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):  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 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):  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):  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. We will also spend significant time exploring the many wonderful applications of linear algebra to such fields as science, economics, business, engineering, computer science and the life sciences.

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. 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 or MATH 263 concurrently

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):  Robert Jensen

Required text(s):  Fundamentals of Differential Equations, by Nagle, Saff, and Snider. 5th edition, or a newer one. 5th edition is ISBN-13: 978-0201338683, ISBN-10: 0201338688.

Prerequisites:  MATH 263 or MATH 263 concurrently

Course description:  A conventional course in ordinary differential equations. Beginning with the definition of a first order differential equation and various techniques for solving them, the course then focuses on linear higher order ordinary differential equations, particularly linear second order differential equations. Then we'll look at systems of ordinary differential equations, and finish the course by introducing some special techniques for solving such as the Laplace transform and power series.

Instructor(s):  Dr. Peter Tingley

Required text(s):  Edwards, Penney and Calvis. Differential Equations and Linear Algebra, 4th edition. Published by Pearson.

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):  Dr. Emily Peters

Required text(s):  Algebra: Abstract and Concrete, by Fred Goodman. Abstract Algebra: Theory and Applications, by Thomas Judson

Textbook notes:  Both textbooks are available online for free: Judson at http://abstract.ups.edu/download.html Goodman at http://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/download.htm

Prerequisites:  MATH 201 and MATH 212

Course description:  Abstract algebra is, at heart, the study of symmetries. What do we mean when we say that a square is more symmetric than a (non-square) rectangle, or that a circle is more symmetric than a square? Which is more symmetric, a cube or an octahedron? The mathematical idea of a 'group' was created to make the idea of symmetry precise, and has taken on a vast life of its own, thanks to its broad applicability. Other examples of groups include: the numbers 0,...,n-1 in arithmetic modulo n; permutations of a group of identical objects; symmetries of the plane; symmetries of the plane that preserve distance (also known as isometries); symmetries of the plane that preserve area; and so forth. This class will be example-driven but also rigorous and abstract. We will study equivalence relations, subgroups, homomorphisms, quotients, products, linear groups, permutation groups, and selected advanced topics.

Instructor(s):  Anne Hupert

Required text(s):  Introduction to Abstract Algebra (fourth edition) by W. Keith Nicholson, published by Wiley Interscience, ISBN-13: 978-1118135358 ISBN-10: 1118135350

Prerequisites:  Math 313

Course description:  The course will cover rings, polynomial rings, integral domains, fields, and, if time permits, Galois Theory. Grades will be based on graded homework, three in-class exams, and a final.

Instructor(s):  Dr. A. Lauve

Required text(s):  Miklós Bóna, A Walk Through Combinatorics: an Introduction to Enumeration and Graph Theory, 3rd Edition (Paperback), World Scientific (2011). ISBN-13: 978-9814460002.

Textbook notes:  There is a newer edition, but buy this cheaper one if you can.

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. 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):  Dr. Stephen Doty

Required text(s):  Maxwell Rosenlicht, Introduction to Analysis, Dover 1986, ISBN-13: 978-0486650388; ISBN-10: 0486650383.

Recommended text(s):  Arthur Mattuck, Introduction to Real Analysis, CreateSpace Independent Publishing Platform (1746).
Michael Spivak, Calculus on Manifolds, CRC Press. ISBN-13: 978-0805390216; ISBN-10: 9780805390216.

Prerequisites:  MATH 351

Course description:  Continuation of Math 351. We will study various topics such as: Compactness in R^m, differentiability and integrability on R^1 and R^m, Taylor's theorem, the change of variable theorem, the inverse and implicit function theorems, and integration of functions. There will be regular assigned homework, at least one midterm exam, and a final exam.

Instructor(s):  Rafal Goebel

Required text(s):  Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering; Steven Strogatz; 2014, second edition, ISBN-13: 978-0813349107, ISBN-10: 0813349109.

Additional notes:  Graduate students taking the class as Math 488 will face more challenging homework problems and may have an opportunity for an in-class presentation.

Prerequisites:  (MATH 212: Linear Algebra and MATH 264: Ordinary Differential Equations) or MATH 266: Linear Algebra and Differential Equations

Course description:  Dynamical systems, which are systems that evolve over time, are everywhere. Continuous-time dynamical systems, like an electrical circuit or a mechanical system consisting of weights and springs (not unlike the shocks in your car), can be described and then analyzed using differential equations. Discrete-time dynamical systems, like the balance of your savings account which (hopefully) increases every month or the population of species measured once every year, can be described using difference equations. Frequently, the differential and difference equations describing these and other systems are nonlinear. Solutions to these equations can tell you what the dynamical system will do in the future, so you can forecast the weather or realize that a species is doomed to extinction, but for nonlinear differential equations, solutions are notoriously hard to find. However, with proper analytical tools, one can predict the behavior of the system anyway. This is what the course is about.

Instructor(s):  Dr. A. Lauve

Required text(s):  Miklós Bóna, A Walk Through Combinatorics: an Introduction to Enumeration and Graph Theory, 3rd Edition (Paperback), World Scientific (2011). ISBN-13: 978-9814460002.

Textbook notes:  There is a newer edition, but buy this cheaper one if you can.

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. Stephen Doty

Required text(s):  Maxwell Rosenlicht, Introduction to Analysis, Dover 1986, ISBN-13: 978-0486650388; ISBN-10: 0486650383.

Recommended text(s):  Arthur Mattuck, Introduction to Real Analysis, CreateSpace Independent Publishing Platform (1746).
Michael Spivak, Calculus on Manifolds, CRC Press. ISBN-13: 978-0805390216; ISBN-10: 9780805390216.

