Instructor(s):  Staff

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

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

Prerequisites:  None

Course description:  Fundamentals of algebra. Graphs of linear equations, polynomials and factoring, first and second-degree equations and inequalities, radicals and exponents, and systems of equations. Word problems emphasized throughout the course.

Syllabus:  Common

Instructor(s):  Staff

Required text(s):  Consortium for Mathematics and Its Applications (COMAP), S. Garfunkel, ed. For All Practical Purposes: Mathematical Literacy in Today's World. 9th ed. ISBN-13: 978-1429243162. New York: W. H. Freeman, 2011. Print.

Prerequisites:  None

Course description:  An introduction to mathematical modeling. Topics chosen from linear programming, probability theory, Markov chains, scheduling problems, coding theory, social choice, voting theory, geometric concepts, game theory, graph theory, combinatorics, networks. Emphasis placed upon demonstrating the usefulness of mathematical models in other disciplines, especially the social science and business.

Syllabus:  Common

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

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

Instructor(s):  Mr. Marius Radulescu

Required text(s):  None

Recommended text(s):  Sullivan, Michael. Precalculus. 10th ed., Pearson, 2015. ISBN-13 : 978-0321979070

Prerequisites:  MATH 100 with a grade of A

Course description:  A corequisite course that provides a rigorous transition from MATH 100 to MATH 118 for students whose high level of proficiency in advanced algebra recommends them for an accelerated path toward transcendental functions and trigonometry. The course will provide students with corequisite support and enrichment for the duration of the target course MATH 118. There are two main objectives of this course: to enrich students’ knowledge pertaining to topics from MATH 117, such as functions transformations and polynomials, through applications and problem-solving strategies, and to offer concurrent support for concepts and skills met along the way in MATH 118 that refer to content covered in MATH 117, such as rate of change, composition of functions and inverse functions.

Instructor(s):  Mrs. Laurie Jordan

Required text(s):  Brown, P., Roediger III, H., & McDaniel, M. (2014). make it stick: The Science of Successful Learning. Cambridge: The Belknap Press of Harvard University Press. Fatima Pirbhai-Illich, S. P. (2017). Cultrually Responsive Pedagogy. Cham, Switzerland: Springer International Publishing. Su, F. (2020). Mathematics for Human Flourshing. New Haven: Yale University Press. Access to current textbooks used for courses in 100-level mathematics and statistics courses will be provided

Prerequisites:  Math 118

Course description:  Students will learn best practices to communicate mathematical concepts and skills to diverse populations. The students will have an opportunity to engage in tutoring mathematics to the undergraduate population at Loyola. This course is designed to promote and encourage engagement and rigor in mathematical concepts and skills among the diverse communities of learners at Loyola. Students will be required to engage in approximately 20 hours of tutoring during the semester. The students will keep a log of the days and times that are devoted to tutoring and will be approved by the Lead Tutor/Supervisor of the Tutoring session. The Loyola Math Club will help facilitate the tutoring for all students in the Loyola undergraduate population. Currently the Loyola Math Club offers tutoring on Monday and Thursday nights from 7-9 pm for all Loyola undergraduates in 100-level Mathematics and Statistics courses. All undergraduate students are welcome to attend the tutoring on a drop-in basis. They may attend the tutoring as many times as they wish and for as long a session as they need to get their questions answered. The Club reserves a room in the STEM center to provide the in-person tutoring but has been tutoring remotely using Zoom.

Instructor(s):  Dr. Gregory J. Matthews

Required text(s):  Modern Data Science with R (2nd edition). Baumer, Kaplan, and Horton PDF of book is available here: https://beanumber.github.io/mdsr2e/index.html

Prerequisites:  None.

Course description:  This course provides students with an introduction to data science using the R programming language covering such topics as data wrangling, data visualization, interacting with databases, principles of reproducible research, building simple statistical models/machine learning and data science ethics.

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):  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

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

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.

Instructor(s):  Dr. Matthew Mills

Required text(s):  Richard Hammack, Book of Proof (3rd edition), Hammack Pub. (2018) ISBN-13 9780989472128 Also available as a PDF on the author's website.

