MATH 100. Intermediate Algebra

Instructor(s):  Staff

Required text(s):  Ron Larson. Intermediate Algebra (WebAssign eBook) 5th ed.​

Textbook notes:  Students are required to have access to WebAssign for this course. Students buying used textbooks should arrange to purchase WebAssign separately

Prerequisites:  None

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

Syllabus:  Common

  

MATH 108. Real World Modeling

Instructor(s):  Staff

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

Prerequisites:  None

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

Syllabus:  Common

  

MATH 117. Precalculus I

Instructor(s):  Staff

Required text(s):  Carl Stitz and Jeff Zeager. Precalculus (WebAssign eBook), 3rd edition.

Stitz Zeager Open Source Mathematics, 4 July 2014. Web. http://www.stitz-zeager.com/.

Prerequisites:  MATH 100 or Math Diagnostic Test

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

Syllabus:  Common

  

MATH 118. Precalculus II

Instructor(s):  Staff

Required text(s):  Carl Stitz and Jeff Zeager. Precalculus (WebAssign eBook), 3rd edition.

Stitz Zeager Open Source Mathematics, 4 July 2014. Web. http://www.stitz-zeager.com/.

Prerequisites:  MATH 117 or Math Diagnostic Test

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

Syllabus:  Common

  

Math 123. Topics in Single Variable Calculus

Instructor(s):  Dr. Peter Tingley

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

Prerequisites:  Prerequisite: MATH131 or 132.

Course description:  This seminar will cover topics from MATH161/162 which are not covered in MATH131/132. The purpose is to allow students who have taken the MATH131/132 sequence to transition to MATH263. The seminar will consist of students working through several booklets, partly in-class and partly as homework. After each, students must pass a quiz. Students must agree to complete this work by week 6 of the semester. The class must be taken pass/fail.

  

MATH 131. Applied Calculus I

Instructor(s):  Staff

Required text(s):  Hughes-Hallett, Deborah, et al. Applied & Single Variable Calculus for Loyola University Chicago, Custom (WebAssign eBook). 4th ed.

Print text (optional): ISBN-13: 9781118747476. Hoboken, NJ: Wiley, 2013.

Prerequisites:  MATH 118 or Math Diagnostic Test

Course description:  An introduction to differential and integral calculus, with an emphasis on applications. This course is intended for students in the life and social sciences, computer science, and business. Topics include: modeling change using functions including exponential and trigonometric functions, the concept of the derivative, computing the derivative, applications of the derivative to business and life, social, and computer sciences, and an introduction to integration. This course is not a substitute for MATH 161.

Syllabus:  Common

  

MATH 132. Applied Calculus II

Instructor(s):  Staff

Required text(s):  Hughes-Hallett, Deborah, et al. Applied & Single Variable Calculus for Loyola University Chicago, Custom (WebAssign eBook). 4th ed.

Print text (optional): ISBN-13: 9781118747476. Hoboken, NJ: Wiley, 2013.

Prerequisites:  MATH 131 or MATH 161

Course description:  A continuation of MATH 131. Topics include: properties of the integral, techniques of integration, numerical methods, improper integrals, applications to geometry, physics, economics, and probability theory, introduction to differential equations and mathematical modeling, systems of differential equations, power series. This course is not a substitute for MATH 162.

Syllabus:  Common

  

MATH 161. Calculus I

Instructor(s):  Staff

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

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

Prerequisites:  MATH 118

Course description:  A traditional introduction to differential and integral calculus. Functions, limits, continuity, differentiation, intermediate and mean-value theorems, curve sketching, optimization problems, related rates, definite and indefinite integrals, fundamental theorem of calculus, logarithmic and exponential functions. Applications to physics and other disciplines.

Syllabus:  Common

  

MATH 162. Calculus II

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

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

Prerequisites:  MATH 161

Course description:  A continuation of MATH 161. Calculus of logarithmic, exponential, inverse trigonometric, and hyperbolic functions. Techniques of integration. Applications of integration to volume, surface area, arc length, center of mass, and work. Numerical sequences and series. Study of power series and the theory of convergence. Taylor's theorem with remainder.

Syllabus:  Common

  

Math 201. Discrete Mathematics and Number Theory

Instructor(s):  Alan Saleski

Required text(s):  1. Richard Hammack, Book of Proof (2nd edition), Hammack Pub. (2013) 2. William LeVeque, Elementary Theory of Numbers, Dover (1962)

Recommended text(s):  Roger Nelson, Proofs Without Words: Exercises in Visual Thinking, volume 1, MAA (1993)

Prerequisites:  Math 161

Course description:  This course in Discrete Mathematics attempts to engage and expose the student to several different topics in discrete mathematics (including induction, naive set theory, number theory, combinatorics, algebraic structures, basic logic, graph theory, equivalence relations, injective and surjective maps, and cardinality.) The primary desired outcome is for the student to learn how to read and write precise and unambiguous mathematical proofs at a beginning level. Such skills should prepare students to enter 300-level courses such as Abstract Algebra and Real Analysis.

