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:  Math Placement Test

Course description:  This course covers the fundamentals of algebra, ranging from linear equations and their graphs through exponents and systems of equations.

Syllabus:  Common

Instructor(s):  Staff

Required text(s):  Quantitative Literacy: Thinking between the lines by Crauder, Evans, Johnson, Noell

Prerequisites:  None

Course description:  This course investigates mathematical modeling applied to a variety of topics such as linear programming, coding information, probability and statistics, scheduling problems and social choice.

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 Placement Test or MATH 100

Course description:  This course covers algebraic topics ranging from functions and their applications to complex numbers to inverse functions to the fundamental theorem of algebra.

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 Placement Test or Math 117

Course description:  This course covers topics ranging from exponential and logarithmic functions to trigonometric functions to the complex plane and elementary optimization problems.

Syllabus:  Common

Instructor(s):  Dr. Darius Wheeler

Required text(s):  None

Recommended text(s):  None

Prerequisites:  None

Course description:  Freshman Mathematics/Statistics Seminar (1-3 Credit Hours): A freshman seminar with no prerequisites on topics in the mathematical sciences drawn from algebra, geometry, statistics, and their applications.

Instructor(s):  Staff

Required text(s):  Hughes-Hallett, Deborah, et al. Applied & Single Variable Calculus for Loyola University Chicago, Custom (WileyPlus eBook).

Prerequisites:  Math Placement Test or Math 118

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.

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:  This course is a continuation of Mathematics 131. Topics include:definition and interpretations of the integral (numerically, graphically, and algebraically), basic techniques for computing anti-derivatives, applications to probability, an introduction to multi-variable calculus and optimization for functions of several variables, and mathematical modeling using differential equations. (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 Placement Test or MATH 118

Course description:  This course provides a standard introduction to differential and integral calculus and covers topics ranging from functions and limits to derivatives and their applications to definite and indefinite integrals and the fundamental theorem of calculus and their applications.

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 Carmen Rovi

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

Prerequisites:  MATH 161

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

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, cardinality, sets, logic, and graph theory. 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 regularly in addition to tests and a final.

Instructor(s):  Dr. Alan Saleski

Required text(s):  Hammack, The Book of Proof, 3rd edition (Also, available for free on Hammack's website.) Supplemental required book: Discrete Structures, zyBook

Prerequisites:  Math 161 (or equivalent)

Course description:  An introduction to writing clear and logical proofs. Topics to include naive set theory, combinatorics, first-order predicate logic, cardinality, number theory, mathematical induction, relations, and functions. We will also discuss mathematical paradoxes and historical themes on the evolution of what constitutes rigor. This course is an essential prerequisite to 300-level courses in analysis, algebra, and topology.

Syllabus:  Biweekly quizzes, weekly written homework, two tests, and a final exam. As this course is writing-intensive, two essays will be assigned.

Instructor(s):  Dr. Anthony Giaquinto

Required text(s):  Strang, Gilbert. Introduction to Linear Algebra. Sixth Edition, Wellesley Cambridge Press, 2023, ISBN 978-1-7331466-7-8

Prerequisites:  MATH 132 or MATH 162

Course description:  Linear algebra is an indispensable tool in the sciences from pure mathematics to physics, engineering, computer science, data science, machine learning and imaging. This course will focus on the traditional topics of linear algebra including vector algebra and geometry, matrices, systems of linear equations, vector spaces, orthogonality, determinants, eigenvalues and eigenvectors with an eye on applications and uses of these concepts.

Instructor(s):  Mr. Marius Radulescu

Required text(s):  Lay, David C., et al. Linear Algebra and Its Applications. 6th ed. Pearson Education Limited, 2021. ISBN-13: 9780136880929

Prerequisites:  MATH 132 or MATH 162 or MATH 162A.

Course description:  This course provides an introduction to linear algebra in abstract vector spaces with an emphasis on Rn, covering topics such as Gaussian elimination, matrix algebra, linear independence and spanning, linear transformations and eigenvalues; software packages such as MAPLE may be used. Outcomes: Students will receive an introduction to abstract mathematics in a setting that encourages the thinking needed in more advanced mathematics courses.

