MATH 100. Intermediate Algebra

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

  

MATH 108. Real World Modeling

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. 10th ed. ISBN-13: 978-1464124730. New York: W. H. Freeman, 2015. 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

  

MATH 117. Precalculus I

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:  The study of functions, their graphs, and their basic properties. Emphasis is placed on polynomial functions, including linear and quadratic functions. Computing real and complex roots of polynomials is explored. Additional topics include: the study of rational functions, absolute value functions, and inverse functions; and solutions of systems of equations.

Syllabus:  Common

  

MATH 118. Precalculus II

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:  A continuation of MATH 117 focusing on exponential, logarithmic, trigonometric, and inverse trigonometric functions, their graphs, and their properties. Techniques for solving equalities involving these functions are examined. Trigonometric identities, sum and difference formulas, double and half-angle formulas, the Laws of Sines and Cosines, and polar coordinates are also considered.

Syllabus:  Common

  

MATH 123. Freshman/Sophomore Seminar

Instructor(s):  Dr. Brian Seguin

Required text(s):  None

Prerequisites:  None

Course description:  This one-credit seminar is designed for freshman and sophomore students who are interested in mathematics, whether or not they intend to major or minor in the subject. It will include presentations facilitated by a number of faculty members. These will cover a wide variety of ideas and applications of mathematics, largely chosen from outside the traditional precalculus-calculus sequence. By the end of the semester you will realize that mathematics isn't just about calculations and finding x, but rather concepts, patterns, and investigating interesting questions. There are no exams, and grades will be based on participation and occasional written homework.

  

MATH 123. Special Topics Seminar

Instructor(s):  Mr. Marius Radulescu

Required text(s):  Dwyer and Gruenwald. Calculus: Resequenced for Students in Stem (WileyPlus eBook). preliminary edition.

Print text (optional): ISBN-13: 978-1119321590.

Prerequisites:  None

Course description:  A freshman/sophomore seminar designed as a corequisite course for MATH 162 and MATH 263. The main goal of the course is to provide a rigorous transition from MATH 131 to MATH 162 and from MATH 132 to Math 263. The focus is on new topics from MATH 161 (Calculus I) and MATH 162 (Calculus II) that are required in MATH 162 and MATH 263, respectively, but are not covered in MATH 131/132. The format of the seminar focuses on problem solving on assigned topics. Students’ academic performance will be assessed based on homework and five quizzes. There is no final exam for this class.

  

MATH 131. Applied Calculus I

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

  

MATH 132. Applied Calculus II

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

  

MATH 161. Calculus I

Instructor(s):  Staff

Required text(s):  Dwyer and Gruenwald. Calculus: Resequenced for Students in Stem (WileyPlus eBook). preliminary edition.

Print text (optional): ISBN-13: 978-1119321590.

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

  

MATH 162. Calculus II

Instructor(s):  Staff

Required text(s):  Dwyer and Gruenwald. Calculus: Resequenced for Students in Stem (WileyPlus eBook). preliminary edition.

Print text (optional): ISBN-13: 978-1119321590.

Prerequisites:  MATH 161

Course description:  This course is a continuation of Calculus I and includes the calculus of various classes of functions, techniques of integration, applications of integral calculus, three-dimensional geometry, and differentiation and integration in two variables.

Syllabus:  Common

  

MATH 162. Calculus II (A)

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 161A

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

  

MATH 201. Introduction to Discrete Mathematics & Number Theory (Section 01W)

Instructor(s):  Dr. Carmen Rovi

Required text(s):  Edward R. Scheinerman. Mathematics: a discrete introduction (3rd edition) ISBN-13: 978-0840049421 ISBN-10: 0840049420

Prerequisites:  MATH 161

Course description:  This course covers topics from discrete mathematics and number theory, areas of mathematics not seen in calculus courses and abundant in applications. The course provides students with the concepts and techniques of mathematical proof needed in 300-level courses in mathematics and will introduce them to the typesetting program LaTex. In particular, students will obtain an understanding of the basic concepts and techniques involved in constructing rigorous proofs of mathematical statements. Class meetings will be very interactive, and students will be encouraged to discuss proofs in class and present their own work. Assessment will be based on homework, two exams, and class participation. In addition, students will work in teams on at least two longer projects and will present their projects to the class.

