MATH 100. Intermediate Algebra

Instructor(s):  Staff

Required text(s):  Angel, Allen and Dennis Runde. Intermediate Algebra for College Students (packaged with MyMathLab). 9th ed. ISBN-10: 0321927370. ISBN-13: 9780321927378. Upper Saddle River, NJ: Pearson-Prentice Hall, 2010. Print.

Textbook notes:  Students are required to have access to MyMathLab for this course. Students buying used textbooks should arrange to purchase MyMathLab 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):  Axler, Sheldon. Precalculus: A Prelude to Calculus. Binder Ready Version w/ Wileyplus ISBN: 9781118562390 or Paperback w/ Wileyplus ISBN: 978-1-118-55625-2. 2nd ed. Hoboken, NJ: Wiley, 2012. Print.

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

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):  Axler, Sheldon. Precalculus: A Prelude to Calculus, 2nd Edition Paperback w/ Wileyplus ISBN: 978-1-118-55625-2. Hoboken, NJ: Wiley, 2012. Print.

Textbook notes:  Students who were enrolled in MATH 117 in Spring 2014 will not need to purchase this new edition of the textbook. (See course instructor for more details.)

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 131. Applied Calculus I

Instructor(s):  Staff

Required text(s):  Hughes-Hallett, Deborah, et al. Applied & Single Variable Calculus for Loyola University Chicago with WebAssign Custom (packaged with WebAssign). 4th ed. ISBN-13: 9781118747476. Hoboken, NJ: Wiley, 2013. Print.

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

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 with WebAssign Custom (packaged with WebAssign). 4th ed. ISBN-13: 9781118747476. Hoboken, NJ: Wiley, 2013. Print.

Textbook notes:  Students are required to have access to WebAssign for this course. Students buying used textbooks should arrange to purchase WebAssign separately. SPECIAL NOTE: this is a change from previous semesters, which required WileyPLUS.

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):  Thomas, George B., Maurice D. Weir, and Joel R. Hass. Thomas' Calculus: Early Transcendentals (Single Variable) (packaged with MyMathLab). 13th edition, ISBN-10: 0321952871. ISBN-13: 9780321952875

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

Prerequisites:  MATH 118 or Math Diagnostic Test

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

Instructor(s):  Staff

Required text(s):  Thomas, George B., Maurice D. Weir, and Joel R. Hass. Thomas' Calculus: Early Transcendentals (Single Variable) (packaged with MyMathLab). 13th ed. ISBN-10: 0321952871. ISBN-13: 9780321952875. Boston: Addison-Wesley, 2009. Print.

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

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. Elementary Number Theory

Instructor(s):  Emily Peters

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

Prerequisites:  MATH 161

Course description:  This course serves primarily as an introduction to understanding and constructing proofs for students planning to take advanced 300-level courses in mathematics. Topics include: mathematical induction, the Euclidean algorithm, congruences, divisibility, counting/combinatorics, and graph theory.

  

MATH 212. Linear Algebra [Doty]

Instructor(s):  Dr. Stephen Doty

Required text(s):  Jim Hefferon, Linear Algebra, 2014; ISBN-13: 978-0989897563. Free PDF version available at http://joshua.smcvt.edu/linearalgebra/, print copy available on Amazon and elsewhere.

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. For example, 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. For many students, linear algebra is the first course involving a higher level of abstraction and demanding increased focus on theory. This standard 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.

  

MATH 212. Linear Algebra

Instructor(s):  Dr. Aaron Greicius

Required text(s):  Anton, Howard. Elementary Linear Algebra. 11th ed. Wiley, 2010. ISBN 978-1-11847350-4.

Prerequisites:  Math 162 or Math 132

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

  

MATH 263. Multivariate Calculus

Instructor(s):  Staff

Required text(s):  Thomas, George B., Maurice D. Weir, and Joel R. Hass. Thomas' Calculus, Multivariable (packaged with MyMathLab), 13th ed. ISBN-13: 9780321953100. New York: Pearson, 2014. Print.

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

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.

