Instructor(s):  Staff

Required text(s):  Ron Larson. Intermediate Algebra (WebAssign eBook) 5th ed.​

Textbook notes:  Students are required to have access to WebAssign for this course. Students buying used textbooks should arrange to purchase WebAssign 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):  Carl Stitz and Jeff Zeager. Precalculus (WebAssign eBook), 3rd edition.

Stitz Zeager Open Source Mathematics, 4 July 2014. Web. http://www.stitz-zeager.com/.

Textbook notes:  Students should register for their section of Math 117 in WebAssign (with eBook).

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):  Carl Stitz and Jeff Zeager. Precalculus (WebAssign eBook), 3rd edition.

Stitz Zeager Open Source Mathematics, 4 July 2014. Web. http://www.stitz-zeager.com/.

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 (WebAssign eBook). 4th ed.

Print text (optional): ISBN-13: 9781118747476. Hoboken, NJ: Wiley, 2013.

Textbook notes:  Students should register for their section of Math 131 in WebAssign (with 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 (WebAssign eBook). 4th ed.

Print text (optional): ISBN-13: 9781118747476. Hoboken, NJ: Wiley, 2013.

Textbook notes:  Students should register for their section of Math 132 in WebAssign (with 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.

Textbook notes:  Students should register for their section of Math 161 in WebAssign (with eBook).

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.

Textbook notes:  Students should register for their section of Math 162 in WebAssign (with eBook).

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. Anne Peters 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. Joseph Mayne

Required text(s):  Lay, David C., Lay, Steven R., and McDonald, Judi J., "Linear Algebra and its Applications," 5th Edition. Packaged with MyMathLab access, Pearson, 2016. ISBN-13: 9780134022697.

Prerequisites:  MATH 162 or MATH 132

Course description:  Linear algebra is widely used in mathematics, science, engineering, and the social sciences. For example, statisticians and economists often employ linear models when trying to analyze problems with many variables. And linear algebra is an important tool in many areas of mathematics itself. Much of functional analysis is devoted to the study of functions preserving linearity and field theory uses linear algebra in the proofs of many results. The course starts with the problem of solving simultaneous linear equations using the Gaussian elimination algorithm. The solution of this important practical problem motivates the definition of many linear algebra concepts: matrices, vectors and vector spaces, linear independence, dimension, and vector subspaces. The emphasis then shifts to general vector spaces and proofs using an axiom system. Most of the results will be for finite dimensional spaces and we will always attempt to visualize theorems in 2 or 3 dimensional Euclidean space. Topics to be covered include: linear transformations, change of basis, determinants, eigenvalues and eigenvectors, and diagonalization. Students will be encouraged to improve their skills at constructing mathematical proofs. There will be three tests, a final examination, and homework assignments, some of which will be submitted on-line using MyMathLab.

Instructor(s):  Dr. Aaron Greicius

Required text(s):  Anton, Howard. Elementary Linear Algebra. 11th ed. Wiley, 2010. ISBN 978-1-11847350-4.

Prerequisites:  MATH 162 or MATH 132.

Course description:  An introduction to linear algebra in abstract vector spaces with particular emphasis on Rn. Topics include: Gaussian elimination, matrix algebra, linear independence, span, basis, linear transformations, projections, Gram-Schmidt,determinants, eigenvalues, eigenvectors, and diagonalization. Some of the basic theorems will be proved rigorously; other results will be demonstrated informally. Software such as Mathematica may be utilized.

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.

Textbook notes:  Students should register for their section of Math 263 in WebAssign (with eBook).

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. Cristina Popovici

Required text(s):  Boyce, William E., and DiPrima, Richard C., Elementary Differential Equations, 10th Edition; ISBN: 978-1-118-61743-4 (E-Text); 978-1-118-15739-8 (Loose-leaf); 978-0-470-45832-7 (Hardcover). Wiley, 2013.

