Instructor(s):  Staff

Required text(s):  Angel, Allen and Dennis Runde. Intermediate Algebra for College Students (packaged with MyMathLab). 9th ed. ISBN-10: 0321927370. ISBN-13: 9780321927378. 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. Precalculus: A Prelude to Calculus, 2nd Edition Paperback w/ Wileyplus ISBN: 978-1-118-55625-2. 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. Precalculus: A Prelude to Calculus, 2nd Edition Paperback w/ Wileyplus ISBN: 978-1-118-55625-2. Hoboken, NJ: Wiley, 2012. Print.

Textbook notes:  Students who were enrolled in MATH 117 in Spring 2014 will not need to purchase this new edition of the textbook. (See course instructor for more details.)

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.

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 & 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 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). 13th edition, ISBN-10: 0321952871. ISBN-13: 9780321952875

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). 13th ed. ISBN-10: 0321952871. ISBN-13: 9780321952875. 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. Marian Bocea

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 course is an introduction to abstract mathematics, with a focus on elementary number theory. It aims to develop the students' ability to understand and construct mathematical proofs, which plays an essential role in advanced 300-level Mathematics courses. Topics include: mathematical induction, the binomial theorem, divisibility, the Euclidean algorithm, prime numbers, congruences, Fermat's little theorem, Wilson's theorem, Euler's phi function, perfect numbers, and Mersenne primes. Homework will be assigned and graded regularly throughout the semester. There will be at least two midterms and a comprehensive final exam.

Instructor(s):  Dr. Emily Peters

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. Aaron Lauve

Required text(s):  Hefferon, Jim. Linear Algebra. Available at joshua.smcvt.edu/linearalgebra/, under Creative Commons license BY-SA 2.5. December, 2013. Web.

Recommended text(s):  Lipschutz, Seymour, and Lipson, Marc. Schaum's Outline of Linear Algebra. 5th ed. ISBN-13: 9780071794565. McGraw-Hill, 2012. Print.

Prerequisites:  MATH 162 or MATH 132

Course description:  Linear systems are ubiquitous in mathematics, science, engineering, and the social sciences. (For example, statisticians and economists often employ linear models to analyze otherwise intractable problems with many variables.) Evidently, a systematic approach for solving linear systems would be immensely valuable. The course begins by giving one approach, the algorithm of Gaussian Elimination, then continues by developing the axioms and theorems of the subject already present in this elegant algorithm. Motivating examples will frequently be illustrated using the computer algebra packages Sage and Mathematica.

Syllabus:  An introduction to linear algebra in abstract vector spaces with particular emphasis on finite dimensional Euclidean space. Topics: Gaussian elimination, matrix algebra, linear independence, span, basis, linear transformations, Gram-Schmidt, determinants, eigenvalues, eigenvectors, and diagonalization. Some of the basic theorems will be proved rigorously; other results will be demonstrated informally. Applications will be emphasized throughout. Assessments: weekly quizzes and online homework; two in-term exams; and a final exam.

Instructor(s):  A. Saleski

Required text(s):  Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence, Linear Algebra (4th edition), Pearson (2002)

Prerequisites:  Math 162 or Math 132

Course description:  This introductory course to linear algebra has two major goals. (a) Studying systems of linear equations in n unknowns and the corresponding matrix algorithms. Basic concepts such as diagonalization, basis, determinants and eigenvalues/eigenvectors will be examined. (b) Studying abstract vector spaces and developing skills in writing proofs. The major definitions (linear independence, spanning set, basis) are examined both in an abstract setting. Inner product spaces will be explored if time permits. This course together with Math 201 (Number Theory) prepares students to take upper-level courses (such as Abstract Algebra and Real Analysis) in which an understanding of proofs is vital. There will be several tests and quizzes as well as a final, and possibly a term project or essay. Occasionally, Mathematica will be used as a computational tool.