  

MATH 201. Introduction to Discrete Mathematics & Number Theory (Section 02W)

Instructor(s):  Dr. Alan Saleski

Required text(s):  Hammack, The Book of Proof, 3rd edition Also available for free on Hammack's website

Prerequisites:  MATH 161

Course description:  An introduction to writing clear and logical proofs. Topics to include naive set theory, combinatorics, first-order predicate logic, cardinality, relations, and functions.

Syllabus:  Biweekly quizzes, written homework, Midterm, and Final exam. As this course is writing-intensive, two essays will be assigned.

  

MATH 212. Linear Algebra

Instructor(s):  Staff

Required text(s):  TBD

Prerequisites:  MATH 132 or MATH 162

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

  

MATH 263. Multivariable Calculus

Instructor(s):  Staff

Required text(s):  Dwyer and Gruenwald. Calculus: Resequenced for Students in Stem (WileyPlus eBook). preliminary edition.

Print text (optional): ISBN-13: 978-1119321590.

Prerequisites:  MATH 162

Course description:  This course covers the differential and integral calculus of multivariable and vector valued functions, and sequences and infinite series, culminating with Green's Theorem, the Divergence Theorem, and Stokes' Theorem; software packages such as MAPLE may be used.

Syllabus:  Common

  

MATH 263. Multivariate Calculus (A)

Instructor(s):  Dr. Brian Seguin

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 162A

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. Software packages such as MAPLE may be used. This course follows a traditional approach to calculus sequencing and is intended only for students with either AP credit or transfer credit equivalent to MATH 161A and MATH 162A.

  

MATH 264. Ordinary Differential Equations

Instructor(s):  Staff

Required text(s):  TBD

Prerequisites:  MATH 263 or MATH 263 corequisite

Course description:  Techniques for solving linear and non-linear first and second-order differential equations, the theory of linear second-order equations with constant coefficients, power series solutions of second-order equation, and topics in systems of linear first-order differential equations. Software such as MAPLE may be utilized.

  

MATH 277. Problem Solving Seminar

Instructor(s):  Dr Stephen London

Required text(s):  None

Prerequisites:  None

Course description:  In a seminar setting, students discuss and present proofs (or computer examples) as solutions to challenging and interesting problems including those from the Putnam and Virginia Tech mathematics competitions. Techniques are drawn from numerous areas of mathematics such as calculus of one and several variables, combinatorics, number theory, geometry, linear algebra, and abstract algebra.

  

MATH 301. History of Mathematics

Instructor(s):  Staff

Required text(s):  TBD

Prerequisites:  MATH 132 or 162. MATH 201 is recommended.

Course description:  This course explores selected topics in the history of mathematics ranging from Babylonian and Egyptian mathematics to Pythagoras and Euclid to the Hindu-Arabic numeration system to Newton and Leibniz to geometries other that Euclid's to the mathematical art of Escher.

  

MATH 304. [ STAT 304 ] Introduction to Probability

Instructor(s):  Dr. Matthew Bourque

Required text(s):  A first course in probablity. Sheldon Ross, Pearson Publishing, 10th edition, ISBN 978-0-13-475311-9.

Prerequisites:  MATH 263

Course description:  Probability is the mathematical study of chance. If you are interested in using math to describe anything that is not deterministic, you will need the tools of probability theory. Therefore, probability theory is foundational for many applied fields, including statistics and finance. This course will cover a discussion of probability, mean, and variance, independence, conditional probability, and random variables. We will consider both discrete probability spaces and probability spaces with continuously differentiable density functions. The course will include study of important probability distributions such as the binomial, exponential, Poisson, and normal distributions, the law of large numbers, and the central limit theorem. If time permits we will also consider Markov processes. Assessment in the course will consist of approximately weekly homework assignments, a few quizzes, two midterms, and a cumulative final exam.

  

MATH 313. [ MATH 413 ] Abstract Algebra

Instructor(s):  Dr. Carmen Rovi

Required text(s):  Goodman, F.. Algebra: abstract and concrete, stressing symmetry. (2003). Judson, Thomas W.. Abstract Algebra: Theory and Applications. (2009).

