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:  Inverse functions, quadratic functions, complex numbers. Detailed study of polynomial functions including zeros, factor theorem, and graphs. Rational functions, exponential and logarithmic functions and their applications. Systems of equations, inequalities, partial fractions, linear programming, sequences and series. Word problems are emphasized throughout the course.

Syllabus:  Common

Instructor(s):  Staff

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

Prerequisites:  MATH 117 or Math Diagnostic Test

Course description:  Functions and change with an emphasis on linear, quadratic, exponential, and logarithmic functions and their graphs. Specific geometric topics include concavity and how transformations affect graphs. Topics in trigonometry include radians, sinusoidal functions, identities, sum/difference formulas, double/half angle formulas, and trigonometric equations. Other topics include polar coordinates.

Syllabus:  Common

Instructor(s):  Dr. Emily Peters

Required text(s):  none

Prerequisites:  Pre or corequisite: Math 131 or 161

Course description:  This one-credit seminar is designed for freshman and sophomore students who are interested in mathematics. It provides a glimpse into the world of mathematics beyond elementary calculus. It aims to be informal, lively and thought-provoking. In the age of enlightenment, scientists used mathematics to model physical phenomena and in doing so changed the world. In the age of information, we are using mathematics to model social phenomena. Find out about the principals behind: *encoding secure information on the internet *fair voting in a democracy *how google decides what order to display search results in *modelling the spread of disease *matching future doctors and hospitals for residency *understanding how information spreads through networks and other topics! There are no exams in this class; grades will be based on participation and occasional written homework.

Instructor(s):  Dr. 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. ISBN 978-0-674-72901-8 Su, F. (2020). Mathematics for Human Flourshing. New Haven: Yale University Press. ISBN 978-0-300-23713-9 Access to current textbooks used for Math courses will be provided.

Prerequisites:  Math 117

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 Loyola Math Club will help facilitate the tutoring. Time will be devoted to each level of mathematics courses and best practices for communicating mathematics. Course Outcomes: Students in this course will deepen their understanding of mathematical concepts and skills and be able to communicate this effectively to diverse communities of learners.

Syllabus:  Students will use each best practice skill to focus on a level of mathematics each week. Although every best practice can be applied to all levels of mathematics, each math course will be used to provide examples and practice each week. Students will be assessed on how well they can apply course content. Assessments may be (but are not limited to) reflections, role play in class, sample lesson demonstrations, use of questioning techniques or designing learning retrieval tasks. Assignments: Journals: Students in the course will be expected to keep journals of their tutoring sessions. Included in the journal will be what went well in the session, what could be improved, what are the obstacles and what are the goals for the next session. (Due weekly) Learning objectives: Each learning objective will require an example of how it was applied to a tutoring session and a reflection on what happened and how it could be handled better. (Due after discussion of each learning objective) Culminating Experience: As a final exercise each student in the course will prepare a presentation or written paper reflecting on how the tutoring sessions made them aware of larger community issues, social structures and topics of social justice. (Due during the final exam slot)

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 towards transcendental functions and trigonometry. The course will provide students with corequisite support and enrichment while taking 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):  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.

Instructor(s):  Dr. Stephen London

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

Prerequisites:  MATH 161

Course description:  The course covers a variety of interesting topics from discrete mathematics including counting number theory, counting, cardinality, sets, and logic. These areas of mathematics have numerous applications in many fields of study. Central to the course is learning not just how to find an answer, but how to write solid mathematical arguments. Students will learn several proof writing techniques which will prepare them for upper level mathematics courses such as real and complex analysis and abstract algebra.

Syllabus:  Students will be given problem sets approximately once a week in addition to two tests and a final.

Instructor(s):  Dr. E. Barron

Required text(s):  Elementary Linear Algebra, Applications version, 12th edition, H.Anton, Rorres, and Kaul, Wiley ISBN-13-9781119584421 WileyPlus is also required

Prerequisites:  MATH 132 or MATH 162

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

Syllabus:  We will have two midterms and a Final Exam as well as five quizzes. Online homework will also be required and graded.

