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

Prerequisites:  None

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

Syllabus:  Common

Instructor(s):  Staff

Required text(s):  Eric Connally, Hughes-Hallett, D., and Gleason, A. M. Functions Modeling Change: A Preparation for Calculus. 6th ed.

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. Study of polynomials includes zeros, factor theorem, and graphs. Additional topics include rational functions, transformations of functions, function composition and inverse functions.

Syllabus:  Common

Instructor(s):  Staff

Required text(s):  Eric Connally, Hughes-Hallett, D., and Gleason, A. M. Functions Modeling Change: A Preparation for Calculus. 6th ed.

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):  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. Su, F. (2020). Mathematics for Human Flourishing. New Haven: Yale University Press.

Recommended text(s):  Fatima Pirbhai-Illich, S. P. (2017). Culturally Responsive Pedagogy. Cham, Switzerland: Springer International Publishing.

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):  Mr. Marius Radulescu

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

Prerequisites:  None

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

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. Emily Peters

Required text(s):  Discrete Mathematics with Ducks, by sarah-marie belcastro. June 21, 2012 by A K Peters/CRC Press Textbook. ISBN 9781466504998

Prerequisites:  MATH 161

Course description:  This course serves primarily as an introduction to understanding and constructing proofs for students planning to take advanced math courses. Topics include: mathematical induction, the Euclidean algorithm, congruences, divisibility, counting/combinatorics, and graph theory; as well as mathematical writing.

Instructor(s):  Dr. Matthew Mills

Required text(s):  No required text

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

Prerequisites:  UCWR 110 and 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):  Staff

Required text(s):  David C. Lay, Steven R. Lay, et al.. Linear Algebra and Its Applications. 6th edition.

Prerequisites:  MATH 132 or MATH 162

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

Instructor(s):  Dr. Christine Haught

Required text(s):  Interactive online python textbook from zyBooks. Details TBA.

Prerequisites:  MATH 132 or MATH 162

Course description:  Math 215 is an introductory programming course for students interested in mathematics and scientific applications, including data science and bioinformatics. No previous programming experience is required. This course is not intended for computer science majors. This course can be used to satisfy the programming requirement in the math major. Students will learn object-oriented programming using the programming language Python. Python is easy to learn and we will quickly be able to solve interesting problems with it. Programming examples will come from mathematics, physics, data science, bioinformatics and other scientific computing applications. We will work with examples from calculus, number theory, statistics, geometry, fractals and linear algebra. The course is programming intensive. There will be weekly programming assignments as well as frequent in-class exercises. There will be two in class exams during the term and a final project.

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. Brian Seguin

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

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

Prerequisites:  MATH 162A

Course description:  Vectors and vector algebra, curves and surfaces in space, functions of several variables, partial derivatives, the chain rule, the gradient vector, LaGrange multipliers, multiple integrals, volume, surface area, the Change of Variables theorem, line integrals, surface integrals, Green's theorem, the Divergence Theorem, and Stokes' Theorem. Software packages such as MAPLE may be used. This course follows a traditional approach to calculus sequencing and is intended only for students with either AP credit or transfer credit equivalent to MATH 161A and MATH 162A.

Instructor(s):  Dr. Darius Wheeler

Required text(s):  Fundamentals of Differential Equations and Boundary Value Problems -- MyLab Math with Pearson eText, Digital Update ISBN-13: 9780137394494 | Published 2021

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. Stephen London

Required text(s):  None

Prerequisites:  None

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

Instructor(s):  Dr. Alan Saleski

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

Recommended text(s):  Bertsekas & Tsitsiklis, Introduction to Probability, 2nd ed, Athena (2008) Sheldon Ross, A First Course in Probability, 10th ed, Pearson (2019)

Additional notes:  This material in this course is vital for students who plan to take the first Actuarial Exam, SOA Exam P.

Prerequisites:  Math 263

Course description:  This course is an introduction to probability theory for students who have studied multivariable calculus. No prior knowledge of probability or statistics is assumed. The topics are: basic combinatorics, random variables, distributions, variance, conditional probability, Bayes’ theorem, joint distributions, covariance, correlation, independence, Chebyshev's inequality, the law of large numbers, and the Central limit theorem. Distribution functions include uniform, binomial, geometric, hypergeometric, Poisson, exponential, normal, gamma, and beta. As time permits, additional topics, such as Markov chains, will be discussed.