Prerequisites:  MATH 263

Course description:  This is an introductory course in ordinary differential equations. Topics to be discussed include linear and nonlinear first order differential equations such as separable, exact, homogeneous, and Bernoulli equations, second order linear equations, the Laplace transform and its applications to solving initial value problems, and systems of linear first-order differential equations. Homework will be assigned regularly throughout the semester. There will be weekly quizzes, two midterms, and a comprehensive final exam.

Instructor(s):  Rafal Goebel

Required text(s):  Introduction to Linear Algebra and Differential Equations, John W. Dettman, Dover Books on Mathematics, revised edition, 0486651916, 978-0486651910

Prerequisites:  Math 263

Course description:  The course is an introduction to linear algebra and differential equations, and is oriented toward students of engineering science.

Instructor(s):  Alan Saleski

Required text(s):  Dimitri P. Bertsekas, John N. Tsitsiklis, Introduction to Probability, 2nd edition, Athena Scientific (2008) ISBN-13: 978-1886529236 ISBN-10: 188652923X

Prerequisites:  Math 263 (Multivariable Calculus)

Course description:  This introductory course will cover basic probability theory: combinatorics, axioms of probability, conditional probablity and independence, Bayes' theorem, random variables, continuous random variables, jointly distributed random variables, expection, moment generating functions, central limit theorem. Math 304 is the best preparation for the first actuarial exam. There will be weekly homework, three tests and a final.

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

Prerequisites:  MATH 304 or 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. Brian Seguin

Required text(s):  Gallian, Joseph A. Contemporary Abstract Algebra. 9th edition. Cengage Learning, 2015 ISBN-13: 978-1305657960

Prerequisites:  MATH 201 and MATH 212

Course description:  This course presents an introduction to the study of abstract algebraic structures with emphasis on the theory of groups and, time permitting, rings. Topics that will be covered include equivalence relations, subgroups, homomorphisms, quotients, products, linear groups, and permutation groups. There will be two exams, weekly homework, periodic quizzes, and a final exam.

Instructor(s):  Dr Stephen Doty

Required text(s):  Sepanski, Mark R. Algebra. Pure and Applied Undergraduate Texts, Volume 11 (2010), American Mathematical Society, Providence, RI. Print ISBN: 978-0-8218-5294-1.

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

Prerequisites:  MATH 313

Course description:  Study of commutative and non-commutative rings, integral domains, and fields. Selected topics may include Galois theory, group representations, modules, and advanced group theory.

This course continues where MATH 313 leaves off. It is a must for students wanting to understand the full story of why 5th degree polynomials are not solvable in terms of radicals. There are also other beautiful applications, such as the proof of impossibility of certain classical problems in Greek geometry (such a squaring the circle). Examples of exotic finite fields will be constructed; these are very useful in algebraic coding theory - mathematics that underlies the coding of information on DVDs and NASA communications.

Modern abstract algebra is increasingly applied. Chemists use it to study crystals and molecules, physicists use it to study elementary particles, biologists use it to study mutations in DNA, and cryptographers use it to protect our security on computer networks. The material in this course is indispensable for anyone wanting to really understand the mathematics behind those contemporary applications.

Instructor(s):  Dr. W. Cary Huffman

Required text(s):  Alan Tucker, Applied Combinatorics, 6th Edition, 2012. ISBN-13: 978-0-470-45838-9. Hoboken, NJ: Wiley, 2012. Print.

Prerequisites:  MATH 162

Course description:  Combinatorics is a branch of mathematics with broad areas of application. There are important uses of combinatorics in computer science, operations research, probability, and statistics. Theoretical thermodynamics uses combinatorial theory to describe ideas such as entropy. Combinatorial analysis is a cornerstone of the study of error-correcting codes; these codes are used to transmit information from deep space or to protect the quality of music on compact discs. Our course will mainly focus on describing and/or counting complicated sets. Often questions which begin “How many ways can you...?” or “How many steps does it take to...?” are answered using combinatorial analysis. Such questions on the surface may appear rather uninteresting, but one can quickly get to questions that are quite engaging. What gambler wouldn’t want to understand the odds at winning a poker hand?

