Instructor(s):  Staff

Required text(s):  McCallum, Connally, Hughes-Hallett et al. Algebra: Form and Function. 2nd edition. (with WileyPlus ebook)

Textbook notes:  Students buying used textbooks should arrange to purchase WileyPlus separately. Instructions for students to obtain the e-book and to use WileyPlus: use your Loyola email address to create a WileyPlus account. Your professor will include details on WileyPlus in the syllabus.

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

Required text(s):  Eric Connally, Hughes-Hallett, D., and Gleason, A. M. Functions Modeling Change: A Preparation for Calculus. 5th ed. New Jersey: Wiley, 2015. Packaged with WileyPlus.​

Prerequisites:  Eric Connally, Hughes-Hallett, D., and Gleason, A. M. Functions Modeling Change: A Preparation for Calculus. 5th ed. New Jersey: Wiley, 2015. Packaged with WileyPlus.​

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):  Eric Connally, Hughes-Hallett, D., and Gleason, A. M. Functions Modeling Change: A Preparation for Calculus. 5th ed. New Jersey: Wiley, 2015. Packaged with WileyPlus.​

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, Custom (WileyPlus eBook).

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, Custom (WileyPlus eBook).

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):  Stewart, James. Calculus: Early Transcendentals (WebAssign eBook). 8th ed.

Print text (optional): ISBN-13: 978-1285741550. Boston: Centage Learning, 2015.

Prerequisites:  MATH 118

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):  Stewart, James. Calculus: Early Transcendentals (WebAssign eBook). 8th ed.

Print text (optional): ISBN-13: 978-1285741550. Boston: Centage Learning, 2015.

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):  Anne Hupert

Required text(s):  Mathematics: A Discrete Introduction (3rd edition) by Edward Scheinerman ISBN-13: 978-0840065285 ISBN-10: 0840065280

Prerequisites:  Math 161

Course description:  This course covers topics from discrete mathematics, primarily from elementary number theory, ranging from induction to congruencies to prime numbers and cardinality, to provide students planning to take advanced 300 level courses in mathematics with an introduction to understanding and constructing proofs. Grades will be bases on daily homework, 3 in-class exams, and a final.

Instructor(s):  Dr. E.N. Barron

Required text(s):  Essentials of Probability and Statistics for Engineers and Scientists, by Walpole, Myers, Myers, and Ye, Pearson. 2013.

Recommended text(s):  Probability and Statistics for Engineering and the Sciences by Jay L. Devore.

Prerequisites:  MATH 162 or 132 (with grade of "C" or better).

Course description:  This is the first rigorous course in Probability and Statistics. It is calculus based and is required of all Statistics and Math majors, as well as Engineering Science students. It is also recommended for Physics, Chemistry, and Biology majors. This class is also excellent preparation for Math/Stat 304 and 305. This course covers the essential topics in Probability and Statistics with derivations of most of the results. It can be used as a stand alone course or a foundation for further study in Statistics for more advanced topics. We will have two midterms and a final exam. A TI-8x is required for this course.

Syllabus:  1. The basics of Probability 2. Random Variables--Distributions, Mean, Variance, Moment Generating Functions 3. Distributions of the Sample Mean and Sample Standard Deviation 4. Statistical Intervals 5. Hypothesis Testing 6. Linear Regression

Instructor(s):  Dr. John G. Del Greco

Required text(s):  Anton, Howard. Elementary Linear Algebra. 11th ed. ISBN-13: 978-1118473504. New York: John Wiley, 2013. Print.

Prerequisites:  MATH 132 or MATH 162

Course description:  This course will be a mathematically rigorous introduction to the basic concepts, theory, and applications of linear algebra. Proofs of basic results will be provided where appropriate. Students may be required to write simple proofs on homework assignments and tests. Linear algebra techniques are important because of their many applications in science, economics, business, engineering, and the life sciences. Moreover, linear algebra constitutes a bridge from basic to more advanced mathematics.

Instructor(s):  Dr. Brian Seguin

Required text(s):  Anton, Howard. Elementary Linear Algebra. 11th ed. ISBN-13: 978-1118473504. New York: John Wiley, 2013. Print.

