MATH 100. Intermediate Algebra
Instructor(s): Staff
Required text(s): Ron Larson. Intermediate Algebra (WebAssign eBook) 5th ed.
Textbook notes: Students are required to have access to WebAssign for this course. Students buying used textbooks should arrange to purchase WebAssign separately
Prerequisites: None
Course description: Fundamentals of algebra. Graphs of linear equations, polynomials and factoring, first and second-degree equations and inequalities, radicals and exponents, and systems of equations. Word problems emphasized throughout the course.
Syllabus: Common
MATH 108. Real World Modeling
Instructor(s): Staff
Required text(s): Consortium for Mathematics and Its Applications (COMAP), S. Garfunkel, ed. For All Practical Purposes: Mathematical Literacy in Today's World. 9th ed. ISBN-13: 978-1429243162. New York: W. H. Freeman, 2011. Print.
Prerequisites: None
Course description: An introduction to mathematical modeling. Topics chosen from linear programming, probability theory, Markov chains, scheduling problems, coding theory, social choice, voting theory, geometric concepts, game theory, graph theory, combinatorics, networks. Emphasis placed upon demonstrating the usefulness of mathematical models in other disciplines, especially the social science and business.
Syllabus: Common
MATH 117. Precalculus I
Instructor(s): Staff
Required text(s): Carl Stitz and Jeff Zeager. Precalculus (WebAssign eBook), 3rd edition.
Stitz Zeager Open Source Mathematics, 4 July 2014. Web. http://www.stitz-zeager.com/.
Textbook notes: Students should register for their section of Math 117 in WebAssign (with eBook).
Prerequisites: MATH 100 or Math Diagnostic Test
Course description: Inverse functions, quadratic functions, complex numbers. Detailed study of polynomial functions including zeros, factor theorem, and graphs. Rational functions, exponential and logarithmic functions and their applications. Systems of equations, inequalities, partial fractions, linear programming, sequences and series. Word problems are emphasized throughout the course.
Syllabus: Common
MATH 118. Precalculus II
Instructor(s): Staff
Required text(s): Carl Stitz and Jeff Zeager. Precalculus (WebAssign eBook), 3rd edition.
Stitz Zeager Open Source Mathematics, 4 July 2014. Web. http://www.stitz-zeager.com/.
Textbook notes: Students should register for their section of Math 118 in WebAssign (with eBook).
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 (WebAssign eBook). 4th ed.
ISBN-13: 9781118747476. Hoboken, NJ: Wiley, 2013. Print.
Textbook notes: Students should register for their section of Math 131 in WebAssign (with eBook).
Prerequisites: MATH 118 or Math Diagnostic Test
Course description: An introduction to differential and integral calculus, with an emphasis on applications. This course is intended for students in the life and social sciences, computer science, and business. Topics include: modeling change using functions including exponential and trigonometric functions, the concept of the derivative, computing the derivative, applications of the derivative to business and life, social, and computer sciences, and an introduction to integration. This course is not a substitute for MATH 161.
Syllabus: Common
MATH 132. Applied Calculus II
Instructor(s): Staff
Required text(s): Hughes-Hallett, Deborah, et al. Applied & Single Variable Calculus for Loyola University Chicago, Custom (WebAssign eBook). 4th ed.
ISBN-13: 9781118747476. Hoboken, NJ: Wiley, 2013. Print.
Textbook notes: Students should register for their section of Math 132 in WebAssign (with 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.
ISBN-13: 978-1285741550. Boston: Centage Learning, 2015. Print.
Textbook notes: Students should register for their section of Math 161 in WebAssign (with eBook).
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.
ISBN-13: 978-1285741550. Boston: Centage Learning, 2015. Print.
Textbook notes: Students should register for their section of Math 162 in WebAssign (with eBook).
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 Math and Number Theory
Instructor(s): Dr. Alan Saleski
Required text(s): Tentative choice: Discrete Mathematics with Ducks, by sarah-marie belcastro. June 21, 2012 by A K Peters/CRC Press Textbook. ISBN 9781466504998 But final decision not yet made.