Instructor(s):  Dr. Xiang Wan

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

Prerequisites:  MATH 132 or MATH 162, or permission of instructor

Course description:  Math 215 is an introductory programming course for students interested in mathematics and scientific applications, including applied math, 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, several exams during the semester, 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. Eric Chang

Required text(s):  William E. Boyce, Richard C. DiPrima, and Douglas B. Meade, Elementary Differential Equations and Boundary Value Problems, 12th Edition, Wiley 2021.

Prerequisites:  MATH 263 or MATH 263A.

Course description:  This course covers the theory, solution techniques, and applications surrounding linear and non-linear first and second-order differential equations, including systems of equations; software packages such as MAPLE may be used.

Instructor(s):  Dr. Tuyen Tran

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

Prerequisites:  MATH263

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

Instructor(s):  Dr. Carmen Rovi

Required text(s):  none

Prerequisites:  Math 161.

Course description:  This course is a sophomore-level seminar covering topics in areas such as number theory, logic, set theory, metric spaces, or history of mathematics. Students will obtain an initial insight into several areas of advanced study in mathematics.

Instructor(s):  Dr. Shuwen Lou

Required text(s):  TBA

Prerequisites:  MATH 263 or MATH 263A.

Course description:  This course provides a calculus based introduction to probability theory, including topics such as combinatorial analysis, random walk, conditional probability, and a variety of statistical distributions.

Instructor(s):  Dr. Matthew Stuart

Required text(s):  Statistical Inference 2nd Edition, George Casella and Roger Berger

Prerequisites:  STAT 304

Course description:  This course is a continuation of STAT 304 and applies the techniques of calculus and probability to the study of advanced topics in statistics. Topics explored include moment generating functions, maximum likelihood, unbiased estimators, most powerful hypothesis tests, and Bayesian statistics.

Instructor(s):  Dr. Emily Peters

Required text(s):  Gallian, Joseph A. Contemporary Abstract Algebra. 10th ed., CRC, Taylor & Francis Group, 2021.

Prerequisites:  MATH 201 and MATH 212

Course description:  This course provides a rigorous introduction to the study of structures such as groups, rings, and fields; emphasis is on the theory of groups with topics such as subgroups, cyclic groups, Abelian groups, permutation groups, homomorphisms, cosets, and factor groups. Prerequisites: MATH 201 and 212. Outcomes: Students will obtain an understanding of abstract structures that will prepare them for advanced work in mathematics.

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

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

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 Goodman's book is available online: https://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/download.htm

Prerequisites:  MATH 313

Course description:  Abstract algebra is more than the study of a collection of mathematical objects. As the great mathematician Emmy Noether, who was influential in the field, wrote in a letter to Hasse in 1931 "My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously" (From the book "Emmy Noether 1882-1935" by Auguste Dick). So abstract algebra is the field that deals with how to think about structure everywhere where it appears. It then has many applications in Mathematics, Physics, Computer Science, and many other areas.

Syllabus:  Topics include: commutative and non-commutative rings, integral domains, and fields. Selected topics will include Galois theory and advanced group theory. 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 414.

Instructor(s):  Dr. Christine Haught

Required text(s):  Hodel, Richard E. An Introduction to mathematical Logic. Dover. 2013. Print. ISBN-13: 978-0-486-49785-3.

Prerequisites:  Math 201

Course description:  This course in modern mathematical logic begins with a study of propositional logic and leads to the study of first-order predicate logic, including quantifiers, models, syntax, semantics, the completeness and compactness theorems, and other selected topics. We will study of the concepts of truth and proof and how they relate to each other. The main topics are propositional logic, first order predicate logic, and decidability. Propositional logic is the study of the expressive power of a language that uses only the Boolean connectives and, or, and not. First-order predicate logic builds on propositional logic and has more expressive power. It adds the ability to refer to properties of individuals through predicates, as well as existential and universal quantifiers. Much of the mathematics that students have encountered can be expressed in first-order logic. We will study some model theory, introduce the concept of decidability and build up to studying the Godel Incompleteness Theorems. Godel’s first Incompleteness Theorem tells us that in any “reasonable” axiomatization of arithmetic, there will be a statement that is true but not provable.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Cryptography: An Introduction (3rd Edition), by Nigel Smart. Self-published by the author at https://homes.esat.kuleuven.be/~nsmart/Crypto_Book/.