Recommended text(s):  Gallian, J. Contemporary Abstract Algebra

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

Prerequisites:  MATH 201 and MATH 212

Course description:  One of the greatest minds working in geometry and algebra in the last decades, Sir Michael Atiyah, once said about algebra: "Algebra is the offer made by the devil to the mathematician. The devil says: I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvelous machine." This is an interesting way to express that abstract algebra, despite all its abstractness, is deeply motivated by the understanding of geometric problems. Some of the original motivations for creating the language of abstract algebra was to tackle questions like understanding symmetries of spaces, or trying to create formulas to find the roots of polynomials. In this course, we will focus on topics in group theory. 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. 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. Nowadays, Abstract Algebra has many applications, even outside of mathematics. Fields like physics, computer science, or cryptography use algebraic structures. This class will be example-driven but also rigorous and abstract. We will study equivalence relations, groups, subgroups, homomorphisms, quotients, products, linear groups, permutation groups, and selected advanced topics.

Syllabus:  There will be two exams, homework, class participation, a small number of quizzes, and a final exam. The students will also work in small teams on group projects and give presentations to the class.

  

MATH 315. [ MATH 415 ] Advanced Topics in Linear Algebra

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Garcia, Stephan Roman, and Horn, Roger A. A Second Course in Linear Algebra (Cambridge Mathematical Textbooks). 1st ed., Cambridge University Press. 2017. ISBN-13 ‏ : ‎ 978-1107103818

Recommended text(s): 

Prerequisites:  MATH 212; MATH 313 (or another proof-based course beyond MATH 201).

Course description:  Linear algebra is a fundamental tool in many fields, including mathematics and statistics, computer science, economics, and the physical and biological sciences. It's expansive and profound theory cannot possibly fit into one course. Enter this Second Course in Linear Algebra, which transitions from basic theory to advanced topics and applications. Topics include: iterative methods for solving matrix equations and finding eigenvectors; important matrix factorizations; singular value decomposition; Jordan canonical form; the spectral theorem; normal matrices; Hermitian matrices (of interest to physics students); and positive definite matrices (of interest to statistics students).

Syllabus:  Assessments: weekly homework (with some programming exercises); fortnightly quizzes; two in-term exams; and a final exam. Graduate students taking MATH 415 will be given assessments commensurate with their standing; and will be responsible for presenting a lecture on an optional/applied topic of their choosing.

  

MATH 351. [ MATH 451 ] Introduction to Real Analysis I

Instructor(s):  Dr. Tuyen Tran

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 rigorous treatment of properties and applications of real numbers and real-valued functions of a real variable. Topics include: metric spaces, sequences and their convergence, continuity and differentiability of functions. After the course, students will be expected to formulate mathematical arguments and proofs. From time to time extra problems on homework/tests will be given for the students taking this class as MATH 451. These questions will count as extra credit for the students taking the class as MATH 351.

  

MATH 353. [ MATH 488 ] Introduction to Complex Analysis

Instructor(s):  Dr. John Del Greco

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

Prerequisites:  MATH 264

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

  

MATH 360. [ MATH 460 ] Game Theory

Instructor(s):  Dr. Peter Tingley

Required text(s):  .

Recommended text(s):  Game Theory: An Introduction, Second Edition, by E. N. Barron, Wiley, 2013, ISBN 978-1-118-21693-4. The text is very useful and a good reference, but I will also be providing a full set of lecture notes, and some people do not find the text is necessary. I highly recommend getting access to it in some form though, since it contains many more examples and more detailed exposition than my notes.

Prerequisites:  MATH 162. Some 200 level math or stats is recommended.

Course description:  This is a mathematically rigorous introduction to the theory of games. Game theory is a branch of applied mathematics founded by John von Neumann with applications to economics, business, political science, optimization, differential equations, optimal transport, etc. It is the theory of finding optimal strategies in conflict or cooperative situations. It brings together most of undergraduate mathematics subjects to produce a subject which is important and fun to study.

  

MATH 366. [ MATH 488 ] Applied Dynamical Systems

Instructor(s):  Dr. 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.

Recommended text(s):  Student Solutions Manual for Nonlinear Dynamics and Chaos; Mitchal Dichter; ISBN-13: 978-0813350547, ISBN-10: 0813350549. (Note: this has solutions to about half of the problems in the book.)

Additional notes:  Graduate students taking the class as Math 488 will face more challenging problems than Math 366 students.

Prerequisites:  (MATH 212: Linear Algebra and MATH 264: Ordinary Differential Equations) or MATH 266: Linear Algebra and Differential Equations. Proficiency in single-variable calculus is essential.

