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. Binder Ready Version w/ Wileyplus ISBN: 9781118562390 or Paperback w/ Wileyplus ISBN: 978-1-118-55625-2. 2nd ed. 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):  Rafal Goebel

Required text(s):  Discrete Mathematics: Elementary and Beyond by Lovasz, Pelikan, and Vesztergombi; Springer 2003; e-book ISBN 978-0-387-21777-2; softcover ISBN 978-0-387-95585-8; hardcover ISBN 978-0-387-95584-1

Prerequisites:  Math 161

Course description:  At an elementary level, number theory takes familiar objects, like natural numbers, and familiar concepts, like divisibility of one natural number by another, and poses interesting and challenging problems. Some of these problems have been solved by the ancient Greeks, who knew, for example, that there exists infinitely many prime numbers. Some of these problems remain challenging today, which helps the Internet data transmission remain secure. Other familiar concepts, like counting things, picking the shortest path for a traveling salesman, or wondering how many different paints one needs to color a map, give rise to combinatorics and graph theory. The course will introduce the student to several theoretical concepts from number theory and to some topics from combinatorics and graph theory, and to satisfying applications of these concepts. One goal of the course is to increase the student's interest in mathematics. Another goal is to develop the student's ability to read, understand, and write rigorous mathematical arguments. After all, as the introduction to the textbook says, ``It is important to realize that there is no mathematics without proofs.'' Topics to be covered include counting principles; mathematical induction; the binomial theorem and Pascal's triangle; Fibonacci numbers; divisibility, prime numbers, Fermat's little theorem, the Euclidean algorithm, congruences, and some special kinds of primes; graphs; trees; and more.

Instructor(s):  Dr. Cristina Popovici

Required text(s):  David Lay, Linear Algebra and its Applications, 4th Edition, Pearson (packaged with MyMathLab). ISBN-10: 0321399145; ISBN-13: 9780321399144. Alternatively, a student may purchase MyMathLab access as a separate entity and use the online version of the book. The ISBN for the MML access only is: 032119991X.

Prerequisites:  MATH 162 Calculus II or MATH 132 Applied Calculus II

Course description:  An introduction to linear algebra in abstract vector spaces with particular emphasis on R^n. Topics include: Gaussian elimination, matrix algebra, linear independence, span, basis, linear transformations, determinants, eigenvalues, eigenvectors, and diagonalization. Some of the basic theorems will be proved rigorously; other results will be demonstrated informally. Homework will be assigned regularly in MyMathLab throughout the semester. There will be at least two midterms and a comprehensive final exam.

Instructor(s):  Dr. Peter Tingley

Required text(s):  Anton, Howard. Elementary Linear Algebra. 10th ed. ISBN-13: 978-0470458211. Hoboken: Wiley, 2010. Print.

Prerequisites:  MATH 162 Calculus II or MATH 132 Applied Calculus II

Course description:  An introduction to linear algebra in abstract vector spaces with particular emphasis on R^n. Topics include: Gaussian elimination, matrix algebra, linear independence, span, basis, linear transformations, determinants, eigenvalues, eigenvectors, and diagonalization. Some of the basic theorems will be proved rigorously; other results will be demonstrated informally.

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. Stephen Doty

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. Print.

Additional notes:  Section 001 (MWF 1:40 - 2:30 PM)

Prerequisites:  MATH 263

Course description:  A differential equation is often used to model a situation that involves change. Such problems as population growth, the amount of liquid flowing out of the bottom of a tank, the concentration of a drug in a patient’s bloodstream, and the position of an object dropped from above the surface of the earth can all be modeled using a differential equation. 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? What about studying equations from a qualitative viewpoint rather than a quantitative one? 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):  Robert Jensen

Required text(s):  "An Introduction to Differential Equations and their Applications" by Stanley J. Farlow ISBN-13: 978-0486445953 ISBN-10: 048644595X

Additional notes:  This is section 002 of Math 264 (i.e., Math 264 002)

Prerequisites:  Math 263

Course description:  This is a traditional course in ordinary differential equations (ODEs). After a brief introduction and definition of ordinary differential equations, we will begin with the study of first order differential equations and techniques for solving them. From there we will move to second order ODEs with concentration on linear second order ODEs (particularly those with constant coefficients) and examples of applications. Then we transition to the development of series solutions for linear second order ODEs (with spatially dependent coefficients). If time permits we will then study systems of first order ODEs.