Recommended text(s): 

• Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman. An Introduction to Mathematical Cryptography, 2nd ed. ISBN-13: 9781493917105. New York: Springer, 2014.
• Steven Levy, Crypto : How the Code Rebels Beat the Government, Saving Privacy in the Digital Age, Penguin 2001. ISBN 978-0140244328.
• Paar, Christof and Jan Pelzl. Understanding Cryptography: A Textbook for Students and Practitioners. ISBN-13: 978-3642041006 (Print). ASIN: B00475ARKM (Kindle). Heidelberg: Springer, 2010. Print and Kindle.

Prerequisites:  (COMP 163 or MATH 313 or MATH 201) and (COMP 125 or COMP 150 or COMP 170 or MATH/COMP 215).

Course description:  This interdisciplinary course treats the mathematical and practical theory of cryptographic systems. That is, the course will be a mixture of theory and practice, involving mathematical proofs, algorithm development (based on the mathematics), and coding—both in lectures and on homework assignments.

The course begins with a survey of historical systems (e.g., from Julius Caesar's time and well before), before spending some time on classical private-key (aka symmetric) systems, such as the Beaufort, Hill, Feistel, and Rijndael ciphers. Our main focus, however, will be public-key (asymmetric) cryptosystems, first appearing the 1970s, and now used EVERYWHERE—in every login to a secure website, in every credit card transaction, every time you ssh into a server to finish your MATH 331 homework, when companies store your password and personal data with hash functions, in Bitcoin, BitTorrent, as well as the modern sale of digital artwork.

We will develop the mathematics needed for Diffie-Hellman, RSA, and elliptic curve cryptography. The RSA algorithm is the gold-standard. WARNING: Quantum computers are coming! They will make RSA obsolete. We will soon need something new. Time permitting, we will also discuss the emerging theory of lattice-based cryptosystems.

Code demonstrations and assignments will be completed in Python 3. This should be available on Loyola-managed machines. Students may wish to install it on their machines as well. (This guide tells you what you need to do if you go the Anaconda route.)

Syllabus:  Planned course assessments will be semiregular quizzes and homework, one midterm exam, a short project, 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

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. Xiang Wan

Required text(s):  N/A

Recommended text(s):  Haberman, Richard. Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow. United States, Society for Industrial and Applied Mathematics, 1988.

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

Course description:  This course will teach students how to use various areas of mathematics to formulate mathematical models in various scenarios, such as physics, biology, computer science, engineering, finance, etc. Centered around Differential Equations, we will explore how different mathematical tools are assembled together to solve questions from modeling, mainly through case study.

Instructor(s):  Dr. Carmen Rovi

Required text(s):  None

Prerequisites:  mostly intended for seniors, but juniors who have completed some upper-level math classes like 313 and/or 351 are also welcome.

Course description:  The Undergraduate Seminar in Mathematics will be a weekly, hour-long seminar where you will hear about some of the many deep and interesting areas of mathematics beyond what you would see in the classroom of most math classes. Students taking this class will be expected to give two brief lectures (one on a familiar topic from the curriculum, and one on a higher level material not customarily from the curriculum), and prepare an extended abstract summarizing the advanced material presented. The topics of student talks will be agreed upon with Dr. Rovi in advance and the students will receive guidance on the chosen topic and on how to give an effective presentation. Students will gain the ability to present material in Mathematics to a general audience. They will be graded based on their performance in presentations and abstracts, and on class participation.

Instructor(s):  Dr. Swarnali Banerjee

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

Recommended text(s):  Introduction to Mathematical Statistics, by Hogg, McKean and Craig (7th edition)

Prerequisites:  MATH/STAT 404

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

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

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

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 Goodman's book is available online: https://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/download.htm

Prerequisites:  MATH 313

Course description:  Abstract algebra is more than the study of a collection of mathematical objects. As the great mathematician Emmy Noether, who was influential in the field, wrote in a letter to Hasse in 1931 "My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously" (From the book "Emmy Noether 1882-1935" by Auguste Dick). So abstract algebra is the field that deals with how to think about structure everywhere where it appears. It then has many applications in Mathematics, Physics, Computer Science, and many other areas.

Syllabus:  Topics include: commutative and non-commutative rings, integral domains, and fields. Selected topics will include Galois theory and advanced group theory. 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 414.