We plan to examine the following topics: permutations and combinations, the inclusion-exclusion principle and other general counting techniques, partitions, generating functions, recurrence relations, Burnside’s Theorem, the cycle index, and Polya’s formula. Other topics may be included as time permits. Emphasis will be on examples rather than theory.

This course is a combined undergraduate/graduate course. The requirements of the course for the graduate students will be different from the requirements for the undergraduates. The material should be comprehensible for any student who has completed Math 162.

Instructor(s):  Dr. Aaron Lauve

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

Prerequisites:  MATH 201 and MATH 212

Course description:  The specific topics and techniques treated in Real Analysis—focused on a rigorous development of the differential calculus—form the foundation of numerical analysis, optimization, dynamical systems, economics, finance, theoretical physics, and more.

As important as the specific topics and techniques alluded to above is the word rigorous that also appears. Beyond working problems, students shall gain and demonstrate proficiency in reading, understanding, formulating, and communicating mathematical arguments and proofs.

Syllabus:  We cover the first five chapters in the Rosenlicht's text: concepts from set theory and logic; the real number system; metric spaces; sequences and their convergence; continuity and differentiability of functions.

There will be weekly homework assignments, two in-class exams, and a final exam.

Instructor(s):  Marian Bocea

Required text(s):  Maxwell Rosenlicht, Introduction to Analysis. Dover Books on Mathematics; ISBN-10: 0-486-65038-3

Prerequisites:  MATH 351

Course description:  This course is a continuation of MATH 351. We will cover most of Chapters VI-X in the textbook. Topics include: Riemann integration, infinite series, partial derivatives, the implicit function theorem, and multiple integrals. A strong emphasis will be placed on conceptual understanding and mathematical rigor. There will be at least two midterms and a comprehensive final exam.

Instructor(s):  David Slavsky

Required text(s):  Felder, Gary N. and Kenny M. Felder. Mathematical Methods in Engineering and Physics. ISBN-13: 978-1118449608. 1st ed. Hoboken, NJ: Wiley, 2015. Print.

Prerequisites:  Math 264

Course description:  Vector calculus, matrices, series solutions of differential equations, special functions; Fourier series, Fourier and Laplace transforms; Partial differential equations, Green's functions, Einstein notation and extensive work in Mathematica. Knowledge of some physics is highly recommended.

Instructor(s):  Robert Jensen

Required text(s):  Oliver, Peter. Introduction to Partial Differential Equations. 1st ed. New York: Springer, 2014. Print. ISBN-13: 978-3319020983 ISBN-10: 3319020986

Prerequisites:  Math 351

Course description:  This course will introduce students to partial differential equations. Partial differential equations are fundamental for modeling objects from physics to biology and economics. For example the the wave equation and the heat equation in physics; reaction diffusion equations in biology; and the Black-Scholes equation in mathematical finance. Solving partial differential equations is much more complicated than solving ordinary differential equations. Indeed there are even linear partial differential equations which are locally unsolvable. We will begin by examining some of the fundamental partial differential equations, such as the wave equation, and looking for different schemes to solve them. One method, separation of variables, allows us to reduce the problem of solving the partial differential equation to a family of connected ordinary differential equations. This context motivates the study of Fourier series, which we will spend some time studying.

Syllabus:  None available

Instructor(s):  Rafal Goebel

Required text(s):  A Gentle Introduction to Optimization, Guenin, Könemann, and Tunçel, 1st edition, Cambridge University Press, ISBN: 1107658799 or 978-1107658790

Recommended text(s):  An Introduction to Continuous Optimization: Foundations and Fundamental Algorithms, Andreasson, Evgrafov, and Patriksson, 3rd edition, Dover, ISBN: 0486802876 or 978-0486802879

Textbook notes:  The required text should be easy to read and serve as a good introduction. The recommended text is certainly not required and provides a more detailed introduction to linear and nonlinear optimization (it excludes graph and integer optimization).

