementation of specific algorithms.

Homework will involve some computer programming as well as solving mathematical problems. Applications to problems such as hashing and digital signing will be considered as time permits.

Instructor(s):  Dr. Emily Peters

Required text(s):  (1) Stillwell, John. Euclid's Elements. ISBN 1-888009-19-5. Santa Fe, NM: Green Lion Press, 2002. Print.

(2) Stillwell, John. The Four Pillars of Geometry. ISBN-13: 978-1441920638. New York: Springer, 2005. Print.

Prerequisites:  Familiarity with Euclidean (high-school) geometry.

Course description:  Geometry in two and three dimensions is both the classical foundation of all of mathematics, and an exciting topic of current research. This course is intended for prospective teachers of mathematics in high school, for math majors, and for graduate students interested in a topics course.

We begin by reviewing classical geometry straight from the source (a translation of Euclid's elements), and go into some depth with straightedge-and-compass constructions. Next we visit the Renaissance topics of perspective and projective geometry. We conclude with the modern study of symmetry, which allows us to discuss non-Euclidean geometries, in which lines parallel to a given line through a point either do not exist (spherical) or are not unique (hyperbolic).

Student grades will be based on homework, quizzes, and a final exam. Graduate students in Math 488 will be asked to do a more in-depth project and give a class presentation, on a topic such as: the impossibility of trisecting an angle with a ruler and compass; Origami constructions and how to trisect angles; classification of polyhedra; Finite geometries; Hilbert's axioms; and further topics in hyperbolic geometry.

Instructor(s):  Dr. Rafal Goebel

Required text(s):  Mattuck, Arthur. Introduction to Analysis. ISBN-13: 978-0130811325. New York: Pearson, 1998. Print.

Recommended text(s):  Thomas, Jr., George B., Maurice D. Weir, and Joel Hass. Thomas' Calculus. 12th ed. ISBN-13: 978-0321587992. New York: Pearson, 2009. Print.

Textbook notes:  Introduction to Analysis is required, and it will be the source of most homework problems. Your old calculus textbook may a good place to read proofs of some of the more fundamental results.

Prerequisites:  MATH 201 and MATH 212

Course description:  A rough and not complete description of Real Analysis would say that it is calculus with proofs. A better description would say that Real Analysis is interested not only in answers to calculus problems but also in if and why the answers exist in the first place. A more formal description would say that Real Analysis begins with the theory behind real numbers and the Euclidean space, studies sequences and their convergence, and applies these concepts to the analysis of functions, of continuity and differentiability of functions, and to integration of functions.

Real Analysis, especially the theory behind convergence, continuity, and approximation forms a foundation upon which many branches of mathematics are built, for example numerical analysis, optimization, and dynamical systems and control. It is also essential in rigorous approaches to economics, finance, theoretical physics, etc.

This course will be an introduction to Real Analysis focusing on real numbers, sequences and series of real numbers, their convergence, and on functions of one variable, especially their continuity and differentiability. Students will be expected to solve problems and, even more importantly, to read, understand, and formulate mathematical arguments and proofs.

Instructor(s):  Dr. Marian Bocea

Required text(s):  Saff, E.B. and A. D. Snider. Fundamentals of Complex Analysis with Applications to Engineering and Science. 3rd ed. ISBN-13: 978-0139078743. Upper Saddle River, NJ: Prentice Hall/Pearson. Print.

Prerequisites:  MATH 264 and MATH 351

Course description:  An introduction to the theory of functions of a complex variable. Topics include analytic functions, contour integrals, Cauchy's integral formula, harmonic functions, Liouville's theorem, Laurent series, residues and poles, and conformal mappings.

Outcomes: Students will gain an understanding of the fundamentals of Complex Analysis that will prepare them for advanced work in Mathematics.

Syllabus:  Syllabus available at: http://www.math.luc.edu/~mbocea/Fall2013MATH353.html

Instructor(s):  Dr. Emmanuel Barron

Required text(s):  Barron, E. N. Game Theory: An Introduction. 2nd ed. ISBN-13: 978-1118216934. New York: John Wiley Interscience, 2013. Print.

Prerequisites:  MATH 162 and STAT 203 or MATH 304. MATH 212 would be helpful but not required.