Instructor(s):  Dr. Christine Haught

Required text(s):  TBA

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):  Staff

Required text(s):  Thomas, George B., Maurice D. Weir, and Joel R. Hass. Thomas' Calculus, Multivariable (packaged with MyMathLab), 13th ed. ISBN-13: 9780321953100. New York: Pearson, 2014. 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. Adam Spiegler

Required text(s):  Nagle, R. Kent, Saff, Edward B., and Edward B. Snider. Fundamentals of Differential Equations. 8th ed. ISBN-13: 978-0321747730. Boston: Addison-Wesley, 2012.

Prerequisites:  MATH 263

Course description:  A differential equation can be used to model a situation that involves change. Examples come from Ecology, Economics, Medicine, Physics, Biology and Chemistry. This course will concentrate on ordinary differential equations. For what equations does a solution exist and when is a solution unique? Can we solve an equation explicitly in mathematical terms? Can we find a numerical solution? Topics will include first order equations, second order linear equations, Laplace Transforms, series solutions, and systems of equations. Applications to modeling will be emphasized.

Instructor(s):  Dr. Steven Jordan

Required text(s):  TBA.

Prerequisites:  MATH 132 or 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, institutions and mathematical genealogy. 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: (As of February 2014.)
• 100 points ~ Biography. Presentation to class with supporting materials
• 100 points ~ Additional topic (e.g., medieval Islamic astronomy) ~ Presentation to class with supporting materials
• 100 points total ~ Several short presentations and homework
• Final exam emphasizing doing mathematics with historical methods
75 points ~ take-home part
25 points ~ in-class part
• 400 points total for course

Instructor(s):  Dr. E.N. Barron

Required text(s):  A First Course in Probability, by S.Ross, 9th edition, ISBN-10: 032179477X | ISBN-13: 978-0321794772 | Edition: 9

Recommended text(s):  Online Notes will be provided

Additional notes:  A TI-83,84,or89 are required.

Prerequisites:  Math 263.

Course description:  The course covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains, a number of more advanced topics, from which we will choose. These topics include transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics.

Syllabus:  We will have regular quizzes on assigned homework, 2 semester exams, and a final exam.

Instructor(s):  Dr. John G. Del Greco

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

Prerequisites:  MATH/STAT 305

Course description:  This course will be a mathematically rigorous introduction to statistics and will require an extensive background in probability. The successful student will need a firm grasp of the following topics from probability theory: axiomatic probability, conditional probability, independence, combinatorial probability, random variables, families of discrete probability distributions (hypergeometric, binomial, Poisson, geometric, negative-binomial), families of continuous distributions (exponential, normal, gammma, beta), expected values, variance, covariance, joint densities, conditional densities, transformations of random variables, order statistics, and moment-generating functions.

Stat 305 will cover the following topics: methods of estimation, properties of estimators (unbiasedness, consistency, sufficiency, efficiency, etc.), minimum-variance unbiased estimators and the Cramer-Rao lower bound, Bayesian estimation, hypothesis testing, uniformly most powerful tests, Neyman-Pearson Lemma, sampling distributions and inferences involving the normal distribution, two-sample tests, goodness-of-fit tests, analysis of variance.

Instructor(s):  Dr. Anthony Giaquinto

Required text(s):  Gallian, Joseph A. Contemporary Abstract Algebra. 8th ed. ISBN-13: 978-1133599708. Boston: Brooks/Cole, Cengage Learning, 2012. 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. Anne Peters Hupert

Required text(s):  Axler, Sheldon. Linear Algebra Done Right (Second Edition). New York: Springer-Verlag, 1997. Print.

Prerequisites:  MATH 212, MATH 313

Course description:  This course offers a rigorous abstract approach to vector spaces and transformations. Topics covered will include eigenvalues, eigenvectors, invariant subspaces, inner product spaces, adjoints, and isometries. Grades will be based on 3 in-class exams, graded homework, and a final.