Prerequisites:  Math 212 and Math 263

Course description:  In Calc I, you learned how to find the minimum or the maximum of a function of one variable over an interval, by using the function's derivative. In Calc III, you (should have) learned how to find the minimum or the maximum of a function of two or three variables over a set in the plane or over a curve in space, by using the function's gradient and 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 a variety of constraints. Optimization is the branch of mathematics which deals with modeling of such real world applications as math problems; with analysis of such problems, which includes proving existence of solutions and writing optimality conditions that characterize the solutions; and with design of computer algorithms that find the solutions. The course is an introduction to optimization and it aims at breadth, rather than depth. Linear, nonlinear, and integer optimization, and optimization on graphs will be discussed. Modeling and analysis will form the core of the course, but computational methods will be presented too. The textbook is similarly broad in its scope. Supplementary material and more challenging problems will come from other sources.

Instructor(s):  Dr. W. Cary Huffman

Required text(s):  None

Prerequisites:  Junior standing or permission of the department chair or assistant chair

Course description:  The overall purpose and objective of this class will be to gain an introductory understanding of numerical mathematics, also called numerical analysis, and present this material in a well-written journal quality final paper. We will study three topics in numerical analysis: numerical solutions of fixed-point problems, quadrature (numerical integration), and numerical solutions of first order ordinary differential equations. Throughout this course homework will be assigned to explore these topics. Some of that homework will require the use of Mathematica. Every homework assignment, and the final paper, will be typeset using LaTeX, which you will learn as the course progresses. Students will be provided with notes on using LaTeX, notes for each of the three topics in numerical analysis, and all of the Mathematica code where required. Major parts of the final paper will be developed in the homework. The class meets weekly on Thursday from 4:00-4:50.

Instructor(s):  Swarnali Banerjee

Required text(s):  Mathematical Statistics with Applications by Dennis D. Wackerly, William Mendenhall III and Richard L. Scheaffer, 7th edition

Recommended text(s):  Statistical Inference by George Casella and Roger L. Berger, 2nd edition

Prerequisites:  MATH/STAT 404

Course description:  A continuation of MATH/STAT 404. Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests).

Instructor(s):  Dr Stephen Doty

Required text(s):  Sepanski, Mark R. Algebra. Pure and Applied Undergraduate Texts, Volume 11 (2010), American Mathematical Society, Providence, RI. Print ISBN: 978-0-8218-5294-1.

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

Prerequisites:  MATH 313

Course description:  Study of commutative and non-commutative rings, integral domains, and fields. Selected topics may include Galois theory, group representations, modules, and advanced group theory.

This course continues where MATH 313 leaves off. It is a must for students wanting to understand the full story of why 5th degree polynomials are not solvable in terms of radicals. There are also other beautiful applications, such as the proof of impossibility of certain classical problems in Greek geometry (such a squaring the circle). Examples of exotic finite fields will be constructed; these are very useful in algebraic coding theory - mathematics that underlies the coding of information on DVDs and NASA communications.

Modern abstract algebra is increasingly applied. Chemists use it to study crystals and molecules, physicists use it to study elementary particles, biologists use it to study mutations in DNA, and cryptographers use it to protect our security on computer networks. The material in this course is indispensable for anyone wanting to really understand the mathematics behind those contemporary applications.

Instructor(s):  Dr. W. Cary Huffman

Required text(s):  Alan Tucker, Applied Combinatorics, 6th Edition, 2012. ISBN-13: 978-0-470-45838-9. Hoboken, NJ: Wiley, 2012. Print.

Prerequisites:  MATH 162

Course description:  Combinatorics is a branch of mathematics with broad areas of application. There are important uses of combinatorics in computer science, operations research, probability, and statistics. Theoretical thermodynamics uses combinatorial theory to describe ideas such as entropy. Combinatorial analysis is a cornerstone of the study of error-correcting codes; these codes are used to transmit information from deep space or to protect the quality of music on compact discs. Our course will mainly focus on describing and/or counting complicated sets. Often questions which begin “How many ways can you...?” or “How many steps does it take to...?” are answered using combinatorial analysis. Such questions on the surface may appear rather uninteresting, but one can quickly get to questions that are quite engaging. What gambler wouldn’t want to understand the odds at winning a poker hand?