Instructor(s):  Alan Saleski

Required text(s):  David Poole,  WebAssign for Linear Algebra: A Modern Introduction, 4th edition ISBN-10: 1337769916 ISBN-13: 9781337769914     

Prerequisites:  Math 162 or Math 132

Course description:  Vectors, systems of equations, matrices, inverse matrices, abstract vector spaces and subspaces, dimension, inner product spaces, orthogonality, determinants, eigenvalues, and eigenvectors, linear transformations, applications as time allows.

Syllabus:  Weekly quizzes (written or oral), one midterm, weekly homework, final exam

Instructor(s):  Staff

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

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

Prerequisites:  MATH 162

Course description:  Vectors and vector algebra, curves and surfaces in space, functions of several variables, partial derivatives, the chain rule, the gradient vector, LaGrange multipliers, multiple integrals, volume, surface area, the Change of Variables theorem, line integrals, surface integrals, Green's theorem, the Divergence Theorem, and Stokes' Theorem.

Syllabus:  Common

Instructor(s):  Dr. Rafal Goebel

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

Prerequisites:  Math 263 is a corequisite. Being comfortable with differentiation and integration is desired.

Course description:  Differential equations can model how things change in time. These things can be population sizes, say for a growing population of bacteria (or zombies!) or for oscillating populations of predators and prey; temperature of your favorite cold beverage when left out in the sun; mechanical systems like weights on a spring or planets around the sun; currents in an electrical circuits; positions of autonomous robots on Mars; amounts of compounds during a chemical reaction; and more. The course will be a fairly standard introduction to differential equations. Students will learn how to model things as listed above, and more, using differential equations; how to solve differential equations, at least those that can be solved; how to predict how solutions to differential equations behave even if the solutions cannot be found explicitly; and possibly how to use mathematical software to help with these learning objective.

Instructor(s):  Dr. Anthony Giaquinto

Required text(s):  Nagle, R. Kent, Saff, Edward B., and Edward B. Snider. Fundamentals of Differential Equations. 9th ed. MyLab Math with Pearson e-Text, ISBN-13: 9780134764832

Prerequisites:  MATH 263 or MATH 263 concurrently

Course description:  This course is an introduction to the study of ordinary differential equations and their appplication to physical systems. Topics will include Solution of First-Order ODE's by analytical, graphical and numerical methods; Linear ODE's, Especially Second Order with Constant Coefficients; Undetermined Coefficients and Variation of Parameters; Series Solutions; Complex Numbers and Exponentials; Laplace Transform Methods; Non-linear Autonomous Systems: Critical Point Analysis and Phase Plane Diagrams.

Instructor(s):  Dr. Peter Tingley

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.

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. Gregory J. Matthews

Required text(s):  Wackerly, D., Mendenhall, W. and Scheaffer, R.L. Mathematical Statistics with Applications 7th Edition. ISBN-13: 978-0495110811

Recommended text(s):  Casella, G. and Berger, R.L. Statistical Inference 2nd edition. 2008.

Prerequisites:  MATH 304 or STAT 304

Course description:  This course will be a mathematically rigorous introduction to statistics and will require an extensive background in probability. The successful student will need a firm grasp of the following topics from probability theory: axiomatic probability, conditional probability, independence, combinatorial probability, random variables, families of discrete probability distributions (hypergeometric, binomial, Poisson, geometric, negative-binomial), families of continuous distributions (exponential, normal, gammma, beta), expected values, variance, covariance, joint densities, conditional densities, transformations of random variables, order statistics, and moment-generating functions.