Prerequisites:  MATH 132 or MATH 162

Course description:  This course will be a mathematically rigorous introduction to the basic concepts, theory, and applications of linear algebra. Proofs of basic results will be provided where appropriate. Students may be required to write simple proofs on homework assignments and tests. Linear algebra techniques are important because of their many applications in science, economics, business, engineering, and the life sciences. Moreover, linear algebra constitutes a bridge from basic to more advanced mathematics.

Instructor(s):  Dr Stephen Doty

Required text(s):  Eric Matthes, Python Crash Course: A Hands-On, Project-Based Introduction to Programming, No Starch Press, 2015. ISBN-10: 1593276036; ISBN-13: 978-1593276034.

Recommended text(s):  Allan M Stavely, Programming and Mathematical Thinking: A Gentle Introduction to Discrete Math Featuring Python, New Mexico Tech Press, 2014. ISBN 978-1-938159-00-8 (pbk.) — 978-1-938159-01-5 (ebook).

Prerequisites:  MATH 162

Course description:  This 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. It is widely used by all major web companies, so knowing something about Python can be helpful in landing a first job after graduation. Programming examples will come from mathematics, physics, 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 and time intensive. There will be frequent programming assignments as well as frequent in-class exercises.

Instructor(s):  Staff

Required text(s):  Stewart, James. Calculus: Early Transcendentals (WebAssign eBook). 8th ed.

Print text (optional): ISBN-13: 978-1285741550. Boston: Cengage Learning, 2015.

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.

Syllabus:  Common

Instructor(s):  Dr. John G. Del Greco

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.

Prerequisites:  MATH 263. Being able to differentiate and integrate functions is an essential skill when studying differential equations. Students will be assumed to be proficient in the techniques of differentiation and integration.

Course description:  This course will be a rigorous treatment of ordinary differential equations. The course will emphasize solutions techniques although some applications will be considered.

Topics will include first- and second-order linear differential equations and methods for their solution: separable of variables and exact equations, integrating factors for linear equations, substitutions and transformations, method of undetermined coefficients, variation of parameters, Laplace transformations, series solutions, systems of differential equations, and phase-plane analysis.

Written homework will be assigned at the end of every class. There should be about 20-25 written homework assignments given during the semester. Each assignment will require at least an hour or two to complete. Homework will count for a significant part of a student's grade.

Instructor(s):  Dr. John G. Del Greco

Required text(s):  Ross, Sheldon. A First Course in Probability. 10th ed. ISBN 9780134753119. Boston: Pearson, 2018. Print.

Prerequisites:  Math 263

Course description:  This course will be a mathematically rigorous introduction to probability theory. The successful student will need a firm grasp of calculus up to multivariate calculus. Topics will include 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, moment-generating functions, and the Central Limit Theorem with applications.

Instructor(s):  Dr. Joseph Mayne

Required text(s):  Sheldon Axler, Linear Algebra Done Right, 3rd Edition, Springer, (2015) ISBN: 978-3-319-11079-0

Prerequisites:  MATH 313

Course description:  This course is a continuation of Mathematics 212, Linear Algebra. The emphasis will be on abstract vector spaces over the fields of real and complex numbers. There will a review of the basic properties of vector spaces and their subspaces. Continuing the study of vector spaces and linear transformations on finite-dimensional spaces, topics will be chosen from: change of basis, trace, determinants, eigenvalues, invariant subspaces, linear functionals, dual spaces, inner product spaces, adjoint transformations, the Spectral Theorem, the characteristic and minimal polynomials, and Jordan canonical form.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Coxeter, H.S.M. and Greitzer, S.L. Geometry Revisited. Math Association of America, 1967. ISBN-13: 978-0883856192.

Recommended text(s):  Densmore and Heath. Euclid’s Elements. Green Lion Press, 2002. ISBN-13: 978-1888009194.
Greenberg. Euclidean and Non-Euclidean Geometries: Development and History, 4th ed. W. H. Freeman, 2007. ISBN-13: 978-0716799481.

