MATH 100. Intermediate Algebra

Instructor(s):  Staff

Required text(s):  McCallum, Connally, Hughes-Hallett et al. Algebra: Form and Function. 2nd edition. (with WileyPlus ebook)

Textbook notes:  Students buying used textbooks should arrange to purchase WileyPlus separately. Instructions for students to obtain the e-book and to use WileyPlus: use your Loyola email address to create a WileyPlus account. Your professor will include details on WileyPlus in the syllabus.

Prerequisites:  None

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

Syllabus:  Common

  

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

Prerequisites:  Math 100 or Math Diagnostic Test

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

Syllabus:  Common

  

MATH 118. Precalculus II

Instructor(s):  Staff

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

Prerequisites:  MATH 117 or Math Diagnostic Test

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

Syllabus:  Common

  

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 (WileyPlus eBook).

Prerequisites:  MATH 118 or Math Diagnostic Test

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

  

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 (WileyPlus eBook).

Prerequisites:  MATH 131 or MATH 161

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

Syllabus:  Common

  

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

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 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):  Dr Stephen Doty

Required text(s):  Mathematics: A Discrete Introduction, (3rd edition), by Edward Scheinerman. ISBN-13: 978-0-8400-4942-1; ISBN-10: 0-8400-4942-0.

Recommended text(s):  Richard Hammack, Book of Proof (3rd edition), Hammack Pub. (2018). See https://www.people.vcu.edu/~rhammack/BookOfProof.

Additional notes:  This is Section 002.

Prerequisites:  MATH 161

Course description:  Math is not just about computing derivatives and integrals! In fact, it really isn't about computing things, so much as it is about proving things. (Of course, each enriches the other.) 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.

  

MATH 212. Linear Algebra

Instructor(s):  Dr. John G. Del Greco Dr. Peter Tingley

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 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. Ordinary Differential Equations (Section 002)

Instructor(s):  Dr. Christine Haught

Required text(s):  Nagle, R. Kent, Saff, Edward B., and Edward B. Snider. Fundamentals of Differential Equations. 8th ed. ISBN-13: 978-0321747730. Boston: Addison-Wesley, 2012. Print.

Prerequisites:  co-requisite MATH 263

Course description:  A differential equation can be used to model a situation that involves change. Examples come from Ecology, Economics, Medicine, Physics, Biology and Chemistry. This course will concentrate on ordinary differential equations. For what equations does a solution exist and when is a solution unique? Can we solve an equation explicitly in mathematical terms? Can we find a numerical solution? Topics will include first order equations, second order linear equations, Laplace Transforms, series solutions, and systems of equations. Applications to modeling will be emphasized. We will use Mathematica for visualization and numerical approximations to solutions. Students will work on a group project on an applied topic of their choice and make a presentation for the class.

Grading will be based on quizzes, Mathematica assignments, projects, an in-class midterm exam and a comprehensive final exam.

  

Math 264. Ordinary Differential Equations

Instructor(s):  Robert Jensen

Required text(s):  Fundamentals of Differential Equations, by Nagle, Saff, and Snider, 9th edition. ISBN-13: 978-0321977069 ISBN-10: 9780321977069

Prerequisites:  MATH 263 or MATH 263 as a co-requisite

Course description:  A traditional 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. We'll also look at systems of ordinary differential equations, and finish the course by introducing some special techniques for solving them, such as the Laplace transform and power series.

  

MATH 266. Differential Equations and Linear Algebra

Instructor(s):  Dr. Peter Tingley

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

Prerequisites:  MATH263

Course description:  The course is an introduction to linear algebra and differential equations, and is oriented toward students of engineering science.

  

Math 304. [ Stat 304 ] Introduction to Probability

Instructor(s):  Dr. E.N.Barron

Required text(s):  First Course in Probability, 10th Edition ISBN-13 978-0-13-475311-9 9th Edition ISBN-13: 978-0321794772 ISBN-10: 9780321794772 Author Sheldon Ross Pearsson

Textbook notes:  An earlier edition may be acceptable except that the problem numbers won't match.

Prerequisites:  Math 263, Stat 203 recommended

Course description:  This is an upper division course on probability and its applications and is required for all math majors. This course is an introduction to probability theory, including a rigorous discussion of basic finite probability theory and a calculus based discussion of probability spaces with continuously differentiable density functions. Topics to be covered include combinatorial analysis, probability spaces and their properties, dependent and independent events, conditional probability, random variables, expectation of random variables and other statistical measures, probability distributions (such as binomial, exponential, and normal), the law of large numbers, the central limit theorem, and some Markov processes. It is strongly recommended that you take this class in preparation for taking the Actuarial Science P-exam!!

  

MATH 313. Abstract Algebra

Instructor(s):  Dr. Aaron Lauve

Required text(s):  T.W. Judson and R.A. Beezer., Abstract Algebra: Theory and Applications. Published online (en español). 2019.