Course description:  Game theory arises in almost every fact of human and inhuman interaction since oftentimes during these communications objectives are opposed or cooperation is viewed as an option. From economics and finance to biology and computer science, researchers and practitioners are often put in complex decision-making scenarios, whether they are interacting with each other or working with evolving technology and artificial intelligence. Acknowledging the role of mathematics in making logical and advantageous decisions, the course uses modern software applications to create, analyze, and implement effective decision-making models.

Game Theory introduces students to the basic theories behind games and presents real-world examples from various fields of study such as economics, political science, military science, finance, biological science as well as general game playing.

Important game theory topics are presented within the following five main areas of coverage:

Two-person zero sum matrix games

Nonzero sum games and the reduction to nonlinear programming

Cooperative games, including discussion of both the Nucleolus concept and the Shapley value

Bargaining, including threat strategies

Evolutionary stable strategies and population games

Mathematica and Gambit Software will be used to assist in the solution of games. No knowledge of programming is required.

We will have at least a midterm and a final and homework will be regularly assigned and graded.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Fallat, M., and Johnson, C.R.. Totally Nonnegative Matrices. ISBN-13: 9780691121574. Princeton: Princeton University Press, 2011. Print.

Additional notes:  Canceled

Prerequisites:  MATH 201 and MATH 212

Course description:  The notion of totally positive matrices stands at the crossroads of many mathematical disciplines, including statistics, mathematical biology, combinatorics, dynamical systems, approximation theory, operator theory, geometry, and representation theory. In this course, we explore the theory of totally positive matrices and their appearances within—and applications to—these many disciplines.

Syllabus:  To keep prerequisites to a minimum, this course will run in a modular fashion. We will spend several weeks at a time on background material in a given discipline before rediscovering totally positive matrices within it. Then we move on to the next application. Aspects of the theory of totally positive matrices (e.g., recognition, factorization, spectra) will be introduced throughout.

Assessments: Short quizzes and homework assignments will accompany each module. A cumulative final exam will revisit the key concepts covered on the quizzes and homework.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  None.

Additional notes:  One Credit.

Prerequisites:  Junior standing or permission from (Assistant) Chair.

Course description:  The undergraduate seminar will cultivate students' presentation skills through: participation in and critical discussion of brief lectures by others on familiar(*) and unfamiliar(**) topics; preparation and presentation of two brief lectures by the student (one on a familiar topic and one on an unfamiliar one); and preparation of a short manuscript, or "extended abstract," summarizing the second presentation.

Outcome: Students will gain the ability to present material in mathematics & statistics and their applications to a general audience.

Notes: (*) by "familiar" is meant "part of the major curriculum," e.g., standard exercises or theorems from calculus, analysis, algebra, and statistics.
(**) by "unfamiliar" is meant "everything else." The instructor will assist students in choosing topics according to their interests and suitable for presentation.

Instructor(s):  Dr. Martin Buntinas

Required text(s):  Wackerly, Dennis, William Mendenhall, and Richard L. Scheaffer. Mathematical Statistics with Applications. 7th ed. ISBN-13:978-0-49-511081-1. Belmont, CA: Duxbury/Brooks/Cole/Thomson, 2008. Print.

Prerequisites:  Some background in statistics (such as STAT 203 or STAT335) or admission into one of our Mathematics Department's MS programs.

Course description:  This is the first semester of a two-semester sequence. The first semester is essentially an exploration of probability as a mathematical model of chance phenomena; the second semester explores the statistical analyses based on these models. In the first semester class, topics to be covered include discrete and continuous random variables, transformations, multivariate distributions, correlation, independence, variance-covariance, special distributions (binomial, Poisson, gamma, chi-square, beta, normal, multivariable normal, t and F), expectations of functions, convergence in probability, convergence in distribution, moment generating functions, and the Central Limit Theorem.

This course requires a good knowledge of calculus, including sums of infinite series, differentiation, and single and double integration. Students needing a review of these concepts should co-enroll in a one-credit review class STAT 396 (Actuarial Seminar)

There will be two quizzes, a midterm exam and a final exam. Homework will be assigned every class, collected, and graded.

Instructor(s):  Dr. W. Cary Huffman

Required text(s):  Friedbreg, Stephen H., Arnold J. Insel, and Lawrence E. Spence. Linear Algebra. 4th ed. ISBN-13: 978-0130084514. Upper Saddle River, NJ: Pearson Education, 2003. Print.