  

Math 264. Ordinary Differential Equations

Instructor(s):  Robert Jensen

Required text(s):  "Differential Equations: A Primer for Scientists and Engineers" by Christian Constanada ISBN-13: 000-1461472962 ISBN-10: 1461472962

Prerequisites:  Math 263

Course description:  A conventional course in ordinary differential equations. Beginning with the definition of a first order differential equation and various techniques for solving them, the course then focuses on linear higher order ordinary differential equations, particularly linear second order differential equations. Then we'll look at systems of ordinary differential equations, and finish the course by introducing some special techniques for solving such as the Laplace transform and power series.

  

MATH 264. Ordinary Differential Equations

Instructor(s):  Dr. Marian Bocea

Required text(s):  Nagle, Saff, and Snider, Fundamentals of Differential Equations, 8th Ed.; ISBN-13: 9780321747730. Pearson, 2012. Print.

Prerequisites:  MATH 263 Multivariable Calculus

Course description:  This course serves as an introduction to ordinary differential equations and their applications. We will discuss linear and nonlinear first and second-order differential equations, including separable and exact equations, integrating factors, substitutions and transformations, the method of undetermined coefficients, variation of parameters, phase-plane analysis, Laplace transforms, series solutions, and systems of linear first-order differential equations. Homework will be assigned regularly throughout the semester, there will be several quizzes, at least two midterms, and a comprehensive final exam.

  

MATH 305. [ STAT 305 ] Probability and Statistics II

Instructor(s):  Dr. John G. Del Greco

Required text(s):  Larson, Richard J. and Morris L. Marx. Introduction to Mathematical Statistics and Its Applications. 5th ed. Boston: Prentice-Hall, 2012. Print.

Prerequisites:  MATH 304 or STAT 304

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

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

  

MATH 313. Abstract Algebra I

Instructor(s):  Anne Hupert

Required text(s):  Dan Saracino, Abstract Algebra, A First Course, Second Edition, Waveland 2008. ISBN : 978-1577665366.

Prerequisites:  Math 201, 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. Grades will be based on required homework, 3 in-class exams, and a required final.

  

MATH 314. [ MATH 414 ] Advanced Topics in Abstract Algebra

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Pinter, Charles. A Book of Abstract Algebra, 2nd ed. Dover, 1990. ISBN-13: 9780486474175. Print.

Recommended text(s):  Scherk, John. Algebra: a Computational Introduction, 2nd ed. Web (CC license), 2009.

Judson, Thomas W., Beezer, Robert A. Abstract Algebra: Theory and Applications. Web (GNU license), 2015.

Prerequisites:  MATH 313

Course description:  Can you, using only ruler and compass, trisect a given angle? or produce a square with the same area as a given circle? These and other simple geometric questions remained open for thousands of years—refusing to yield to proofs using purely geometric methods. In the nineteenth century, these ancient pillars were finally toppled by reaching beyond geometry to the study of abstract algebra. More specifically, to the main goal of this course: the fundamental theorem of Galois theory. (Answer: "No, you cannot.")

We have not left group theory (studied in Math 313) completely behind, but they take a back seat for awhile. We begin with an introduction to rings and fields, with an emphasis on integral domains and rings of polynomials. We study commutative and non-commutative rings, and finite and infinite fields (both characteristic 0 and characteristic p). After this "survey" portion of the course, we zero-in on Galois theory and the famous impossibilities. Along the way, we learn about extension fields, splitting fields, algebraic closure, and several other (modern-day) applications of abstract algebra.

Syllabus:  We cover most of Chapters 17 through 33 in Pinter's book. Students' course grade will be based on a midterm, a comprehensive final, several quizzes, and 10-12 written assignments. The written assignments will account for more than 25% of the grade and are an integral part of the class. (Math 414 students will work additional homework and exam problems, as well as present supplemental material to the entire class.)

  

MATH 328. [ COMP 328 COMP 428 MATH 428 ] Algebraic Coding Theory

Instructor(s):  Dr. W. Cary Huffman

Required text(s):  Huffman, W. Cary, and Vera Pless. Fundamentals of Error-Correcting Codes. Cambridge University Press, 2003.