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 primarily consist of classical lectures, but students will be required to present some of their own proofs during class time. There will be weekly homework sets to help illustrate core concepts and other projects may be assigned depending on the interests of registered students.

Instructor(s):  Dr. Peter Tingley

Required text(s):  Anton, Howard. Elementary Linear Algebra. 11th ed. ISBN-13: 978-1118473504. New York: John Wiley, 2013. Print. Note: there is a 12th edition, but the 11th edition is cheaper, and I plan to follow that.

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):  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

Instructor(s):  Dr. Christine Haught

Required text(s):  Nagle, R. Kent, Saff, Edward B., and Edward B. Snider. Fundamentals of Differential Equations. 8th ed. ISBN-13: 978-0321747730. Boston: Addison-Wesley, 2012. Print.

Prerequisites:  MATH 263 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, Laplace transforms, and topics in systems of linear first-order differential equations. Applications and modelling will be emphasized.

Instructor(s):  Dr. Stuart Wick

Required text(s):  Fundamentals of Differential Equations, Eighth edition, by Nagle, Saff and Snider.

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.

Instructor(s):  Dr. Tuyen Tran

Required text(s):  Edwards, Penney and Calvis. Differential Equations and Linear Algebra, 4th edition. Published by Pearson. ISBN: 978-0134497181

Prerequisites:  MATH263

Course description:  The course is an introduction to linear algebra and differential equations, and is oriented toward students of engineering science. Topics include first and second-order differential equations, systems of first-order differential equations, systems of linear algebraic equations, matrix algebra, bases and dimension for vector spaces, linear independence, linear transformations, determinants, eigenvalues, and eigenvectors. Students will learn fundamental results and methods in ordinary differential equations and linear algebra.

Instructor(s):  Dr. John G. Del Greco

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

Prerequisites:  MATH 263

Course description:  An introduction to probability, including random variables, mean, variance, and basic theorems such as the Law of Large Numbers and the Central Limit Theorem.

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Mathematical Statistics by Wackerly, Mendenhall and Scheaffer, (7th edition).

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

Prerequisites:  MATH/STAT 304

Course description:  In continuation of MATH/STAT 304, MATH/STAT 305 explores the statistical analyses based on the distribution models. Topics to be covered include Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests). Evaluation for this course would include weekly homework assignments, 2 Midterm examinations and 1 final examination.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  T.W. Judson and R.A. Beezer., Abstract Algebra: Theory and Applications. Published online (en español). 2019.

Textbook notes:  For additional examples and exercises, or alternative presentation of the material, I can also recommend the cheap book by Pinter (Dover publishing) and the free books by Goodman and Scherk.

Additional notes:  (1) Students will gain some experience in using the powerful computer algebra package, SageMath. Indeed, many of the examples in the course text have code accompanying them that you can use to experiment with the objects we'll be studying.

(2) There is a zero-credit, unscheduled "lab" component to this course (MATH 313-002). If at all possible, please leave these two blocks free in your Spring schedule. Wednesdays, 2:00–3:00 and Thursdays, 1:00–2:00.

Prerequisites:  MATH 201 and MATH 212

Course description:  The techniques and results of modern abstract algebra have found purchase in a wide variety of disciplines, ranging from physical chemistry and quantum physics to cryptography, coding theory (allowing the Cassini satellite to send you pictures of Saturn's moons) and even voting theory. At the root of it all, not surprisingly, is the centuries old study of roots of algebraic equations—so we are headed back to high school!

In this course, we study groups, the first pillar of abstract algebra, which may be viewed as the search for symmetry in objects. (Continuing the theme started in the preceding paragraph, as examples of such "objects" I might mention here algebraic equations, differential equations, geometric objects, …) Students will be introduced to permutation groups, matrix groups, subgroups, isomorphisms, equivalence relations, factor groups, and more. Over the course of the semester, we will consider some applications of abstract algebra, but the main focus will be on the "pure" study of the algebraic structures themselves. Examples motivating the theory will appear throughout.

Syllabus:  We will cover the first 12 chapters completely, and select topics from 13–18 as time permits. Assessment will be as follows: weekly homework, two midterms, a group presentation, and a comprehensive final exam. Graduate Students will be assigned additional reading and more in-depth homework, with exams and presentations adjusted accordingly.