Syllabus:  None available

Instructor(s):  Alan Saleski

Required text(s):  Sheldon Ross, A First Course in Probability, 9th edition, Pearson (2012)

Prerequisites:  MATH 263

Course description:  This introductory course will cover basic probability theory: Combinatorics, Axioms of probability, Conditional probablity and independence, Random variables, Continuous random variables, jointly distributed random variables, Expection, Moment generating functions, Central limit theorem. This course is the best preparation for the first actuarial exam. There will be three tests, several quizzes, and a final.

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 304

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):  Anne Hupert

Required text(s):  Dan Saracino, Abstract Algebra, A First Course, Second Edition, Waveland 2008. ISBN : 978-1577665366.

Recommended text(s):  None

Textbook notes:  None

Additional notes:  None

Prerequisites:  Math 201, Math 212

Course description:  This course provides a rigorous introduction to the study of structures such as groups, rings, and fields; emphasis is on the theory of groups with topics such as subgroups, cyclic groups, Abelian groups, permutation groups, homomorphisms, cosets, and factor groups.

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 313

Course description:  This course is a continuation of MATH 313 and will focus mainly on the rings and fields. Most of the topics in Chapters 12 - 23 and 32 of the Gallian text will be studied, with special emphasis will be on factorization/divisibility, polynomial rings, finite fields and Galois theory.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Miklós Bóna, A Walk Through Combinatorics: an Introduction to Enumeration and Graph Theory, 3rd Edition, World Scientific (2011). ISBN: 978-9814-46000-2 (paperback); 978-9814-33523-2 (hardcover).

Prerequisites:  MATH 162

Course description:  Combinatorial problems from enumeration and graph theory and methods for their solution. Prior experience with abstraction and proofs is helpful, but not necessary. Graduate students will complete more advanced exercises than the undergraduate students and will present some supplemental topics from independent reading.

Syllabus:  Topics: Permutations, binomial theorem, compositions, partitions, Stirling numbers, Catalan numbers, graphs, trees, Eulerian walks, Hamiltionian cycles, electrical networks, graph colorings, chromatic polynomials, combinatorial algorithms, optimization, among others. Techniques: Pigeon-hole principle, mathematical induction, inclusion-exclusion principle, recurrence relations, generating functions, matrix-tree theorem, Polya theory, Ramsey theory, pattern avoidance, probabilistic methods, partial orders, combinatorial algorithms, among others.

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 or permission of instructor.

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. E.N.Barron

Required text(s):  Mathematics for Finance: An Introduction to Financial Engineering (Springer Undergraduate Mathematics Series) Paperback – November 25, 2010 by Marek Capinski , Tomasz Zastawniak ISBN-13: 978-0857290816 ISBN-10: 0857290819 Edition: 2nd ed. 2011

Prerequisites:  Math/Stat 304, 263, and 264.

Course description:  The aim of the course is to give an introduction to the mathematical theory of modern financial markets with the emphasis on pricing and hedging of derivative securities. Topics covered by this course include: probability review, introduction to securities markets, the modelling of riskless and risky securities, the concept of arbitrage, the risk-neutral probabilities (equivalent martingale measures) and their applications, the fundamental theorem of asset pricing, the study of complete and incomplete market models, the pricing and hedging of options of European and American style, the put-call parity relationship, the binomial options pricing model and the CRR call option pricing formula, the Brownian motion, the Black-Scholes model and the derivation of the Black-Scholes call option pricing formula.

Syllabus:  Linear contracts: forwards, futures and swaps. Arbitrage. Cash and carry arguments. Introduction to the valuation of options, binomial tree approach, delta-hedging argument in discrete time. and Monte Carlo simulation. Basic properties of the Brownian Motion, stochastic integral and Itō's lemma. Black-Scholes-Merton model. Delta-hedging argument in continuous time. Greek letters. Volatility smiles.

Instructor(s):  Dr. Joseph H. Mayne

Required text(s):  Arthur Mattuck, Introduction to Analysis, Prentice-Hall, (1999). ISBN: 0-13-081132-7.