Stat 305 will cover the following topics: methods of estimation, properties of estimators (unbiasedness, consistency, sufficiency, efficiency, etc.), minimum-variance unbiased estimators and the Cramer-Rao lower bound, Bayesian estimation, hypothesis testing, uniformly most powerful tests, Neyman-Pearson Lemma, sampling distributions and inferences involving the normal distribution, two-sample tests, goodness-of-fit tests, analysis of variance.

Instructor(s):  Dr. Antonio Mastroberardino

Required text(s):  Sauer, Timothy. Numerical Analysis. 3rd edition. Pearson. 2018. Print. ISBN-13: 978-0134696454.

Textbook notes:  Students may choose to purchase the eText. ISBN-13: 978-0134697376.

Additional notes:  Graduate students will be required to complete more advanced homework exercises and present a supplemental topic from independent reading at the end of the semester.

Prerequisites:  COMP 170 or MATH/COMP 215, MATH 212, and MATH 264

Course description:  Numerical analysis is a branch of mathematics that deals with the development and use of algorithmic methods for solving mathematical problems that are often too complicated to solve analytically. Topics that will be covered include floating point computation, rootfinding, direct and iterative methods for solving systems of linear equations, interpolation, method of least squares, numerical quadrature, numerical solutions of ordinary and partial differential equations, and if time permits, various matrix decompositions. Homework assignments will include computational exercises requiring the use of the high-level programming language MATLAB, although no previous programming experience will be assumed.

Instructor(s):  Dr. Anthony Giaquinto

Required text(s):  Stewart, Ian. Galois Theory. 4th ed., Chapman and Hall/CRC, 2015, ISBN 9781482245820

Textbook notes:  Any edition and format of the text is acceptable.

Prerequisites:  MATH 313

Course description:  Abstract algebra is about the definition and study of various algebraic structures (e.g., groups, rings, fields, vector spaces) which have arisen in mathematics in the last 200 years or so. One of the original motivations for the study of these systems was to find a formula to solve a general fifth degree polynomial equation in terms of radicals. Such formulas exist for polynomials of degree 2, 3 and 4; in degree 2 the formula is the well-known quadratic formula which we learn in high-school algebra. The Norwegian mathematician Niels Henrik Abel eventually around 1822 proved that the fifth degree polynomial equation cannot be solved by such a formula, and the French mathematician Evariste Galois gave in 1832 a complete theory which tells us precisely which polynomial equations can be solved in terms of radicals. Later it was shown by similar techniques that it is impossible to trisect a given angle solely by means of ruler and compass, and also it is impossible to construct (by ruler and compass) a square whose area is the same as a given circle. Nowadays many of the algebraic structures used in these problems have applications far beyond their original motivation. For example, communication systems use algebraic coding theory to encode the information so that errors can be minimized, and public key cryptography, which banks use to verify electronic transactions, is rooted in the algebraic structures studied in this course. This course will focus mainly on selected topics in classical algebra, field and ring theory, polynomials and Galois theory.

Instructor(s):  Dr. A. Lauve

Required text(s):  Bogart, Kenneth, Combinatorics Through Guided Discovery, PreTeXt edition (2017), http://bogart.openmathbooks.org/.

Textbook notes:  The PreTeXt source code for the Bogart text is released under the GNU Free Documentation Licence (FDL). It does not look much like a traditional mathematics textbook. Being written for (guided) self-discovery, you won't find many carefully worded definitions or theorems. If you are looking for some of that, Brualdi and Bona have both written nice textbooks. (I will provide additional notes or resources, as needed.)

Prerequisites:  Math 162

Course description:  Combinatorial problems from enumeration and graph theory and methods for their solution. Prior experience with abstraction and proofs is helpful, but not necessary. Graduate students will: complete more advanced exercises than the undergraduate students; help compile carefully worded definitions and theorems, with proofs; and will present some supplemental topics from independent reading.