Recommended text(s): Burton’s Elementary Number Theory
Prerequisites: MATH 161
Course description: This course in Discrete Mathematics attempts to engage and expose the student to several different topics in discrete mathematics (including induction, naive set theory, number theory, combinatorics, algebraic structures, basic logic, graph theory, equivalence relations, injective and surjective maps, and cardinality.) The primary desired outcome is for the student to learn how to read and write precise and unambiguous mathematical proofs at a beginning level. Such skills should prepare students to enter 300-level courses such as Abstract Algebra and Real Analysis.
MATH 201. Discrete Math and Number Theory
Instructor(s): Dr. Anne Peters Hupert
Required text(s): Mathematics: A Discrete Introduction (3rd edition) by Edward Scheinerman ISBN-13: 978-0840065285 ISBN-10: 0840065280
Prerequisites: MATH 161
Course description: This course covers topics from discrete mathematics, primarily from elementary number theory, ranging from induction to congruencies to prime numbers and cardinality, to provide students planning to take advanced 300 level courses in mathematics with an introduction to understanding and constructing proofs. Grades will be bases on daily homework, 3 in-class exams, and a final.
MATH 212. Linear Algebra
Instructor(s): Drs. John G. Del Greco and 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 215. [ COMP 215 ] Object-Oriented Programming for Mathematics
Instructor(s): Dr. Aaron Lauve
Required text(s): Allan M. Stavely, Programming and Mathematical Thinking: A Gentle Introduction to Discrete Math Featuring Python. 1st ed. ISBN: 978-1-938159-00-8 (pbk.), 978-1-938159-01-5 (ebook). Socorro, New Mexico: New Mexico Tech Press, 2014. (eBook available from instructor on first day of class.)
Recommended text(s): Andrew Harrington, Hands-On Python Tutorial; Robert Sedgewick, et al., Introduction to Programming in Python BookSite.
Additional notes: This course is programming intensive. Students will submit assignments as Jupyter Notebooks within SageMathCloud. For information on SageMathCloud, see here. For a demo on these notebooks, see here.
Prerequisites: MATH 162 or MATH 132 or permission of the instructor
Course description: Math 215/Comp 215 is a first course in programming for students interested in mathematics and scientific applications. No previous programming experience is required. Students will learn object-oriented programming using the programming language Python. Python is easy to learn and we will quickly be able to solve interesting problems with it drawn from a variety of scientific computing realms. Special focus will be given to mathematical examples arising in calculus, number theory, statistics, geometry, and linear algebra.
(Note: This course is a substitute for Comp 170 in most CS curricula. As such, the Comp 170 course description, course goals, and course outcomes apply here as well.)
Syllabus: There will be weekly programming assignments as well as frequent in-class exercises. Final course grade will be based on the programming assignments, near-weekly quizzes, a final project, and a final exam.
MATH 263. Multivariate Calculus
Instructor(s): Staff
Required text(s): Stewart, James. Calculus: Early Transcendentals (WebAssign eBook). 8th ed.
ISBN-13: 978-1285741550. Boston: Centage Learning, 2015. Print.
Textbook notes: Students should register for their section of Math 263 in WebAssign (with eBook).
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
Instructor(s): Dr. W. Cary Huffman
Required text(s): R. Kent Nagle, Edward B. Saff, and Arthur David Snider, Fundamentals of Differential Equations, 8th Edition, 2012. ISBN-13: 978-0-321-74773-0. Boston: Addison-Wesley, 2012. Print.
Prerequisites: MATH 263
Course description:
Differential equations arise in many fields of study including physics, biology, chemistry, engineering, and economics. This course will focus primarily on techniques for solving families of first-order and second-order ordinary differential equations as well as systems of these equations. We will also consider questions of existence and uniqueness of solutions to ordinary differential equations. Along the way applications leading to differential equations will be presented. As time permits, other topics related to solutions of ordinary differential equations will be explored.