Prerequisites:  MATH 201, MATH 212

Course description:  This course serves as an introduction to the foundations of real analysis emphasizing careful definitions and proofs. Much of the course consists of examining concepts originally studied in the calculus sequence, but now revisited from a more rigorous standpoint. Topics will include: a review of set theory, properties of the real number system, sequences and limits, completeness of the real numbers, infinite series, power series, functions and limits, continuous functions and the intermediate value function, the definition and properties of the derivative, the mean-value theorem, and Taylor’s theorem.

Instructor(s):  Robert Jensen

Required text(s):  "Introduction to Analysis" by Maxwell Rosenlicht ISBN-13: 978-0486650388 ISBN-10: 0486650383

Prerequisites:  Math 351

Course description:  This course is a continuation of Math 351 and will cover the material on integration and partial derivatives in chapters VI through X of "Introduction to Analysis" by Maxwell Rosenlicht.

Instructor(s):  Dr. John G. Del Greco

Required text(s): 

(1) Vanderbei, Robert J. Linear Programming: Foundations and Extensions (International Series in Operations Research & Management Science). 4th ed. ISBN-13: 978-1461476290. New York: Springer, 2014. Print.

(2) Fourer, Robert, David M. Gay, and Brian W. Kernighan. AMPL: A Modeling Language for Mathematical Programming. 2nd ed. ISBN-13: 978-0534388096. Belmont, CA: Brooks/Cole, 2003. Print.

Prerequisites:  MATH 212

Course description:  Math 358 will be an introductory course on operations research methodology which will focus primarily on the linear programming problem and its many extensions and applications. There will be take-home exams and written homework assignments. The exams and homeworks will include programming in AMPL.

We will study the following topics from linear programming:

• Simplex Method for solving linear programming problems
• Duality theory and the dual simplex method
• Revised simplex method
• Sensitivity and parametric analysis
• Convex analysis
• Applications to game theory
• Financial applications: portfolio selection and options pricing
• Spanning trees and bases
• Primal and dual network simplex method
• Transportation and assignment problems
• Shortest path problem
• Integer programming models
• Traveling salesman problem
• Branch and bound algorithm for integer programming

Instructor(s):  Dr. Marian Bocea

Required text(s):  Walter A. Strauss, Partial Differential Equations: An Introduction, Second Edition (2008), Wiley, ISBN-10: 0470054565 ISBN-13: 978-0470054567.

Prerequisites:  MATH 263 Multivariable Calculus and MATH 264 Ordinary Differential Equations

Course description:  This is an introductory course on partial differential equations (PDE). A PDE is a differential equation involving the partial derivatives of an unknown function depending of more than one variable. Such equations model many real-world phenomena and, as such, arise in various disciplines. Typical examples are the heat equation, which governs the evolution of temperature in a conductive material, the wave equation, which governs propagation of waves, or Laplace's equation, satisfied by the stream function of an incompressible fluid. The course will serve as a conceptual introduction to the theory of PDE; although we will learn how to find explicit solutions for certain PDE (this is a problem that very often doesn't have a tractable solution, even for the simplest linear equations), the focus will be on studying qualitative properties of solutions which will help us understand phenomena encountered in applications. For example, the "maximum principle" for the heat equation explains why heat doesn't collect at "hot points".

Syllabus:  In addition to first order PDE (such as the transport equation) we will study in detail the main types of second order PDE (as illustrated by the Laplace equation, the heat equation, and the wave equation), with an emphasis on understanding the different qualitative behavior of the solutions. This will include the treatment of both homogeneous and inhomogeneous equations and boundary conditions. We will cover selected topics from Chapters 1-7 of the textbook. 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. Earvin Balderama

Required text(s):  Wackerly, D., Mendenhall, W., Scheaffer, R.L. Mathematical Statistics with Applications, 7th edition. Duxbury/Brooks/Cole/Thomson. 2007. 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" is not the same.

Prerequisites:  MATH/STAT 404

Course description:  This is a continuation of MATH/STAT 404. This course is designed to provide the basic tools of statistical inference to graduate students. It should prepare the students to understand the foundations behind statistical inference, and enable them to formulate appropriate statistical procedures. It should further hone their problem solving skills, as well as prepare them to handle more advanced courses.