Prerequisites:  MATH 313, or the equivalent, or permission of the instructor.

Course description:  Many problems in applied mathematics, physics, and engineering involve systems of equations that may be very difficult to solve. Sometimes the first approximation to solving such systems is to linearize them and solve these linearized systems using various theoretical and applied techniques. This class will be a second course in linear algebra, where advanced topics will be considered. These topics will be chosen from inner product spaces, Gram-Schmidt orthogonalization, normal and self-adjoint operators, unitary and orthogonal operators, bilinear and quadratic forms, and Jordan and rational canonical forms. There will be applications of these ideas to least squares problems and regression, orthogonal polynomials, exponential functions with matrix exponents, time contraction in Einstein's Theory of relativity, and others. The course will begin with a review of some necessary material from MATH 212 and MATH 313.

This course is a combined undergraduate/graduate course. The requirements of the course for the graduate students will be different from the requirements for the undergraduates.

Instructor(s):  Dr. Stephen Doty

Required text(s):  Paar, Christof and Jan Pelzl. Understanding Cryptography: A Textbook for Students and Practitioners. ISBN-13: 978-3642041006 (Print). ASIN: B00475ARKM (Kindle). Heidelberg: Springer, 2010. Print and Kindle.

Prerequisites:  Mathematics (one of COMP 163, MATH 313 or MATH 201) and Programming (COMP 125, COMP 170, COMP 215, or equivalent).

Course description:  This interdisciplinary course applies number theory from mathematics in order to construct modern "asymmetric" cryptosystems for use in public-key cryptography. Some mathematical maturity along with a prior exposure to computer programming is required (see specific prerequisites above). The course will look at both the underlying mathematical concepts as well as issues of implementation of specific algorithms.

Homework will involve some computer programming as well as solving mathematical problems. Applications to problems such as hashing and digital signing will be considered as time permits.

Instructor(s):  Dr. Emmanuel Barron

Required text(s):  Barron, E. N. Game Theory: An Introduction. 2nd ed. ISBN-13: 978-1118216934. New York: John Wiley Interscience, 2013. Print.

Prerequisites:  MATH 162 and STAT 203 or MATH 304. MATH 212 would be helpful but not required.

Course description:  Game theory arises in almost every fact of human and inhuman interaction since oftentimes during these communications objectives are opposed or cooperation is viewed as an option. From economics and finance to biology and computer science, researchers and practitioners are often put in complex decision-making scenarios, whether they are interacting with each other or working with evolving technology and artificial intelligence. Acknowledging the role of mathematics in making logical and advantageous decisions, the course uses modern software applications to create, analyze, and implement effective decision-making models.

Game Theory introduces students to the basic theories behind games and presents real-world examples from various fields of study such as economics, political science, military science, finance, biological science as well as general game playing.

Important game theory topics are presented within the following five main areas of coverage:

Two-person zero sum matrix games

Nonzero sum games and the reduction to nonlinear programming

Cooperative games, including discussion of both the Nucleolus concept and the Shapley value

Bargaining, including threat strategies

Evolutionary stable strategies and population games

Mathematica and Gambit Software will be used to assist in the solution of games. No knowledge of programming is required.

We will have at least a midterm and a final and homework will be regularly assigned and graded.

Instructor(s):  Dr. Emily Peters

Required text(s):  (1) Stillwell, John. Euclid's Elements. ISBN 1-888009-19-5. Santa Fe, NM: Green Lion Press, 2002. Print.

(2) Stillwell, John. The Four Pillars of Geometry. ISBN-13: 978-1441920638. New York: Springer, 2005. Print.

Prerequisites:  Familiarity with Euclidean (high-school) geometry.

Course description:  Geometry in two and three dimensions is both the classical foundation of all of mathematics, and an exciting topic of current research. This course is intended for prospective teachers of mathematics in high school, for math majors, and for graduate students interested in a topics course.

We begin by reviewing classical geometry straight from the source (a translation of Euclid's elements), and go into some depth with straightedge-and-compass constructions. Next we visit the Renaissance topics of perspective and projective geometry. We conclude with the modern study of symmetry, which allows us to discuss non-Euclidean geometries, in which lines parallel to a given line through a point either do not exist (spherical) or are not unique (hyperbolic).