Textbook notes:  Recommended texts will be placed on reserve in Cudahy Library for the entire semester.

Prerequisites:  Math 162

Course description:  Having its origins in the systematic study of the heavens (for agriculture; and because who doesn't wonder at the heavens?), Geometry is surely the foundation for all mathematics. In this course, we endeavor to look carefully at this foundation, including its shakier parts, and how it has weathered the 5000(!) years from the Babylonians to the present day. Well, almost. We will not make it all the way to the modern work of Perelman and Mirzakhani---nor will we spend much time looking further back than 300 B.C.---but we will visit the Euclidean, projective, and hyperbolic corners of this fascinating subject.

Most of our time will be spent working through the "classic hits" in Euclidean geometry, like the theorems of Menelaus, Pappus and Brahmagupta (and of course, SAS and ASA), as well as more modern gems due to Pascal, Desargues, Euler, Brianchon, Morley, and others. The shaky parts alluded to above are mistakes and redundancies in Euclid's Elements, as well as the infamous parallel postulate. We'll give a fair amount of attention to these. Next we turn to the work of Klein (symmetries and transformation) and Bolyai-Lobachevski (hyperbolic geometry). If time is not running short, we'll give more than a cursory inspection of elliptic and Riemannian geometry.

Syllabus:  Student grades will be based on homework, quizzes, an in-term project, and a final exam.

Graduate students in Math 488 will be asked to do a more in-depth project and to give a class presentation. Possible topics include: the impossibility of trisecting an angle with a ruler and compass; origami constructions and how to trisect angles; classification of polyhedra; finite geometries; elliptic geometry; Riemannian geometry; Ptolemy’s model of the heavens and the Islamic geometers’ extensions; classical curves; Japanese anchor-ring problems and Ford circles; or Archimedes' "mechanical theorems".

Instructor(s):  Rafal Goebel

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

Prerequisites:  Math 201, Math 212

Course description:  A rough and not complete description of introductory Real Analysis would say that it is calculus with proofs. A better description would say that Real Analysis is interested not only in answers to calculus problems problems but also in if and why the answers exist in the first place. Real Analysis, especially the theory behind convergence, continuity, and approximation forms a foundation upon which many branches of mathematics are built, for example numerical analysis, optimization, dynamical systems, etc. It is also essential in rigorous approaches to economics, finance, theoretical physics, and more. This course will be an introduction to Real Analysis. It will review concepts from set theory and logic and then focus on the real number system, metric spaces, sequences and their convergence, continuity and differentiability of functions. Students will be expected to solve problems and, more importantly, to read, understand, and formulate mathematical arguments and proofs.

Instructor(s):  Dr Stephen Doty

Required text(s):  Saff, E. B and Snider, A. D., Fundamentals of Complex Analysis with Applications to Engineering and Science. 3rd ed. New Jersey: Pearson, 2003. Print. ISBN-13: 978-0134689487 ISBN-10: 0134689488

Prerequisites:  Math 264

Course description:  In complex analysis we are interested in extending results of basic calculus over the real numbers to analogous results over complex numbers. This reveals striking unexpected features, such as a relation between derivatives and integrals which is different from the fundamental theorem of calculus. Important 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; for instance certain improper integrals (over the real numbers) are most easily evaluated using complex analysis. We will study analytic functions, integration, infinite series, residue theory and, time permitting, conformal mappings. Grading will be based on homework sets, quizzes, a midterm exam and a final exam.

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:  MATH162. Some 200 level math or stats recommended.

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. There will be two midterms and a cumulative final exam, and homework will be regularly assigned and graded.

Instructor(s):  Dr. John G. Del Greco

Required text(s):  Chartrand, Gary and Ping Zhang. A First Course in Graph Theory. ISBN-13: 978-0-48-6483689. Dover reprint of Introduction to Graph Theory. New York: McGraw-Hill Book Company, Inc., 2004. Print.