Course description:  Relatively simple systems of nonlinear differential equations, like those modeling a virus outbreak or a zombie infestation, may be very hard or just impossible to "solve by hand". Still, there are analytical methods and tools that let us predict the short-term and long-term behavior of solutions, and so tell if the virus will turn into a pandemic or if a small size of the zombie population will be stable. Much of the course is about this. (The methods and the tools, not the zombies...) Also, relatively simple dynamics may generate sequences with very exotic and unexpected behaviors, i.e., "chaos". Some of the course is about that. The course will be light on theorems and proofs, and will stress problem-solving. Proficiency in single-variable calculus --- differentiation, graphing, integration, etc. --- will be very helpful. (If you need to refresh your calculus skills, say for a GRE exam, this course will make you do that!)

  

MATH 413. [ MATH 313 ] Abstract Algebra

Instructor(s):  Dr. Carmen Rovi

Required text(s):  Goodman, F.. Algebra: abstract and concrete, stressing symmetry. (2003). Judson, Thomas W.. Abstract Algebra: Theory and Applications. (2009).

Recommended text(s):  Gallian, J. Contemporary Abstract Algebra

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

Prerequisites:  MATH 201 and MATH 212

Course description:  One of the greatest minds working in geometry and algebra in the last decades, Sir Michael Atiyah, once said about algebra: "Algebra is the offer made by the devil to the mathematician. The devil says: I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvelous machine." This is an interesting way to express that abstract algebra, despite all its abstractness, is deeply motivated by the understanding of geometric problems. Some of the original motivations for creating the language of abstract algebra was to tackle questions like understanding symmetries of spaces, or trying to create formulas to find the roots of polynomials. In this course, we will focus on topics in group theory. 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. 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. Nowadays, Abstract Algebra has many applications, even outside of mathematics. Fields like physics, computer science, or cryptography use algebraic structures. This class will be example-driven but also rigorous and abstract. We will study equivalence relations, groups, subgroups, homomorphisms, quotients, products, linear groups, permutation groups, and selected advanced topics.

Syllabus:  There will be two exams, homework, class participation, a small number of quizzes, and a final exam. The students will also work in small teams on group projects and give presentations to the class.

  

MATH 415. [ MATH 315 ] Advanced Topics in Linear Algebra

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Garcia, Stephan Roman, and Horn, Roger A. A Second Course in Linear Algebra (Cambridge Mathematical Textbooks). 1st ed., Cambridge University Press. 2017. ISBN-13 ‏ : ‎ 978-1107103818

Recommended text(s): 

Prerequisites:  MATH 212; MATH 313 (or another proof-based course beyond MATH 201).

Course description:  Linear algebra is a fundamental tool in many fields, including mathematics and statistics, computer science, economics, and the physical and biological sciences. It's expansive and profound theory cannot possibly fit into one course. Enter this Second Course in Linear Algebra, which transitions from basic theory to advanced topics and applications. Topics include: iterative methods for solving matrix equations and finding eigenvectors; important matrix factorizations; singular value decomposition; Jordan canonical form; the spectral theorem; normal matrices; Hermitian matrices (of interest to physics students); and positive definite matrices (of interest to statistics students).

Syllabus:  Assessments: weekly homework (with some programming exercises); fortnightly quizzes; two in-term exams; and a final exam. Graduate students taking MATH 415 will be given assessments commensurate with their standing; and will be responsible for presenting a lecture on an optional/applied topic of their choosing.

  

MATH 451. [ MATH 351 ] Introduction to Real Analysis I

Instructor(s):  Dr. Tuyen Tran

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 rigorous treatment of properties and applications of real numbers and real-valued functions of a real variable. Topics include: metric spaces, sequences and their convergence, continuity and differentiability of functions. After the course, students will be expected to formulate mathematical arguments and proofs. From time to time extra problems on homework/tests will be given for the students taking this class as MATH 451. These questions will count as extra credit for the students taking the class as MATH 351.

  

MATH 460. [ MATH 360 ] Game Theory

Instructor(s):  Dr. Peter Tingley

Required text(s):  .

Recommended text(s):  Game Theory: An Introduction, Second Edition, by E. N. Barron, Wiley, 2013, ISBN 978-1-118-21693-4. The text is very useful and a good reference, but I will also be providing a full set of lecture notes, and some people do not find the text is necessary. I highly recommend getting access to it in some form though, since it contains many more examples and more detailed exposition than my notes.