Hardcover: ISBN-10: 0521782805; ISBN-13: 978-0521782807
Paperback: ISBN-10: 0521131707; ISBN-13: 978-0521131704

Prerequisites:  MATH 212 (Linear Algebra) or the equivalent or permission of the instructor.

Course description:  Error-correcting codes are used to recover data distorted by noise or by deterioration over time when retransmission or reconstruction of data is impossible. One of the first codes, developed by Richard Hamming in the late 1940s, helped to prevent the shutdown of the Bell Laboratories Model V computer when an error was encountered during the execution of a program. The code he developed became the foundation for the extensive and important field known today as coding theory. Without error-correcting codes CDs would sound much like phonographs, distorting the sound whenever there is a bit of dust on the CD or the slightest flaw in the material. Deep space satellite communication would be virtually impossible without error-correcting capabilities. In order to insure high fidelity reception, error-correcting codes are built into the communication standards for digital television, for optical and audio communication systems, and for multimedia broadcast/multicast service.

In this course we will study the major types of error-correcting codes, how to encode and decode them, and their main properties. The codes we examine will include the Hamming, Golay, BCH, cyclic, quadratic residue, Reed-Solomon, and Reed-Muller codes. As time permits, we will examine applications of coding theory, for instance to its use with CD players. There will be weekly homework assignments, a (probably takehome) midterm, and (probably takehome) final.

This course will require students to understand proofs. A few proofs will be included in homework and exams, but computation will be emphasized. It would be advisable to review the basics of Linear Algebra, although I will attempt to remind you of what is necessary as we go along.

  

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 or permission of instructor

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 science, 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 at least 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 and MATH 212

Course description:  A rough and not complete description of 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 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, even more importantly, to read, understand, and formulate mathematical arguments and proofs.

  

MATH 352. [ MATH 452 ] Introduction to Real Analysis II

Instructor(s):  Dr. Brian Seguin

Required text(s):  Rosenlicht, Maxwell. Introduction to Analysis Dover Publications, Inc. ISBN-10: 0-486-650383

Prerequisites:  MATH 351

Course description:  This course continues the careful derivation of the basic results first learned in calculus. We will cover most of what is in Chapters VI-X in the required book. This includes, but is not limited to, Riemann integration in R and R^n, derivatives in higher dimensions and partial derivatives, the implicit and inverse function theorems, and infinite series. The course will focus on the learning and understanding of concepts in analysis and the application of these concepts to prove results.

  

MATH 355. [ PHYS 301 ] Methods of Applied Mathematics

Instructor(s):  David Slavsky

Required text(s):  Felder, Gary N. and Kenny M. Felder. Mathematical Methods in Engineering and Physics. ISBN-13: 978-1118449608. 1st ed. Hoboken, NJ: Wiley, 2015. Print.

Prerequisites:  Math 264

Course description:  Vector calculus, matrices, series solutions of differential equations, special functions; Fourier series, Fourier and Laplace transforms; Partial differential equations, Green's functions, Einstein notation and extensive work in Mathematica.

  

MATH 358. [ MATH 458 ] Methods of Operations Research

Instructor(s):  Dr. John G. Del Greco

Required text(s): 

(1) Vanderbei, Robert J. Linear Programming: Foundations and Extensions (International Series in Operations Research & Management Science). 4th ed. ISBN-13: 978-1461476290. New York: Springer, 2014. Print.

(2) Fourer, Robert, David M. Gay, and Brian W. Kernighan. AMPL: A Modeling Language for Mathematical Programming. 2nd ed. ISBN-13: 978-0534388096. Belmont, CA: Brooks/Cole, 2003. Print.

Prerequisites:  MATH 212

Course description:  Math 358 will be an introductory course on operations research methodology which will focus primarily on the linear programming problem and its many extensions and applications. There will be take-home exams and written homework assignments. The exams and homeworks will include programming in AMPL.

We will study the following topics from linear programming:

  

Math 388. [ Math 488 ] Special Topics in Mathematics: Introduction to Differential Geometry

Instructor(s):  Dr. Adam Spiegler

Required text(s):  Pressley, Andrew. Elementary Differential Geometry, 2nd edition. ISBN-13: 978-1848828902. Springer 2010.