Student grades will be based on homework, quizzes, and a final exam. Graduate students in Math 488 will be asked to do a more in-depth project and give a class presentation, on a topic such as: the impossibility of trisecting an angle with a ruler and compass; Origami constructions and how to trisect angles; classification of polyhedra; Finite geometries; Hilbert's axioms; and further topics in hyperbolic geometry.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Fallat, M., and Johnson, C.R.. Totally Nonnegative Matrices. ISBN-13: 9780691121574. Princeton: Princeton University Press, 2011. Print.

Additional notes:  Canceled

Prerequisites:  MATH 201 and MATH 212

Course description:  The notion of totally positive matrices stands at the crossroads of many mathematical disciplines, including statistics, mathematical biology, combinatorics, dynamical systems, approximation theory, operator theory, geometry, and representation theory. In this course, we explore the theory of totally positive matrices and their appearances within—and applications to—these many disciplines.

Syllabus:  To keep prerequisites to a minimum, this course will run in a modular fashion. We will spend several weeks at a time on background material in a given discipline before rediscovering totally positive matrices within it. Then we move on to the next application. Aspects of the theory of totally positive matrices (e.g., recognition, factorization, spectra) will be introduced throughout.

Assessments: Short quizzes and homework assignments will accompany each module. A cumulative final exam will revisit the key concepts covered on the quizzes and homework.

Instructor(s):  Dr. Changwon Lim

Required text(s):  Buntinas, Martin and Gerald Funk. Statistics for the Sciences. ISBN-13: 978-0534387747. Belmont, CA: Duxbury/Thomson/Brooks/Cole, 2005. Print.

Prerequisites:  MATH 132 or 162.

Course description:  Our society is increasingly dependent upon statistics. For example, decisions about the safety and effectiveness of drugs, changes in tax laws that affect the economy, and environmental regulations that strive to improve our lives all involve the use of statistics. In spite of this importance, there is widespread ignorance about the proper application of statistics. In this course we will look at examples of the use and misuse of statistics using methods of differential and integral calculus to justify results. We will study some standard statistical methods and learn how to determine when they should be used and how they should be applied. The goal is to understand how these methods work and how they can be applied correctly.

Instructor(s):  Dr. John G. Del Greco

Required text(s):  Larson, Richard J., and Morris L. Marx. An Introduction to Mathematical Statistics and Its Applications. 5th ed. ISBN-13: 978-0321693945. Boston: Prentice Hall, 2012. Print.

Prerequisites:  Statistics majors: MATH 263, STAT 203
Mathematics majors: MATH 263

Course description:  This course will be a rigorous treatment of mathematical probability with an eye toward statistics which will be the subject of the follow-up course, STAT 305.

In STAT 304 we will cover axiomatic probability, combinatorial probability, conditional probability and Bayes Theorem, and independence. We will then turn to a study of random variables, both discrete and continuous, and their various distributions. Joint distributions, marginal distributions, and conditional distributions of two or more random variables will also be discussed.

Advanced topics will include order statistics, moment-generating functions, and the Central Limit Theorem. Time permitting, a discussion of the Bayesian approach to probability and statistics will be included as well.

There will be two midterm exams, a final exam, and multiple written homework assignments during the semester which may include computer exercises using R or Minitab.

Instructor(s):  Dr. Changwon Lim

Required text(s):  Abraham, Bovas and Johannes Ledolter. Introduction to Regression Modeling (with CD-ROM). ISBN-13: 978-0534420758. Belmont, CA: Duxbury/Thomson/Brooks/Cole, 2006. Print.

Prerequisites:  STAT 203 or STAT 335.

Course description:  This course provides students with a thorough introduction to applied regression methodology. The concept of simple linear regression will be reviewed and discussed using matrices, and multiple linear regression, transformations, diagnostics, polynomial regression, indicator variables, model building and multicollinearity will be discussed, as will be nonlinear and generalized linear regression. The course will focus on applications such as those from biometry and biostatistics (clinical trials, HIV studies, etc.), sports, engineering, agriculture and environmental science.

Instructor(s):  Dr. Gerald Funk

Required text(s):  Morgan, Byron J. T. Applied Stochastic Modelling. 2nd ed. ISBN-13: 978-1584886662. Boca Raton, FL: Chapman and Hall/CRC Press, 2008. Print.