Instructor(s):  Dr. W. Cary Huffman

Required text(s):  I. Martin Isaacs, Geometry for College Students. ISBN-10: 0821847945, ISBN-13: 978-0821847947.

Textbook notes:  There are two covers for the book. One is red and white, the other is green and white; the contents are identical and you can purchase either one.

Prerequisites:  MATH 132 or 162.

Course description:  For many people, the word “geometry” conjures up thoughts of the first course in high school that required proofs; for some this is a pleasant memory, for others rather unpleasant. Often lost in this memory is the beauty of geometry. In this class, the hope is that you rediscover, or discover for the first time, the real beauty of geometry.

Geometry arose in many early cultures as a tool for measurement. As a mathematical discipline, geometry was first axiomatized by Euclid in his Elements published about 2300 years ago. The geometry described by Euclid with his axioms is called Euclidean geometry. There are non-Euclidean geometries that have a similar axiomatic flavor such as projective and hyperbolic geometry. Euclidean geometry will be the main focus of this course. Some of the remarkably beautiful results we will examine include the nine-point circle, Morley’s Theorem, the Butterfly Theorem, Ceva’s Theorem, and Menelaus’ Theorem.

Syllabus:  In this course, I will provide you with a list of the theorems, lemmas, and corollaries that we will cover. This list will used on the regularly assigned homework and will be available for the three in-class exams and the final exam. On the homework, you will be able to turn in corrections for partial credit.

Instructor(s):  Robert Jensen

Required text(s):  "Introduction to Analysis" by Maxwell Rosenlicht Dover Books on Mathematics ISBN 0-486-65038-3

Prerequisites:  As listed

Course description:  In this course we will rigorously examine the foundations of real analysis and revisit with precision the concepts of continuity and differentiability of real valued functions of a real valued variable. We will begin with a review of the basics of set theory and proceed to the axioms for the real numbers and the implications of these axioms. Important among these is the topology induced by the axioms. Special attention will be placed on the notions of open sets, closed sets, and compactness. We take a brief time to define metric spaces and show that the set of real numbers is an example of a metric space. Next we will revisit the concept of continuity and rigorously establish important theorems such as the intermediate value theorem and theorems about the existence of maximums and minimums for continuous functions. Finally we will revisit the concept of a derivative and carefully construct proofs to important theorems from differential calculus, including the mean value theorem and Taylor's theorem.

Instructor(s):  Dr. Joseph Mayne

Required text(s):  Saff, E. B. and Snider, A. D., Fundamentals of Complex Analysis with Applications to Engineering and Science, 3rd Edition. New Jersey: Pearson, 2003. Print. ISBN-13: 9780139078743

Prerequisites:  MATH 264

Course description:  In complex analysis we are interested in extending results using real numbers in algebra and analysis to analogous results using the field of complex numbers. Applications of this extension occur in electrical engineering, signal processing, quantum mechanics, and various mathematical fields such as number theory and real analysis. Many concepts and results that seem non-intuitive when encountered in real analysis become “natural” when extended to their complex versions. We will study analytic functions, integration, infinite series, residue theory and conformal mappings. Grading will be based on homework, three tests during the semester, a project, and the final examination.

Instructor(s):  Dr. Peter Tingley

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 is not required.

Course description:  Throughout many fields (economics, biology, politics, engineering, sports...most of life really) people must work towards goals while other forces are acting against them. Any such situation can be thought of as a game, where the "players" make various decisions while trying to achieve goals which may be in conflict. Game theory studies methods of making "good" decisions. Often this reduces to quite elegant mathematics. We will study that math, and consider some applications. Mathematica and/or Gambit Software will be used at times, although no prior knowledge of programming is required. There will be two midterms and a cumulative final exam, and homework will be regularly assigned and graded.