Prerequisites:  Math 212 and Math 263

Course description:  This course is an introduction to differential geometry. Differential geometry studies the properties of curves, surfaces, and higher-dimensional curved spaces using tools from calculus and linear algebra. The use of calculus in geometry brings about paths of study that extend beyond classical geometry. A large variety of curves, surfaces and manifolds naturally arise in areas of study that employ geometry. To address these objects, various branches of mathematics can be applied to the study of expanding field of geometry. Differential geometry contains some of the most beautiful results in mathematics, and yet most of them can be understood without extensive background knowledge. The only pre-requisites for this course are good working knowledge of multivariable calculus and linear algebra.

Syllabus:  Differential geometry questions often fall into two categories: local properties, by which one means properties of a curve or surface defined in the neighborhood of a point, or global properties which refer to properties of the curve or surface taken as a whole. We will begin by discussing local properties of curves such as curvature and torsion, and then move on to global properties of curves such as the four vertex theorem. Next we will turn our attention to the study of the geometry of surfaces in space. Topics will include how to measure length (the first fundamental form), how to measure curvature (the second fundamental form), and finally (time permitting) discuss Gauss' Theorema Egregium which is one of Gauss' most important discoveries about surfaces.

  

MATH 405. [ STAT 405 ] Probability & Statistics II

Instructor(s):  Dr. Adriano Zanin Zambom

Required text(s):  Statistical Inference - George Casella and Roger L. Berger - Second Edition

Prerequisites:  MATH/STAT 404

Course description:  A continuation of MATH/STAT 404. Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests)

  

MATH 414. [ MATH 314 ] Advanced Topics in Abstract Algebra

Instructor(s):  Dr. Aaron Lauve

Required text(s):  Pinter, Charles. A Book of Abstract Algebra, 2nd ed. Dover, 1990. ISBN-13: 9780486474175. Print.

Recommended text(s):  Scherk, John. Algebra: a Computational Introduction, 2nd ed. Web (CC license), 2009.

Judson, Thomas W., Beezer, Robert A. Abstract Algebra: Theory and Applications. Web (GNU license), 2015.

Prerequisites:  MATH 313

Course description:  Can you, using only ruler and compass, trisect a given angle? or produce a square with the same area as a given circle? These and other simple geometric questions remained open for thousands of years—refusing to yield to proofs using purely geometric methods. In the nineteenth century, these ancient pillars were finally toppled by reaching beyond geometry to the study of abstract algebra. More specifically, to the main goal of this course: the fundamental theorem of Galois theory. (Answer: "No, you cannot.")

We have not left group theory (studied in Math 313) completely behind, but they take a back seat for awhile. We begin with an introduction to rings and fields, with an emphasis on integral domains and rings of polynomials. We study commutative and non-commutative rings, and finite and infinite fields (both characteristic 0 and characteristic p). After this "survey" portion of the course, we zero-in on Galois theory and the famous impossibilities. Along the way, we learn about extension fields, splitting fields, algebraic closure, and several other (modern-day) applications of abstract algebra.

Syllabus:  We cover most of Chapters 17 through 33 in Pinter's book. Students' course grade will be based on a midterm, a comprehensive final, several quizzes, and 10-12 written assignments. The written assignments will account for more than 25% of the grade and are an integral part of the class. (Math 414 students will work additional homework and exam problems, as well as present supplemental material to the entire class.)

  

MATH 428. [ COMP 328 COMP 428 MATH 328 ] Algebraic Coding Theory

Instructor(s):  Dr. W. Cary Huffman

Required text(s):  Huffman, W. Cary, and Vera Pless. Fundamentals of Error-Correcting Codes. Cambridge University Press, 2003.

Hardcover: ISBN-10: 0521782805; ISBN-13: 978-0521782807
Paperback: ISBN-10: 0521131707; ISBN-13: 978-0521131704

Prerequisites:  MATH 212 (Linear Algebra) or the equivalent or permission of the instructor.