Syllabus: 
We discover the joy and power of counting. (What a funny thing to say!) To some extent, the topics and techniques below show up in other domains of mathematics and computer science. So you could call this an applications course (indeed combinatorists at MIT are members of the "Applied Mathematics" department). But we'll mostly just be having fun, learning, all over again, how to count.

Topics: Basic counting principles, induction and recursion in combinatorics and graph theory, distribution problems, generating functions. Advanced topics, as time permits may include: the principle of inclusion-exclusion, groups acting on sets, Catalan objects, graph walks, graph colorings, chromatic polynomials, combinatorial algorithms, optimization, pattern avoidance, probabilistic methods, partial orders, among others.

Techniques: Pigeon-hole principle, mathematical induction, inclusion-exclusion principle, recurrence relations, bijections, generating functions, matrix-tree theorem, Polya theory, Ramsey theory, combinatorial algorithms, among others.

Instructor(s):  Dr. Shuwen Lou

Required text(s):  Ross, Sheldon, Elementary Introduction to Mathematical Finance, Third Edition (2011).

Prerequisites:  MATH 264 and MATH 304, or acceptance into the MS Mathematics/Statistics program.

Course description:  The course provides an introduction to the mathematical theory of option pricing. Topics include arbitrage, the Black–Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model.

Instructor(s):  Dr. Brian Seguin

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

Prerequisites:  MATH 201 and MATH 212

Course description:  This course provides a rigorous development of the differential calculus. Students are expected to have had experience understanding and writing proofs. Topics covered include: numerical sequences, limit theorems for sequences, completeness property, nested intervals theorem, Bolzano-Weierstrass theorem, Cauchy sequences, infinite series, convergence tests, rearrangements, power series, functions, continuity, intermediate value theorem, compactness, uniform continuity, the derivative, mean value theorem, l'Hopital's rule, convexity, Taylor's theorem with Lagrange remainder.

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. Robert McNees

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. Rafal Goebel

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

Additional notes:  Graduate students taking the class as Math 488 will face more challenging 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:  Dynamical systems, which are systems that evolve over time, are everywhere. Continuous-time dynamical systems, like an electrical circuit or a mechanical system consisting of weights and springs (not unlike the shocks in your car), can be described and then analyzed using differential equations. Discrete-time dynamical systems, like the balance of your savings account which (hopefully) increases every month or the population of species measured once every year, can be described using difference equations. Frequently, the differential and difference equations describing these and other systems are nonlinear. Solutions to these equations can tell you what the dynamical system will do in the future, so you can forecast the weather or realize that a species is doomed to extinction, but for nonlinear differential equations, solutions are notoriously hard to find. However, with proper analytical tools, one can predict the behavior of the system anyway. This is what the course is about. 

Instructor(s):  Dr. Xiaoli Kong

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

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

Textbook notes:  ISBN-13: 978-0495110811 ISBN-10: 0495110817

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).

Instructor(s):  Dr. Antonio Mastroberardino

Required text(s):  Sauer, Timothy. Numerical Analysis. 3rd edition. Pearson. 2018. Print. ISBN-13: 978-0134696454.

Textbook notes:  Students may choose to purchase the eText. ISBN-13: 978-0134697376.

Additional notes:  Graduate students will be required to complete more advanced homework exercises and present a supplemental topic from independent reading at the end of the semester.

Prerequisites:  COMP 170 or MATH/COMP 215, MATH 212, and MATH 264

Course description:  Numerical analysis is a branch of mathematics that deals with the development and use of algorithmic methods for solving mathematical problems that are often too complicated to solve analytically. Topics that will be covered include floating point computation, rootfinding, direct and iterative methods for solving systems of linear equations, interpolation, method of least squares, numerical quadrature, numerical solutions of ordinary and partial differential equations, and if time permits, various matrix decompositions. Homework assignments will include computational exercises requiring the use of the high-level programming language MATLAB, although no previous programming experience will be assumed.