Instructor(s):  Dr. Rafael S. González D'León

Required text(s):  Judson, Thomas W.. Abstract Algebra: Theory and Applications. (2009).

Recommended text(s):  Robinson, Derek J. S.. Abstract Algebra: An Introduction with Applications. 3rd ed., De Gruyter. (2022).

Textbook notes:  Judson's book is available online for free in English and Spanish: http://abstract.ups.edu/download.html

Prerequisites:  MATH 201 and MATH 212

Course description:  The subject of algebra can be traced back to the work of the Persian mathematician Al-Khwarizmi in which he presented methods to find roots of linear and quadratic polynomials. The word algebra (al-jabr) comes from the title of his book on calculation by completion and balancing. The abstract formalism of having a set of operations "acting" on objects has appeared in many different contexts since then: from the problem of finding roots of polynomials to the understanding of the concept of symmetry. As an example the symmetries of a solid object can be composed and reversed giving rise to the structure known as a "group". It is precisely the theory of groups that is the focus of this first course in abstract algebra. Applications of this theory are plentiful and can be found in computer science, physics, chemistry, and engineering.

Syllabus:  Topics include: equivalence relations, groups, subgroups, homomorphisms, quotients, products, groups acting on sets, and a selection of advanced topics. Students will learn to formulate mathematical arguments and formal proofs within this area. The evaluation will be comprised of two exams, homework, and a final exam. The students will also work in small teams on group projects and give presentations to the class. Extra problems on homework sets will be given for the students taking this class as MATH 413.

Instructor(s):  Dr. Anthony Giaquinto

Required text(s):  Strang, Gilbert.Linear Algebra and Learning from Data. 1st ed., Wellesley-Cambridge Press, 2019. ISBN-13: 9780692196380

Recommended text(s): 

• Garcia, Stephan Ramon, and Roger A. Horn. Matrix Mathematics: A Second Course in Linear Algebra. 2nd ed., Cambridge University Press, 2023. ISBN-13: 9781108938426
• Strang, Gilbert.Linear Algebra and its Applications. 4th ed., Cengage Learning, 2006. ISBN-13: 9780030105678

Prerequisites:  MATH 212 - Linear Algebra; Abstract algebra MATH 313 will not be a prerequisite for this course.

Course description:  Linear algebra is a fundamental tool in many fields, including mathematics and statistics, data science, computer science, economics, and the biological and physical sciences. This second course on linear algebra will transition from the basic theory found in MATH 212 to more advanced topics of linear algebra. After a quick review of the basics of matrices and linear algebra, the course will transition to topics such as the singular value decomposition, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Applications to effective computation and modern data analysis will be highlighted throughout.

There will be regular written homework assignments as well as two midterms and a final exam.

Instructor(s):  Mr. Marius Radulescu

Required text(s):  Greenberg, Marvin J. Euclidean and Non-Euclidean Geometries: Development and History. 3rd ed. W. H. Freeman, 2007. ISBN-13: 978-0716799481.

Recommended text(s):  Venema, Gerard Foundations of Geometry. Pearson, 2012. ISBN-13: 978-0136020585

Coxeter, H.S.M. and Greitzer, S.L. Geometry Revisited. Math Association of America, 1967. ISBN-13: 978-0883856192.

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

Course description:  This course is designed as an exploration of the traditional axiomatic treatment of geometry, including topics such as Euclid's Elements, axiomatic systems, the parallel postulates, neutral geometry, Euclidean geometry, hyperbolic geometry, constructions, transformations, and the classical models for non-Euclidean geometry. The course is intended to give a deeper understanding of geometry and measurement with an emphasis on reasoning and presentation of mathematical ideas. We will use small group work to explore some of the unknown beautiful problems of classic geometry, revisit axiomatic systems and learn how to develop arguments based on logic. Students will be graded based on homework, quizzes, a midterm exam and a final exam.