Additional notes:  (1) Students will gain some experience in using the powerful computer algebra package, SageMath. Indeed, many of the examples in the course text have code accompanying them that you can use to experiment with the objects we'll be studying.

(2) There is a zero-credit, unscheduled "lab" component to this course (MATH 313-002). If at all possible, please leave these two blocks free in your Spring schedule. Wednesdays, 2:00–3:00 and Thursdays, 1:00–2:00.

Prerequisites:  MATH 201 and MATH 212

Course description:  The techniques and results of modern abstract algebra have found purchase in a wide variety of disciplines, ranging from physical chemistry and quantum physics to cryptography, coding theory (allowing the Cassini satellite to send you pictures of Saturn's moons) and even voting theory. At the root of it all, not surprisingly, is the centuries old study of roots of algebraic equations—so we are headed back to high school!

In this course, we study groups, the first pillar of abstract algebra, which may be viewed as the search for symmetry in objects. (Continuing the theme started in the preceding paragraph, as examples of such "objects" I might mention here algebraic equations, differential equations, geometric objects, …) Students will be introduced to permutation groups, matrix groups, subgroups, isomorphisms, equivalence relations, factor groups, and more. Over the course of the semester, we will consider some applications of abstract algebra, but the main focus will be on the "pure" study of the algebraic structures themselves. Examples motivating the theory will appear throughout.

Syllabus:  We will cover the first 12 chapters completely, and select topics from 13–18 as time permits. There will be weekly homework, semi-regular quizzes, two midterms, and a comprehensive final exam.

  

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

Instructor(s):  Dr. Anthony Giaquinto

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

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

Prerequisites:  MATH 313

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

  

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

Instructor(s):  Dr Stephen Doty

Required text(s):  Cryptography: An Introduction (3rd Edition), by Nigel Smart. Self-published by the author at http://people.cs.bris.ac.uk/~nigel/Crypto_Book.

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

Course description:  This is a course about the mathematical theory of cryptography, with a focus of the relatively recent development (since the 1970s) of public-key cryptosystems. We wil study the underlying mathematical principles, which essentially belong to discrete mathematics and abstract algebra, as well as some of the algorithms used. We will also study implementation of said algorithms (in Python). It is important that you have a solid math background, with some experience in understanding and writing proofs, as well as a previous programming course (in any high-level language).

  

MATH 351. Introduction to Real Analysis I

Instructor(s):  Dr. Joseph H. Mayne

Required text(s):  Arthur Mattuck, Introduction to Analysis, Prentice-Hall (1999), ISBN: 0-13-081132-7

Prerequisites:  MATH 201, MATH 212

Course description:  This course serves as an introduction to the foundations of real analysis emphasizing careful definitions and proofs. Much of the course consists of examining concepts originally studied in the calculus sequence, but now revisited from a more rigorous standpoint. Topics will include: a review of set theory, properties of the real number system, sequences and limits, completeness of the real numbers, infinite series, power series, functions and limits, continuous functions and the intermediate value function, the definition and properties of the derivative, the mean-value theorem, and Taylor’s theorem.

  

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

Instructor(s):  Rafal Goebel

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

Textbook notes:  Supplementary reading material will be provided when needed.

Prerequisites:  Math 351: Introduction to Real Analysis I

Course description:  Math 352 is a natural continuation of Math 351. After a brief review and reinforcement of key topics from Math 351, like sequences and their convergence and functions and their continuity and differentiability, the course will cover Riemann integration, with a brief and intense review of elements of Calc II and with an excursion to Lebesque integrability; infinite series of numbers, with a brief and intense review of elements of Calc III, and sequences of functions; the fixed point theorem and its application to differential equations, with a brief and intense review of elements of Differential Equations; the implicit function theorem; and selected other topics. Students enrolled in Math 452 will see the same material but will face tougher problems and higher standards.

  

MATH 356. Mathematical Modeling

Instructor(s):  Dr. Brian Seguin

Required text(s):  None.

Recommended text(s):  None.

Textbook notes:  None.

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

Course description:  Mechanics, being the study of forces acting on bodies and their resultant motion, is an important subject one must understand to describe many different physical phenomena. In this course you will learn how to model forces, bodies and their motion using mathematical concepts from linear algebra and vector calculus for several different mechanical systems, including systems of particles, rigid bodies, and deformable bodies. Some of the specific topics to be covered are kinematics (motion), balance laws, frames of reference, constitutive laws, and more. There will be 2-3 exams, and an equal number of quizzes during the course the semester. Weekly homework will also be assigned. There will be no textbook, but my handwritten lecture notes will be provided.

Syllabus:  None.