Instructor(s):  Dr. Emily Peters

Required text(s):  Willard, Stephen. General Topology. Mineaola: Dover, 2004. ISBN 9780486434797. Print. Hatcher, Allen. Algebraic Topology. Cambridge: Cambridge University Press. ISBN 9780521795401. Print.

Textbook notes:  Please note that Hatcher's Algebraic Topology is available for free from his personal webpage.

Prerequisites:  MATH 351 (Real Analysis I) is a prerequisite, and MATH 313 (Abstract Algebra I) is a corequisite.

Course description:  Topology is the qualitative study of space — as opposed to geometry, the quantitative study of space. Instead of distances, angles, and curvatures, topology studies spaces through their open and closed subsets. The first half of this class will cover point-set topology, which is a generalization of real anaylsis (generalizing away the “real” part). In the second half of the class, we’ll move closer to the ‘rubber-sheet geometry’ aspects of topology. We’ll classify orientable and non-orientable two-dimensional spaces, and study homotopy and the fundamental group. Because these last topics require some algebra, Math 313 (Abstract Algebra I) is a prerequisite/corequisite for this class. In more detail, we will study metric spaces, open and closed sets, continuity, connectedness, path-connectedness, compactness, and product spaces; as well as classification of surfaces, homotopy and the fundamental group. Additional topics may include space-filling curves, quotient spaces, topological dimension, and Hausdorff (fractal) dimension.

Instructor(s):  Dr. Peter Tingley

Required text(s):  None

Prerequisites:  Senior Standing, including completion of Math 304/Stat 304 or Math 313 or Math 351

Course description:  The purpose of this seminar is to develop skills in communicating advanced mathematics. Students will give at least one presentation to their peers on material beyond the standard curriculum, and produce an accompanying set of lecture notes. Students will also attend a number of lectures on a range of topics, some given by their peers, some by Loyola faculty, and some by outside faculty (as part of the undergraduate colloquium series). Students will be expected to interact with speakers and ask questions as appropriate, and will write short expositions recapping some of the talks.

Instructor(s):  Dr. Earvin Balderama

Required text(s):  Dennis Wackerly, William Mendenhall, Richard L. Scheaffer, Mathematical Statistics with Applications, 7th edition (2007), Duxbury/Brooks/Cole/Thomson. ISBN-10: 0-495-11081-7 (ISBN-13:978-0-49-511081-1)

Textbook notes:  It is important to have the 7th edition. The international edition does not have the same Exercise sets used for homework assignments.

Prerequisites:  Some background in statistics or admission into one of our Math 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).

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

Instructor(s):  Dr. Anne Peters Hupert

Required text(s):  Axler, Sheldon. Linear Algebra Done Right (Second Edition). New York: Springer-Verlag, 1997. Print.

Prerequisites:  MATH 212, MATH 313

Course description:  This course offers a rigorous abstract approach to vector spaces and transformations. Topics covered will include eigenvalues, eigenvectors, invariant subspaces, inner product spaces, adjoints, and isometries. Grades will be based on 3 in-class exams, graded homework, and a final.

Instructor(s):  Dr. Peter Tingley

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 is not required.

Course description:  Throughout many fields (economics, biology, politics, engineering, sports...most of life really) people must work towards goals while other forces are acting against them. Any such situation can be thought of as a game, where the "players" make various decisions while trying to achieve goals which may be in conflict. Game theory studies methods of making "good" decisions. Often this reduces to quite elegant mathematics. We will study that math, and consider some applications. Mathematica and/or Gambit Software will be used at times, although no prior knowledge of programming is required. There will be two midterms and a cumulative final exam, and homework will be regularly assigned and graded.