We plan to examine the following topics: permutations and combinations, the inclusion-exclusion principle and other general counting techniques, partitions, generating functions, recurrence relations, Burnside’s Theorem, the cycle index, and Polya’s formula. Other topics may be included as time permits. Emphasis will be on examples rather than theory.

This course is a combined undergraduate/graduate course. The homework, quizzes, and exams for graduate students will be different from the homework, quizzes, and exams for undergraduates. Additionally, graduate students will research a topic in combinatorics that is not covered in class and will write a paper on that topic.

Instructor(s):  Marian Bocea

Required text(s):  Maxwell Rosenlicht, Introduction to Analysis. Dover Books on Mathematics; ISBN-10: 0-486-65038-3

Prerequisites:  MATH 351

Course description:  This course is a continuation of MATH 351. We will cover most of Chapters VI-X in the textbook. Topics include: Riemann integration, infinite series, partial derivatives, the implicit function theorem, and multiple integrals. A strong emphasis will be placed on conceptual understanding and mathematical rigor. There will be at least two midterms and a comprehensive final exam.

Instructor(s):  Rafal Goebel

Required text(s):  A Gentle Introduction to Optimization, Guenin, Könemann, and Tunçel, 1st edition, Cambridge University Press, ISBN: 1107658799 or 978-1107658790

Recommended text(s):  An Introduction to Continuous Optimization: Foundations and Fundamental Algorithms, Andreasson, Evgrafov, and Patriksson, 3rd edition, Dover, ISBN: 0486802876 or 978-0486802879

Textbook notes:  The required text should be easy to read and serve as a good introduction. The recommended text is certainly not required and provides a more detailed introduction to linear and nonlinear optimization (it excludes graph and integer optimization).

Prerequisites:  Math 212 and Math 263

Course description:  In Calc I, you learned how to find the minimum or the maximum of a function of one variable over an interval, by using the function's derivative. In Calc III, you (should have) learned how to find the minimum or the maximum of a function of two or three variables over a set in the plane or over a curve in space, by using the function's gradient and 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 a variety of constraints. Optimization is the branch of mathematics which deals with modeling of such real world applications as math problems; with analysis of such problems, which includes proving existence of solutions and writing optimality conditions that characterize the solutions; and with design of computer algorithms that find the solutions. The course is an introduction to optimization and it aims at breadth, rather than depth. Linear, nonlinear, and integer optimization, and optimization on graphs will be discussed. Modeling and analysis will form the core of the course, but computational methods will be presented too. The textbook is similarly broad in its scope. Supplementary material and more challenging problems will come from other sources.

Instructor(s):  Staff

Required text(s):  Illowsky, Barbara, and Susan Dean. Introductory Statistics (WebAssign eBook). 1st ed.

Print text (optional): ISBN-13 978-1-938168-20-8. Houston: Open Stax College, 2013.

Textbook notes:  Students should register for their section of Stat 103 in WebAssign (with eBook).

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):  Probability & Statistics, by E.N.Barron and J. Del Greco, Preliminary version. Available only at the book store.

Prerequisites:  Math 132 or Math 162 (with a grade of at least C). Math 263 is recommended as a prerequisite or taken concurrently.

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 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

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

Prerequisites:  MATH 304 or 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. Earvin Balderama

Required text(s):  Agresti, A. (2007). An Introduction to Categorical Data Analysis, Second Edition. John Wiley & Sons, Inc. ISBN 978-0-471-22618-5

Prerequisites:  STAT 203 or STAT 335, or instructor consent. STAT 308 is recommended.

Course description:  Normally distributed response variables lead statistical practitioners to use linear modeling 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 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. 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. Exams, projects and take-home assignments will be used to determine the final grade in the course. The R statistical software will be used throughout the course, although no previous programming experience is necessary.

Instructor(s):  Dr. Gregory J. Matthews

Required text(s):  Rosner, Bernard. Fundamentals of Biostatistics. 7th ed. Boston: Cengage Learning, 2011. Print.