  

Math 388. [ Math 488 ] Special Topics in Mathematics: Algebraic Topology

Instructor(s):  Emily Peters

Required text(s):  Allen Hatcher, "Algebraic Topology," available at https://pi.math.cornell.edu/~hatcher/AT/AT.pdf .

Prerequisites:  Math 313

Course description:  Topology is what happens when you care about shapes but not about measurements: To a topologist, a donut and a coffee cup are the same -- each has exactly one hole! Mathematically, the way we can tell when surfaces are the same (or different) is by looking at paths on those shapes, and how one path can smoothly move to another path. It turns out that the paths on a surface form a group (called the fundamental group), and we can use this group to tell a one-holed donut apart from a two-holed donut (and a great number of other things). In this class, we will explore the construction of surfaces and other topologically interesting objects (such as knots), the fundamental group, and another interesting algebraic invariant called homology.

  

MATH 390. Undergraduate Seminar

Instructor(s):  Dr Stephen London

Required text(s):  None

Prerequisites:  Senior standing, including completion of MATH/STAT 304 or MATH 313 or MATH 351

Course description:  Students will explore interesting and challenging areas of mathematics chosen by the instructor in this senior seminar. Each student will then explore specific topics in more depth chosen in conjunction with the instructor and will write up and share their results.

  

MATH 405. [ STAT 405 ] Probability and Statistics II

Instructor(s):  Dr. Shuwen Lou

Required text(s):  Introduction to Mathematical Statistics, 8th Edition, by Robert V. Hogg, Joseph W. McKean, and Allen T. Craig.

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. Anthony Giaquinto

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

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

Prerequisites:  MATH 313

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

  

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

Instructor(s):  Dr Stephen Doty

Required text(s):  Cryptography: An Introduction (3rd Edition), by Nigel Smart. Self-published by the author at http://people.cs.bris.ac.uk/~nigel/Crypto_Book.

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

Course description:  This is a course about the mathematical theory of cryptography, with a focus of the relatively recent development (since the 1970s) of public-key cryptosystems. We wil study the underlying mathematical principles, which essentially belong to discrete mathematics and abstract algebra, as well as some of the algorithms used. We will also study implementation of said algorithms (in Python). It is important that you have a solid math background, with some experience in understanding and writing proofs, as well as a previous programming course (in any high-level language).

  

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

Instructor(s):  Rafal Goebel

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

Textbook notes:  Supplementary reading material will be provided when needed.

Prerequisites:  Math 351: Introduction to Real Analysis I

Course description:  Math 352 is a natural continuation of Math 351. After a brief review and reinforcement of key topics from Math 351, like sequences and their convergence and functions and their continuity and differentiability, the course will cover Riemann integration, with a brief and intense review of elements of Calc II and with an excursion to Lebesque integrability; infinite series of numbers, with a brief and intense review of elements of Calc III, and sequences of functions; the fixed point theorem and its application to differential equations, with a brief and intense review of elements of Differential Equations; the implicit function theorem; and selected other topics. Students enrolled in Math 452 will see the same material but will face tougher problems and higher standards.

  

Math 488. [ Math 388 ] Special Topics in Mathematics: Algebraic Topology

Instructor(s):  Emily Peters

Required text(s):  Allen Hatcher, "Algebraic Topology," available at https://pi.math.cornell.edu/~hatcher/AT/AT.pdf .

Prerequisites:  Math 313

Course description:  Topology is what happens when you care about shapes but not about measurements: To a topologist, a donut and a coffee cup are the same -- each has exactly one hole! Mathematically, the way we can tell when surfaces are the same (or different) is by looking at paths on those shapes, and how one path can smoothly move to another path. It turns out that the paths on a surface form a group (called the fundamental group), and we can use this group to tell a one-holed donut apart from a two-holed donut (and a great number of other things). In this class, we will explore the construction of surfaces and other topologically interesting objects (such as knots), the fundamental group, and another interesting algebraic invariant called homology.

  

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. Introduction to Probability and Statistics

Instructor(s):  Swarnali Banerjee

Required text(s):  Probability and Statistics for Engineering and the Sciences by Jay L. Devore.

Recommended text(s):  Essentials of Probability and Statistics for Engineers and Scientists by Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying Ye

Prerequisites:  MATH 162 or 132 (with grade of "C" or better).

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

  

Stat 304. [ Math 304 ] Introduction to Probability

Instructor(s):  Dr. E.N.Barron

Required text(s):  First Course in Probability, 10th Edition ISBN-13 978-0-13-475311-9 9th Edition ISBN-13: 978-0321794772 ISBN-10: 9780321794772 Author Sheldon Ross Pearsson

Textbook notes:  An earlier edition may be acceptable except that the problem numbers won't match.