The first-order equations we will examine include separable, linear, and exact equations. For other first-order equations, solution techniques such as integrating factors, substitution, and transformations will be presented. For second-order equations we will focus on techniques such as undetermined coefficients and variation of parameters to solve linear equations. For first- and second-order equations where general techniques fail, power series solutions become an option.
The Laplace Transform is a particularly important tool for solving systems of linear differential equations where certain discontinuities can arise. The LaPlace Transform converts a differential equation to an algebraic equation. We will study properties of this transform and how it can be used to solve differential equations.
Grades in the course will be based on homework and exams.
MATH 264. Ordinary Differential Equations
Instructor(s): Dr. Cristina Popovici
Required text(s): Boyce, William E., and DiPrima, Richard C., Elementary Differential Equations, 10th Edition; ISBN: 978-1-118-61743-4 (E-Text); 978-1-118-15739-8 (Loose-leaf); 978-0-470-45832-7 (Hardcover). Wiley, 2013.
Prerequisites: MATH 263
Course description: This is an introductory course in ordinary differential equations. Topics to be discussed include linear and nonlinear first order differential equations such as separable, exact, homogeneous, and Bernoulli equations, second order linear equations, the Laplace transforms and its applications to solving initial value problems, and systems of linear first-order differential equations. Homework will be assigned regularly throughout the semester. There will be two midterms and a comprehensive final exam.
MATH 304. [ STAT 304 ] Introduction to Probability
Instructor(s): Dr. Robert Jensen
Required text(s): Probability Theory: A Concise Course (Dover Books on Mathematics) by Y.A. Rozanov (Author) ISBN-13: 080-0759635443 ISBN-10: 0486635449
Recommended text(s): A First Course in Probability (6th Edition) 6th Edition by Sheldon Ross (Author) ISBN-13: 978-0131856622 ISBN-10: 0131856626
Textbook notes: It is highly recommended that students get the (recommended) text, "A First Course in Probability" (6th Edition) 6th Edition by Sheldon Ross (Author). Students may substitute a more recent edition of this text.
Prerequisites: MATH 263
Course description: 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.
MATH 313. Abstract Algebra I
Instructor(s): Dr. Stephen Doty
Required text(s): Sepanski, Mark R. Algebra. Pure and Applied Undergraduate Texts, Volume 11 (2010), American Mathematical Society, Providence, RI. Print ISBN: 978-0-8218-5294-1.
Recommended text(s): Pinter, Charles C. A Book of Abstract Algebra. Dover ed. ISBN-13: 978-0486474175. New York: McGraw-Hill, 1990. Print.
Prerequisites: MATH 201 and MATH 212
Course description: This course provides a rigorous introduction to the study of structures such as groups, rings, and fields; emphasis is on the theory of groups with topics such as subgroups, cyclic groups, Abelian groups, permutation groups, homomorphisms, cosets, and factor groups.
Groups are mathematical systems that codify symmetry. Originally developed by Lagrange and Galois in order to study roots of polynomials, the theory of groups (and abstract algebra more generally) has seen increasing application to such diverse areas as particle physics, crystals in chemistry, DNA in biology, encoding DVDs and space communications, geometry and topology, cryptography, and functional programming languages in computer science. If you wish to find out why the general quintic (5th degree polynomial) equation is not solvable in terms of radicals, or why it is impossible to trisect an angle by ruler and compass, then you need the ideas of this course. If you want to understand how strong public-key cryptosystems work to protect your privacy on the internet, then you need to know about groups. And so on.
Grades will be based on required homework, in-class exams, and a required final.
MATH 315. [ MATH 415 ] Topics in Linear Algebra
Instructor(s): Dr. Joseph Mayne
Required text(s): Sheldon Axler, Linear Algebra Done Right, 3rd Edition, Springer, (2015). ISBN: 978-3-319-11079-0.