Instructor(s):  Dr. Tuyen Tran

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

Recommended text(s):  Arthur Mattuck, Introduction to Analysis

Prerequisites:  MATH 201, MATH 162

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

Instructor(s):  Dr. John G Del Greco

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

Prerequisites:  MATH 263

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

Instructor(s):  Dr. Peter Tingley

Required text(s):  None

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

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

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

Instructor(s):  Dr. Xiang Wan

Required text(s):  Applied Partial Differential Equations (3rd ed) by J. Logan, 2015. ISBN-13: 978-3319124926

Recommended text(s):  Partial Differential Equations: An Introduction (2nd edition) by Walter A. Strauss, 2008. ISBN-13: 978-0470260715

Textbook notes:  Required text Amazon link: https://www.amazon.com/Applied-Differential-Equations-Undergraduate-Mathematics/dp/3319124927/ref=sr_1_4?crid=14CUDER9S4LK6&keywords=Applied+Partial+Differential+Equations+3rd+ed+J+logan&qid=1679896133&s=books&sprefix=applied+partial+differential+equations+3rd+ed+j+logan%2Cstripbooks%2C93&sr=1-4

Recommended text Amazon link: https://www.amazon.com/Student-Solutions-accompany-Differential-Equations/dp/0470260718/ref=sr_1_4?crid=3V444NIXGA8HK&keywords=Partial+Differential+Equations%3A+An+Introduction+solution&qid=1679894683&s=books&sprefix=partial+differential+equations+an+introduction+solu%2Cstripbooks%2C154&sr=1-4&ufe=app_do%3Aamzn1.fos.006c50ae-5d4c-4777-9bc0-4513d670b6bc

Prerequisites:  MATH 264 or MATH 266

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

Syllabus:  https://loyolauniversitychicago-my.sharepoint.com/:b:/g/personal/xwan1_luc_edu/EYz3iYUf-zlDub0LbNhOcmEB93mb8wHco7teoweuGZYKMw?e=QxcZxo

Instructor(s):  Dr. Carmen Rovi

Required text(s):  None.

Recommended text(s):  - Aigner, M., Ziegler, G.M. Proofs from THE BOOK. Springer, 6th ed., 2018.

- Krantz, S.G. How to Teach Mathematics. American Mathematical Society, 3rd ed., 2015.

Additional readings provided throughout the semester. Drawn from, e.g.,

- Felder, R.M., Brent, R. Teaching and Learning STEM: A Practical Guide. Jossey-Bass, 2016.

- Hagelgans, N.L., el al., eds. Practical Guide to Cooperative Learning in Collegiate Mathemat- ics. MAA, 1995.

- Henrich, A.K., et al., eds. Living Proof: Stories of Resilience. AMS & MAA, 2019.

- Higham, N.J. Handbook of Writing for the Mathematical Sciences. SIAM, 2nd ed., 1998.

- Krantz, S.G. A Mathematician’s Survival Guide: Graduate School and Early Career Development. American Mathematical Society, 2003.

- Kung, D., Speer, N. What Could They Possibly be Thinking!?!, MAA, 2020.

- Levy, R., Laugesen, R. BIG Jobs Guide: Business, Industry, and Government Careers for Mathematical Scientists, SIAM, 2018.

- Su, F. Mathematics for Human Flourishing. Yale UP, 2000.

Prerequisites:  Graduate standing

Course description:  This is a professional development seminar for the beginning graduate student. Through short lectures, faculty panels, career panels, regular reading and writing assignments, and assorted workshops, it provides the student with the tools they need to succeed in the program, and beyond.

Instructor(s):  Dr. Shuwen Lou

Required text(s):  Introduction to Mathematical Statistics by Hogg, McKean and Craig, 8th edition.

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

Course description:  This is the first semester of a two-semester sequence. The first semester (STAT 404) is essentially an exploration of probability as a mathematical model of chance phenomena. (The second semester, STAT 405, explores the statistical analyses based on these models.) Topics to be covered in STAT 404 include discrete and continuous random variables, transformations, multivariate distributions, correlation, independence, variance-covariance, special distributions (binomial, Poisson, gamma, chi-square, beta, normal, multivariate normal, t, and F), expectations of functions, convergence in probability, convergence in distribution, moment generating functions, and the central limit theorem.

Instructor(s):  Dr. Rafael S. González D'León

Required text(s):  Judson, Thomas W.. Abstract Algebra: Theory and Applications. (2009).

Recommended text(s):  Robinson, Derek J. S.. Abstract Algebra: An Introduction with Applications. 3rd ed., De Gruyter. (2022).