Syllabus:  This course covers topics from discrete mathematics and number theory, areas of mathematics not seen in calculus courses and abundant in applications, that provide students with the concepts and techniques of mathematical proof needed in 300 level courses in mathematics. Outcome: Students will obtain an understanding of the basic concepts and techniques involved in constructing rigorous proofs of mathematical statements.

  

Math 201. Discrete Mathematics and Number Theory

Instructor(s):  Anne E Hupert

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

Prerequisites:  Math 161

Course description:  This course covers topics from discrete mathematics, primarily from elementary number theory, ranging from induction to congruencies to prime numbers and cardinality, to provide students planning to take advanced 300 level courses in mathematics with an introduction to understanding and constructing proofs. Grades will be based on daily homework, 3 in-class exams, and a final.

  

MATH 212. Linear Algebra

Instructor(s):  Dr. John G. Del Greco

Required text(s):  Anton, Howard. Elementary Linear Algebra. 11th ed. ISBN-13: 978-1118473504. New York: John Wiley, 2013. Print.

Prerequisites:  MATH 132 or MATH 162

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

  

MATH 212. Linear Algebra

Instructor(s):  Dr. Joseph Mayne

Required text(s):  Lay, David C., Lay, Steven R., and McDonald, Judi J., "Linear Algebra and its Applications," 5th Edition. Packaged with MyMathLab access, Pearson, 2016. ISBN-13: 9780134022697.

Prerequisites:  MATH 132 or MATH 162

Course description:  Linear algebra is widely used in mathematics, science, engineering, and the social sciences. For example, statisticians and economists often employ linear models when trying to analyze problems with many variables. And linear algebra is an important tool in many areas of mathematics itself. Much of functional analysis is devoted to the study of functions preserving linearity and field theory uses linear algebra in the proofs of many results. The course starts with the problem of solving simultaneous linear equations using the Gaussian elimination algorithm. The solution of this important practical problem motivates the definition of many linear algebra concepts: matrices, vectors and vector spaces, linear independence, dimension, and vector subspaces. The emphasis then shifts to general vector spaces and proofs using an axiom system. Most of the results will be for finite dimensional spaces and we will always attempt to visualize theorems in 2 or 3 dimensional Euclidean space. Topics to be covered include: linear transformations, change of basis, determinants, eigenvalues and eigenvectors, and diagonalization. Students will be encouraged to improve their skills at constructing mathematical proofs. There will be three tests, a final examination, and homework assignments, some of which will be submitted on-line using MyMathLab

  

MATH 215. [ COMP 215 ] Object-Oriented Programming for Mathematics

Instructor(s):  Dr. Aaron Lauve

Required text(s):  R. Sedgewick, K. Wayne, R. Dondero. Introduction to Programming in Python: An Interdisciplinary Approach. 1st ed. ISBN-13: 978-0134076430. New York: Addison-Wesley / Pearson, 2015. Print.

Recommended text(s):  Andrew Harrington, Hands-On Python Tutorial;

Allan M. Stavely, Programming and Mathematical Thinking: A Gentle Introduction to Discrete Math Featuring Python. 1st ed. ISBN: 978-1-938159-00-8 (pbk.), 978-1-938159-01-5 (ebook). Socorro, New Mexico: New Mexico Tech Press, 2014. (eBook available from instructor on first day of class.)

Additional notes:  Students will submit assignments as Jupyter Notebooks within COCALC ("Collaborative Calculation in the Cloud"). For information on COCALC, see here. For a demo on these notebooks, see here.

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

Course description:  Math 215/Comp 215 is a first course in programming for students interested in mathematics and scientific applications. Though no previous programming experience is required, the course is programming intensive.

(Note: This course is a substitute for Comp 170 in most CS curricula. As such, the Comp 170 course description, course goals, and course outcomes apply here as well.)

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 drawn from a variety of scientific computing realms. Specifically, we cover built-in data types, input/output, loops, functions, and classes (essentially, the first three chapters of the course textbook). Special focus will be given to mathematical examples arising in calculus, number theory, statistics, geometry, and linear algebra.

Syllabus:  There will be weekly programming assignments as well as frequent in-class exercises. Final course grade will be based on the programming assignments, near-weekly quizzes, a final project, and a final exam.

  

MATH 263. Multivariate Calculus

Instructor(s):  Staff

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

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

Prerequisites:  MATH 162

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

Syllabus:  Common

  

MATH 264. Introduction to Differential Equations

Instructor(s):  Dr. E.N. Barron

Required text(s):  Zill, Dennis. A First Course in Differential Equations with Modeling Applications, with WebAssign Printed Access Card, 11th Edition, Single-Term, Cengage ISBN 9781337652469

Prerequisites:  MATH 263

Course description:  This course is about ordinary differential equations used in many areas of applications, like engineering, physics, chemistry, biology, economics, etc. It covers first and second order differential equations and uses real models throughout the semester. Analytical techniques for solving and analyzing solutions of differential equations will be the focus of the course. Homework is on WebAssign. We will have two semester exams and a final exam. Several quizzes will also be given in class.