Syllabus:  Content includes limit theorems, point and interval estimation, hypothesis testing, maximum likelihood, Neyman-Pearson Lemma, likelihood ratio, nonparametric statistics. Two midterms and a final exam will be given and homework will be assigned weekly.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Miklós Bóna, A Walk Through Combinatorics: an Introduction to Enumeration and Graph Theory, 3rd Edition, World Scientific (2011). ISBN: 978-9814-46000-2 (paperback); 978-9814-33523-2 (hardcover).

Prerequisites:  MATH 162

Course description:  Combinatorial problems from enumeration and graph theory and methods for their solution. Prior experience with abstraction and proofs is helpful, but not necessary. Graduate students will complete more advanced exercises than the undergraduate students and will present some supplemental topics from independent reading.

Syllabus:  Topics: Permutations, binomial theorem, compositions, partitions, Stirling numbers, Catalan numbers, graphs, trees, Eulerian walks, Hamiltionian cycles, electrical networks, graph colorings, chromatic polynomials, combinatorial algorithms, optimization, among others. Techniques: Pigeon-hole principle, mathematical induction, inclusion-exclusion principle, recurrence relations, generating functions, matrix-tree theorem, Polya theory, Ramsey theory, pattern avoidance, probabilistic methods, partial orders, combinatorial algorithms, among others.

Instructor(s):  Dr. E.N.Barron

Required text(s):  Mathematics for Finance: An Introduction to Financial Engineering (Springer Undergraduate Mathematics Series) Paperback – November 25, 2010 by Marek Capinski , Tomasz Zastawniak ISBN-13: 978-0857290816 ISBN-10: 0857290819 Edition: 2nd ed. 2011

Prerequisites:  Math/Stat 304, 263, and 264.

Course description:  The aim of the course is to give an introduction to the mathematical theory of modern financial markets with the emphasis on pricing and hedging of derivative securities. Topics covered by this course include: probability review, introduction to securities markets, the modelling of riskless and risky securities, the concept of arbitrage, the risk-neutral probabilities (equivalent martingale measures) and their applications, the fundamental theorem of asset pricing, the study of complete and incomplete market models, the pricing and hedging of options of European and American style, the put-call parity relationship, the binomial options pricing model and the CRR call option pricing formula, the Brownian motion, the Black-Scholes model and the derivation of the Black-Scholes call option pricing formula.

Syllabus:  Linear contracts: forwards, futures and swaps. Arbitrage. Cash and carry arguments. Introduction to the valuation of options, binomial tree approach, delta-hedging argument in discrete time. and Monte Carlo simulation. Basic properties of the Brownian Motion, stochastic integral and Itō's lemma. Black-Scholes-Merton model. Delta-hedging argument in continuous time. Greek letters. Volatility smiles.

Instructor(s):  Robert Jensen

Required text(s):  "Introduction to Analysis" by Maxwell Rosenlicht ISBN-13: 978-0486650388 ISBN-10: 0486650383

Prerequisites:  Math 351

Course description:  In addition to the material on integration and partial derivatives in chapters VI through X of "Introduction to Analysis" by Maxwell Rosenlicht, I will assign independent reading on measure theory and Lebesgue integration.

Syllabus:  None available

Instructor(s):  Dr. John G. Del Greco

Required text(s): 

(1) Vanderbei, Robert J. Linear Programming: Foundations and Extensions (International Series in Operations Research & Management Science). 4th ed. ISBN-13: 978-1461476290. New York: Springer, 2014. Print.

(2) Fourer, Robert, David M. Gay, and Brian W. Kernighan. AMPL: A Modeling Language for Mathematical Programming. 2nd ed. ISBN-13: 978-0534388096. Belmont, CA: Brooks/Cole, 2003. Print.

Prerequisites:  MATH 212

Course description:  Math 358 will be an introductory course on operations research methodology which will focus primarily on the linear programming problem and its many extensions and applications. There will be take-home exams and written homework assignments. The exams and homeworks will include programming in AMPL.