Textbook notes:  Judson's book is available online for free in English and Spanish: http://abstract.ups.edu/download.html

Prerequisites:  MATH 201 and MATH 212

Course description:  The subject of algebra can be traced back to the work of the Persian mathematician Al-Khwarizmi in which he presented methods to find roots of linear and quadratic polynomials. The word algebra (al-jabr) comes from the title of his book on calculation by completion and balancing. The abstract formalism of having a set of operations "acting" on objects has appeared in many different contexts since then: from the problem of finding roots of polynomials to the understanding of the concept of symmetry. As an example the symmetries of a solid object can be composed and reversed giving rise to the structure known as a "group". It is precisely the theory of groups that is the focus of this first course in abstract algebra. Applications of this theory are plentiful and can be found in computer science, physics, chemistry, and engineering.

Syllabus:  Topics include: equivalence relations, groups, subgroups, homomorphisms, quotients, products, groups acting on sets, and a selection of advanced topics. Students will learn to formulate mathematical arguments and formal proofs within this area. The evaluation will be comprised of two exams, homework, and a final exam. The students will also work in small teams on group projects and give presentations to the class. Extra problems on homework sets will be given for the students taking this class as MATH 413.

Instructor(s):  Dr. Anthony Giaquinto

Required text(s):  Strang, Gilbert.Linear Algebra and Learning from Data. 1st ed., Wellesley-Cambridge Press, 2019. ISBN-13: 9780692196380

Recommended text(s): 

• Garcia, Stephan Ramon, and Roger A. Horn. Matrix Mathematics: A Second Course in Linear Algebra. 2nd ed., Cambridge University Press, 2023. ISBN-13: 9781108938426
• Strang, Gilbert.Linear Algebra and its Applications. 4th ed., Cengage Learning, 2006. ISBN-13: 9780030105678

Prerequisites:  MATH 212 - Linear Algebra; Abstract algebra MATH 313 will not be a prerequisite for this course.

Course description:  Linear algebra is a fundamental tool in many fields, including mathematics and statistics, data science, computer science, economics, and the biological and physical sciences. This second course on linear algebra will transition from the basic theory found in MATH 212 to more advanced topics of linear algebra. After a quick review of the basics of matrices and linear algebra, the course will transition to topics such as the singular value decomposition, spectral theorem, QR factorization, normal matrices, Hermitian matrices, and positive definite matrices. Applications to effective computation and modern data analysis will be highlighted throughout.

There will be regular written homework assignments as well as two midterms and a final exam.

Instructor(s):  Mr. Marius Radulescu

Required text(s):  Greenberg, Marvin J. Euclidean and Non-Euclidean Geometries: Development and History. 3rd ed. W. H. Freeman, 2007. ISBN-13: 978-0716799481.

Recommended text(s):  Venema, Gerard Foundations of Geometry. Pearson, 2012. ISBN-13: 978-0136020585

Coxeter, H.S.M. and Greitzer, S.L. Geometry Revisited. Math Association of America, 1967. ISBN-13: 978-0883856192.

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

Course description:  This course is designed as an exploration of the traditional axiomatic treatment of geometry, including topics such as Euclid's Elements, axiomatic systems, the parallel postulates, neutral geometry, Euclidean geometry, hyperbolic geometry, constructions, transformations, and the classical models for non-Euclidean geometry. The course is intended to give a deeper understanding of geometry and measurement with an emphasis on reasoning and presentation of mathematical ideas. We will use small group work to explore some of the unknown beautiful problems of classic geometry, revisit axiomatic systems and learn how to develop arguments based on logic. Students will be graded based on homework, quizzes, a midterm exam and a final exam.

Instructor(s):  Dr. Tuyen Tran

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

Recommended text(s):  Arthur Mattuck, Introduction to Analysis

Prerequisites:  MATH 201, MATH 162

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

Instructor(s):  Dr. John G Del Greco

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

Prerequisites:  MATH 263

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

Instructor(s):  Dr. Peter Tingley

Required text(s):  None

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

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

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

Instructor(s):  Dr. Xiang Wan

Required text(s):  Applied Partial Differential Equations (3rd ed) by J. Logan, 2015. ISBN-13: 978-3319124926

Recommended text(s):  Partial Differential Equations: An Introduction (2nd edition) by Walter A. Strauss, 2008. ISBN-13: 978-0470260715