Prerequisites:  Math 212

Course description:  This course will cover the fundamental concepts of graph theory: simple graphs, directed graphs, Eulerian and Hamiltonian graphs, trees, matchings, networks, paths and cycles, graph colorings, and planar graphs. There are many well-known problems in mathematics that can be formulated in terms of graphs: the four color problem (coloring regions on a map using only four colors so that adjacent regions have different colors), the network flow problem (maximizing flow in a network), the marriage problem (matching partners into compatible pairs), the assignment problem (filling n jobs in the best way), and the traveling salesman problem (visiting n cities at minimum cost), etc.

Instructor(s):  Dr. Shuwen Lou

Required text(s):  Introduction to Mathematical Statistics, by Robert Hogg, Joseph McKean, and Allen Craig

Prerequisites:  STAT 203 or STAT 335

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. Topics to be covered include discrete and continuous random variables, transformations, multivariate distributions, correlation, independence, variance-covariance, special distributions (binomial, Poisson, gamma, normal, multivariable normal, t), expectations of functions, convergence in probability, convergence in distribution, moment generating functions, and the central limit theorem.

Instructor(s):  Dr. Joseph Mayne

Required text(s):  Sheldon Axler, Linear Algebra Done Right, 3rd Edition, Springer, (2015) ISBN: 978-3-319-11079-0

Prerequisites:  MATH 313

Course description:  This course is a continuation of Mathematics 212, Linear Algebra. The emphasis will be on abstract vector spaces over the fields of real and complex numbers. There will a review of the basic properties of vector spaces and their subspaces. Continuing the study of vector spaces and linear transformations on finite-dimensional spaces, topics will be chosen from: change of basis, trace, determinants, eigenvalues, invariant subspaces, linear functionals, dual spaces, inner product spaces, adjoint transformations, the Spectral Theorem, the characteristic and minimal polynomials, and Jordan canonical form.

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:  MATH162. Some 200 level math or stats recommended.

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. There will be two midterms and a cumulative final exam, and homework will be regularly assigned and graded.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Coxeter, H.S.M. and Greitzer, S.L. Geometry Revisited. Math Association of America, 1967. ISBN-13: 978-0883856192.

Recommended text(s):  Densmore and Heath. Euclid’s Elements. Green Lion Press, 2002. ISBN-13: 978-1888009194.
Greenberg. Euclidean and Non-Euclidean Geometries: Development and History, 4th ed. W. H. Freeman, 2007. ISBN-13: 978-0716799481.

Textbook notes:  Recommended texts will be placed on reserve in Cudahy Library for the entire semester.

Prerequisites:  Math 162

Course description:  Having its origins in the systematic study of the heavens (for agriculture; and because who doesn't wonder at the heavens?), Geometry is surely the foundation for all mathematics. In this course, we endeavor to look carefully at this foundation, including its shakier parts, and how it has weathered the 5000(!) years from the Babylonians to the present day. Well, almost. We will not make it all the way to the modern work of Perelman and Mirzakhani---nor will we spend much time looking further back than 300 B.C.---but we will visit the Euclidean, projective, and hyperbolic corners of this fascinating subject.

Most of our time will be spent working through the "classic hits" in Euclidean geometry, like the theorems of Menelaus, Pappus and Brahmagupta (and of course, SAS and ASA), as well as more modern gems due to Pascal, Desargues, Euler, Brianchon, Morley, and others. The shaky parts alluded to above are mistakes and redundancies in Euclid's Elements, as well as the infamous parallel postulate. We'll give a fair amount of attention to these. Next we turn to the work of Klein (symmetries and transformation) and Bolyai-Lobachevski (hyperbolic geometry). If time is not running short, we'll give more than a cursory inspection of elliptic and Riemannian geometry.

Syllabus:  Student grades will be based on homework, quizzes, an in-term project, and a final exam.

Graduate students in Math 488 will be asked to do a more in-depth project and to give a class presentation. Possible topics include: the impossibility of trisecting an angle with a ruler and compass; origami constructions and how to trisect angles; classification of polyhedra; finite geometries; elliptic geometry; Riemannian geometry; Ptolemy’s model of the heavens and the Islamic geometers’ extensions; classical curves; Japanese anchor-ring problems and Ford circles; or Archimedes' "mechanical theorems".