We will study the following topics from linear programming:

• Simplex Method for solving linear programming problems
• Duality theory and the dual simplex method
• Revised simplex method
• Sensitivity and parametric analysis
• Convex analysis
• Applications to game theory
• Financial applications: portfolio selection and options pricing
• Spanning trees and bases
• Primal and dual network simplex method
• Transportation and assignment problems
• Shortest path problem
• Integer programming models
• Traveling salesman problem
• Branch and bound algorithm for integer programming

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 or permission of instructor.

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. Marian Bocea

Required text(s):  Walter A. Strauss, Partial Differential Equations: An Introduction, Second Edition (2008), Wiley, ISBN-10: 0470054565 ISBN-13: 978-0470054567.

Prerequisites:  MATH 263 Multivariable Calculus and MATH 264 Ordinary Differential Equations

Course description:  This is an introductory course on partial differential equations (PDE). A PDE is a differential equation involving the partial derivatives of an unknown function depending of more than one variable. Such equations model many real-world phenomena and, as such, arise in various disciplines. Typical examples are the heat equation, which governs the evolution of temperature in a conductive material, the wave equation, which governs propagation of waves, or Laplace's equation, satisfied by the stream function of an incompressible fluid. The course will serve as a conceptual introduction to the theory of PDE; although we will learn how to find explicit solutions for certain PDE (this is a problem that very often doesn't have a tractable solution, even for the simplest linear equations), the focus will be on studying qualitative properties of solutions which will help us understand phenomena encountered in applications. For example, the "maximum principle" for the heat equation explains why heat doesn't collect at "hot points".

Syllabus:  In addition to first order PDE (such as the transport equation) we will study in detail the main types of second order PDE (as illustrated by the Laplace equation, the heat equation, and the wave equation), with an emphasis on understanding the different qualitative behavior of the solutions. This will include the treatment of both homogeneous and inhomogeneous equations and boundary conditions. We will cover selected topics from Chapters 1-7 of the textbook. Homework will be assigned and graded regularly throughout the semester. There will be at least two midterms and a comprehensive final exam.

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 005 [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. E.N.Barron

Required text(s):  The book will be provided through OpenIntro. For online homework and quizzes we use Introduction to the Practice of Statistics, 8th Edition, Moore, McCabe, Craig, W.H. Freeman Press, All you need is the stand-alone Stats Portal access card is: 1464190658 This includes an ebook. You may get this either from the bookstore or online.

Textbook notes:  Make sure the book comes with an Access Code.

Prerequisites:  Prerequisites: Math 132 or Math 162

Course description:  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. The class requires two semesters of calculus as a prerequisite.

Syllabus:  Syllabus: 1.Data and distributions, 2. Numerical summary measures, 3. Bivariate and multivariate data and distributions, 4. Probability and sampling distributions, 5. Estimation, 6. Testing hypotheses, 7. Analysis of variance, 8. Regression and correlation.

Instructor(s):  Alan Saleski

Required text(s):  Sheldon Ross, A First Course in Probability, 9th edition, Pearson (2012)

Prerequisites:  MATH 263

Course description:  This introductory course will cover basic probability theory: Combinatorics, Axioms of probability, Conditional probablity and independence, Random variables, Continuous random variables, jointly distributed random variables, Expection, Moment generating functions, Central limit theorem. This course is the best preparation for the first actuarial exam. There will be three tests, several quizzes, and a final.

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 304

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. Tim O'Brien

Required text(s):  “Design and Analysis of Experiments” by Angela Dean & Daniel Voss, 1999, Springer-Verlag New York, ISBN/10: 0387985611, ISBN/13: 978-0387985619.

Prerequisites:  STAT-203 or STAT-335 or equivalent, or permission of the instructor.

Course description:  As no subject is more central to the development of statistical methods, this course provides students with a thorough introduction to statistical experimental design and to the statistical methods used to analyze the resulting data. The concepts of comparative experiments, analysis of variance (ANOVA) and mean separation procedures will be reviewed; blocking (complete and incomplete) will be discussed, as will be factorial designs, fractional factorial designs, and confounding. The course will focus on biometric applications such as clinical trials, HIV studies, and environmental and agricultural research, but industrial and other examples will occasionally be provided to show the breadth of application of experimental design ideas. Students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. Grading is based on regular homework assignments, a project/paper, two exams and a final.