Instructor(s):  Rafal Goebel

Required text(s):  Title: Elementary Functional Analysis Author: Barbara MacCluer Series: Graduate Texts in Mathematics (Book 253) Hardcover: 208 pages Publisher: Springer; 1st Edition. 2nd Printing. 2008 edition (March 5, 2009) ISBN-10: 0387855289 ISBN-13: 978-0387855288

Recommended text(s):  Title: Functional Analysis Author: George Bachmand and Lawrence Narici Series: Dover Books on Mathematics Paperback: 544 pages Publisher: Dover Publications; 2 Unabridged edition (January 29, 1998) ISBN-10: 0486402517 ISBN-13: 978-0486402512

Textbook notes:  The required text should be a pleasure to learn from. The recommended text can serve as a reference for many years. The former is not expensive. The latter is even more not expensive.

Prerequisites:  Real Analysis I Math 351, Abstract Algebra I Math 313, graduate standing or permission of instructor

Course description:  This course is an introduction to functional analysis, building on previously acquired knowledge of real analysis and linear algebra. Real analysis, at an early stage, studies real numbers and functions of a real variable, with later extensions to functions of two or more real variables. Linear algebra studies linear operations on finite-dimensional Euclidean spaces. Functional analysis goes much further and studies linear operations and functionals defined on general, infinite-dimensional spaces. While this may appear too abstract, one should note that the definite integral, studied as early as in a calculus class, is an example of a linear functional defined on the infinite-dimensional space of continuous functions. Many other examples will be featured in the course, along with material on Hilbert spaces, linear operator theory, the famous and important results like the Hahn-Banach Theorem, the Principle of Uniform Boundedness, and the Open Mapping and Closed Graph , and more. A potential student should know too that despite the abstract setting, functional analysis finds a plethora of applications, to approximation theory, mathematical physics, optimization, ordinary and partial differential equations, and more.

Instructor(s):  Dr. Emily Peters

Required text(s):  Willard, Stephen. General Topology. Mineaola: Dover, 2004. ISBN 9780486434797. Print. Hatcher, Allen. Algebraic Topology. Cambridge: Cambridge University Press. ISBN 9780521795401. Print.

Textbook notes:  Please note that Hatcher's Algebraic Topology is available for free from his personal webpage.

Prerequisites:  MATH 351 (Real Analysis I) is a prerequisite, and MATH 313 (Abstract Algebra I) is a corequisite.

Course description:  Topology is the qualitative study of space — as opposed to geometry, the quantitative study of space. Instead of distances, angles, and curvatures, topology studies spaces through their open and closed subsets. The first half of this class will cover point-set topology, which is a generalization of real anaylsis (generalizing away the “real” part). In the second half of the class, we’ll move closer to the ‘rubber-sheet geometry’ aspects of topology. We’ll classify orientable and non-orientable two-dimensional spaces, and study homotopy and the fundamental group. Because these last topics require some algebra, Math 313 (Abstract Algebra I) is a prerequisite/corequisite for this class. In more detail, we will study metric spaces, open and closed sets, continuity, connectedness, path-connectedness, compactness, and product spaces; as well as classification of surfaces, homotopy and the fundamental group. Additional topics may include space-filling curves, quotient spaces, topological dimension, and Hausdorff (fractal) dimension.

Instructor(s):  Dr. W. Cary Huffman

Required text(s):  I. Martin Isaacs, Geometry for College Students. ISBN-10: 0821847945, ISBN-13: 978-0821847947.

Textbook notes:  There are two covers for the book. One is red and white, the other is green and white; the contents are identical and you can purchase either one.

Prerequisites:  MATH 132 or 162.

Course description:  For many people, the word “geometry” conjures up thoughts of the first course in high school that required proofs; for some this is a pleasant memory, for others rather unpleasant. Often lost in this memory is the beauty of geometry. In this class, the hope is that you rediscover, or discover for the first time, the real beauty of geometry.