Prerequisites:  STAT 203 or STAT 335

Course description:  This course uses SAS and R languages to address statistical modelling and to conduct statistical simulations to assess linear, generalized linear, nonlinear and complex models and experimental designs. Outcome: Students will gain practical experience and knowledge in real-world statistical situations for which underlying theory is cumbersome or intractable.

Instructor(s):  Mr. Bret Longman

Required text(s):  D’Agostino, Ralph, Lisa Sullivan, and Alexa Beiser. Introductory Applied Biostatistics. 1st ed. ISBN-13: 978-0534423995. New York: Brooks/Cole, 2006. Print.

Prerequisites:  STAT 335 or permission of instructor

Course description:  This course covers the basics of hypothesis testing, sample size and power calculations, categorical data techniques, experimental design and ANOVA, repeated measures ANOVA, simple and multiple linear regression, analysis of covariance (ANCOVA), generalized linear models, maximum likelihood estimation, logistic regression, survival analysis, and if time allows, relative potency and drug synergy. The emphasis is on applications instead of statistical theory, and students are required to analyze real-life datasets using output from statistical packages such as Minitab and SAS, although no previous programming experience is assumed.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  None.

Additional notes:  One Credit.

Prerequisites:  Junior standing or permission from (Assistant) Chair.

Course description:  The undergraduate seminar will cultivate students' presentation skills through: participation in and critical discussion of brief lectures by others on familiar(*) and unfamiliar(**) topics; preparation and presentation of two brief lectures by the student (one on a familiar topic and one on an unfamiliar one); and preparation of a short manuscript, or "extended abstract," summarizing the second presentation.

Outcome: Students will gain the ability to present material in mathematics & statistics and their applications to a general audience.

Notes: (*) by "familiar" is meant "part of the major curriculum," e.g., standard exercises or theorems from calculus, analysis, algebra, and statistics.
(**) by "unfamiliar" is meant "everything else." The instructor will assist students in choosing topics according to their interests and suitable for presentation.

Instructor(s):  Dr. Timothy O'Brien

Required text(s):  Broverman, Samuel A. ACTEX Calculus Review Study Manual. 2005 ed. ISBN-13: 978-1566985116. Winsted, CT: ACTEX Publications, 2005. Print.

Prerequisites:  One year of calculus including differential and integral calculus.

Course description:  This course reviews basic differential and integral calculus methods and covers multivariable calculus techniques needed for further study in statistics and/or to pass the first actuarial exam (Exam P). Grading is based on in-class presentations and quizzes.

Instructor(s):  Dr. Timothy E. O’Brien

Required text(s):  Kleinman, Ken, and Nicholas J. Horton. SAS and R: Data Management, Statistical Analysis, and Graphics. ISBN-13: 978-1420070576. Boca Raton, FL: CRC Press, 2010. Print.

Recommended text(s):  Der, Geoff, and Brian S. Everitt. Statistical Analysis of Medical Data Using SAS. ISBN: 1-58488-469-X. Boca Raton, FL: Chapman & Hall/CRC, 2006. Print.

Textbook notes:  Programs from Cody and Smith's SAS book (not required) as well as solutions to odd numbered problems are available at www.prenhall.com/cody. Examples and data sets for Der and Everitt's book (recommended) are available at support.sas.com/documentation/onlinedoc/code.samples.html

Prerequisites:  Some exposure to sampling distributions, confidence intervals, hypothesis tests (z- and t-tests, chi-square tests, etc.), linear regression and ANOVA (including interaction)

Course description:  This course is an introduction to the use of the statistical software packages SAS and R, two of the most popular statistical packages available on the market. In many industries, SAS is considered the “gold standard”, perhaps due to its outstanding database management capabilities. Additionally, since it is open-source freeware, R is the lingua franca of statistics.

In addition to data management and programming, this course will also focus on applications and explanations of SAS and R output. For more information, visit www.sas.com and http://www.r-project.org/

Students will develop expertise using the SAS computer package, although no previous programming experience will be assumed. Grading is based on weekly homework assignments, a project/paper, and exams.

Instructor(s):  Dr. Martin Buntinas

Required text(s):  Wackerly, Dennis, William Mendenhall, and Richard L. Scheaffer. Mathematical Statistics with Applications. 7th ed. ISBN-13:978-0-49-511081-1. Belmont, CA: Duxbury/Brooks/Cole/Thomson, 2008. Print.