Instructor(s):  Dr. Anthony Giaquinto

Required text(s):  Stewart, Ian. Galois Theory. 4th ed., Chapman and Hall/CRC, 2015, ISBN 9781482245820

Textbook notes:  Any edition and format of the text is acceptable.

Prerequisites:  MATH 313

Course description:  Abstract algebra is about the definition and study of various algebraic structures (e.g., groups, rings, fields, vector spaces) which have arisen in mathematics in the last 200 years or so. One of the original motivations for the study of these systems was to find a formula to solve a general fifth degree polynomial equation in terms of radicals. Such formulas exist for polynomials of degree 2, 3 and 4; in degree 2 the formula is the well-known quadratic formula which we learn in high-school algebra. The Norwegian mathematician Niels Henrik Abel eventually around 1822 proved that the fifth degree polynomial equation cannot be solved by such a formula, and the French mathematician Evariste Galois gave in 1832 a complete theory which tells us precisely which polynomial equations can be solved in terms of radicals. Later it was shown by similar techniques that it is impossible to trisect a given angle solely by means of ruler and compass, and also it is impossible to construct (by ruler and compass) a square whose area is the same as a given circle. Nowadays many of the algebraic structures used in these problems have applications far beyond their original motivation. For example, communication systems use algebraic coding theory to encode the information so that errors can be minimized, and public key cryptography, which banks use to verify electronic transactions, is rooted in the algebraic structures studied in this course. This course will focus mainly on selected topics in classical algebra, field and ring theory, polynomials and Galois theory.

Instructor(s):  Dr. A. Lauve

Required text(s):  Bogart, Kenneth, Combinatorics Through Guided Discovery, PreTeXt edition (2017), http://bogart.openmathbooks.org/.

Textbook notes:  The PreTeXt source code for the Bogart text is released under the GNU Free Documentation Licence (FDL). It does not look much like a traditional mathematics textbook. Being written for (guided) self-discovery, you won't find many carefully worded definitions or theorems. If you are looking for some of that, Brualdi and Bona have both written nice textbooks. (I will provide additional notes or resources, as needed.)

Prerequisites:  Math 162

Course description:  Combinatorial problems from enumeration and graph theory and methods for their solution. Prior experience with abstraction and proofs is helpful, but not necessary. Graduate students will: complete more advanced exercises than the undergraduate students; help compile carefully worded definitions and theorems, with proofs; and will present some supplemental topics from independent reading.

Syllabus: 
We discover the joy and power of counting. (What a funny thing to say!) To some extent, the topics and techniques below show up in other domains of mathematics and computer science. So you could call this an applications course (indeed combinatorists at MIT are members of the "Applied Mathematics" department). But we'll mostly just be having fun, learning, all over again, how to count.

Topics: Basic counting principles, induction and recursion in combinatorics and graph theory, distribution problems, generating functions. Advanced topics, as time permits may include: the principle of inclusion-exclusion, groups acting on sets, Catalan objects, graph walks, graph colorings, chromatic polynomials, combinatorial algorithms, optimization, pattern avoidance, probabilistic methods, partial orders, among others.

Techniques: Pigeon-hole principle, mathematical induction, inclusion-exclusion principle, recurrence relations, bijections, generating functions, matrix-tree theorem, Polya theory, Ramsey theory, combinatorial algorithms, among others.

Instructor(s):  Dr. Shuwen Lou

Required text(s):  Ross, Sheldon, Elementary Introduction to Mathematical Finance, Third Edition (2011).

Prerequisites:  MATH 264 and MATH 304, or acceptance into the MS Mathematics/Statistics program.

Course description:  The course provides an introduction to the mathematical theory of option pricing. Topics include arbitrage, the Black–Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model.