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):  Swarnali Banerjee

Required text(s):  Rosner, Bernard. Fundamentals of Biostatistics. 7th ed. Boston: Cengage Learning, 2011. Print.

Prerequisites:  MATH 132 or 162; BIOL 102, 112

Course description:  An introduction to statistical methods used in designing biological experiments and in data analyses. Topics include probability and sampling distribution, designed biological experiments and analysis of variance, regression and correlation, stochastic processes, and frequency distributions. Computer laboratory assignments with biological data.

Instructor(s):  Bret A Longman

Required text(s):  Rosner, Bernard. Fundamentals of Biostatistics. 7th ed. Boston: Cengage Learning, 2011. Print.

Prerequisites:  MATH 132/162 and BIOL 102

Course description:  This course provides an introduction to statistical methods used in designing biological experiments and in data analysis. Topics include descriptive statistics, probability, discrete probability distributions, the normal distribution, sampling distributions, confidence intervals, hypothesis testing for one and two samples involving means and proportions, chi-square tests, one way ANOVA, and simple linear regression. 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. Exams, take-home assignments, and one paper will be used to determine the final grade in the course.

Instructor(s):  Bret A Longman

Required text(s):  Vittinghoff, Glidden, Shiboski & McCulloch (2012), Regression Methods in Biostatistics: Linear, Logistic, Survival, and Repeated Measures Models, 2nd Edition, Springer, ISBN: 9781461413523.

Prerequisites:  STAT 203 or STAT 335 or equivalent.

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, repeated measures designs and analysis (longitudinal data 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 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):  Dr. Timothy E. O'Brien

Required text(s):  Lee, J.K., ed., Statistical Bioinformatics, Wiley, ISBN: 978-0471-692720.

Prerequisites:  STAT-203 or STAT-335 or equivalent.

Course description:  Predicting which conditions and diseases will develop in animals and human subjects based on its gene and protein characteristics must involve drawing conclusions from well-designed studies. As such, meaningful decisions hinge upon the correct use of statistical hypothesis testing, prediction and estimation. The most likely conclusions are also drawn from probabilistic and stochastic arguments, and a wisely chosen experimental (study) design removes biases and allows researchers to generalize from small studies to the larger population. 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. The focus in this course will be on the application of these techniques and on meaningful interpretation of results. As such, this course will be project-focused and will entail student participation. Grading will be based on student projects and presentations, homework and exam(s). Although no prior knowledge is assumed, students will become familiar with programming in the R (or R-Studio) language. This course neither assumes nor requires any specialized background in Biology or Bioinformatics – it focusing on the quantitative aspects of work in these fields.

Instructor(s):  Adriano Zanin Zambom

Required text(s):  - Hollander, M; Wolfe, D.A., and Chicken E. “Nonparametric Statistical Methods”, 3rd Edition. - Gibbons, J. D. and Chakraborti, S. “Nonparametric Statistical Inference”, Fourth Edition, Marcel Dekker, New York. - Eubank, R. L. “Nonparametric Regression and Spline Smoothing”, Second Edition, Marcel Dekker, New York. - Wasserman, L. “All of Nonparametric Statistics”, Springer.

Prerequisites:  Exposure to basic statistics concepts and basic calculus.

Course description:  This course will cover the basic principles of nonparametric methods in statistics including: one, two and K sample location methods; tests of randomness; tests of goodness of fit; nonlinear correlation; histogram; density estimation; nonparametric regression.

Instructor(s):  Gregory J. Matthews

Required text(s):  "ggplot2 book." Hadley Wickham. http://ggplot2.org/book/

Recommended text(s):  "Handbook of Missing Data Methodology." Geert Molenberghs, Garrett Fitzmaurice, Michael G. Kenward, Anastasios Tsiatis, Geert Verbeke. ISBN 9781439854617. "The Truthful Art." Alberto Cairo. http://www.thefunctionalart.com/p/the-truthful-art-book.html "The Functional Art." Alberto Cairo. http://www.thefunctionalart.com/p/about-book.html

Prerequisites:  STAT 308/408.