Prerequisites:  Some background in statistics (such as STAT 203 or STAT335) or admission into one of our Mathematics Department's MS programs.

Course description:  This is the first semester of a two-semester sequence. The first semester is essentially an exploration of probability as a mathematical model of chance phenomena; the second semester explores the statistical analyses based on these models. In the first semester class, topics to be covered include discrete and continuous random variables, transformations, multivariate distributions, correlation, independence, variance-covariance, special distributions (binomial, Poisson, gamma, chi-square, beta, normal, multivariable normal, t and F), expectations of functions, convergence in probability, convergence in distribution, moment generating functions, and the Central Limit Theorem.

This course requires a good knowledge of calculus, including sums of infinite series, differentiation, and single and double integration. Students needing a review of these concepts should co-enroll in a one-credit review class STAT 396 (Actuarial Seminar)

There will be two quizzes, a midterm exam and a final exam. Homework will be assigned every class, collected, and graded.

Instructor(s):  Dr. Changwon Lim

Required text(s):  Abraham, Bovas and Johannes Ledolter. Introduction to Regression Modeling (with CD-ROM). ISBN-13: 978-0534420758. Belmont, CA: Duxbury/Thomson/Brooks/Cole, 2006. Print.

Prerequisites:  STAT 203 or STAT 335.

Course description:  This course provides students with a thorough introduction to applied regression methodology. The concept of simple linear regression will be reviewed and discussed using matrices, and multiple linear regression, transformations, diagnostics, polynomial regression, indicator variables, model building and multicollinearity will be discussed, as will be nonlinear and generalized linear regression. The course will focus on applications such as those from biometry and biostatistics (clinical trials, HIV studies, etc.), sports, engineering, agriculture and environmental science.

Instructor(s):  Dr. Liping Tong

Required text(s):  Collett, David. Modelling Survival Data in Medical Research. 2nd ed. ISBN-13: 978-1584883258. Boca Raton, FL: Chapman & Hall / CRC Prss, 2003. Print.

Recommended text(s):  Kleinbaum, David G. and Mitchel Klein. Survival Analysis: A Self-Learning Text. 3rd ed. ISBN-13: 978-1441966452. New York: Springer, 2011. Print.

Prerequisites:  This course require students to have background on linear algebra, statistical inferences such as hypothesis testing, maximum likelihood parameter estimations, linear regressions, etc. We are going to use the software R and SAS for all the programming and calculation. Familarity in R and SAS is not required, but is a big plus for this course.

Course description:  Modern statistical methods are covered to analyze data that is right-, left- and/or interval-censored. Both parametric methods (such as those based on the Exponential and Weibull distribution) and non-parametric approaches (such as the Kaplan-Meier estimation technique, log-rank test and proportional-hazards model) are considered. Accelerated failure time models and nonlinear models are also discussed. Students will develop expertise using the statistical software (such as R or SAS).

Instructor(s):  Dr. Gerald Funk

Required text(s):  Morgan, Byron J. T. Applied Stochastic Modelling. 2nd ed. ISBN-13: 978-1584886662. Boca Raton, FL: Chapman and Hall/CRC Press, 2008. Print.

Prerequisites:  STAT 203 or STAT 335

Course description:  This course uses SAS and R languages to address statistical modelling and to conduct statistical simulations to assess linear, generalized linear, nonlinear and complex models and experimental designs. Outcome: Students will gain practical experience and knowledge in real-world statistical situations for which underlying theory is cumbersome or intractable.

Instructor(s):  Dr. Timothy O'Brien

Required text(s):  Cabrera, Javier, and Andrew McDougall. Statistical Consulting. ISBN-13: 978-0387988634. New York: Springer-Verlag, 2002. Print.

Prerequisites:  One year of MS full-time study in the Applied Statistics program (previous coursework in regression, SAS/programming and experimental design; categorical data analysis and survival analysis also recommended), or obtain the permission of the instructor.

Course description:  (Section 001) This course serves as a program capstone course for the MS program in Applied Statistics; as such it synthesizing the course material in the context of actual statistical consulting sessions. Students are required to assist in analyzing real-life data sets using the Minitab, SAS and R statistical packages. Students also learn to sharpen their verbal, written and non-verbal communication skills.

Grading is based on in-class presentations and consulting sessions and practicum, quizzes and a course project.