Prerequisites:  MATH 162. Some 200 level math or stats is recommended.

Course description:  This is a mathematically rigorous introduction to the theory of games. Game theory is a branch of applied mathematics founded by John von Neumann with applications to economics, business, political science, optimization, differential equations, optimal transport, etc. It is the theory of finding optimal strategies in conflict or cooperative situations. It brings together most of undergraduate mathematics subjects to produce a subject which is important and fun to study.

  

MATH 488. [ MATH 366 ] Applied Dynamical Systems

Instructor(s):  Dr. 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.

Recommended text(s):  Student Solutions Manual for Nonlinear Dynamics and Chaos; Mitchal Dichter; ISBN-13: 978-0813350547, ISBN-10: 0813350549. (Note: this has solutions to about half of the problems in the book.)

Additional notes:  Graduate students taking the class as Math 488 will face more challenging problems than Math 366 students.

Prerequisites:  (MATH 212: Linear Algebra and MATH 264: Ordinary Differential Equations) or MATH 266: Linear Algebra and Differential Equations. Proficiency in single-variable calculus is essential.

Course description:  Relatively simple systems of nonlinear differential equations, like those modeling a virus outbreak or a zombie infestation, may be very hard or just impossible to "solve by hand". Still, there are analytical methods and tools that let us predict the short-term and long-term behavior of solutions, and so tell if the virus will turn into a pandemic or if a small size of the zombie population will be stable. Much of the course is about this. (The methods and the tools, not the zombies...) Also, relatively simple dynamics may generate sequences with very exotic and unexpected behaviors, i.e., "chaos". Some of the course is about that. The course will be light on theorems and proofs, and will stress problem-solving. Proficiency in single-variable calculus --- differentiation, graphing, integration, etc. --- will be very helpful. (If you need to refresh your calculus skills, say for a GRE exam, this course will make you do that!)

  

MATH 488. [ MATH 353 ] Introduction to Complex Analysis

Instructor(s):  Dr. John Del Greco

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

Prerequisites:  MATH 264

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

  

STAT 103. Fundamentals of Statistics

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.

  

STAT 203. Introduction to Probability and Statistics

Instructor(s):  Dr. Nan Miles Xi

Required text(s):  Probability and Statistics for Engineering and the Sciences 9th Edtion by Jay L. Devore.

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

Course description:  An introduction to statistical methodology and theory using the techniques of one-variable calculus. Topics include: Descriptive statistics, probability, random variables, probability distributions, random sample, point estimation, confidence interval, tests of hypotheses.

  

STAT 303. SAS Programming and Applied Statistics

Instructor(s):  Dr. Michael Perry

Required text(s):  None

Recommended text(s):  Cody, Ron P. and Jeffrey K. Smith, Applied Statistics and the SAS Programming Language, 5th ed., Pearson, 2006 ISBN-13: 978-0131465329

Prerequisites:  STAT 103 or STAT 203 or STAT 335

Course description:  This course is an introduction to writing and executing SAS programs under the Windows environment in the context of applied statistics problems. SAS procedures are used to read and analyze various types of data sets as they apply to t-tests, simple and multiple regressions, ANOVA, categorical analysis, and repeated measures.

Syllabus:  Grade calculation Test 1: 20% Test 2: 30% Homework: 30% Project/Presentation 20%

  

STAT 304. [ MATH 304 ] Introduction to Probability

Instructor(s):  Dr. Matthew Bourque

Required text(s):  A first course in probablity. Sheldon Ross, Pearson Publishing, 10th edition, ISBN 978-0-13-475311-9.

Prerequisites:  MATH 263

Course description:  Probability is the mathematical study of chance. If you are interested in using math to describe anything that is not deterministic, you will need the tools of probability theory. Therefore, probability theory is foundational for many applied fields, including statistics and finance. This course will cover a discussion of probability, mean, and variance, independence, conditional probability, and random variables. We will consider both discrete probability spaces and probability spaces with continuously differentiable density functions. The course will include study of important probability distributions such as the binomial, exponential, Poisson, and normal distributions, the law of large numbers, and the central limit theorem. If time permits we will also consider Markov processes. Assessment in the course will consist of approximately weekly homework assignments, a few quizzes, two midterms, and a cumulative final exam.