Instructor(s):  Dr. Brian Seguin

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

Prerequisites:  MATH 201 and MATH 212

Course description:  This course provides a rigorous development of the differential calculus. Students are expected to have had experience understanding and writing proofs. Topics covered include: numerical sequences, limit theorems for sequences, completeness property, nested intervals theorem, Bolzano-Weierstrass theorem, Cauchy sequences, infinite series, convergence tests, rearrangements, power series, functions, continuity, intermediate value theorem, compactness, uniform continuity, the derivative, mean value theorem, l'Hopital's rule, convexity, Taylor's theorem with Lagrange remainder.

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

Additional notes:  Graduate students taking the class as Math 488 will face more challenging 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:  Dynamical systems, which are systems that evolve over time, are everywhere. Continuous-time dynamical systems, like an electrical circuit or a mechanical system consisting of weights and springs (not unlike the shocks in your car), can be described and then analyzed using differential equations. Discrete-time dynamical systems, like the balance of your savings account which (hopefully) increases every month or the population of species measured once every year, can be described using difference equations. Frequently, the differential and difference equations describing these and other systems are nonlinear. Solutions to these equations can tell you what the dynamical system will do in the future, so you can forecast the weather or realize that a species is doomed to extinction, but for nonlinear differential equations, solutions are notoriously hard to find. However, with proper analytical tools, one can predict the behavior of the system anyway. This is what the course is about. 

Instructor(s):  Staff

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

Prerequisites:  None

Course description:  An introduction to statistical reasoning. Students learn how statistics has helped to solve major problems in economics, education, genetics, medicine, physics, political science, and psychology. Topics include: design of experiments, descriptive statistics, mean and standard deviation, the normal distribution, the binomial distribution, correlation and regression, sampling, estimation, and testing of hypothesis.

Syllabus:  Common

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.

Instructor(s):  Dr. Michael Perry

Required text(s):  none

Recommended text(s):  R. Cody & Smith, Applied Statistics and the SAS Programming

Additional notes:  Laptop and SAS On Demand account is required. We will set up a SAS On Demand account on the first day of class.

Prerequisites:  STAT 103, STAT 203 or STAT 335

Course description:  This course is an introduction to writing and executing SAS programs in the context of applied statistics problems. Students will learn some basic computer coding techniques such as if-statements and do-loops as well as how to code pre-defined SAS procedures to analyze statistical output various statistical methods such as t-tests, simple and multiple regressions, ANOVA, Chi-squared tests, and repeated measures. Students will be graded on homework, quizzes, one take home test and one project with a presentation. The course will require a significant amount of computer coding.

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. Gregory J. Matthews

Required text(s):  Wackerly, D., Mendenhall, W. and Scheaffer, R.L. Mathematical Statistics with Applications 7th Edition. ISBN-13: 978-0495110811

Recommended text(s):  Casella, G. and Berger, R.L. Statistical Inference 2nd edition. 2008.

Prerequisites:  MATH 304 or STAT 304

Course description:  This course will be a mathematically rigorous introduction to statistics and will require an extensive background in probability. The successful student will need a firm grasp of the following topics from probability theory: axiomatic probability, conditional probability, independence, combinatorial probability, random variables, families of discrete probability distributions (hypergeometric, binomial, Poisson, geometric, negative-binomial), families of continuous distributions (exponential, normal, gammma, beta), expected values, variance, covariance, joint densities, conditional densities, transformations of random variables, order statistics, and moment-generating functions.

Stat 305 will cover the following topics: methods of estimation, properties of estimators (unbiasedness, consistency, sufficiency, efficiency, etc.), minimum-variance unbiased estimators and the Cramer-Rao lower bound, Bayesian estimation, hypothesis testing, uniformly most powerful tests, Neyman-Pearson Lemma, sampling distributions and inferences involving the normal distribution, two-sample tests, goodness-of-fit tests, analysis of variance.

Instructor(s):  Dr. Xiaoli Kong

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, nonparametric regression and time series analysis will be discussed. 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. Quizzes, exams, and take-home assignments and projects will be used to determine the final grade in the course.

Instructor(s):  Dr. Tim O'Brien

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.)