Instructor(s):  Dr. Anthony Giaquinto

Required text(s):  Artin, Michael Algebra. Second Edition, Pearson, 2018. ISBN: 9780137980994 (ebook) or 9780134689609 (print copy)

Recommended text(s):  Hungerford, Thomas Algebra. Springer Graduate Texts in Mathematics, Volume 73, 1974, ISBN: 9781461261018 (ebook), 978-1461261032 (print copy)

Prerequisites:  Restricted to graduate students

Course description:  This is a survey course in algebra with three parts. Part one covers topics in group theory such as group operations, the Sylow Theorems, classification of finte groups, generators and relations, and the Todd-Coxeter algorithm. Part two covers basic ring theory including many examples, integral domains, and fraction fields. Modules over rings will be studied leading to the classification of finite abelian groups. The course will close with a selection of contemporary algebraic topics.

Instructor(s):  Dr. Christine Haught

Required text(s):  Hodel, Richard E. An Introduction to mathematical Logic. Dover. 2013. Print. ISBN-13: 978-0-486-49785-3.

Prerequisites:  Math 201

Course description:  This course in modern mathematical logic begins with a study of propositional logic and leads to the study of first-order predicate logic, including quantifiers, models, syntax, semantics, the completeness and compactness theorems, and other selected topics. We will study of the concepts of truth and proof and how they relate to each other. The main topics are propositional logic, first order predicate logic, and decidability. Propositional logic is the study of the expressive power of a language that uses only the Boolean connectives and, or, and not. First-order predicate logic builds on propositional logic and has more expressive power. It adds the ability to refer to properties of individuals through predicates, as well as existential and universal quantifiers. Much of the mathematics that students have encountered can be expressed in first-order logic. We will study some model theory, introduce the concept of decidability and build up to studying the Godel Incompleteness Theorems. Godel’s first Incompleteness Theorem tells us that in any “reasonable” axiomatization of arithmetic, there will be a statement that is true but not provable.

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Cryptography: An Introduction (3rd Edition), by Nigel Smart. Self-published by the author at https://homes.esat.kuleuven.be/~nsmart/Crypto_Book/.

Recommended text(s): 

• Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman. An Introduction to Mathematical Cryptography, 2nd ed. ISBN-13: 9781493917105. New York: Springer, 2014.
• Steven Levy, Crypto : How the Code Rebels Beat the Government, Saving Privacy in the Digital Age, Penguin 2001. ISBN 978-0140244328.
• Paar, Christof and Jan Pelzl. Understanding Cryptography: A Textbook for Students and Practitioners. ISBN-13: 978-3642041006 (Print). ASIN: B00475ARKM (Kindle). Heidelberg: Springer, 2010. Print and Kindle.

Prerequisites:  (COMP 163 or MATH 313 or MATH 201) and (COMP 125 or COMP 150 or COMP 170 or MATH/COMP 215).

Course description:  This interdisciplinary course treats the mathematical and practical theory of cryptographic systems. That is, the course will be a mixture of theory and practice, involving mathematical proofs, algorithm development (based on the mathematics), and coding—both in lectures and on homework assignments.

The course begins with a survey of historical systems (e.g., from Julius Caesar's time and well before), before spending some time on classical private-key (aka symmetric) systems, such as the Beaufort, Hill, Feistel, and Rijndael ciphers. Our main focus, however, will be public-key (asymmetric) cryptosystems, first appearing the 1970s, and now used EVERYWHERE—in every login to a secure website, in every credit card transaction, every time you ssh into a server to finish your MATH 331 homework, when companies store your password and personal data with hash functions, in Bitcoin, BitTorrent, as well as the modern sale of digital artwork.

We will develop the mathematics needed for Diffie-Hellman, RSA, and elliptic curve cryptography. The RSA algorithm is the gold-standard. WARNING: Quantum computers are coming! They will make RSA obsolete. We will soon need something new. Time permitting, we will also discuss the emerging theory of lattice-based cryptosystems.

Code demonstrations and assignments will be completed in Python 3. This should be available on Loyola-managed machines. Students may wish to install it on their machines as well. (This guide tells you what you need to do if you go the Anaconda route.)

Syllabus:  Planned course assessments will be semiregular quizzes and homework, one midterm exam, a short project, 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

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. Xiang Wan

Required text(s):  N/A

Recommended text(s):  Haberman, Richard. Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow. United States, Society for Industrial and Applied Mathematics, 1988.

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

Course description:  This course will teach students how to use various areas of mathematics to formulate mathematical models in various scenarios, such as physics, biology, computer science, engineering, finance, etc. Centered around Differential Equations, we will explore how different mathematical tools are assembled together to solve questions from modeling, mainly through case study.