  

STAT 307. Statistical Design and Analysis of Experiments

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Douglas C. Montgomery Design and Analysis of Experiments, 8th edition, Wiley (2012), ISBN-10: ‎ 1118146921; ISBN-13: ‎ 978-1118146927

Recommended text(s):  Robert O. Kuehl, Design of Experiments: Statistical Principles of Research Design and Analysis, 2nd edition, Duxbury Press, Brooks/Cole (2000), ISBN: 0534368344

Prerequisites:  STAT 203/335 and STAT 308 and the maturity to move quickly through new material.

Course description:  In order to understand how medical or industrial processes work, researchers in engineering, biology, chemistry, medical science and agronomy set up studies to answer fundamental questions. The field of statistical experimental design is a branch of statistics that is devoted to finding efficient and practical ways to run these studies. Once the study is run and the data are obtained, the statistician is called upon to analyze the data, to interpret the results, to reach the corresponding conclusions, and to communicate these conclusions back to the original researchers or decision-makers. As such, this course provides students with a thorough introduction to statistical experimental design, and to the statistical methods used to analyze the resulting data. The concepts of comparative experiments, analysis of variance (ANOVA) and mean separation procedures will be reviewed; blocking (complete and incomplete) will be discussed, as will be factorial designs, fractional factorial designs, and confounding. The course will focus on biometric applications such as clinical trials, HIV studies, and environmental and agricultural research, but industrial and other examples will occasionally be provided to show the breadth of application of experimental design ideas. Students will develop expertise R, although no previous programming experience will be assumed. At the discretion of the instructor, grading is based on participation, homework assignments, Midterm, a project/paper/presentation and a final.

  

STAT 308. Applied Regression Analysis

Instructor(s):  Staff

Required text(s):  TBD

Prerequisites:  STAT 203 or STAT 335

Course description:  Simple and multiple linear regression methods including weighted least squares and polynomial regression. Multiple comparison estimation procedures, residual analysis, and other methods for studying the aptness of a proposed regression model. Use of packaged computer programs such as R. For those interested in the actuarial profession, this course satisfies the Applied Statistical Methods VEE requirement.

  

STAT 311. [ STAT 411 ] Applied Survival Analysis

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

Required text(s):  David Collett, Modelling Survival Data in Medical Research, 3rd edition (2015), CRC Press: Boca Raton, FL., ISBN: 978-1-4398-5678-9

Textbook notes:  (Note that we'll be using the 3rd edition of Collett's Survival book.)

Prerequisites:  STAT 308 (with a grade of C- or higher)

Course description:  This course will provide students with the background, knowledge, and means to analyze survival, reliability and failure-time data. These types of data arise in situations where the actual response measurements are not precisely known, but are known to be below or above a threshold or within an interval. Right-censored data result when the response involves time-to-event-data (such as time for a cancer-survivor to remain tumor-free or time for a recovering addict to remain substance-free) and the event does not occur at the end of the study or evaluation period. Other situations can involve left- or interval-censored data. In this course, we examine various parametric and non-parametric models including the log-rank tests and Cox proportional hazards and the accelerated failure time models. Time permitting, additional topics may include time-dependent covariates, interval-censored methods, and/or frailty (longitudinal) methods. Students will be required to analyze and interpret real-life survival data using R and SAS statistical packages. Assessment will be based on homework assignments, an exam, and hands-on student projects.

  

STAT 321. [ STAT 421 ] Modeling & Simulation

Instructor(s):  Dr. Mena Whalen

Required text(s):  Jones, O., Maillardet, R, and Robinson, A. Introduction to Scientific Programming and Simulation Using R. CRC Press. Taylor and Francis Group. 2009. ISBN 13-978-1-4200-6872-6 Tanner, M. A. (1996). Tools for statistical inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions. Springer. ISBN 978-0-387-94688-7

Prerequisites:  STAT 308

Course description:  This course will use the R language to solve statistical problems through simulation techniques. Topics covered will include random number generation, bootstrapping, permutation testing, monte carlo approaches, markov chain monte carlo (MCMC) algorithms, and parallel computing.