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).

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 313

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. In this course, we will encounter algebraic constructions like groups, rings, or vector spaces. Some of the original motivations for creating this whole language of algebra was to tackle questions like understanding symmetries of spaces, or trying to create formulas to find the roots of polynomials. 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 commutative and non-commutative rings, integral domains, and fields. Selected topics may include Galois theory, group representations, modules, and advanced group theory. Students will be assessed based on weekly homework, two midterms, group projects and presentations, a small number of quizzes, and class participation.

Instructor(s):  Dr. Rafal Goebel

Required text(s):  Introduction to Analysis, Maxwell Rosenlicht, Dover Books on Mathematics, ISBN 978-0486650388 or 0486650383

Recommended text(s):  Your old Calc I textbook.

Prerequisites:  Math 201 and Math 212

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

Instructor(s):  Dr. Tuyen Tran

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

Textbook notes:  Supplementary reading material will be provided when needed.

Prerequisites:  MTH 351: Introduction to Real Analysis I

Course description:  This course is a continuation of MTH 351. After a brief review of key topics from Math 351, like sequences and their convergence, functions and their continuity, and differentiability, the course will cover Riemann integration with emphasis on the one variable case, infinite series, the fixed point theorem, the implicit function theorem, and elements of convex analysis, dealing with convex sets and functions. There will be 2-3 exams, and bi-weekly homework will also be assigned.

Instructor(s):  Dr. Mahvand Khamesian

Required text(s):  TBA

Prerequisites:  MATH 264

Course description:  A wide spectrum of topics with applications to physics, engineering, economics, and the social sciences. Topics include Green's functions and solutions to ordinary differential equations, integral equations, the calculus of variations and optimization, and partial differential equations. This class is cross-listed with PHYS 301. Register under PHYS 301.

Instructor(s):  Dr. Brian Seguin

Required text(s):  None, but hand written lecture notes will be provided to you.

Prerequisites:  MATH 266 or (MATH 212 and MATH 264)

Course description:  Mechanics, being the study of forces acting on bodies and their resultant motion, is an important subject one must understand to describe many different physical phenomena. In this course you will learn how to model forces, bodies, and their motion using mathematical concepts from linear algebra and vector calculus for several different mechanical systems, including systems of particles, rigid bodies, and deformable bodies. Some of the specific topics to be covered are kinematics (motion), balance laws, frames of reference, constitutive laws, and more. There will be 2 exams and a few quizzes during the course the semester. Weekly homework will also be assigned. There will be no textbook, but my handwritten lecture notes will be provided.

Instructor(s):  Dr. Rafal Goebel

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

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 as an optimality condition. 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. The course will cover a majority of the textbook: Chapter 1: Introduction, Chapter 2: Solving linear programs, Chapter 3: Duality through examples, Chapter 4: Duality theory, Chapter 5: Applications of duality, Chapter 6: Solving integer programs, and Chapter 7: Nonlinear optimization, in varying depth.

Instructor(s):  Dr. Anthony Giaquinto

Required text(s):  Stillwell, John, Naive Lie theory. Undergraduate Texts in Mathematics. Springer, New York, 2008. ISBN: 978-0-387-78214-0

Prerequisites:  MATH 212 and MATH 263

Course description:  This course will be an introduction to Lie groups and Lie algebras using primarily concepts from linear algebra and calculus. Lie groups are simultaneously algebraic and geometric objects which have extensive uses and applications in a variety of topics such as topology, particle physics, computer graphics, quantum computing and Riemannian geometry. The main object of study in this course will be matrix groups which are certain sets of invertible matrices. Motivating examples are rotations in two, three and four real, complex or quaternion dimensions. These examples extend to rotations in higher dimensions and yield the classical simple Lie groups in a geometric way. Calculus is then used to discover the tangent spaces to these groups via the usual logarithm and exponential functions. We will discover that, surprisingly, the curved structure of a Lie group is almost completely determined by the flat structure of its Lie algebra. There will be regular written homework assignments as well as two midterms and a final exam.

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Mathematical Statistics by Wackerly, Mendenhall and Scheaffer, (7th edition).