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:  This course provides an introduction to statistical reasoning and techniques in descriptive and inferential statistics and their applications in economics, education, genetics, medicine, physics, political science, and psychology. Not open to students who have completed ISOM 241.

Instructor(s):  Dr. Shuwen Lou

Required text(s):  TBD.

Prerequisites:  MATH 132 or MATH 162 or MATH 162A; MATH 162 may also be taken concurrently as a co-requisite.

Course description:  This course is a Calculus-based rigorous introduction to basic topics in probability (distributions, expectations, variance, central limit theorem and the law of large numbers, moment generating functions, etc.) and statistics (estimation, hypothesis testing, regression, design of experiments) needed in engineering and science applications. Outcomes: The students will obtain required knowledge in probability and statistics useful in every area of engineering and science. They will learn how to assess data and outcomes of experiments.

Instructor(s):  Dr. Michael Perry

Required text(s):  Devore, Jay L. , Probability and Statistics for Engineering and the Sciences 9th, Cengage Learning, 2016

Additional notes:  CALCULATORS: A four function or standard scientific calculator is necessary for the class. No graphing calculators, calculators to perform numerical integration or calculators that perform statistical tests on tests. The only statistics the calculator may calculate are mean, median, standard deviation and variance. We will use R (R- Studio) for some very limited work.

Prerequisites:  Math 132 or Math 162 (Stat 203 may be taken as a co-requisite with Math 162 only)

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

Syllabus:  Grade calculation: Homework: 20% Quizzes: 15% Midterm 1: 20% Midterm 2: 20% Final: 25%

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: 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. Michael Perry

Required text(s):  None

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

Prerequisites:  STAT 103 or STAT 203 or STAT 335

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

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

Instructor(s):  Dr. Shuwen Lou

Required text(s):  TBA

Prerequisites:  MATH 263 or MATH 263A.

Course description:  This course provides a calculus based introduction to probability theory, including topics such as combinatorial analysis, random walk, conditional probability, and a variety of statistical distributions.

Instructor(s):  Dr. Matthew Stuart

Required text(s):  Statistical Inference 2nd Edition, George Casella and Roger Berger

Prerequisites:  STAT 304

Course description:  This course is a continuation of STAT 304 and applies the techniques of calculus and probability to the study of advanced topics in statistics. Topics explored include moment generating functions, maximum likelihood, unbiased estimators, most powerful hypothesis tests, and Bayesian statistics.

Instructor(s):  Dr. Matthew Stuart

Required text(s):  None

Prerequisites:  STAT 203 or 335

Course description:  This course discusses simple and multiple linear regression methods, multiple comparison estimation procedures, residual analysis, and other methods for studying the aptness of a proposed regression model; the packaged computer program R will be used extensively.

Instructor(s):  Dr. Tim O'Brien

Required text(s):  Kleinbaum, D.G. & Klein, M., 2010, Logistic Regression: A Self-Learning Text, 3rd Edition, Springer, ISBN: 978-1-4419-1741-6

Prerequisites:  (STAT 203 or STAT 335 with C- or better) and (STAT 303 or STAT 308 with C- or better)

Course description:  Normal response variables lead applied statisticians to use simple linear model procedures such as simple and multiple regression, one- or two-way ANOVA or ANOCOV, but other types of data often leaves practitioners confused, leading some to applying these procedures incorrectly. As a result, these simple techniques have been extended to handle nominal, ordinal, count and binary data under the general heading of categorical data analysis. Modern-day extensions to the chi-square test include logistic regression and log-linear modeling techniques, which are the focus of this course – as will be the unified perspective, based on ‘generalized linear models’, that connects these methods with standard regression methods for normally-distributed data. In this larger framework, this course addresses the fundamental questions encountered with regression and ANOVA for count data. Specialized methods for ordinal data, small samples, multi-category data, and matched pairs 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.

Instructor(s):  Sheila Suresh

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

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

Prerequisites:  BIOL 102, MATH 132 or MATH 162 (as pre-requisite or co-requisite) or MATH 162A; Students may take MATH 162 as a prerequisite for STAT/BIOL 335 or take it concurrently as a corequisite with STAT/BIOL 335; For Bioinformatics Majors: only BIOL 101, MATH 132 or MATH 162 (as pre-requisite or co-requisite) or MATH 162A

Course description:  An introduction to statistical methods used in designing biological experiments and in data analyses. Topics include probability and sampling distribution, designed biological experiments and analysis of variance, regression and correlation, stochastic processes, and frequency distributions. Computer laboratory assignments with biological data. (Note: Students may not receive credit for both STAT 203 & 335.)