  

MATH 264. Introduction to Differential Equations

Instructor(s):  Dr. Brian Seguin

Required text(s):  Zill, Dennis. A First Course in Differential Equations with Modeling Applications, with WebAssign Printed Access Card, 11th Edition, Single-Term, Cengage ISBN 9781337652469

Prerequisites:  MATH 263

Course description:  This course is about ordinary differential equations used in many areas of applications, like engineering, physics, chemistry, biology, economics, etc. It covers first and second order differential equations and uses real models throughout the semester. Analytical techniques for solving and analyzing solutions of differential equations will be the focus of the course. Homework is on WebAssign. We will have two semester exams and a final exam. Several quizzes will also be given in class.

  

MATH 277. Problem Solving Seminar

Instructor(s):  Dr. Peter Tingley

Required text(s):  None.

Prerequisites:  MATH 162.

Course description:  This is a one credit seminar in mathematical problem solving. The focus will be on creative mathematical thinking and open-ended exploration. The meetings will consist mainly of collaborative problem solving activities. Students will also be expected to produce some written solutions and proofs, and to give informal presentations of their solutions to the class.

Meetings will be Thursdays, 2:30-4:00

  

MATH 304. [ STAT 304 ] Probability and Statistics I

Instructor(s):  Dr. John G. Del Greco

Required text(s):  Grimmett, Geoffrey and Dominic Welsh. Probability: An Introduction. 2nd ed. ISBN-13: 978-0-19-870997. New York: Oxford University Press, 2014. Print.

Prerequisites:  Math 263

Course description:  This course will be a mathematically rigorous introduction to probability theory. The successful student will need a firm grasp of calculus up to multivariate calculus. Topics will include axiomatic probability, conditional probability, independence, combinatorial probability, random variables, families of discrete probability distributions (hypergeometric, binomial, Poisson, geometric, negative-binomial), families of continuous distributions (exponential, normal, gammma, beta), expected values, variance, covariance, joint densities, conditional densities, transformations of random variables, order statistics, moment-generating functions, and the Central Limit Theorem with applications.

  

MATH 313. Abstract Algebra

Instructor(s):  Dr. Emily Peters

Required text(s):  Algebra: Abstract and Concrete, by Fred Goodman.

Textbook notes:  The textbook is no longer in print, but is available as a PDF from http://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/download.htm

Prerequisites:  MATH 201 and MATH 212

Course description:  Abstract algebra is, at heart, the study of symmetries. What do we mean when we say that a square is more symmetric than a (non-square) rectangle, or that a circle is more symmetric than a square? Which is more symmetric, a cube or an octahedron? The mathematical idea of a 'group' was created to make the idea of symmetry precise, and has taken on a vast life of its own, thanks to its broad applicability. Other examples of groups include: the numbers 0,...,n-1 in arithmetic modulo n; permutations of a group of identical objects; symmetries of the plane; symmetries of the plane that preserve distance (also known as isometries); symmetries of the plane that preserve area; and so forth. This class will be example-driven but also rigorous and abstract. We will study equivalence relations, subgroups, homomorphisms, quotients, products, linear groups, permutation groups, and selected advanced topics.

  

MATH 315. [ MATH 415 ] Topics in Linear Algebra

Instructor(s):  Dr. W. Cary Huffman

Required text(s):  Friedbreg, Stephen H., Arnold J. Insel, and Lawrence E. Spence. Linear Algebra. 4th ed. ISBN-13: 978-0130084514. Upper Saddle River, NJ: Pearson Education, 2003. Print.

Prerequisites:  MATH 313, or the equivalent, or permission of the instructor.

Course description:  Many problems in applied mathematics, physics, and engineering involve systems of equations that may be very difficult to solve. Sometimes the first approximation to solving such systems is to linearize them and solve these linearized systems using various theoretical and applied techniques. This class will be a second course in linear algebra, where advanced topics will be considered. These topics will be chosen from inner product spaces, Gram-Schmidt orthogonalization, normal and self-adjoint operators, unitary and orthogonal operators, bilinear and quadratic forms, and Jordan and rational canonical forms. There will be applications of these ideas to least squares problems and regression, orthogonal polynomials, exponential functions with matrix exponents, time contraction in Einstein's Theory of relativity, and others. The course will begin with a review of some necessary material from MATH 212 and MATH 313.

This course is a combined undergraduate/graduate course. The requirements of the course for the graduate students will be different from the requirements for the undergraduates.

  

MATH 320. [ MATH 420 ] Mathematical Logic

Instructor(s):  Dr. Christine Haught

Required text(s):  Smullyan, Raymond A Beginner's Guide to Mathematical Logic. Dover Publications (July 16, 2014). Print.

Recommended text(s):  Soare, Robert I. Turing Computability: Theory and Applications. Spring-Verlag (2016). Print.

Textbook notes:  The additional text on computability (Turing Computability: Theory and Applications by Robert I. Soare) will be required for students in Math 420.