Prerequisites:  MATH 351

Course description:  Continuation of Math 351. We will study various topics such as: Compactness in R^m, differentiability and integrability on R^1 and R^m, Taylor's theorem, the change of variable theorem, the inverse and implicit function theorems, and integration of functions. There will be regular assigned homework, at least one midterm exam, and a final exam.

Instructor(s):  Rafal Goebel

Required text(s):  Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering; Steven Strogatz; 2014, second edition, ISBN-13: 978-0813349107, ISBN-10: 0813349109.

Additional notes:  Graduate students taking the class as Math 488 will face more challenging homework problems and may have an opportunity for an in-class presentation.

Prerequisites:  (MATH 212: Linear Algebra and MATH 264: Ordinary Differential Equations) or MATH 266: Linear Algebra and Differential Equations

Course description:  Dynamical systems, which are systems that evolve over time, are everywhere. Continuous-time dynamical systems, like an electrical circuit or a mechanical system consisting of weights and springs (not unlike the shocks in your car), can be described and then analyzed using differential equations. Discrete-time dynamical systems, like the balance of your savings account which (hopefully) increases every month or the population of species measured once every year, can be described using difference equations. Frequently, the differential and difference equations describing these and other systems are nonlinear. Solutions to these equations can tell you what the dynamical system will do in the future, so you can forecast the weather or realize that a species is doomed to extinction, but for nonlinear differential equations, solutions are notoriously hard to find. However, with proper analytical tools, one can predict the behavior of the system anyway. This is what the course is about.

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

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

Recommended text(s):  Essentials of Probability and Statistics for Engineers and Scientists by Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying Ye

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

Course description:  An introduction to statistical methodology and theory using the techniques of one-variable calculus. Topics include: experimental design, descriptive statistics, probability theory, sampling theory, inferential statistics, estimation theory, testing hypotheses, correlation theory, and regression.

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

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

Textbook notes:  Note: the listed textbook (Agresti's Intro book) will be updated to the 3rd Edition if it publishes before January 2019.

Prerequisites:  STAT-203 or STAT-335 or equivalent; a course in regression is recommended (or at least exposure to concepts of regression).

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. Xiaoli Kong, Dr. Shuwen Lou

Required text(s):  Rosner, Bernard. Fundamentals of Biostatistics. 8th edition. Boston: Cengage Learning, 2015.

Additional notes:  We will use R for some assignments.

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. Additionally, the course will include programming in R and analyzing R output. (Note: Students may not receive credit for both STAT 203 & 335.)

Instructor(s):  Mr. Bret A. Longman

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):  Swarnali Banerjee

Required text(s):  Computational Genome Analysis: An Introduction (Statistics for Biology & Health S) by Richard C. Deonier, Simon Tavaré and Michael S. Waterman.

Recommended text(s):  1.Statistical Methods in Bioinformatics: An Introduction (Statistics for Biology and Health) 2nd Edition by Warren J. Ewens and Gregory R. Grant 2. Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids 1st Edition by Richard Durbin, Sean R. Eddy, Anders Krogh and Graeme Mitchison.

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. Xiaoli Kong

Required text(s):  Applied Multivariate Statistical Analysis (6th ed.) R. A. Johnson & D. W. Wichern, Prentice Hall, 2001

Recommended text(s):  Methods of Multivariate Analysis (3rd ed.), A. C. Rencher & W. F. Christensen Wiley, 2012 Modern Multivariate Statistical Techniques, A. J. Izenman, Springer, 2008 An Introduction to Multivariate Statistical Analysis (3rd ed.), T. W. Anderson, Wiley, 2003

Prerequisites:  MATH/STAT 305/405 or permission of instructor.

Course description:  Study of multivariate normal distribution, estimation and tests of hypotheses for multivariate populations, principal components, factor analysis, discriminant analysis. The course will include programing experience with the statistical software R and packages for multivariate data analysis.

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

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

Textbook notes:  Note: the listed textbook (Agresti's Intro book) will be updated to the 3rd Edition if it publishes before January 2019.

Prerequisites:  STAT-203 or STAT-335 or equivalent; a course in regression is recommended (or at least exposure to concepts of regression).

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):  Swarnali Banerjee

Required text(s):  Computational Genome Analysis: An Introduction (Statistics for Biology & Health S) by Richard C. Deonier, Simon Tavaré and Michael S. Waterman.

Recommended text(s):  1.Statistical Methods in Bioinformatics: An Introduction (Statistics for Biology and Health) 2nd Edition by Warren J. Ewens and Gregory R. Grant 2. Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids 1st Edition by Richard Durbin, Sean R. Eddy, Anders Krogh and Graeme Mitchison.

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. Xiaoli Kong

Required text(s):  Applied Multivariate Statistical Analysis (6th ed.) R. A. Johnson & D. W. Wichern, Prentice Hall, 2001

Recommended text(s):  Methods of Multivariate Analysis (3rd ed.), A. C. Rencher & W. F. Christensen Wiley, 2012 Modern Multivariate Statistical Techniques, A. J. Izenman, Springer, 2008 An Introduction to Multivariate Statistical Analysis (3rd ed.), T. W. Anderson, Wiley, 2003

Prerequisites:  MATH/STAT 305/405 or permission of instructor.

Course description:  Study of multivariate normal distribution, estimation and tests of hypotheses for multivariate populations, principal components, factor analysis, discriminant analysis. The course will include programing experience with the statistical software R and packages for multivariate data analysis.