Textbook notes:  Required text Amazon link: https://www.amazon.com/Applied-Differential-Equations-Undergraduate-Mathematics/dp/3319124927/ref=sr_1_4?crid=14CUDER9S4LK6&keywords=Applied+Partial+Differential+Equations+3rd+ed+J+logan&qid=1679896133&s=books&sprefix=applied+partial+differential+equations+3rd+ed+j+logan%2Cstripbooks%2C93&sr=1-4

Recommended text Amazon link: https://www.amazon.com/Student-Solutions-accompany-Differential-Equations/dp/0470260718/ref=sr_1_4?crid=3V444NIXGA8HK&keywords=Partial+Differential+Equations%3A+An+Introduction+solution&qid=1679894683&s=books&sprefix=partial+differential+equations+an+introduction+solu%2Cstripbooks%2C154&sr=1-4&ufe=app_do%3Aamzn1.fos.006c50ae-5d4c-4777-9bc0-4513d670b6bc

Prerequisites:  MATH 264 or MATH 266

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

Syllabus:  https://loyolauniversitychicago-my.sharepoint.com/:b:/g/personal/xwan1_luc_edu/EYz3iYUf-zlDub0LbNhOcmEB93mb8wHco7teoweuGZYKMw?e=QxcZxo

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. 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 or MATH 162A (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. Alan Saleski

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

Recommended text(s):  Bertsekas & Tsitsiklis, Introduction to Probability, 2nd ed, Athena (2008) Sheldon Ross, A First Course in Probability, 10th ed, Pearson (2019)

Additional notes:  This material in this course is vital for students who plan to take the first Actuarial Exam, SOA Exam P.

Prerequisites:  Math 263

Course description:  This course is an introduction to probability theory for students who have studied multivariable calculus. No prior knowledge of probability or statistics is assumed. The topics are: basic combinatorics, random variables, distributions, variance, conditional probability, Bayes’ theorem, joint distributions, covariance, correlation, independence, Chebyshev's inequality, the law of large numbers, and the Central limit theorem. Distribution functions include uniform, binomial, geometric, hypergeometric, Poisson, exponential, normal, gamma, and beta. As time permits, additional topics, such as Markov chains, will be discussed.

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

Required text(s):  Oehlert, Gary W., A First Course in Design and Analysis of Experiments, 2010, freely downloaded from: http://users.stat.umn.edu/~gary/book/fcdae.pdf

Prerequisites:  An introductory class such as STAT 203 or STAT 335 or equivalent or permission of the instructor. It is highly recommended that students have taken a course in applied regression (such as STAT 308 or 408).

Course description:  As no subject is more central to the development of statistical methods, this course provides students with a thorough introduction to statistical experimental design and to the statistical methods used to analyze the resulting data. The concepts of comparative experiments, analysis of variance (ANOVA) and mean separation procedures will be covered; blocking (complete and incomplete) will be discussed, as will be factorial designs, fractional factorial designs, and confounding. The course will focus on biometric applications such as clinical trials, HIV studies, and environmental and agricultural research, but industrial and other examples will occasionally be provided to show the breadth of application of experimental design ideas.

In this course, students will develop expertise using the SAS, R and Minitab computer packages, although no previous programming experience will be assumed. Grading will be based on participation, homework assignments, a project/paper, exam(s) and a final.

Instructor(s):  Dr. Matthew Stuart

Required text(s):  None

Prerequisites:  STAT 203 or STAT 335

Course description:  Simple and multiple linear regression methods including weighted least squares and polynomial regression. Multiple comparison estimation procedures, residual analysis, and other methods for studying the aptness of a proposed regression model. Use of packaged computer programs such as R, though no previous coding experience required. Evaluation will be made through take home exams as well as a semester long group project.

Instructor(s):  Dr. Matthew Stuart

Required text(s):  None

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. Use of packaged computer programs such as R will be utilized, though no previous coding experience required. Evaluation will be made through homework assignments, take home exams, and a semester long project. (Note: Students may not receive credit for both STAT 203 & 335.)

Instructor(s):  Mr. Bret A Longman

Required text(s):  A course packet will be given based on the Samuels/Witmer/Schaffner book but it is not necessary to buy this book.