Course description:  Error-correcting codes are used to recover data distorted by noise or by deterioration over time when retransmission or reconstruction of data is impossible. One of the first codes, developed by Richard Hamming in the late 1940s, helped to prevent the shutdown of the Bell Laboratories Model V computer when an error was encountered during the execution of a program. The code he developed became the foundation for the extensive and important field known today as coding theory. Without error-correcting codes CDs would sound much like phonographs, distorting the sound whenever there is a bit of dust on the CD or the slightest flaw in the material. Deep space satellite communication would be virtually impossible without error-correcting capabilities. In order to insure high fidelity reception, error-correcting codes are built into the communication standards for digital television, for optical and audio communication systems, and for multimedia broadcast/multicast service.

In this course we will study the major types of error-correcting codes, how to encode and decode them, and their main properties. The codes we examine will include the Hamming, Golay, BCH, cyclic, quadratic residue, Reed-Solomon, and Reed-Muller codes. As time permits, we will examine applications of coding theory, for instance to its use with CD players. There will be weekly homework assignments, a (probably takehome) midterm, and (probably takehome) final.

This course will require students to understand proofs. A few proofs will be included in homework and exams, but computation will be emphasized. It would be advisable to review the basics of Linear Algebra, although I will attempt to remind you of what is necessary as we go along.

  

MATH 452. [ MATH 352 ] Introduction to Real Analysis II

Instructor(s):  Dr. Brian Seguin

Required text(s):  Rosenlicht, Maxwell. Introduction to Analysis Dover Publications, Inc. ISBN-10: 0-486-650383

Prerequisites:  MATH 351

Course description:  This course continues the careful derivation of the basic results first learned in calculus. We will cover most of what is in Chapters VI-X in the required book. This includes, but is not limited to, Riemann integration in R and R^n, derivatives in higher dimensions and partial derivatives, the implicit and inverse function theorems, and infinite series. The course will focus on the learning and understanding of concepts in analysis and the application of these concepts to prove results.

  

MATH 458. [ MATH 358 ] Methods of Operations Research

Instructor(s):  Dr. John G. Del Greco

Required text(s): 

(1) Vanderbei, Robert J. Linear Programming: Foundations and Extensions (International Series in Operations Research & Management Science). 4th ed. ISBN-13: 978-1461476290. New York: Springer, 2014. Print.

(2) Fourer, Robert, David M. Gay, and Brian W. Kernighan. AMPL: A Modeling Language for Mathematical Programming. 2nd ed. ISBN-13: 978-0534388096. Belmont, CA: Brooks/Cole, 2003. Print.

Prerequisites:  MATH 212

Course description:  Math 358 will be an introductory course on operations research methodology which will focus primarily on the linear programming problem and its many extensions and applications. There will be take-home exams and written homework assignments. The exams and homeworks will include programming in AMPL.

We will study the following topics from linear programming:

  

Math 488. [ Math 388 ] Special Topics in Mathematics: Introduction to Differential Geometry

Instructor(s):  Dr. Adam Spiegler

Required text(s):  Pressley, Andrew. Elementary Differential Geometry, 2nd edition. ISBN-13: 978-1848828902. Springer 2010.

Prerequisites:  Math 212 and Math 263

Course description:  This course is an introduction to differential geometry. Differential geometry studies the properties of curves, surfaces, and higher-dimensional curved spaces using tools from calculus and linear algebra. The use of calculus in geometry brings about paths of study that extend beyond classical geometry. A large variety of curves, surfaces and manifolds naturally arise in areas of study that employ geometry. To address these objects, various branches of mathematics can be applied to the study of expanding field of geometry. Differential geometry contains some of the most beautiful results in mathematics, and yet most of them can be understood without extensive background knowledge. The only pre-requisites for this course are good working knowledge of multivariable calculus and linear algebra.

Syllabus:  Differential geometry questions often fall into two categories: local properties, by which one means properties of a curve or surface defined in the neighborhood of a point, or global properties which refer to properties of the curve or surface taken as a whole. We will begin by discussing local properties of curves such as curvature and torsion, and then move on to global properties of curves such as the four vertex theorem. Next we will turn our attention to the study of the geometry of surfaces in space. Topics will include how to measure length (the first fundamental form), how to measure curvature (the second fundamental form), and finally (time permitting) discuss Gauss' Theorema Egregium which is one of Gauss' most important discoveries about surfaces.