Prerequisites:  Math 201, 313 or permission of instructor

Course description:  This course is a mathematical study of the concepts of truth and proof and how they relate to each other. The main topics are propositional logic, predicate logic, predicate logic with quantifiers, completeness and incompleteness phenomena, decidability and computability. Propositional logic is the study of the expressive power of a language that uses only the Boolean connectives and, or, and not. First-order 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 we are familiar with can be expressed in first-order logic. At the end of the course we will study the notion of decidability and Godel's incompleteness theorems, which tells us that in any first-order theory strong enough to formalize arithmetic, and in which the axioms are decidable, there is a statement that is true but not provable. Grades will be determined by weekly written homework assignments, three in class exams, a project and a final exam.

  

MATH 331. [ COMP 331 COMP 431 MATH 431 ] Cryptography

Instructor(s):  Dr. Aaron Greicius

Required text(s):  Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman. An Introduction to Mathematical Cryptography, 2nd ed. ISBN-13: 9781493917105. New York: Springer, 2014.

Prerequisites:  (MATH 201 or COMP 363) and ( COMP 125 or COMP 150 or COMP 170 or COMP/MATH 215)

Course description:  This interdisciplinary course applies number theory from mathematics in order to construct modern "asymmetric" cryptosystems for use in public-key cryptography. The course will look at both the underlying mathematical concepts (e.g., primes, congruences, finite fields, elliptic curves) as well as issues of implementation of specific algorithms. We will cover some subset of the following topics: conventional encryption techniques, the Hill cipher, DES and SDES, RSA, the Rijndael cipher, discrete logarithms and the Diffie-Hellman key exchange, and elliptic curve cryptography. Homework will involve some computer programming in Python as well as solving mathematical problems.

  

MATH 344. [ MATH 488 ] Geometry

Instructor(s):  Dr. Cristina Popovici

Required text(s):  None. Lecture notes will be provided.

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

Course description:  The main goal of the course is to provide a concise treatment of fundamental results in Euclidean Geometry, starting from the most basic axioms about geometrical figures in the plane and leading to a number of deep, strikingly beautiful results. Geometry is a deductive subject, with theorems and proofs. As such, students will learn how to draw valid conclusions from hypotheses, detect and avoid invalid reasoning, and will have the opportunity to further develop their ability to understand and construct mathematical proofs, a skill that plays an essential role in more advanced 300-level Mathematics courses and beyond. Homework will be assigned regularly throughout the semester. There will be two midterms and a comprehensive final exam.

  

Math 351. Introduction to Real Analysis I

Instructor(s):  Rafal Goebel

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

Prerequisites:  Math 201, Math 212

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

  

Math 353. Introduction to Complex Analysis

Instructor(s):  Robert Jensen

Required text(s):  "Complex Analysis" (Undergraduate Texts in Mathematics) Aug 6, 2010 by Joseph Bak and Donald J. Newman, 3rd Edition (2010) ISBN-13: 978-1441972873 ISBN-10: 1441972870; or reprint in paperback (2012) ISBN-13: 978-1461426363; ISBN-10: 1461426367

Prerequisites:  Math 264, Math 351

Course description:  This is a traditional course on complex analysis. After a brief review of the complex numbers we will study complex valued functions of a complex variable. This includes differentiation and the connection between differentiable functions and analytic functions; and integration, where the line integral from multivariable calculus provides the connection between integration and differentiation. We will prove the Cauchy representation theorem and the residue theorem and examine their consequences and applications.

  

Math 360. [ Math 460 ] Theory of Games

Instructor(s):  Dr. Peter Tingley

Required text(s):  Barron, E. N. Game Theory: An Introduction. 2nd ed. ISBN-13: 978-1118216934. New York: John Wiley Interscience, 2013. Print.

Prerequisites:  MATH 212 and a stats course equivalent to STAT 203

Course description:  Throughout many fields (economics, biology, politics, engineering, sports...most of life really) people must work towards goals while other forces are acting against them. Any such situation can be thought of as a game, where the "players" make various decisions while trying to achieve goals which may be in conflict. Game theory studies methods of making "good" decisions. Often this reduces to quite elegant mathematics. We will study that math, and consider some applications. Mathematica and/or Gambit Software will be used at times, although no prior knowledge of programming is required. There will be two midterms and a cumulative final exam, and homework will be regularly assigned and graded.

  

MATH 404. [ STAT 404 ] Probability and Statistics I

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Mathematical Statistics with Applications, 7th Edition by Dennis D. Wackerly, William Mendenhall III and Richard L. Sceaffer Statistical Inference by George Casella and Roger L. Berger

Prerequisites:  STAT 203 or 335

Course description:  This is the first semester of a two-semester sequence. The first semester is essentially an exploration of probability as a mathematical model of chance phenomena. The second semester explores the statistical analyses based on these models. Topics to be covered 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.

  

MATH 415. [ MATH 315 ] Topics in Linear Algebra

Instructor(s):  Dr. W. Cary Huffman

Required text(s):  Friedbreg, Stephen H., Arnold J. Insel, and Lawrence E. Spence. Linear Algebra. 4th ed. ISBN-13: 978-0130084514. Upper Saddle River, NJ: Pearson Education, 2003. Print.