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

Prerequisites:  MATH/STAT 404

Course description:  In continuation of MATH/STAT 404, MATH/STAT 405 explores the statistical analyses based on the distribution models. Topics to be covered include Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests). Evaluation for this course will include weekly homework assignments, 2 Midterm examinations and 1 final examination.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  T.W. Judson and R.A. Beezer., Abstract Algebra: Theory and Applications. Published online (en español). 2019.

Textbook notes:  For additional examples and exercises, or alternative presentation of the material, I can also recommend the cheap book by Pinter (Dover publishing) and the free books by Goodman and Scherk.

Additional notes:  (1) Students will gain some experience in using the powerful computer algebra package, SageMath. Indeed, many of the examples in the course text have code accompanying them that you can use to experiment with the objects we'll be studying.

(2) There is a zero-credit, unscheduled "lab" component to this course (MATH 313-002). If at all possible, please leave these two blocks free in your Spring schedule. Wednesdays, 2:00–3:00 and Thursdays, 1:00–2:00.

Prerequisites:  MATH 201 and MATH 212

Course description:  The techniques and results of modern abstract algebra have found purchase in a wide variety of disciplines, ranging from physical chemistry and quantum physics to cryptography, coding theory (allowing the Cassini satellite to send you pictures of Saturn's moons) and even voting theory. At the root of it all, not surprisingly, is the centuries old study of roots of algebraic equations—so we are headed back to high school!

In this course, we study groups, the first pillar of abstract algebra, which may be viewed as the search for symmetry in objects. (Continuing the theme started in the preceding paragraph, as examples of such "objects" I might mention here algebraic equations, differential equations, geometric objects, …) Students will be introduced to permutation groups, matrix groups, subgroups, isomorphisms, equivalence relations, factor groups, and more. Over the course of the semester, we will consider some applications of abstract algebra, but the main focus will be on the "pure" study of the algebraic structures themselves. Examples motivating the theory will appear throughout.

Syllabus:  We will cover the first 12 chapters completely, and select topics from 13–18 as time permits. Assessment will be as follows: weekly homework, two midterms, a group presentation, and a comprehensive final exam. Graduate Students will be assigned additional reading and more in-depth homework, with exams and presentations adjusted accordingly.

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).

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 313

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. In this course, we will encounter algebraic constructions like groups, rings, or vector spaces. Some of the original motivations for creating this whole language of algebra was to tackle questions like understanding symmetries of spaces, or trying to create formulas to find the roots of polynomials. 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 commutative and non-commutative rings, integral domains, and fields. Selected topics may include Galois theory, group representations, modules, and advanced group theory. Students will be assessed based on weekly homework, two midterms, group projects and presentations, a small number of quizzes, and class participation.

Instructor(s):  Dr. Tuyen Tran

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

Textbook notes:  Supplementary reading material will be provided when needed.

Prerequisites:  MTH 351: Introduction to Real Analysis I

Course description:  This course is a continuation of MTH 351. After a brief review of key topics from Math 351, like sequences and their convergence, functions and their continuity, and differentiability, the course will cover Riemann integration with emphasis on the one variable case, infinite series, the fixed point theorem, the implicit function theorem, and elements of convex analysis, dealing with convex sets and functions. There will be 2-3 exams, and bi-weekly homework will also be assigned.

Instructor(s):  Dr. Rafal Goebel

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

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 as an optimality condition. 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. The course will cover a majority of the textbook: Chapter 1: Introduction, Chapter 2: Solving linear programs, Chapter 3: Duality through examples, Chapter 4: Duality theory, Chapter 5: Applications of duality, Chapter 6: Solving integer programs, and Chapter 7: Nonlinear optimization, in varying depth.

Instructor(s):  Dr. Brian Seguin

Required text(s):  None, but hand written lecture notes will be provided to you.

Prerequisites:  MATH 266 or (MATH 212 and MATH 264)

Course description:  Mechanics, being the study of forces acting on bodies and their resultant motion, is an important subject one must understand to describe many different physical phenomena. In this course you will learn how to model forces, bodies, and their motion using mathematical concepts from linear algebra and vector calculus for several different mechanical systems, including systems of particles, rigid bodies, and deformable bodies. Some of the specific topics to be covered are kinematics (motion), balance laws, frames of reference, constitutive laws, and more. There will be 2 exams and a few quizzes during the course the semester. Weekly homework will also be assigned. There will be no textbook, but my handwritten lecture notes will be provided.