  

STAT 335. [ BIOL 335 ] Introduction to Biostatistics

Instructor(s):  Dr. Izuchukwu Eze

Required text(s):  Samuels, Witmer, Schaffner. Statistics for the Life Sciences, 5th edition, Pearson Grant Publishing

Prerequisites:  BIOL 102, and MATH 132 or MATH 162. For Bioinformatics majors only: BIOL 101, and MATH 132 or MATH 162

Course description:  This course is an introduction to statistical methods used in designing biological experiments and analyzing biomedical, ecological and environmental data. Topics covered include basic probability, frequency distributions, design of experiments, chi-square methods, interval estimation, tests of hypotheses, correlation and regression – all with a focus on biological and medical data, and analysis of variance. Assessment will be based on homework assignments, exams, and final project. Additionally, the course will include computer laboratory assignments using R.

  

STAT 335. Introduction to Biostatistics

Instructor(s):  Staff

Required text(s):  Varies - please consult individual instructor's syllabus.

Prerequisites:  MATH 162 or 132; BIOL 102

Course description:  An introduction to statistical methods used in data analysis. Topics include descriptive statistics, probability and sampling distribution, design of biological experiments, hypothesis testing, analysis of variance, and regression and correlation. Additionally, the course may include programming in R and analyzing R output. (Note: Students may not receive credit for both STAT 203 & 335.)

  

STAT 336. Advanced Biostatistics

Instructor(s):  Mr. Bret A Longman

Required text(s):  None

Prerequisites:  STAT 335

Course description:  This course covers multi-variate analysis, including advanced ANOVA, 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/or R statistical packages, although no previous programming experience is assumed. Grading will be based on homework assignments, a course project/paper, exams and a final.

  

STAT 338. [ STAT 488 ] Predictive Analytics

Instructor(s):  Dr. Gregory J. Matthews

Required text(s):  James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning, with Applications in R, (Second Edition), Springer. ISBN/10: 1461471370, ISBN/13: 978-1461471370. https://www.statlearning.com/

Recommended text(s):  Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition, (corrected 10th printing), Springer. ISBN-13: 978-0387848570 ISBN-10: 0387848576.

Textbook notes:  Note that an electronic copy of the required text is freely available for download at: https://hastie.su.domains/ISLR2/ISLRv2_website.pdf

Prerequisites:  Some background in basic statistical methods or biostatistics including chi-square, ANOVA and simple regression, and maturity to get through somewhat sophisticated material. (STAT 308 or STAT 408 recommended)

Course description:  This course will cover a variety of statistical and machine learning techniques used to to predict and forecast future events. This will include supervised and unsupervised learning methods including potentially linear regression and classification, naive Bayes classifiers, cross-validation concepts, EM algorithm, generalized additive models (GAMS), tree based methods, boosting, neural networks, support vector machines, clustering, and random forests.

  

STAT 370. Data Science Consulting

Instructor(s):  Dr. Swarnali Banerjee

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

Prerequisites:  STAT 308

Course description:  Students will be placed into groups of 3-5 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 student 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.

  

STAT 396. Actuarial Seminar I

Instructor(s):  Dr. Matthew Bourque

Required text(s):  Exam P Sample Questions. Society of Actuaries. https://www.soa.org/globalassets/assets/Files/Edu/edu-exam-p-sample-quest.pdf.

Prerequisites:  MATH 263. MATH/STAT 304 is strongly recommended as a prerequisite or corequisite.

Course description:  This seminar is for students who want to prepare for Society of Actuaries exam P, or (CAS Exam 1), Probability. Students will work and discuss problems from practice materials published by the Society of Actuaries. 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. Assessment in the course will be on the basis of participation in weekly seminar meetings.

  

STAT 407. Statistical Design and Analysis of Experiments

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Douglas C. Montgomery Design and Analysis of Experiments, 8th edition, Wiley (2012), ISBN-10: ‎ 1118146921; ISBN-13: ‎ 978-1118146927

Recommended text(s):  Robert O. Kuehl, Design of Experiments: Statistical Principles of Research Design and Analysis, 2nd edition, Duxbury Press, Brooks/Cole (2000), ISBN: 0534368344

Prerequisites:  STAT 203/335 and STAT 308 and the maturity to move quickly through new material.