  

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 or permission of instructor

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 science, 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 at least two midterms and a comprehensive final exam.

  

STAT 103. Fundamentals of Statistics

Instructor(s):  Dr. Gregory J. Matthews

Required text(s):  Gould, R. and Ryan, C Introductory Statistics: Exploring the World Through Data. 2nd ed. ISBN-13: 978-0-321-97827-1. Boston: Pearson, 2016. Print.

Recommended text(s):  Diez, D.M., Barr, C.D., and Centinkaya-Rundel, M. OpenIntro Statistics. 3rd ed. https://www.openintro.org/stat/textbook.php?stat_book=os

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 103. Fundamentals of Statistics

Instructor(s):  Staff

Required text(s):  Gould, Robert N. and Coleen N. Ryan. Introductory Statistics Plus NEW MyStatLab with Pearson eText -- Access Card Package, 2nd ed. ISBN-13: 978-0133956504. New York: Pearson, 2015. Print.

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. A TI-83 (or equivalent) calculator is required for this course.

Syllabus:  Common

  

STAT 203. Introduction to Probability & Statistics

Instructor(s):  Dr. Earvin Balderama

Required text(s):  TBD.

Prerequisites:  MATH 132 or MATH 162

Course description:  This course introduces the student to the common topics in probability and statistics found in engineering and science applications. It is a calculus-based rigorous introduction to basic probability theory (law of large numbers, distributions of random variables, expectations, variance, central limit theorem, moment generating functions, etc.) and statistical inference (estimation, hypothesis testing, regression, design of experiments). It also prepares the student for the in-depth classes Math/Stat 304 (Probability) and Math/Stat 305 (Mathematical Statistics).

  

STAT 305. [ MATH 305 ] Probability and Statistics II

Instructor(s):  Dr. John G. Del Greco

Required text(s):  Larson, Richard J. and Morris L. Marx. Introduction to Mathematical Statistics and Its Applications. 5th ed. Boston: Prentice-Hall, 2012. Print.

Prerequisites:  MATH 304 or STAT 304

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

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

  

STAT 310. [ STAT 410 ] Categorical Data Analysis

Instructor(s):  Dr. Molly K. Walsh

Required text(s):  Alan Agresti. An Introduction to Categorical Data Analysis. 2nd Ed. Wiley, 2007.

Prerequisites:  STAT 335 or permission of instructor

Course description:  Normally distributed response variables lead statistical practitioners to use simple linear models procedures such as simple and multiple regression or one- or two-way ANOVA, but other types of data cannot be analyzed in the same ways. Thus, these simple (regression) techniques have been generalized to handle nominal, ordinal, count and binary data under the general heading of categorical data analysis. Contingency table analyses, generalized linear models, logistic regression and log-linear modeling are the focus of this course. This course also addresses the fundamental questions encountered with regression and ANOVA for count data. Specialized methods for ordinal data, small samples, multi-category data, matched pairs, marginal models and random effects models 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. Quizzes, exams, a group project and take-home assignments will be used to determine the final grade in the course.

  

STAT 335. [ BIOL 335 ] Intro to Biostatistics

Instructor(s):  Dr. Adriano Zanin Zambom

Required text(s):  TBA

Prerequisites:  MATH 132 or 162; BIOL 102, 112.

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.

  

STAT 335. [ BIOL 335 ] Introduction to Biostatistics

Instructor(s):  Dr. Molly K. Walsh Dr. Michael Perry

Required text(s):  TBA

Recommended text(s):  Bernard Rosner. Fundamentals of Biostatistics, 7th Edition. Cengage Learning.

Additional notes:  Students may not receive credit for both STAT 203 & 335

Prerequisites:  MATH 132/162 and BIOL 102

Course description:  This course provides an introduction to statistical methods used in designing biological experiments and in data analysis. Topics include descriptive statistics, probability, discrete probability distributions, the normal distribution, sampling distributions, confidence intervals, hypothesis testing for one and two samples involving means and proportions, chi-square tests, one way ANOVA, and simple linear regression. The emphasis is on applications instead of statistical theory, and students are required to analyze real-life datasets using output from statistical packages such as Minitab and SAS, although no previous programming experience is assumed. Quizzes, exams, and take-home assignments will be used to determine the final grade in the course.