Prerequisites: MATH 313
Course description: This course is a continuation of Mathematics 212, Linear Algebra. The emphasis will be on abstract vector spaces primarily over the fields of real and complex numbers. There will a review of the basic properties of vector spaces and their subspaces. Continuing the study of vector spaces and linear transformations on finite-dimensional spaces, topics will be chosen from: change of basis, trace, determinant, eigenvalues, invariant subspaces, linear functionals, dual spaces, inner product spaces, adjoint transformations, the spectral theorem, the characteristic and minimal polynomials, and Jordan canonical form. Grading will based on the scores of three tests, a final examination, and regular homework assignments.
MATH 351. Introduction to Real Analysis I
Instructor(s): Dr. Marian Bocea
Required text(s): Rosenlicht, Maxwell, Introduction to Analysis. Dover Books on Mathematics; ISBN-10: 0-486-65038-3
Prerequisites: MATH 201 and MATH 212
Course description: This course offers an introduction to Real Analysis, from the foundations of the subject to the development of key concepts such as continuity and differentiability. Topics include: the real number system, metric spaces, open and closed sets, compactness, connectedness, sequences, limits, continuity, uniform continuity, and differentiability. A strong emphasis will be placed on conceptual understanding and mathematical rigor. The students will be expected to understand and formulate mathematical proofs, and will have ample opportunities to demonstrate their problem-solving skills. There will be at least two midterms and a comprehensive final exam.
MATH 353. [ MATH 453 ] Introduction to Complex Analysis
Instructor(s): Dr. Brian Seguin
Required text(s): Saff, E. B., and Snider, A. D. Fundamentals of Complex Analysis with Applications to Engineering and Science ISBN 0-13-907874-6. 3rd ed. Person Education, Inc. 2003. Print.
Prerequisites: MATH 351
Course description: This is a traditional course on complex analysis. After a brief review of the complex numbers we will study complex valued functions of a complex variable. This includes differentiation and the connection between differentiable functions and analytic functions; and integration, where the line integral from multivariable calculus provides the connection between integration and differentiation. We will prove the Cauchy representation theorem and the residue theorem and examine their consequences and applications.
MATH 360. [ MATH 460 ] Game Theory
Instructor(s): Dr. E. N. Barron
Required text(s): Game Theory: An Introduction, 2nd edition, by E.N.Barron, Wiley, ISBN-13: 978-1118216934 ISBN-10: 1118216938
Textbook notes: A solutions manual is also available but is totally optional. Solution Manual to Accompany Game Theory: An Introduction, by E.N.Barron ISBN-13: 978-1118274286 ISBN-10: 1118274288
Prerequisites: You should know how to multiply matrices and find an inverse of a matrix. Some elementary probability is also used. You should have 2 semesters of calculus. You certainly have enough if you have had MATH 212 and MATH 304 or MATH 203.
Course description: This class is a modern introduction to all of the major topics in game theory. We will cover 2-person zero sum games as an introduction, them move to N-person nonzero sum games. These are non-cooperative. Then we cover bargaining and cooperative games, both the von-Neumann and Shapley theories. Applications are emphasized throughout the course. Applications to economics, political science, transportation, fair apportionment, warfare, etc., will be covered. This class will have two midterms and a final.
MATH 388. [ MATH 488 ] Special Topics in Mathematics: Knot Theory
Instructor(s): Emily Peters
Required text(s): The Knot Book, by Colin Adams.
Prerequisites: Math 201 and 212.
Course description: If you’ve ever played with one of those puzzles where you have to remove a bead from a rope wound around a wooden base, a brass ring, and a horseshoe, then you understand that the question of whether two knots are the same is frustratingly difficult and fascinating. In mathematics, a knot is a flexible piece of string in three-dimensional space whose ends have been joined together. (In other words, your shoelaces are not a knot, mathematically speaking, but an extension cord plugged into itself is.) Telling knots apart from each other is surprisingly difficult! Even identifying whether a knot can be unknotted (ie, manipulated into a simple loop, without breaking and reconnecting the string) is surprisingly hard. This, of course, is where mathematics comes in. Mathematicians have developed a number of knot invariants: ways of assigning something simpler than a knot (perhaps a number, or a collection of numbers, or a polynomial) to a depiction of a knot, in such a way that allowed manipulations don’t change the value of the invariant. A very simple example — can the knot be colored with three different colors, according to some simple rules? — produces either the answer “yes” or “no”, and can tell us that some knots cannot be unknotted. In the first part of this class, we will investigate knots and their invariants: first, we’ll mathematically define a knot and when two knots are equivalent; then, we’ll construct maps from the set of knot equivalence classes into … other things. (Colors, numbers, polynomials, 2D surfaces in 3D space, etc.) Along the way, we’ll notice some interesting digressions into linear algebra, continued fractions, group theory, geometry, and topology. In the second part of the class, student interest will determine which of these digressions we develop further. Grades will be based on homework, an in-class midterm, and a final exam. Graduate students will also do an independent project which will include an in-class presentation.