Instructor(s):  Dr. Anthony Giaquinto

Required text(s):  Stillwell, John, Naive Lie theory. Undergraduate Texts in Mathematics. Springer, New York, 2008. ISBN: 978-0-387-78214-0

Prerequisites:  MATH 212 and MATH 263

Course description:  This course will be an introduction to Lie groups and Lie algebras using primarily concepts from linear algebra and calculus. Lie groups are simultaneously algebraic and geometric objects which have extensive uses and applications in a variety of topics such as topology, particle physics, computer graphics, quantum computing and Riemannian geometry. The main object of study in this course will be matrix groups which are certain sets of invertible matrices. Motivating examples are rotations in two, three and four real, complex or quaternion dimensions. These examples extend to rotations in higher dimensions and yield the classical simple Lie groups in a geometric way. Calculus is then used to discover the tangent spaces to these groups via the usual logarithm and exponential functions. We will discover that, surprisingly, the curved structure of a Lie group is almost completely determined by the flat structure of its Lie algebra. There will be regular written homework assignments as well as two midterms and a final exam.

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.

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 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):  Dr. Swarnali Banerjee

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. The course evaluation involves weekly homework assignments, 2 midterm examinations and one final examination.

Instructor(s):  Dr. Mike 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:  None

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:  Grading: Approximately 7 homework assignments - 25% 4 quizzes - 20% 1 Take home test - 30% 1 Project with Presentation (2 papers and slide presentation) - 25%

Instructor(s):  Dr. John G. Del Greco

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

Prerequisites:  MATH 263

Course description:  An introduction to probability, including random variables, mean, variance, and basic theorems such as the Law of Large Numbers and the Central Limit Theorem.

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Mathematical Statistics by Wackerly, Mendenhall and Scheaffer, (7th edition).

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

Prerequisites:  MATH/STAT 304

Course description:  In continuation of MATH/STAT 304, MATH/STAT 305 explores the statistical analyses based on the distribution models. Topics to be covered include Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests). Evaluation for this course would include weekly homework assignments, 2 Midterm examinations and 1 final examination.

Instructor(s):  Dr. Izuchukwu Eze

Required text(s):  Applied Regression Analysis and Other Multivariable Methods 5th Edition - Kleinbaum, Kupper, Nizam, Rosenberg. (Customized version for Loyola)

Textbook notes:  ISBN-13: 978-1285051086 ISBN-10: 1285051084

Prerequisites:  STAT 203 or STAT 335 (or permission of instructor)

Course description:  This course provides students with a thorough introduction to applied regression methodology. The concept of simple linear regression will be reviewed, and multiple linear regression, transformations, indicator variables, multicollinearity, diagnostics, model building, polynomial regression, logistic regression. The course will focus on applications such as those from biometry and biostatistics (clinical trials, HIV studies, etc.), sports, engineering, agriculture and environmental science. Students are required to analyze real-life datasets using the R statistical software, although no previous programming experience is assumed. Two exams, and 6 projects will be used to determine the final grade in the course.

Instructor(s):  Dr. Mena Whalen

Required text(s):  “An Introduction to Categorical Data Analysis” by Alan Agresti, 2019, 3rd Edition, Wiley, ISBN: 978-1-119-40526-9. (NB - this is NOT the same as Agresti's "Categorical Data Analysis" book, also 3rd Edition and by Wiley, but published in 2013.)

Prerequisites:  STAT 203 or STAT 335 with C- or better and STAT 308 with C- or better

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. As such, 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, binary logistic regression, polytomous and ordinal logistic modeling are the focus of this course in the context of epidemiology, biostatistics and predictive modeling. This course also addresses the fundamental questions encountered with regression and ANOVA for count data. Specialized methods for ordinal data, small samples, 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 as emphasized. Using categorical data, students will develop expertise using R computer packages, although no previous programming experience will be assumed. Grading is based on regular homework assignments, article review(s), and paper/project(s).

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.)