  

STAT 336. [ BIOL 336 ] Advanced Biostatistics

Instructor(s):  Dr. Molly K. Walsh

Required text(s):  TBA

Recommended text(s):  Bernard Rosner. Fundamentals of Biostatistics, 7th Edition. Cengage Learning.

Prerequisites:  STAT 335 or permission of instructor

Course description:  This course covers the basics of hypothesis testing, sample size and power calculations, categorical data techniques, experimental design and ANOVA, repeated measures ANOVA, randomized complete block design, two way ANOVA, multiple linear regression, analysis of covariance, logistic regression, and survival analysis. The emphasis is on applications instead of statistical theory, and students are required to analyze real-life datasets using output from statistical packages such as Minitab and SAS, although no previous programming experience is assumed. Quizzes, exams, a group project and take-home assignments will be used to determine the final grade in the course. Students (in small groups) will complete an original data analysis project using at least one of the methods covered during the course. Use of computer software such as Minitab and/or SAS is highly recommended for computations.

  

STAT 337. Quantitative Methods in Bioinformatics

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

Required text(s):  (1) Durbin, Eddy, Krogh & Mitchison, 1998, Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids, Cambridge, ISBN 0-521-62971-3, and (2) Norman Matloff, 2011, The Art of R Programming: A Tour of Statistical Software Design, No Starch Press, ISBN 978-1-59327-384-2

Prerequisites:  STAT-203 or STAT-335

Course description:  Predicting which conditions and diseases will develop in animals and human subjects based on its gene and protein characteristics must involve drawing conclusions from well-designed studies. As such, meaningful decisions hinge upon the correct use of statistical hypothesis testing, prediction and estimation. The most likely conclusions are also drawn from probabilistic and stochastic arguments, and a wisely chosen experimental (study) design removes biases and allows researchers to generalize from small studies to the larger population. This course explores recently developed mathematical, probabilistic and statistical methods currently used in the fields of bioinformatics and DNA microarray and protein array data analysis. These include stochastic processes, (hidden and traditional) Markov chains, microarray and other techniques. Our focus in this course is on the application of these techniques and on meaningful interpretation of results. Grading will be based on participation, homework assignments, exams, and a course paper. Additionally, although no prior knowledge is assumed, students will become familiar with programming in the R (or R-Studio) language.

  

STAT 388. [ STAT 488 ] Introduction to Nonparametric Statistics

Instructor(s):  Dr. Gregory Matthews

Required text(s):  Hollander, Myles, Douglas A. Wolfe, and Eric Chicken. Nonparametric Statistical Methods, 3rd ed. ISBN: 978-0-470-38737-5. New York: Wiley, 2013. Print.

Prerequisites:  At least one statistics course such as STAT 203 or STAT 335.

Course description:  Most basic statistical techniques are based upon normal or binomial distributional assumptions which may not be appropriate in practice. This course introduces and illustrates rank-based methods, permutation tests, bootstrap methods, and curve smoothing useful to analyze data when normal and/or binomial assumptions are not valid. 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 weekly homework assignments, quizzes and exams.

  

STAT 388. [ STAT 488 ] Applied Bayesian Statistics

Instructor(s):  Dr. Earvin Balderama

Required text(s):  Kruschke, J. K., (2014). Doing Bayesian Data Analysis, Second Edition. Elsevier Academic Press. ISBN-13: 978-0124058880.

Prerequisites:  At least one course in probability such as STAT 203 or STAT 335 or MATH/STAT 304

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.

Syllabus:  The first part of the course will introduce the Bayesian approach, including comparison with frequentist methods, Bayesian learning, common prior distributions, and summarizing posterior distributions. In the second part of the course we will study modern Bayesian computing methods, mostly MCMC and mostly using R. The main topics include Monte Carlo approximation, Gibbs sampling, convergence diagnostics, and JAGS. With these computational tools at hand, we will begin applying Bayesian methods using multiple linear regression, generalized linear models, and hierarchical models. Grading is based on homework assignments, midterm and final.