Prerequisites:  MATH 313, or the equivalent, or permission of the instructor.

Course description:  Many problems in applied mathematics, physics, and engineering involve systems of equations that may be very difficult to solve. Sometimes the first approximation to solving such systems is to linearize them and solve these linearized systems using various theoretical and applied techniques. This class will be a second course in linear algebra, where advanced topics will be considered. These topics will be chosen from inner product spaces, Gram-Schmidt orthogonalization, normal and self-adjoint operators, unitary and orthogonal operators, bilinear and quadratic forms, and Jordan and rational canonical forms. There will be applications of these ideas to least squares problems and regression, orthogonal polynomials, exponential functions with matrix exponents, time contraction in Einstein's Theory of relativity, and others. The course will begin with a review of some necessary material from MATH 212 and MATH 313.

This course is a combined undergraduate/graduate course. The requirements of the course for the graduate students will be different from the requirements for the undergraduates.

  

MATH 420. [ MATH 320 ] Mathematical Logic

Instructor(s):  Dr. Christine Haught

Required text(s):  Smullyan, Raymond A Beginner's Guide to Mathematical Logic. Dover Publications (July 16, 2014). Print.

Recommended text(s):  Soare, Robert I. Turing Computability: Theory and Applications. Spring-Verlag (2016). Print.

Textbook notes:  The additional text on computability (Turing Computability: Theory and Applications by Robert I. Soare) will be required for students in Math 420.

Prerequisites:  Math 201, 313 or permission of instructor

Course description:  This course is a mathematical study of the concepts of truth and proof and how they relate to each other. The main topics are propositional logic, predicate logic, predicate logic with quantifiers, completeness and incompleteness phenomena, decidability and computability. Propositional logic is the study of the expressive power of a language that uses only the Boolean connectives and, or, and not. First-order 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 we are familiar with can be expressed in first-order logic. At the end of the course we will study the notion of decidability and Godel's incompleteness theorems, which tells us that in any first-order theory strong enough to formalize arithmetic, and in which the axioms are decidable, there is a statement that is true but not provable. Grades will be determined by weekly written homework assignments, three in class exams, a project and a final exam.

  

MATH 431. [ COMP 331 COMP 431 MATH 331 ] Cryptography

Instructor(s):  Dr. Aaron Greicius

Required text(s):  Jeffrey Hoffstein, Jill Pipher, and Joseph H. Silverman. An Introduction to Mathematical Cryptography, 2nd ed. ISBN-13: 9781493917105. New York: Springer, 2014.

Prerequisites:  (MATH 201 or COMP 363) and ( COMP 125 or COMP 150 or COMP 170 or COMP/MATH 215)

Course description:  This interdisciplinary course applies number theory from mathematics in order to construct modern "asymmetric" cryptosystems for use in public-key cryptography. The course will look at both the underlying mathematical concepts (e.g., primes, congruences, finite fields, elliptic curves) as well as issues of implementation of specific algorithms. We will cover some subset of the following topics: conventional encryption techniques, the Hill cipher, DES and SDES, RSA, the Rijndael cipher, discrete logarithms and the Diffie-Hellman key exchange, and elliptic curve cryptography. Homework will involve some computer programming in Python as well as solving mathematical problems.

  

Math 460. [ Math 360 ] Theory of Games

Instructor(s):  Dr. Peter Tingley

Required text(s):  Barron, E. N. Game Theory: An Introduction. 2nd ed. ISBN-13: 978-1118216934. New York: John Wiley Interscience, 2013. Print.

Prerequisites:  MATH 212 and a stats course equivalent to STAT 203

Course description:  Throughout many fields (economics, biology, politics, engineering, sports...most of life really) people must work towards goals while other forces are acting against them. Any such situation can be thought of as a game, where the "players" make various decisions while trying to achieve goals which may be in conflict. Game theory studies methods of making "good" decisions. Often this reduces to quite elegant mathematics. We will study that math, and consider some applications. Mathematica and/or Gambit Software will be used at times, although no prior knowledge of programming is required. There will be two midterms and a cumulative final exam, and homework will be regularly assigned and graded.

  

MATH 488. [ MATH 344 ] Geometry

Instructor(s):  Dr. Cristina Popovici

Required text(s):  None. Lecture notes will be provided.

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

Course description:  The main goal of the course is to provide a concise treatment of fundamental results in Euclidean Geometry, starting from the most basic axioms about geometrical figures in the plane and leading to a number of deep, strikingly beautiful results. Geometry is a deductive subject, with theorems and proofs. As such, students will learn how to draw valid conclusions from hypotheses, detect and avoid invalid reasoning, and will have the opportunity to further develop their ability to understand and construct mathematical proofs, a skill that plays an essential role in more advanced 300-level Mathematics courses and beyond. Homework will be assigned regularly throughout the semester. There will be two midterms and a comprehensive final exam.

  

STAT 103. Fundamentals of Statistics

Instructor(s):  Staff

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

Prerequisites:  None

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

Syllabus:  Common

  

STAT 203. Statistics

Instructor(s):  Dr. John G. Del Greco

Required text(s):  Barron, E. N. and John G. Del Greco, Probability & Statistics , Preliminary version. Available only at the book store.