Instructor(s):  Robert Jensen

Required text(s):  A Gentle Introduction to Optimization by B. Guenin, J. Konemann, and L. Tuncel (Paperback) ISBN-13: 978-1107658790 ISBN-10: 1107658799

Prerequisites:  Math 212 and Math 263

Course description:  One of the important topics/applications in the first semester of calculus the use of a function's derivative to find the minimum or the maximum of a function of one variable over an interval. In the third semester of calculus this is extended in two ways. The functions depend on two or three variables, and there may be constraints imposed on the variables. This is accomplished by use of the gradient of the function and a method called, Lagrange multipliers. In real world applications, for example involving personnel or production scheduling, route planning, stock portfolio design, traffic flow, planting and harvesting, etc., one may want to minimize or maximize a function of many, even hundreds or thousands, of variables subject to multiple constraints. Optimization is the branch of mathematics which deals with the mathematical modeling of such real world applications; with the mathematical analysis of such problems, which includes proving existence of solutions and writing optimality conditions that characterize the solutions; and with the construction of computer algorithms that "find" the solutions. This course is an introduction to optimization. We shall aim at breadth rather than depth in covering the material. Linear, nonlinear, integer optimization, and optimization on graphs will be discussed. Modeling and analysis will form the core of the course, but I will endeavor to include computational methods as well.

Instructor(s):  Staff

Required text(s):  C.H. Brase and C.P. Brase. Understanding Basic Statistics, 7th ed (WebAssign eBook). Cengage.

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.

Syllabus:  Common

Instructor(s):  Dr. E.N. Barron

Required text(s):  Essentials of Probability and Statistics for Engineers and Scientists, by Walpole, Myers, Myers, and Ye, Pearson. 2013.

Recommended text(s):  Probability and Statistics for Engineering and the Sciences by Jay L. Devore.

Prerequisites:  MATH 162 or 132 (with grade of "C" or better).

Course description:  This is the first rigorous course in Probability and Statistics. It is calculus based and is required of all Statistics and Math majors, as well as Engineering Science students. It is also recommended for Physics, Chemistry, and Biology majors. This class is also excellent preparation for Math/Stat 304 and 305. This course covers the essential topics in Probability and Statistics with derivations of most of the results. It can be used as a stand alone course or a foundation for further study in Statistics for more advanced topics. We will have two midterms and a final exam. A TI-8x is required for this course.

Syllabus:  1. The basics of Probability 2. Random Variables--Distributions, Mean, Variance, Moment Generating Functions 3. Distributions of the Sample Mean and Sample Standard Deviation 4. Statistical Intervals 5. Hypothesis Testing 6. Linear Regression

Instructor(s):  Timothy E. O’Brien, Ph.D.

Required text(s):  Oehlert, Gary W., A First Course in Design and Analysis of Experiments, 2010, download from: http://users.stat.umn.edu/~gary/book/fcdae.pdf (free download is authorized by the author)

Prerequisites:  STAT-203 or STAT-335 or equivalent, or permission of the instructor. It is highly recommended that students have taken a course in applied regression (such as STAT-308 or 408).

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. In this course, students will develop expertise using the Minitab, R and SAS computer packages, although no previous programming experience will be assumed. Grading will be based on participation, homework assignments, a project/paper, exam(s) and a final.

Instructor(s):  Staff

Required text(s):  Regression Methods in Biostatistics: Linear, Logisitic, Survival and Repeated Measures Models, Vittinghoff/Glidden/ Shiboski/McCulloch, 2nd Edition, Springer (ISBN: 978-1461413523)

Prerequisites:  STAT 203 OR STAT 335

Course description:  This course covers multi-variate analysis, including linear regression, logistic regression and survival analysis. 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 R statistical packages, although no previous programming experience is assumed. Grading will be based on homework assignments, a course project/paper, quiz(zes)/exam(s) and a final.

Instructor(s):  Timothy E. O’Brien, Ph.D.

Required text(s):  Kabacoff, Robert I., 2015, R in Action: Data Analysis and Graphics with R, Shelter Island, N.Y.: Manning Publications, ISBN-13: 978-1-617291-38-8; ISBN: 1-617291-38-2.