Geometry arose in many early cultures as a tool for measurement. As a mathematical discipline, geometry was first axiomatized by Euclid in his Elements published about 2300 years ago. The geometry described by Euclid with his axioms is called Euclidean geometry. There are non-Euclidean geometries that have a similar axiomatic flavor such as projective and hyperbolic geometry. Euclidean geometry will be the main focus of this course. Some of the remarkably beautiful results we will examine include the nine-point circle, Morley’s Theorem, the Butterfly Theorem, Ceva’s Theorem, and Menelaus’ Theorem.

Syllabus:  In this course, I will provide you with a list of the theorems, lemmas, and corollaries that we will cover. This list will used on the regularly assigned homework and will be available for the three in-class exams and the final exam. On the homework, you will be able to turn in corrections for partial credit.

Instructor(s):  Dr. Joseph Mayne

Required text(s):  Saff, E. B. and Snider, A. D., Fundamentals of Complex Analysis with Applications to Engineering and Science, 3rd Edition. New Jersey: Pearson, 2003. Print. ISBN-13: 9780139078743

Prerequisites:  Math 264

Course description:  In complex analysis we are interested in extending results using real numbers in algebra and analysis to analogous results using the field of complex numbers. Applications of this extension occur in electrical engineering, signal processing, quantum mechanics, and various mathematical fields such as number theory and real analysis. Many concepts and results that seem non-intuitive when encountered in real analysis become “natural” when extended to their complex versions. We will study analytic functions, integration, infinite series, residue theory and conformal mappings. Grading will be based on homework, three tests during the semester, a project, and the final examination.

Instructor(s):  Staff

Required text(s):  Freedman, David, Robert Pisani, and Roger Purves, Statistics. 4th ed. ISBN-13: 978-0393929720. New York: W. W. Norton & Company, 2007. Print.

Sections 003 and 004 [Dr. Adam Spiegler] will use the following text:

Lock, Robin H. et al. Statistics: Unlocking the Power of Data. ISBN-13: 978-0470601877. Hoboken, NJ: Wiley, 2012.

Prerequisites:  None

Course description:  An introduction to statistical reasoning. Students learn how statistics has helped to solve major problems in economics, education, genetics, medicine, physics, political science, and psychology. Topics include: design of experiments, descriptive statistics, mean and standard deviation, the normal distribution, the binomial distribution, correlation and regression, sampling, estimation, and testing of hypothesis. A TI-83 (or equivalent) calculator is required for this course.

Syllabus:  Common

Instructor(s):  Dr. Earvin Balderama

Required text(s):  Buntinas, Martin. Statistics for the Sciences. 1st ed. ISBN-13: 9780534387747. Stamford, CT: Centage Learning, 2005. Print.

Textbook notes:  Student Solution manual available, ISBN-13 978-0-321-78399-8

Prerequisites:  Math 132 or Math 162

Course description:  This is a one semester foundation class in probability and statistics. The class is meant to introduce the student to the basics of probability and statistics for science and engineering majors. It introduces the probability needed to form a foundation for the statistics methods which are the focus of the course. Statistics is the scientific method used in order to be able to reach a decision about the result of an experiment which has random outcomes. Such experiments arise in all areas of science and medicine. The scientific method involves controlled randomized experiments so that the method of comparison can be used to reach a conclusion about the compared groups. Statistics and probability is the mathematical basis for the method of comparison. We will have at least two exams plus a final, as well as assigned homework from the book and quizzes on WebWork. The class requires two semesters of calculus as a prerequisite.

Instructor(s):  Dr. E.N. Barron

Required text(s):  A First Course in Probability, by S.Ross, 9th edition, ISBN-10: 032179477X | ISBN-13: 978-0321794772 | Edition: 9

Recommended text(s):  Online Notes will be provided

Additional notes:  A TI-83,84,or89 are required.

Prerequisites:  Math 263.

Course description:  The course covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains, a number of more advanced topics, from which we will choose. These topics include transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics.

Syllabus:  We will have regular quizzes on assigned homework, 2 semester exams, and a final exam.