Math 390. Undergraduate Seminar in Mathematics
Instructor(s): Robert Jensen
Required text(s): None
Textbook notes: Students will be expected to find their own resources for material on the topic they choose.
Prerequisites: Senior Standing, including completion of Math 304/Stat 304 or Math 313 or Math 351
Course description: In this seminar students will pick a topic from the theory of special functions (i.e., one of the special functions such as the gamma function, beta function, zeta function, Hermite polynomials, Laguerre polynomials, Legendre polynomials, hypergeometric functions, and etc.); and give a short computer aided presentation (I anticipate using the Beamer LaTex module for this) describing the topic, its utility, and "proving" an advanced result about the topic.
MATH 415. [ MATH 315 ] Topics in Linear Algebra
Instructor(s): Dr. Joseph Mayne
Required text(s): Sheldon Axler, Linear Algebra Done Right, 3rd Edition, Springer, (2015). ISBN: 978-3-319-11079-0.
Prerequisites: MATH 313
Course description: This course is a continuation of Mathematics 212, Linear Algebra. The emphasis will be on abstract vector spaces primarily over the fields of real and complex numbers. There will a review of the basic properties of vector spaces and their subspaces. Continuing the study of vector spaces and linear transformations on finite-dimensional spaces, topics will be chosen from: change of basis, trace, determinant, eigenvalues, invariant subspaces, linear functionals, dual spaces, inner product spaces, adjoint transformations, the spectral theorem, the characteristic and minimal polynomials, and Jordan canonical form. Grading will based on the scores of three tests, a final examination, and regular homework assignments.
MATH 453. [ MATH 353 ] Introduction to Complex Analysis
Instructor(s): Dr. Brian Seguin
Required text(s): Saff, E. B., and Snider, A. D. Fundamentals of Complex Analysis with Applications to Engineering and Science ISBN 0-13-907874-6. 3rd ed. Person Education, Inc. 2003. Print.
Prerequisites: MATH 351
Course description: This is a traditional course on complex analysis. After a brief review of the complex numbers we will study complex valued functions of a complex variable. This includes differentiation and the connection between differentiable functions and analytic functions; and integration, where the line integral from multivariable calculus provides the connection between integration and differentiation. We will prove the Cauchy representation theorem and the residue theorem and examine their consequences and applications.
MATH 460. [ MATH 360 ] Game Theory
Instructor(s): Dr. E. N. Barron
Required text(s): Game Theory: An Introduction, 2nd edition, by E.N.Barron, Wiley, ISBN-13: 978-1118216934 ISBN-10: 1118216938
Textbook notes: A solutions manual is also available but is totally optional. Solution Manual to Accompany Game Theory: An Introduction, by E.N.Barron ISBN-13: 978-1118274286 ISBN-10: 1118274288
Prerequisites: You should know how to multiply matrices and find an inverse of a matrix. Some elementary probability is also used. You should have 2 semesters of calculus. You certainly have enough if you have had MATH 212 and MATH 304 or MATH 203.
Course description: This class is a modern introduction to all of the major topics in game theory. We will cover 2-person zero sum games as an introduction, them move to N-person nonzero sum games. These are non-cooperative. Then we cover bargaining and cooperative games, both the von-Neumann and Shapley theories. Applications are emphasized throughout the course. Applications to economics, political science, transportation, fair apportionment, warfare, etc., will be covered. This class will have two midterms and a final.