Additional notes:  This one-credit is required only of STAT major who declared their STAT major before Fall 2018. Students who declare during or after Fall 2018, are not required to complete STAT-390.

Prerequisites:  Senior standing and the completion of STAT-304.

Course description:  The seminar will cultivate students' presentation skills through participation in and critical discussion of brief lectures on familiar and unfamiliar topics; preparation and presentation of two brief lectures by the student (one on a familiar topic from the curriculum, one on a higher level material not customarily from the curriculum); and preparation of an extended abstract summarizing the advanced material presented. Outcomes: Students will gain the ability to present material in Statistics, and their applications to a general audience.

Instructor(s):  Dr. Xiaoli Kong

Required text(s):  None

Prerequisites:  MATH 263, MATH 212, STAT 304 are strongly recommended.

Course description:  This seminar is for students who want to prepare for Society of Actuaries exam P, or (CAS Exam 1), Probability. Topics include general probability including conditional probability and Bayes rule, univariate distributions, including binomial, hypergeometric, Poisson, beta, Pareto, gamma, Weibull and normal, and multivariate distributions including joint moment generating functions and transformation techniques. May be repeated for credit.

Instructor(s):  Dr. Shuwen Lou

Required text(s):  Introduction to Mathematical Statistics, by Robert Hogg, Joseph McKean, and Allen Craig

Prerequisites:  STAT 203 or STAT 335

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. Topics to be covered include discrete and continuous random variables, transformations, multivariate distributions, correlation, independence, variance-covariance, special distributions (binomial, Poisson, gamma, normal, multivariable normal, t), expectations of functions, convergence in probability, convergence in distribution, moment generating functions, and the central limit theorem.

Instructor(s):  Timothy E. O’Brien, Ph.D.

Required text(s):  Oehlert, Gary W., A First Course in Design and Analysis of Experiments, 2010, download from: http://users.stat.umn.edu/~gary/book/fcdae.pdf (free download is authorized by the author)

Prerequisites:  STAT-203 or STAT-335 or equivalent, or permission of the instructor. It is highly recommended that students have taken a course in applied regression (such as STAT-308 or 408).

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. In this course, students will develop expertise using the Minitab, R and SAS computer packages, although no previous programming experience will be assumed. Grading will be based on participation, homework assignments, a project/paper, exam(s) and a final.

Instructor(s):  Dr. Xiaoli Kong

Required text(s):  Kutner, M., Nachtsheim, C., Neter, J. and Li, W. (2004) Applied Linear Statistical Models. 5th Edition, McGraw-Hill

Recommended text(s):  Faraway, J. (2014) Linear Models with R. 2nd Edition. Elsevier Academic Press

Prerequisites:  Acceptance into the MS Statistics program, or instructor consent.

Course description:  This course provides students with a thorough introduction to applied regression methodology. The concept of simple linear regression will be reviewed and discussed using matrices, and multiple linear regression, transformations, diagnostics, polynomial regression, indicator variables, model building and multicolinearity will be discussed, as will be nonlinear and generalized linear regression. Coding will be introduced using the statistical software R. The course will focus on applications of linear regression as a tool for the analysis of real, possibly messy, data.

Instructor(s):  Dr. Xiaoli Kong

Required text(s):  None

Recommended text(s):  Cabrera, J. and McDougall, A. Statistical Consulting, Chapman & Hall.

Prerequisites:  Stat 404/405 and Stat 408 or permission of instructor.

Course description:  Students will be placed into groups of 4-5 students and assigned a client to work with for the duration of the semester. Each group will provide regular updates on the progress of the project via an oral presentation approximately every few weeks. Additionally, at the end of the semester each group will submit a well-written report documenting the problem, the data, the work they did, and future idea for new directions. In addition to this group project, each individual will be required to present topics previously chosen (needs approval). Presentations must be accompanied by well written, informative slides. Student will also be graded based on their participation during class. This includes, but is not limited to, asking relevant questions during the group and individual presentations.