Instructor(s):  Dr. John G. Del Greco

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

Prerequisites:  MATH/STAT 305

Course description:  This course will be a mathematically rigorous introduction to statistics and will require an extensive background in probability. The successful student will need a firm grasp of the following topics from probability theory: axiomatic probability, conditional probability, independence, combinatorial probability, random variables, families of discrete probability distributions (hypergeometric, binomial, Poisson, geometric, negative-binomial), families of continuous distributions (exponential, normal, gammma, beta), expected values, variance, covariance, joint densities, conditional densities, transformations of random variables, order statistics, and moment-generating functions.

Stat 305 will cover the following topics: methods of estimation, properties of estimators (unbiasedness, consistency, sufficiency, efficiency, etc.), minimum-variance unbiased estimators and the Cramer-Rao lower bound, Bayesian estimation, hypothesis testing, uniformly most powerful tests, Neyman-Pearson Lemma, sampling distributions and inferences involving the normal distribution, two-sample tests, goodness-of-fit tests, analysis of variance.

Instructor(s):  Dr. Molly K. Walsh

Required text(s):  Mendenhall, William and Sincich, Terry. A Second Course in Statistics: Regression Analysis. 7th ed. ISBN-13: 978-0321691699. Boston: Prentice Hall, 2012. Print.

Prerequisites:  STAT 203, STAT 335 or permission of instructor

Course description:  This course provides students with a thorough introduction to applied regression methodology. The concept of simple linear regression will be reviewed, and multiple linear regression, transformations, indicator variables, multicollinearity, diagnostics, model building, polynomial regression, logistic regression and nonparametric regression will be discussed. The course will focus on applications such as those from biometry and biostatistics (clinical trials, HIV studies, etc.), sports, engineering, agriculture and environmental science. 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. Practice problems will be given for every topic studied, and several short quizzes based on the practice problems will be given during the course. Two quiz scores may be dropped. Quizzes make up 25% of the final grade. Two midterm exams and a final exam will also be given, and each is worth 25% of the final grade.

Instructor(s):  Staff

Required text(s):  Samuels, Myra L., Jeffrey A. Witmer, and Andrew A. Schaffner. Statistics for the Life Sciences. 4th ed. ISBN-13: 978-0321652805. New York: Prentice Hall, 2012. Print.

Additional notes:  Students may not receive credit for both STAT 203 and STAT 335

Prerequisites:  BIOL 102 and MATH 162 or MATH 132

Course description:  An introduction to statistical methods used in designing biological experiments and in data analysis. Topics include frequency distributions, probability and sampling distribution, design of biological experiments, interval estimation, tests of hypotheses, analysis of variance, correlation and regression. This course will have two quizzes, two exams, regularly assigned homework, a course project, and computer laboratory assignments in MINITAB with biological data.

Instructor(s):  Staff

Required text(s):  D’Agostino, Sullivan & Beiser, Introductory Applied Biostatistics, Brooks/Cole, 2006. ISBN: 978-0-534-42399-5.

Prerequisites:  STAT 335 or with the permission of the 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. Gerald M. Funk

Required text(s):  David W. Hosmer, Jr., Stanley Lemeshow & Susanne May. Applied Survival Analysis: Regression Modeling of Time to Event Data, 2nd Edition. John Wiley & Sons. ISBN: 978-0-471-75499-2, ©2008

Prerequisites:  STAT 203 or STAT 335

Course description:  Time-to-event data, also referred to as survival data or failure-time data arise in situations where the actual response measurements are not known, but are known to be below or above a threshold or within an interval. This course focuses on methods for analyzing such data. We first consider descriptive methods for survival data including the survival function and its estimation using the Kaplan-Meier method and how to use and compare estimated survival functions. Then we discuss several important regression models for survival data: semi-parametric models such as proportional hazards regression models and parametric models including exponential, Weibull and log-logistic regression models. Using ideas not unlike those used in linear regression models we will describe techniques for model development, including selecting covariates, identifying influential and poorly fit subjects, and assessing overall goodness-of-fit. In this course, students will be required to analyze real-life data sets using the Minitab, R and/or SAS statistical packages. Grading will be based on participation, homework assignments, a course project/paper/presentation, and exams.