Course description:  This course will explore data visualization techniques and missing data analysis using the R program language.

Instructor(s):  Adriano Zanin Zambom

Required text(s):  TBA

Prerequisites:  Senior standing; completion of STAT-304.

Course description:  This one-credit capstone 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 statistics. As such, students will be required to read course texts, actively participate in discussions, and give several presentations to their peers (on material beyond the standard curriculum). 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):  Swarnali Banerjee

Required text(s):  Mathematical Statistics with Applications by Dennis D. Wackerly, William Mendenhall III and Richard L. Scheaffer, 7th edition

Recommended text(s):  Statistical Inference by George Casella and Roger L. Berger, 2nd edition

Prerequisites:  MATH/STAT 404

Course description:  A continuation of MATH/STAT 404. Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests).

Instructor(s):  Dr. Earvin Balderama

Required text(s):  Agresti, A. (2007). An Introduction to Categorical Data Analysis, Second Edition. John Wiley & Sons, Inc. ISBN 978-0-471-22618-5

Prerequisites:  STAT 203 or STAT 335, or instructor consent. STAT 308 is recommended.

Course description:  Normally distributed response variables lead statistical practitioners to use linear modeling 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 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. 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. Exams, projects and take-home assignments will be used to determine the final grade in the course. The R statistical software will be used throughout the course, although no previous programming experience is necessary.

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

Required text(s):  Lee, J.K., ed., Statistical Bioinformatics, Wiley, ISBN: 978-0471-692720.

Prerequisites:  STAT-203 or STAT-335 or equivalent.

Course description:  Predicting which conditions and diseases will develop in animals and human subjects based on its gene and protein characteristics must involve drawing conclusions from well-designed studies. As such, meaningful decisions hinge upon the correct use of statistical hypothesis testing, prediction and estimation. The most likely conclusions are also drawn from probabilistic and stochastic arguments, and a wisely chosen experimental (study) design removes biases and allows researchers to generalize from small studies to the larger population. 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. The focus in this course will be on the application of these techniques and on meaningful interpretation of results. As such, this course will be project-focused and will entail student participation. Grading will be based on student projects and presentations, homework and exam(s). Although no prior knowledge is assumed, students will become familiar with programming in the R (or R-Studio) language. This course neither assumes nor requires any specialized background in Biology or Bioinformatics – it focusing on the quantitative aspects of work in these fields.

Instructor(s):  Adriano Zanin Zambom

Required text(s):  - Hollander, M; Wolfe, D.A., and Chicken E. “Nonparametric Statistical Methods”, 3rd Edition. - Gibbons, J. D. and Chakraborti, S. “Nonparametric Statistical Inference”, Fourth Edition, Marcel Dekker, New York. - Eubank, R. L. “Nonparametric Regression and Spline Smoothing”, Second Edition, Marcel Dekker, New York. - Wasserman, L. “All of Nonparametric Statistics”, Springer.

Prerequisites:  Exposure to basic statistics concepts and basic calculus.

Course description:  This course will cover the basic principles of nonparametric methods in statistics including: one, two and K sample location methods; tests of randomness; tests of goodness of fit; nonlinear correlation; histogram; density estimation; nonparametric regression.

Instructor(s):  Gregory J. Matthews

Required text(s):  "ggplot2 book." Hadley Wickham. http://ggplot2.org/book/

Recommended text(s):  "Handbook of Missing Data Methodology." Geert Molenberghs, Garrett Fitzmaurice, Michael G. Kenward, Anastasios Tsiatis, Geert Verbeke. ISBN 9781439854617. "The Truthful Art." Alberto Cairo. http://www.thefunctionalart.com/p/the-truthful-art-book.html "The Functional Art." Alberto Cairo. http://www.thefunctionalart.com/p/about-book.html

Prerequisites:  STAT 308/408.

Course description:  This course will explore data visualization techniques and missing data analysis using the R program language.