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):  Mr. Bret A Longman

Required text(s):  None

Prerequisites:  STAT 335

Course description:  This course covers multi-variate analysis, including advanced ANOVA, linear regression, logistic regression and survival analysis. The emphasis of the course is on applications instead of statistical theory, and students are required to analyze real-life datasets using the Minitab, SAS and/or R statistical packages, although no previous programming experience is assumed. Grading will be based on homework assignments, a course project/paper, exams and a final.

Instructor(s):  Dr. Matthew Stuart

Required text(s):  None

Recommended text(s):  ACTEX Exam P Study Materials

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

Course description:  The seminar provides a comprehensive review of the probability topics that most commonly appear on Actuarial Exam P. Topics covered include: axiomatic probability, combinatorial probability, conditional probability and Bayes' Theorem, independence, random variables and their various distributions, joint distributions, marginal distributions, conditional distributions of tow of more random variables. Students will also learn test-taking strategies and will have the opportunity to take practice tests.

Instructor(s):  Dr. Michael Perry

Required text(s):  None

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

Prerequisites:  None

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

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

Instructor(s):  Dr. Shuwen Lou

Required text(s):  Introduction to Mathematical Statistics by Hogg, McKean and Craig, 8th edition.

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

Course description:  This is the first semester of a two-semester sequence. The first semester (STAT 404) is essentially an exploration of probability as a mathematical model of chance phenomena. (The second semester, STAT 405, explores the statistical analyses based on these models.) Topics to be covered in STAT 404 include discrete and continuous random variables, transformations, multivariate distributions, correlation, independence, variance-covariance, special distributions (binomial, Poisson, gamma, chi-square, beta, normal, multivariate normal, t, and F), expectations of functions, convergence in probability, convergence in distribution, moment generating functions, and the central limit theorem.

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

Required text(s):  Oehlert, Gary W., A First Course in Design and Analysis of Experiments, 2010, freely downloaded from: http://users.stat.umn.edu/~gary/book/fcdae.pdf

Prerequisites:  An introductory class such as STAT 203 or STAT 335 or equivalent or permission of the instructor. It is highly recommended that students have taken a course in applied regression (such as STAT 308 or 408).

Course description:  As no subject is more central to the development of statistical methods, this course provides students with a thorough introduction to statistical experimental design and to the statistical methods used to analyze the resulting data. The concepts of comparative experiments, analysis of variance (ANOVA) and mean separation procedures will be covered; blocking (complete and incomplete) will be discussed, as will be factorial designs, fractional factorial designs, and confounding. The course will focus on biometric applications such as clinical trials, HIV studies, and environmental and agricultural research, but industrial and other examples will occasionally be provided to show the breadth of application of experimental design ideas.

In this course, students will develop expertise using the SAS, R and Minitab computer packages, although no previous programming experience will be assumed. Grading will be based on participation, homework assignments, a project/paper, exam(s) and a final.

Instructor(s):  Dr. Nan Miles Xi

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

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

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

Course description:  This course provides students with a thorough introduction to applied regression methodology. The concept of simple linear regression will be reviewed and discussed using matrices, and multiple linear regression, transformations, diagnostics, polynomial regression, indicator variables, model building, and multicollinearity will be discussed, as will be nonlinear and generalized linear regression. Coding will be introduced using the statistical software R. The course will focus on applications of linear regression as a tool for the analysis of real, possibly messy, data.

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Survival Analysis Techniques for Censored and Truncated Data by Klein and Moeschberger (2nd Edition)

Prerequisites:  Some background in basic statistical methods or biostatistics, or permission of instructor.

Course description:  Modern statistical methods are covered to analyze data that is right-, left- and/or interval-censored. Nonparametric approaches such as the Kaplan-Meier estimation technique, log-rank test and proportional-hazards model are considered as are parametric methods such as those based on the Exponential and Weibull distribution. Accelerated failure time models and nonlinear models are also discussed. Students will develop expertise using the SAS (and R) computer packages, although no previous programming experience will be assumed.

Instructor(s):  Dr. Mena Whalen

Required text(s):  Grolemund, Garrett, and Hadley Wickham. R for Data Science. O’Reilly Media, 2017 Baumer, B.S., Kaplan, D.T., & Horton, N.J. (2021). Modern Data Science with R (2nd ed.). Chapman and Hall/CRC. Both found online.

Prerequisites:  None

Course description:  Learning to use the programming language R and the tidyverse package to wrangle and manage data in a pipeline for data analysis.