Prerequisites:  Math 263, Stat 203 recommended

Course description:  This is an upper division course on probability and its applications and is required for all math majors. This course is an introduction to probability theory, including a rigorous discussion of basic finite probability theory and a calculus based discussion of probability spaces with continuously differentiable density functions. Topics to be covered include combinatorial analysis, probability spaces and their properties, dependent and independent events, conditional probability, random variables, expectation of random variables and other statistical measures, probability distributions (such as binomial, exponential, and normal), the law of large numbers, the central limit theorem, and some Markov processes. It is strongly recommended that you take this class in preparation for taking the Actuarial Science P-exam!!

  

STAT 308. Applied Regression Analysis

Instructor(s):  Dr. Michael Perry

Required text(s):  Applied Regression Analysis and Other Multivariable Methods 5th Edition - Kleinbaum, Kupper, Nizam, Rosenberg.

Prerequisites:  STAT 203 or STAT 335 (or permission of instructor)

Course description:  This course provides students with a thorough introduction to applied regression methodology. The concept of simple linear regression will be reviewed, and multiple linear regression, transformations, indicator variables, multicollinearity, diagnostics, model building, polynomial regression, logistic regression, nonparametric regression and time series analysis will be discussed. The course will focus on applications such as those from biometry and biostatistics (clinical trials, HIV studies, etc.), sports, engineering, agriculture and environmental science. Students are required to analyze real-life datasets using the R statistical software, although no previous programming experience is assumed. Quizzes, exams, and take-home assignments and projects will be used to determine the final grade in the course.

  

STAT 335. Introduction to Biostatistics

Instructor(s):  Staff

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

Additional notes:  We will use 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. Additionally, the course will include programming in R and analyzing R output. (Note: Students may not receive credit for both STAT 203 & 335.)

  

STAT 336. Advanced Biostatistics

Instructor(s):  Mr. Bret A. Longman

Required text(s):  Regression Methods in Biostatistics: Linear, Logisitic, Survival and Repeated Measures Models, Vittinghoff/Glidden/ Shiboski/McCulloch, 2nd Edition, Springer (ISBN: 978-1461413523)

Prerequisites:  STAT 203 OR STAT 335

Course description:  This course covers multi-variate analysis, including linear regression, logistic regression and survival analysis. The emphasis of the course is on applications instead of statistical theory, and students are required to analyze real-life datasets using the Minitab, SAS and 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 337. [ BIOL 337 ] Quantitative Bioinformatics

Instructor(s):  Swarnali Banerjee

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

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

Prerequisites:  STAT 203 or 335 or equivalent

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

  

STAT 338. [ STAT 488 ] Topics in Statistics-Multivariate Statistical Analysis

Instructor(s):  Dr. Xiaoli Kong

Required text(s):  Applied Multivariate Statistical Analysis (6th ed.) R. A. Johnson & D. W. Wichern, Prentice Hall, 2001

Recommended text(s):  Methods of Multivariate Analysis (3rd ed.), A. C. Rencher & W. F. Christensen Wiley, 2012 Modern Multivariate Statistical Techniques, A. J. Izenman, Springer, 2008 An Introduction to Multivariate Statistical Analysis (3rd ed.), T. W. Anderson, Wiley, 2003

Prerequisites:  MATH/STAT 305/405 or the permission of the instructor.

Course description:  Study of the multivariate normal distribution, estimation and tests of hypotheses for multivariate populations, principal components, factor analysis, discriminant analysis. The course will include programing experience with the statistical software R and packages for multivariate data analysis.

  

STAT 390. Undergraduate Seminar in Statistics

Instructor(s):  Swarnali Banerjee, Ph.D.

Required text(s):  TBD

Prerequisites:  Senior standing; 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 and Statistics II

Instructor(s):  Dr. Shuwen Lou

Required text(s):  Introduction to Mathematical Statistics, 8th Edition, by Robert V. Hogg, Joseph W. McKean, and Allen T. Craig.

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 437. Quantitative Bioinformatics

Instructor(s):  Swarnali Banerjee

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

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

Prerequisites:  STAT 203 or 335 or equivalent

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

  

STAT 488. [ STAT 338 ] Topics in Statistics-Multivariate Statistical Analysis

Instructor(s):  Dr. Xiaoli Kong

Required text(s):  Applied Multivariate Statistical Analysis (6th ed.) R. A. Johnson & D. W. Wichern, Prentice Hall, 2001

Recommended text(s):  Methods of Multivariate Analysis (3rd ed.), A. C. Rencher & W. F. Christensen Wiley, 2012 Modern Multivariate Statistical Techniques, A. J. Izenman, Springer, 2008 An Introduction to Multivariate Statistical Analysis (3rd ed.), T. W. Anderson, Wiley, 2003

Prerequisites:  MATH/STAT 305/405 or the permission of the instructor.

Course description:  Study of the multivariate normal distribution, estimation and tests of hypotheses for multivariate populations, principal components, factor analysis, discriminant analysis. The course will include programing experience with the statistical software R and packages for multivariate data analysis.