  

STAT 390. Undergraduate Seminar in Statistics

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

Required text(s):  (1) Kaiser Fung, Number-Sense: How to Use Big Data to Your Advantage, 2013, McGraw-Hill, ISBN 978-0-07179966-9 (2) Alex Reinhart, Statistics Done Wrong: The Woefully Complete Guide, 2015, No Starch Press, ISBN 978-1-59327-6201 and (3) Andrew Vickers, What is a P-Value Anyway?, 2010, Pearson, ISBN 0321-629302

Prerequisites:  Senior Standing, including completion of STAT-304

Course description:  This one-credit capstone seminar will help students to develop skills in communicating statistical topics of interest in the larger context and to an audience outside of academe and statistics. As such, students will be required to read course texts, actively participate in discussions, and give several presentations to their peers (on material beyond the standard curriculum). Students will be expected to interact with speakers and ask questions as appropriate, and will write short expositions recapping some of the talks. Grading will be based on the quality of presentations, writing and oral communication of statistical concepts.

  

STAT 405. [ MATH 405 ] Probability & Statistics II

Instructor(s):  Dr. Adriano Zanin Zambom

Required text(s):  Statistical Inference - George Casella and Roger L. Berger - Second Edition

Prerequisites:  MATH/STAT 404

Course description:  A continuation of MATH/STAT 404. Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests)

  

STAT 410. [ STAT 310 ] Categorical Data Analysis

Instructor(s):  Dr. Molly K. Walsh

Required text(s):  Alan Agresti. An Introduction to Categorical Data Analysis. 2nd Ed. Wiley, 2007.

Prerequisites:  STAT 335 or permission of instructor

Course description:  Normally distributed response variables lead statistical practitioners to use simple linear models procedures such as simple and multiple regression or one- or two-way ANOVA, but other types of data cannot be analyzed in the same ways. Thus, these simple (regression) techniques have been generalized to handle nominal, ordinal, count and binary data under the general heading of categorical data analysis. Contingency table analyses, generalized linear models, logistic regression and log-linear modeling are the focus of this course. This course also addresses the fundamental questions encountered with regression and ANOVA for count data. Specialized methods for ordinal data, small samples, multi-category data, matched pairs, marginal models and random effects models 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. Quizzes, exams, a group project and take-home assignments will be used to determine the final grade in the course.

  

STAT 488. [ STAT 388 ] Introduction to Nonparametric Statistics

Instructor(s):  Dr. Gregory Matthews

Required text(s):  Hollander, Myles, Douglas A. Wolfe, and Eric Chicken. Nonparametric Statistical Methods, 3rd ed. ISBN: 978-0-470-38737-5. New York: Wiley, 2013. Print.

Prerequisites:  At least one statistics course such as STAT 203 or STAT 335.

Course description:  Most basic statistical techniques are based upon normal or binomial distributional assumptions which may not be appropriate in practice. This course introduces and illustrates rank-based methods, permutation tests, bootstrap methods, and curve smoothing useful to analyze data when normal and/or binomial assumptions are not valid. 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 weekly homework assignments, quizzes and exams.

  

STAT 488. [ STAT 388 ] Applied Bayesian Statistics

Instructor(s):  Dr. Earvin Balderama

Required text(s):  Kruschke, J. K., (2014). Doing Bayesian Data Analysis, Second Edition. Elsevier Academic Press. ISBN-13: 978-0124058880.

Prerequisites:  At least one course in probability such as STAT 203 or STAT 335 or MATH/STAT 304

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.

Syllabus:  The first part of the course will introduce the Bayesian approach, including comparison with frequentist methods, Bayesian learning, common prior distributions, and summarizing posterior distributions. In the second part of the course we will study modern Bayesian computing methods, mostly MCMC and mostly using R. The main topics include Monte Carlo approximation, Gibbs sampling, convergence diagnostics, and JAGS. With these computational tools at hand, we will begin applying Bayesian methods using multiple linear regression, generalized linear models, and hierarchical models. Grading is based on homework assignments, midterm and final.