Additional notes:  This course has been thoroughly revised: using R (and some SAS), we'll focus on logistic and multicategory logit regression, as well as correlated/mixed models data.

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 modelling. This course also addresses the fundamental questions encountered with regression and ANOVA for count data. Specialized methods for ordinal data, small samples, multi-category data, matched pairs, marginal models and random effects models (correlated data and GEEs) will also be discussed. The focus throughout this course will be on applications and real-life data sets; as such, theorems and proofs will not be emphasized. Using categorical data, students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. Grading is based on regular homework assignments, article review(s), a project/paper, as well as exams.

Instructor(s):  Staff

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

Additional notes:  Students may be asked to do some computer coding in R for this course.

Prerequisites:  MATH 162 or 132; BIOL 102

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

Instructor(s):  Dr. Antonio Mastroberardino

Required text(s):  Rosner, Bernard. Fundamentals of Biostatistics. 8th edition. Boston: Cengage Learning, 2015. ISBN-13: 9781305268920.

Prerequisites:  MATH 162 or 132; BIOL 102

Course description:  This course 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 programming in R and analyzing R output. (Note: Students may not receive credit for both STAT 203 & 335.)

Instructor(s):  Mr. Bret A Longman

Required text(s):  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. Swarnali Banerjee

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

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

Prerequisites:  STAT 203 or 335 or equivalent

Course description:  This course explores recently developed mathematical, probabilistic and statistical methods currently used in the fields of bioinformatics and DNA microarray and protein array data analysis. These include stochastic processes, (hidden and traditional) Markov chains, tree- and clustering techniques (including principal components analysis and biplots), discriminant analysis, experimental design strategies and ANOVA methods. Our focus in this course is on the application of these techniques and on meaningful interpretation of results.

Instructor(s):  Dr. Shuwen Lou

Required text(s):  Ross, Sheldon, Elementary Introduction to Mathematical Finance, Third Edition (2011).

Prerequisites:  MATH 264 and MATH 304, or acceptance into the MS Mathematics/Statistics program.

Course description:  The course provides an introduction to the mathematical theory of option pricing. Topics include arbitrage, the Black–Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model.

Instructor(s):  Dr. Xiaoli Kong

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

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

Textbook notes:  ISBN-13: 978-0495110811 ISBN-10: 0495110817

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).

Instructor(s):  Dr. Tim O'Brien

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.)

Additional notes:  This course has been thoroughly revised: using R (and some SAS), we'll focus on logistic and multicategory logit regression, as well as correlated/mixed models data.

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 modelling. This course also addresses the fundamental questions encountered with regression and ANOVA for count data. Specialized methods for ordinal data, small samples, multi-category data, matched pairs, marginal models and random effects models (correlated data and GEEs) will also be discussed. The focus throughout this course will be on applications and real-life data sets; as such, theorems and proofs will not be emphasized. Using categorical data, students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. Grading is based on regular homework assignments, article review(s), a project/paper, as well as exams.

Instructor(s):  Dr. Swarnali Banerjee

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

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

Prerequisites:  STAT 203 or 335 or equivalent

Course description:  This course explores recently developed mathematical, probabilistic and statistical methods currently used in the fields of bioinformatics and DNA microarray and protein array data analysis. These include stochastic processes, (hidden and traditional) Markov chains, tree- and clustering techniques (including principal components analysis and biplots), discriminant analysis, experimental design strategies and ANOVA methods. Our focus in this course is on the application of these techniques and on meaningful interpretation of results.

Instructor(s):  Dr. Shuwen Lou

Required text(s):  Ross, Sheldon, Elementary Introduction to Mathematical Finance, Third Edition (2011).

Prerequisites:  MATH 264 and MATH 304, or acceptance into the MS Mathematics/Statistics program.

Course description:  The course provides an introduction to the mathematical theory of option pricing. Topics include arbitrage, the Black–Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model.