Instructor(s):  Dr. Timothy O'Brien

Required text(s):  Hedeker, D and Gibbons, R.D., Longitudinal Data Analysis, Wiley, 2006, ISBN-10: 0471420271, ISBN-13: 978-0-471-42027-9.

Prerequisites:  STAT 203, STAT 335, or permission of instructor.

Course description:  Course description: This course explores methods for the analysis of longitudinal data for linear models, generalized linear models, and nonlinear models. Focusing on applications, this course explores: the analysis of repeated measures ANOVA, multivariate approaches, random-effects regression, covariance-pattern models, generalized-estimating equations, and generalizations. Students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. Grading is based on weekly homework assignments, a project/paper, and exams.

Instructor(s):  Dr. Timothy O'Brien

Required text(s):  The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century, by David Salsburg, 2001: Holt Paperbacks, ISBN-10: 0805071342, ISBN-13: 978-0-8050-7134-4

Prerequisites:  Senior Standing, including completion of STAT-304

Course description:  This seminar will help students to develop skills in communicating statistical topics of interest in the larger context and to an audience outside of academe and math/statistics. As such, students will be required to actively participate in discussions and blog-posts, and give at least one presentation to their peers on material beyond the standard curriculum. As opportunities arise, students will also attend a number of lectures on a range of topics, some given by their peers, some by Loyola faculty, and some by outside faculty (as part of the undergraduate colloquium series). Students will be expected to interact with speakers and ask questions as appropriate, and will write short expositions recapping some of the talks. Grading will be based on the quality of presentations, writing and oral communication of statistical concepts.

Instructor(s):  Dr. John G. Del Greco
Dr. Alan J. Saleski

Required text(s):  The focus will be on problem solving throughout the course. Problem sheets will be distributed to students who will have to prepare solutions and present them to the class.

Prerequisites:  MATH 263 (required)
STAT 304 (recommended)

Course description:  The purpose of Stat 396 is solely to prepare students to take the SOA Actuarial Examination P. Stat 396 will be one-credit course and will consist of a rigorous and comprehensive review of the probability topics that most commonly appear on the SOA P exam. The course will cover axiomatic probability, combinatorial probability, conditional probability and Bayes' Theorem, independence, 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. Other topics will include order statistics, moment-generating functions, the Central Limit Theorem, and risk analysis.

A discussion of test-taking skills will be included in the course, and students will have the opportunity to take practice tests under conditions similar to those of the actual test.

Instructor(s):  Dr. Michael Perry

Required text(s):  Cody & Smith, Applied Statistics & the SAS Programming Language, 5th Ed., Pearson, 2005, ISBN-10: 0131465325, ISBN-13: 978-0131465329

Textbook notes:  Programs from Cody and Smith's book 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 (not required) are available at support.sas.com/documentation/onlinedoc/code.samples.html.

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

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. Earvin Balderama

Required text(s):  Dennis Wackerly, William Mendenhall, Richard L. Scheaffer, Mathematical Statistics with Applications, 7th edition (2007), Duxbury/Brooks/Cole/Thomson. ISBN-10: 0-495-11081-7 (ISBN-13:978-0-49-511081-1)

Textbook notes:  It is important to have the 7th edition. The international edition does not have the same Exercise sets used for homework assignments.

Prerequisites:  Some background in statistics or admission into one of our Math 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).

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

Instructor(s):  Dr. Gregory J. Matthews

Required text(s):  Kutner, M., Nachtsheim, C., Neter, J. Applied Linear Statistical Models. 5th ed. ISBN-13: 978-0073108742. McGraw-Hill Europe. 2004. Print.