Prerequisites:  Math 132 or Math 162 (with a grade of at least C). Math 263 is recommended as a prerequisite or taken concurrently.

Course description:  Stat 203 will be a rigorous course in probability and statistics. It is calculus based and is required of all statistics and mathematics majors as well as engineering science students. It is recommended for physics, chemistry, and biology majors. Stat 203 covers the essential topics in probability and statistics with derivations of most of the results. It can be used as a stand-alone course or a foundation for advanced study in probability and statistics. We will have two midterms and a final exam. A TI-8x is required for this course. The following topics will be covered: axiomatic probability, random variables (distributions, mean, variance, moment-generating functions), sampling distributions for the normal random variable, statistical intervals, hypotheses testing, and linear regression.

  

STAT 304. [ MATH 304 ] Probability and Statistics I

Instructor(s):  Dr. John G. Del Greco

Required text(s):  Grimmett, Geoffrey and Dominic Welsh. Probability: An Introduction. 2nd ed. ISBN-13: 978-0-19-870997. New York: Oxford University Press, 2014. Print.

Prerequisites:  Math 263

Course description:  This course will be a mathematically rigorous introduction to probability theory. The successful student will need a firm grasp of calculus up to multivariate calculus. Topics will include axiomatic probability, conditional probability, independence, combinatorial probability, random variables, families of discrete probability distributions (hypergeometric, binomial, Poisson, geometric, negative-binomial), families of continuous distributions (exponential, normal, gammma, beta), expected values, variance, covariance, joint densities, conditional densities, transformations of random variables, order statistics, moment-generating functions, and the Central Limit Theorem with applications.

  

STAT 307. [ STAT 407 ] Statistical Design and Analysis of Experiments

Instructor(s):  Timothy E. O’Brien, Ph.D.

Required text(s):  Montgomery, Douglas C. (2013), Design and Analysis of Experiments, 8th Edition, Wiley, ISBN: 9781118146927.

Prerequisites:  STAT-203 or STAT-335 or equivalent, or permission of the instructor.

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 reviewed; blocking (complete and incomplete) will be discussed, as will be factorial designs, fractional factorial designs, and confounding. The course will focus on biometric applications such as clinical trials, HIV studies, and environmental and agricultural research, but industrial and other examples will occasionally be provided to show the breadth of application of experimental design ideas. Students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. Grading is based on participation, homework assignments, a project/paper, exam(s) and a final.

  

STAT 335. [ BIOL 335 ] Introduction to Biostatistics (Section 004)

Instructor(s):  Dr. Michael Perry

Required text(s):  Rosner, Bernard. Fundamentals of Biostatistics. 7th ed. Boston: Cengage Learning, 2011. Print.

Additional notes:  We will use Minitab and possibly R for some assignments.

Prerequisites:  MATH 162 or 132; BIOL 102

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

  

STAT 336. Advanced Biostatistics

Instructor(s):  Staff

Required text(s):  Vittinghoff, Glidden, Shiboski & McCulloch (2012), Regression Methods in Biostatistics: Linear, Logistic, Survival, and Repeated Measures Models, 2nd Edition, Springer, ISBN: 9781461413523.

Additional notes:  Extensive additional Lecture Notes and Computer Code/Programs will be distributed in class.

Prerequisites:  STAT 203 or STAT 335 or equivalent.

Course description:  This course covers experimental design (interaction, analysis of covariance, crossover designs, etc.) and the analysis of designed studies, simple and multiple linear regression, generalized linear and nonlinear regression, bioassay, relative potency and drug synergy, repeated measures designs and analysis (longitudinal data analysis), and survival analysis of censored data (Cox proportional odds model, log-rank tests, Kaplan-Meier estimation). 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 R statistical packages, although no previous programming experience is assumed. Grading will be based on homework assignments, a course project/paper, quiz(zes)/exam(s) and a final.

  

STAT 388. [ STAT 411 ] Applied Survival Analysis

Instructor(s):  Dr. Michael Perry

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

Recommended text(s):  Allison, Paul D. Survival Analysis Using SAS: A Practical Guide 2nd, SAS Institute, 2010 Lee, Elisa and John Wang, Statistical Methods for Survival Data Analysis

Textbook notes:  The Allison textbook is a good resource for learning the SAS code. I have a pdf file for those preferring to use R, but it is not a comprehensive. There is no comprehensive book in R for Survival Analysis.

Additional notes:  STAT 308/408 recommend. There is significant regression analysis involved with this class.

Prerequisites:  STAT 203, STAT 335

Course description:  Time-to-event data, also referred to as survival data or failure-time data arise in situations where the actual response measurements are not known, but are known to be below or above a threshold or within an interval. This course focuses on methods for analyzing such data. We first consider descriptive methods for survival data including the survival function and its estimation using the Kaplan-Meier method and how to use and compare estimated survival functions. Then we discuss several important regression models for survival data: semi-parametric models such as proportional hazards regression models and parametric models including exponential, Weibull and log-logistic regression models. Using ideas not unlike those used in linear regression models we will describe techniques for model development, including selecting covariates, identifying influential and poorly fit subjects, and assessing overall goodness-of-fit. In this course, students will be required to analyze real-life data sets using the Minitab, R and/or SAS statistical packages.