Instructor(s):  Dr. Tim O'Brien

Required text(s):  “An Introduction to Categorical Data Analysis” by Alan Agresti, 2007, 2nd Edition, Wiley, ISBN/10: 0471226181, ISBN/13: 978-0471226185.

Prerequisites:  STAT-203 or STAT-335 or equivalent, or permission of the instructor. (Send me an email at tobrie1@luc.edu if you have any questions.)

Course description:  Normally distributed response variables lead statistical practitioners to use simple linear models procedures such as simple and multiple regression or one- or two-way ANOVA, but other types of data cannot be analyzed in the same ways. Thus, these simple (regression) techniques have been generalized to handle nominal, ordinal, count and binary data under the general heading of categorical data analysis. Contingency table analyses, generalized linear models, logistic regression and log-linear modeling are the focus of this course in the context of predictive modelling. This course also addresses the fundamental questions encountered with regression and ANOVA for count data. Specialized methods for ordinal data, small samples, multi-category data, matched pairs, marginal models and random effects models will also be discussed. The focus throughout this course will be on applications and real-life data sets; as such, theorems and proofs will not be emphasized. Students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. Grading is based on regular homework assignments, a project/paper, two exams and a final.

Instructor(s):  Dr. Michael Perry (Section 002)
Mr. Bret Longman (Sections 001, 003)

Required text(s):  Myra L. Samuels, Jeffrey A. Witmer, and Andrew A. Schaffner, Statistics for the Life Sciences, Prentice Hall, 4th edition Prentice Hall (2012), ISBN: 10: 0-321-65280-0; 13: 978-0-32165280-5

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

Prerequisites:  Calculus II (Math 162 or 132); Introduction to Biology II (Biol 102)

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):  Dr. Gregory J. Matthews

Required text(s):  Diez, David M., Barr, Christophe D., and Cetinkaya-Rundel, Mine. OpenIntro Statistics: Second Edition. CreateSpace Independent Publishing Platform, 2012. OpenIntro.org. Web. July 26, 2012

Prerequisites:  MATH 162 or 132; BIOL 102

Course description:  An introduction to statistical methods used in designing biological experiments and in data analysis. Topics include probability and sampling distribution, design of biological experiments and analysis of variance, regression and correlation, stochastic processes, and frequency distributions. Computer laboratory assignments with biological data. (Note: Students may not receive credit for both STAT 203 & 335.)

Instructor(s):  Dr. Molly K. Walsh

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. Practice problems will be given for every topic studied, and quizzes based on the practice problems will be given during most weeks of the course. Two quiz scores may be dropped. Quizzes make up 40% of the final grade. Students (in small groups) will complete an original data analysis project using at least one of the methods covered during the course. Use of computer software such as Minitab and/or SAS is highly recommended for computations. The project represents 20% of the final grade. A midterm and a final exam will be given, and each is worth 20% of the final grade.

Instructor(s):  Dr. Gregory J. Matthews

Required text(s):  Deonier, Richard C., Tavare, Simon, and Waterman, M. Computational Genome Analysis: An Introduction. Springer, 2007. Print.

Prerequisites:  STAT 203 or 335 or equivalent.

Course description:  This course explores recently developed mathematical, probabilistic and statistical methods currently used in the fields of bioinformatics and DNA microarray and protein array data analysis. These include stochastic processes, (hidden and traditional) Markov chains, tree- and clustering techniques (including principal components analysis and biplots), discriminant analysis, experimental design strategies and ANOVA methods. Our focus in this course is on the application of these techniques and on meaningful interpretation of results.

Instructor(s):  Dr. Earvin Balderama

Required text(s):  Wackerly, D., Mendenhall, W., Scheaffer, R.L. Mathematical Statistics with Applications, 7th edition. Duxbury/Brooks/Cole/Thomson. 2007. 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" is not the same.

Prerequisites:  MATH/STAT 404

Course description:  This is a continuation of MATH/STAT 404. This course is designed to provide the basic tools of statistical inference to graduate students. It should prepare the students to understand the foundations behind statistical inference, and enable them to formulate appropriate statistical procedures. It should further hone their problem solving skills, as well as prepare them to handle more advanced courses.