Instructor(s):  Mrs. Sheila Suresh

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

Recommended 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:  Introduction to Biostatistics is 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 computer laboratory assignments using R.

Instructor(s):  Mr. Bret A Longman

Required text(s):  No Textbook is used for this class.

Prerequisites:  STAT 203 or STAT 335

Course description:  This course is an extension of Stat 335 and 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 and 3 exams.

Instructor(s):  Dr. Nan Miles Xi

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. Mike Perry

Required text(s):  -

Recommended text(s):  Higgins, James J. "Introduction to Modern Nonparametric Statistics." Brooks/Cole. 2004 Hollander, M; Wolfe, D.A., and Chicken E. “Nonparametric Statistical Methods”, 3rd Edition. Wiley. 2014

Prerequisites:  STAT 308 if enrolling for STAT 351. None for STAT 488

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):  Dr. Mena Whalen

Required text(s):  Applied Multivariate Statistical Analysis, 6th Edition by Johnson & Wichern 2008 ISBN-13: 9780131877153 AND An Introduction to Applied Multivariate Analysis with R by Everitt & Hothorn 2011 ISBN 978-1-4419-9650-3

Additional notes:  Linear algebra knowledge is recommended.

Prerequisites:  STAT 305

Course description:  This course covers advanced-level multivariate statistical methods, including assumptions of multivariate statistical procedures, MANOVA, factor analysis, canonical correlation analysis, cluster analysis, and principal components analysis. The focus of this course will be on conceptual understanding and computer applications in R, with an introduction to the mathematical underpinnings of the procedures examined. Evaluations will be performed through written homework, paper reviews(s), and projects(s).

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Mathematical Statistics by Wackerly, Mendenhall and Scheaffer, (7th edition).

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

Prerequisites:  MATH/STAT 404

Course description:  In continuation of MATH/STAT 404, MATH/STAT 405 explores the statistical analyses based on the distribution models. Topics to be covered include Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests). Evaluation for this course will include weekly homework assignments, 2 Midterm examinations and 1 final examination.

Instructor(s):  Dr. Mena Whalen

Required text(s):  “An Introduction to Categorical Data Analysis” by Alan Agresti, 2019, 3rd Edition, Wiley, ISBN: 978-1-119-40526-9. (NB - this is NOT the same as Agresti's "Categorical Data Analysis" book, also 3rd Edition and by Wiley, but published in 2013.)

Prerequisites:  STAT 203 or STAT 335 with C- or better and STAT 308 with C- or better

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. As such, 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, binary logistic regression, polytomous and ordinal logistic modeling are the focus of this course in the context of epidemiology, biostatistics and predictive modeling. This course also addresses the fundamental questions encountered with regression and ANOVA for count data. Specialized methods for ordinal data, small samples, 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 as emphasized. Using categorical data, students will develop expertise using R computer packages, although no previous programming experience will be assumed. Grading is based on regular homework assignments, article review(s), and paper/project(s).

Instructor(s):  Dr. Nan Miles Xi

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. Mike Perry

Required text(s):  -

Recommended text(s):  Higgins, James J. "Introduction to Modern Nonparametric Statistics." Brooks/Cole. 2004 Hollander, M; Wolfe, D.A., and Chicken E. “Nonparametric Statistical Methods”, 3rd Edition. Wiley. 2014

Prerequisites:  STAT 308 if enrolling for STAT 351. None for STAT 488

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):  Dr. Mena Whalen

Required text(s):  Applied Multivariate Statistical Analysis, 6th Edition by Johnson & Wichern 2008 ISBN-13: 9780131877153 AND An Introduction to Applied Multivariate Analysis with R by Everitt & Hothorn 2011 ISBN 978-1-4419-9650-3

Additional notes:  Linear algebra knowledge is recommended.

Prerequisites:  STAT 305

Course description:  This course covers advanced-level multivariate statistical methods, including assumptions of multivariate statistical procedures, MANOVA, factor analysis, canonical correlation analysis, cluster analysis, and principal components analysis. The focus of this course will be on conceptual understanding and computer applications in R, with an introduction to the mathematical underpinnings of the procedures examined. Evaluations will be performed through written homework, paper reviews(s), and projects(s).