  

STAT 388. [ STAT 488 ] Applied Bayesian Statistics

Instructor(s):  Dr. Earvin Balderama

Required text(s):  Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2014) Bayesian Data Analysis, Third Edition. Chapman & Hall/CRC. ISBN: 978-1-439-84095-5.

Recommended text(s):  Hoff, P. D. (2009) A First Course in Bayesian Statistical Methods. Springer. ISBN: 978-0-387-92299-7 Kruschke, J. K. (2014) Doing Bayesian Data Analysis, Second Edition. Elsevier Academic Press. ISBN: 978-0-124-05888-0. McElreath, R. (2016) Statistical Rethinking. Chapman & Hall/CRC Press. ISBN: 978-1-482-25344-3.

Prerequisites:  At least one course in probability such as STAT 203 or STAT 335 or MATH/STAT 304; STAT 308 or 408 recommended; Computing experience (e.g., with R) recommended (although not required).

Course description:  "Classical" statistics, encapsulating well-known methods such as t-tests, ANOVA, etc. are from the frequentist school of statistical thought. The basic idea of frequentist statistics is that the world is described by parameters that are fixed and unknown. Since these parameters are unknown, we do not know their exact values. Since they are fixed, however, we cannot discuss them in probabilistic terms. Probabilistic reasoning can only be applied to random variables---and parameters are not random, in the eyes of a frequentist. The Bayesian says, “Who cares?!”

It turns out that we can use probabilities not only to express the chance that something will occur, but we can also use them to express the extent to which we believe something, and all the math still works. The frequentist can only apply probabilities to the act of repeating an experiment, while the Bayesian can apply probabilities directly to their knowledge of the world.

Bayesian statistics are rippling through everything from physics to cancer research, ecology to psychology, law to politics, even sports analytics. Enthusiasts say they are allowing scientists to solve problems that would have been considered impossible just 20 years ago. It is proving especially useful in approaching complex problems, such as in the search for the crashed Air France Flight 447 in 2011.

Data gathering is frequently expensive compared with data analysis. It is sensible then that hard-won data be inspected from many different viewpoints. In the selection of viewpoints, Bayesian methods allow greater emphasis to be given to scientific interest and less to mathematical convenience. This course is designed to provide an introduction to fundamental conceptual, computational, and practical methods of Bayesian data analysis.

  

STAT 396. Actuarial Seminar I

Instructor(s):  Dr. Adriano Zanin Zambom

Required text(s):  None

Prerequisites:  MATH 263, MATH 212, STAT 304 are strongly recommended.

Course description:  This seminar is for students who want to prepare for Society of Actuaries exam P, or (CAS Exam 1), Probability. Topics include general probability including conditional probability and Bayes rule, univariate distributions, including binomial, hypergeometric, Poisson, beta, Pareto, gamma, Weibull and normal, and multivariate distributions including joint moment generating functions and transformation techniques.

  

STAT 404. [ MATH 404 ] Probability and Statistics I

Instructor(s):  Dr. Swarnali Banerjee

Required text(s):  Mathematical Statistics with Applications, 7th Edition by Dennis D. Wackerly, William Mendenhall III and Richard L. Sceaffer Statistical Inference by George Casella and Roger L. Berger

Prerequisites:  STAT 203 or 335

Course description:  This is the first semester of a two-semester sequence. The first semester is essentially an exploration of probability as a mathematical model of chance phenomena. The second semester explores the statistical analyses based on these models. Topics to be covered 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.

  

STAT 407. [ STAT 307 ] Statistical Design and Analysis of Experiments

Instructor(s):  Timothy E. O’Brien, Ph.D.

Required text(s):  Montgomery, Douglas C. (2013), Design and Analysis of Experiments, 8th Edition, Wiley, ISBN: 9781118146927.

Prerequisites:  STAT-203 or STAT-335 or equivalent, or permission of the instructor.

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 reviewed; blocking (complete and incomplete) will be discussed, as will be factorial designs, fractional factorial designs, and confounding. The course will focus on biometric applications such as clinical trials, HIV studies, and environmental and agricultural research, but industrial and other examples will occasionally be provided to show the breadth of application of experimental design ideas. Students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. Grading is based on participation, homework assignments, a project/paper, exam(s) and a final.

  

STAT 408. Applied Regression Analysis

Instructor(s):  Dr. Adriano Zanin Zambom

Required text(s):  Kutner, M., Nachtsheim, C., Neter, J. and Li, W. (2004) Applied Linear Statistical Models. 5th Edition, McGraw-Hill.

Recommended text(s):  Kutner, M., Nachtsheim, C. and Neter, J. Applied Linear Regression Models. 4th Edition, McGraw-Hill. Faraway, J.J. (2014) Linear Models with R. 2nd Edition. Elsevier Academic Press.