Syllabus:  Content includes limit theorems, point and interval estimation, hypothesis testing, maximum likelihood, Neyman-Pearson Lemma, likelihood ratio, nonparametric statistics. Two midterms and a final exam will be given and homework will be assigned weekly.

Instructor(s):  Dr. Tim O'Brien

Required text(s):  “Design and Analysis of Experiments” by Angela Dean & Daniel Voss, 1999, Springer-Verlag New York, ISBN/10: 0387985611, ISBN/13: 978-0387985619.

Prerequisites:  STAT-203 or STAT-335 or equivalent, or permission of the instructor.

Course description:  As no subject is more central to the development of statistical methods, this course provides students with a thorough introduction to statistical experimental design and to the statistical methods used to analyze the resulting data. The concepts of comparative experiments, analysis of variance (ANOVA) and mean separation procedures will be reviewed; blocking (complete and incomplete) will be discussed, as will be factorial designs, fractional factorial designs, and confounding. The course will focus on biometric applications such as clinical trials, HIV studies, and environmental and agricultural research, but industrial and other examples will occasionally be provided to show the breadth of application of experimental design ideas. Students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. Grading is based on regular homework assignments, a project/paper, two exams and a final.

Instructor(s):  Dr. Tim O'Brien

Required text(s):  “An Introduction to Categorical Data Analysis” by Alan Agresti, 2007, 2nd Edition, Wiley, ISBN/10: 0471226181, ISBN/13: 978-0471226185.

Prerequisites:  STAT-203 or STAT-335 or equivalent, or permission of the instructor. (Send me an email at tobrie1@luc.edu if you have any questions.)

Course description:  Normally distributed response variables lead statistical practitioners to use simple linear models procedures such as simple and multiple regression or one- or two-way ANOVA, but other types of data cannot be analyzed in the same ways. Thus, these simple (regression) techniques have been generalized to handle nominal, ordinal, count and binary data under the general heading of categorical data analysis. Contingency table analyses, generalized linear models, logistic regression and log-linear modeling are the focus of this course in the context of predictive modelling. This course also addresses the fundamental questions encountered with regression and ANOVA for count data. Specialized methods for ordinal data, small samples, multi-category data, matched pairs, marginal models and random effects models will also be discussed. The focus throughout this course will be on applications and real-life data sets; as such, theorems and proofs will not be emphasized. Students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. Grading is based on regular homework assignments, a project/paper, two exams and a final.

Instructor(s):  Molly K. Walsh, PhD

Required text(s):  Vittinghoff, Eric, David Glidden, Stephen Shiboski and Charles McCulloch. Regression Methods in Biostatistics. 2nd ed. ISBN-13: 978-1461413523. New York: Springer, 2012. Print.

Prerequisites:  Graduate level course

Course description:  This course covers experimental design (interaction, analysis of covariance, crossover designs, etc.) and the analysis of designed studies, simple and multiple linear regression, generalized linear and nonlinear regression, bioassay, relative potency and drug synergy, multivariate analysis (MANOVA and multivariate regression), repeated measures designs and analysis, and survival analysis of censored data (Cox proportional odds model, log-rank tests, Kaplan-Meier estimation). The emphasis of the course is on applications instead of statistical theory, and students are required to analyze real-life datasets using the Minitab, SAS and/or R statistical packages, although no previous programming experience is assumed. Grading will be based on homework assignments, quizzes, exams and a project presentation.

Instructor(s):  Dr. Gregory J. Matthews

Required text(s):  Deonier, Richard C., Tavare, Simon, and Waterman, M. Computational Genome Analysis: An Introduction. Springer, 2007. Print.

Prerequisites:  STAT 203 or 335 or equivalent.

Course description:  This course explores recently developed mathematical, probabilistic and statistical methods currently used in the fields of bioinformatics and DNA microarray and protein array data analysis. These include stochastic processes, (hidden and traditional) Markov chains, tree- and clustering techniques (including principal components analysis and biplots), discriminant analysis, experimental design strategies and ANOVA methods. Our focus in this course is on the application of these techniques and on meaningful interpretation of results.