Instructor(s):  Bret A Longman

Required text(s):  No required text

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):  Bret A Longman

Required text(s):  No required text

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. Nan Miles Xi

Required text(s):  There is no required textbook. The lecture notes will be posted on Sakai.

Recommended text(s):  Introduction to Bioinformatics with R: A Practical Guide for Biologists (2020). Edward Curry. CRC Press. Statistical Modeling and Machine Learning for Molecular Biology (2016). Alan Moses. CRC Press. An Introduction to Statistical Learning with Applications in R. Second Edition (2021). Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani. Springer.

Prerequisites:  STAT 203 or 335 or equivalent

Course description:  Introduction to statistical and machine learning methods in computational biology and bioinformatics. Emphasize understanding basic statistical and machine learning concepts and the ability to use those tools to solve biological problems. The tentative topics include: review of introductory probability and statistics, introduction to R programming language, statistical inference, multiple testing, clustering, dimension reduction, measure of association, linear regression, classification, resampling.

Required text(s):  None

Prerequisites:  None

Course description:  Students will work on a research project with a client acting as a consultant on the statistical and computational aspects of the project. Students are required to meet with a client, develop a strategy for addressing their problem, and present their results to the client (and their classmates).

Instructor(s):  Dr. Mena Whalen

Required text(s):  An Introduction to Applied Multivariate Analysis with R by Everitt & Hothorn 2011 ISBN 978-1-4419-9650-3

Additional notes:  Linear algebra knowledge is recommended.

Prerequisites:  STAT 203

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

Instructor(s):  Dr. Swarnali Banerjee

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

Recommended text(s):  Introduction to Mathematical Statistics, by Hogg, McKean and Craig (7th edition)

Prerequisites:  MATH/STAT 404

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

Instructor(s):  Dr. Tim O'Brien

Required text(s):  Bilder, Christopher R. and Loughin, Thomas M., 2015, Analysis of Categorical Data with R, CRC Press/Chapman and Hall: Boca Raton, FL., ISBN-13: 978-1-4398-5567-6

Prerequisites:  Restricted to Graduate School students. It is advised that students have had some exposure to linear regression methods such as multiple regression.

Course description:  Normal response variables lead applied statisticians to use simple linear model procedures such as simple and multiple regression, one- or two-way ANOVA or ANOCOV, but other types of data often leaves practitioners confused, leading some to applying these procedures incorrectly. As a result, these simple techniques have been extended to handle nominal, ordinal, count and binary data under the general heading of categorical data analysis. Modern-day extensions to the chi-square test include logistic regression and log-linear modeling techniques, which are the focus of this course – as will be the unified perspective, based on ‘generalized linear models’, that connects these methods with standard regression methods for normally-distributed data. In this larger framework, this course addresses the fundamental questions encountered with regression and ANOVA for count data. Specialized methods for ordinal data, small samples, multi-category data, and matched pairs 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.

Instructor(s):  Dr. Nan Miles Xi

Required text(s):  There is no required textbook. The lecture notes will be posted on Sakai.

Recommended text(s):  Introduction to Bioinformatics with R: A Practical Guide for Biologists (2020). Edward Curry. CRC Press. Statistical Modeling and Machine Learning for Molecular Biology (2016). Alan Moses. CRC Press. An Introduction to Statistical Learning with Applications in R. Second Edition (2021). Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani. Springer.

Prerequisites:  STAT 203 or 335 or equivalent

Course description:  Introduction to statistical and machine learning methods in computational biology and bioinformatics. Emphasize understanding basic statistical and machine learning concepts and the ability to use those tools to solve biological problems. The tentative topics include: review of introductory probability and statistics, introduction to R programming language, statistical inference, multiple testing, clustering, dimension reduction, measure of association, linear regression, classification, resampling.

Instructor(s):  Dr. Mena Whalen

Required text(s):  An Introduction to Applied Multivariate Analysis with R by Everitt & Hothorn 2011 ISBN 978-1-4419-9650-3

Additional notes:  Linear algebra knowledge is recommended.

Prerequisites:  STAT 203

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