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

Course description:  This course provides students with a thorough introduction to applied regression methodology. The concept of simple linear regression will be reviewed and discussed using matrices, and multiple linear regression, transformations, diagnostics, polynomial regression, indicator variables, model building and multicolinearity will be discussed, as will be nonlinear and generalized linear regression. The course will focus on applications such as those from biometry and biostatistics (clinical trials, HIV studies, etc.), sports, engineering, agriculture and environmental science.

Syllabus:  Evaluation: Midterm 1 20% Midterm 2 20% Final 20% Project 20% Homework 20%

  

STAT 411. [ STAT 388 ] Applied Survival Analysis

Instructor(s):  Dr. Michael Perry

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

Recommended text(s):  Allison, Paul D. Survival Analysis Using SAS: A Practical Guide 2nd, SAS Institute, 2010 Lee, Elisa and John Wang, Statistical Methods for Survival Data Analysis

Textbook notes:  The Allison textbook is a good resource for learning the SAS code. I have a pdf file for those preferring to use R, but it is not a comprehensive. There is no comprehensive book in R for Survival Analysis.

Additional notes:  STAT 308/408 recommend. There is significant regression analysis involved with this class.

Prerequisites:  STAT 203, STAT 335

Course description:  Time-to-event data, also referred to as survival data or failure-time data arise in situations where the actual response measurements are not known, but are known to be below or above a threshold or within an interval. This course focuses on methods for analyzing such data. We first consider descriptive methods for survival data including the survival function and its estimation using the Kaplan-Meier method and how to use and compare estimated survival functions. Then we discuss several important regression models for survival data: semi-parametric models such as proportional hazards regression models and parametric models including exponential, Weibull and log-logistic regression models. Using ideas not unlike those used in linear regression models we will describe techniques for model development, including selecting covariates, identifying influential and poorly fit subjects, and assessing overall goodness-of-fit. In this course, students will be required to analyze real-life data sets using the Minitab, R and/or SAS statistical packages.

  

STAT 488. Statistical Consulting

Instructor(s):  Dr. Adriano Zanin Zambom

Required text(s):  None

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

Prerequisites:  Stat 404/405 and Stat 408 or permission of instructor.

Course description:  Students will be placed into groups of 4-5 students and assigned a client to work with for the duration of the semester. Each group will provide regular updates on the progress of the project via an oral presentation approximately every few weeks. Additionally, at the end of the semester each group will submit a well-written report documenting the problem, the data, the work they did, and future idea for new directions. In addition to this group project, each individual will be required to present topics previously chosen (needs approval). Presentations must be accompanied by well written, informative slides. Student will also be graded based on their participation during class. This includes, but is not limited to, asking relevant questions during the group and individual presentations.

  

STAT 488. [ STAT 388 ] Applied Bayesian Statistics

Instructor(s):  Dr. Earvin Balderama

Required text(s):  Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2014) Bayesian Data Analysis, Third Edition. Chapman & Hall/CRC. ISBN: 978-1-439-84095-5.

Recommended text(s):  Hoff, P. D. (2009) A First Course in Bayesian Statistical Methods. Springer. ISBN: 978-0-387-92299-7 Kruschke, J. K. (2014) Doing Bayesian Data Analysis, Second Edition. Elsevier Academic Press. ISBN: 978-0-124-05888-0. McElreath, R. (2016) Statistical Rethinking. Chapman & Hall/CRC Press. ISBN: 978-1-482-25344-3.

Prerequisites:  At least one course in probability such as STAT 203 or STAT 335 or MATH/STAT 304; STAT 308 or 408 recommended; Computing experience (e.g., with R) recommended (although not required).

Course description:  "Classical" statistics, encapsulating well-known methods such as t-tests, ANOVA, etc. are from the frequentist school of statistical thought. The basic idea of frequentist statistics is that the world is described by parameters that are fixed and unknown. Since these parameters are unknown, we do not know their exact values. Since they are fixed, however, we cannot discuss them in probabilistic terms. Probabilistic reasoning can only be applied to random variables---and parameters are not random, in the eyes of a frequentist. The Bayesian says, “Who cares?!”

It turns out that we can use probabilities not only to express the chance that something will occur, but we can also use them to express the extent to which we believe something, and all the math still works. The frequentist can only apply probabilities to the act of repeating an experiment, while the Bayesian can apply probabilities directly to their knowledge of the world.

Bayesian statistics are rippling through everything from physics to cancer research, ecology to psychology, law to politics, even sports analytics. Enthusiasts say they are allowing scientists to solve problems that would have been considered impossible just 20 years ago. It is proving especially useful in approaching complex problems, such as in the search for the crashed Air France Flight 447 in 2011.

Data gathering is frequently expensive compared with data analysis. It is sensible then that hard-won data be inspected from many different viewpoints. In the selection of viewpoints, Bayesian methods allow greater emphasis to be given to scientific interest and less to mathematical convenience. This course is designed to provide an introduction to fundamental conceptual, computational, and practical methods of Bayesian data analysis.