Course description:  In order to understand how medical or industrial processes work, researchers in engineering, biology, chemistry, medical science and agronomy set up studies to answer fundamental questions. The field of statistical experimental design is a branch of statistics that is devoted to finding efficient and practical ways to run these studies. Once the study is run and the data are obtained, the statistician is called upon to analyze the data, to interpret the results, to reach the corresponding conclusions, and to communicate these conclusions back to the original researchers or decision-makers. As such, this course provides students with a thorough introduction to statistical experimental design, and to the statistical methods used to analyze the resulting data. The concepts of comparative experiments, analysis of variance (ANOVA) and mean separation procedures will be reviewed; blocking (complete and incomplete) will be discussed, as will be factorial designs, fractional factorial designs, and confounding. The course will focus on biometric applications such as clinical trials, HIV studies, and environmental and agricultural research, but industrial and other examples will occasionally be provided to show the breadth of application of experimental design ideas. Students will develop expertise R, although no previous programming experience will be assumed. At the discretion of the instructor, grading is based on participation, homework assignments, Midterm, a project/paper/presentation and a final.

  

STAT 408. Applied Regression Analysis

Instructor(s):  Dr. Nan Miles Xi

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

Recommended text(s):  Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani. (2021) An Introduction to Statistical Learning with Applications in R. Second Edition. Springer.

Prerequisites:  A basic statistical methods class (such as STAT-203 or 335 or equivalent)

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 multicollinearity 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.

  

STAT 411. [ STAT 311 ] Applied Survival Analysis

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

Required text(s):  David Collett, Modelling Survival Data in Medical Research, 3rd edition (2015), CRC Press: Boca Raton, FL., ISBN: 978-1-4398-5678-9

Textbook notes:  (Note that we'll be using the 3rd edition of Collett's Survival book.)

Prerequisites:  STAT 308 (with a grade of C- or higher)

Course description:  This course will provide students with the background, knowledge, and means to analyze survival, reliability and failure-time data. These types of data arise in situations where the actual response measurements are not precisely known, but are known to be below or above a threshold or within an interval. Right-censored data result when the response involves time-to-event-data (such as time for a cancer-survivor to remain tumor-free or time for a recovering addict to remain substance-free) and the event does not occur at the end of the study or evaluation period. Other situations can involve left- or interval-censored data. In this course, we examine various parametric and non-parametric models including the log-rank tests and Cox proportional hazards and the accelerated failure time models. Time permitting, additional topics may include time-dependent covariates, interval-censored methods, and/or frailty (longitudinal) methods. Students will be required to analyze and interpret real-life survival data using R and SAS statistical packages. Assessment will be based on homework assignments, an exam, and hands-on student projects.

  

STAT 421. [ STAT 321 ] Modeling & Simulation

Instructor(s):  Dr. Mena Whalen

Required text(s):  Jones, O., Maillardet, R, and Robinson, A. Introduction to Scientific Programming and Simulation Using R. CRC Press. Taylor and Francis Group. 2009. ISBN 13-978-1-4200-6872-6 Tanner, M. A. (1996). Tools for statistical inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions. Springer. ISBN 978-0-387-94688-7

Prerequisites:  STAT 308

Course description:  This course will use the R language to solve statistical problems through simulation techniques. Topics covered will include random number generation, bootstrapping, permutation testing, monte carlo approaches, markov chain monte carlo (MCMC) algorithms, and parallel computing.

  

STAT 488. Statistical Consulting

Instructor(s):  Dr. Swarnali Banerjee

Required 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 3-5 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 student 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.

  

STAT 488. [ STAT 338 ] Predictive Analytics

Instructor(s):  Dr. Gregory J. Matthews

Required text(s):  James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning, with Applications in R, (Second Edition), Springer. ISBN/10: 1461471370, ISBN/13: 978-1461471370. https://www.statlearning.com/

Recommended text(s):  Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition, (corrected 10th printing), Springer. ISBN-13: 978-0387848570 ISBN-10: 0387848576.

Textbook notes:  Note that an electronic copy of the required text is freely available for download at: https://hastie.su.domains/ISLR2/ISLRv2_website.pdf

Prerequisites:  Some background in basic statistical methods or biostatistics including chi-square, ANOVA and simple regression, and maturity to get through somewhat sophisticated material. (STAT 308 or STAT 408 recommended)

Course description:  This course will cover a variety of statistical and machine learning techniques used to to predict and forecast future events. This will include supervised and unsupervised learning methods including potentially linear regression and classification, naive Bayes classifiers, cross-validation concepts, EM algorithm, generalized additive models (GAMS), tree based methods, boosting, neural networks, support vector machines, clustering, and random forests.