MATH 488. [ MATH 388 ] Special Topics in Mathematics: Knot Theory
Instructor(s): Emily Peters
Required text(s): The Knot Book, by Colin Adams.
Prerequisites: Math 201 and 212.
Course description: If you’ve ever played with one of those puzzles where you have to remove a bead from a rope wound around a wooden base, a brass ring, and a horseshoe, then you understand that the question of whether two knots are the same is frustratingly difficult and fascinating. In mathematics, a knot is a flexible piece of string in three-dimensional space whose ends have been joined together. (In other words, your shoelaces are not a knot, mathematically speaking, but an extension cord plugged into itself is.) Telling knots apart from each other is surprisingly difficult! Even identifying whether a knot can be unknotted (ie, manipulated into a simple loop, without breaking and reconnecting the string) is surprisingly hard. This, of course, is where mathematics comes in. Mathematicians have developed a number of knot invariants: ways of assigning something simpler than a knot (perhaps a number, or a collection of numbers, or a polynomial) to a depiction of a knot, in such a way that allowed manipulations don’t change the value of the invariant. A very simple example — can the knot be colored with three different colors, according to some simple rules? — produces either the answer “yes” or “no”, and can tell us that some knots cannot be unknotted. In the first part of this class, we will investigate knots and their invariants: first, we’ll mathematically define a knot and when two knots are equivalent; then, we’ll construct maps from the set of knot equivalence classes into … other things. (Colors, numbers, polynomials, 2D surfaces in 3D space, etc.) Along the way, we’ll notice some interesting digressions into linear algebra, continued fractions, group theory, geometry, and topology. In the second part of the class, student interest will determine which of these digressions we develop further. Grades will be based on homework, an in-class midterm, and a final exam. Graduate students will also do an independent project which will include an in-class presentation.
STAT 103. Fundamentals of Statistics
Instructor(s): Staff
Required text(s): Illowsky, Barbara, and Susan Dean. Introductory Statistics (WebAssign eBook). 1st ed.
ISBN-13 978-1-938168-20-8. Houston: Open Stax College, 2013. Print.
Textbook notes: Students should register for their section of Stat 103 in WebAssign (with eBook).
Prerequisites: None
Course description: An introduction to statistical reasoning. Students learn how statistics has helped to solve major problems in economics, education, genetics, medicine, physics, political science, and psychology. Topics include: design of experiments, descriptive statistics, mean and standard deviation, the normal distribution, the binomial distribution, correlation and regression, sampling, estimation, and testing of hypothesis.
Syllabus: Common
STAT 203. Statistics
Instructor(s): Dr. Adriano Zanin Zambom
Required text(s): Walpole, Myers, Myers and Ye. Essentials of Probability and Statistics for Engineers and Scientists. Pearson.
Prerequisites: MATH 132 or MATH 162
Course description: This course is a Calculus-based rigorous introduction to basic topics in probability (distributions, expectations, variance, central limit theorem and the law of large numbers, moment generating functions, etc.) and statistics (estimation, hypothesis testing, regression, design of experiments) needed in engineering and science applications. Prerequisite: MATH 132 or 162 (with grade of C or better) Outcomes: The students will obtain required knowledge in probability and statistics useful in every area of engineering and science. They will learn how to assess data and outcomes of experiments.
STAT 304. [ MATH 304 ] Introduction to Probability
Instructor(s): Dr. Robert Jensen
Required text(s): Probability Theory: A Concise Course (Dover Books on Mathematics) by Y.A. Rozanov (Author) ISBN-13: 080-0759635443 ISBN-10: 0486635449
Recommended text(s): A First Course in Probability (6th Edition) 6th Edition by Sheldon Ross (Author) ISBN-13: 978-0131856622 ISBN-10: 0131856626
Textbook notes: It is highly recommended that students get the (recommended) text, "A First Course in Probability" (6th Edition) 6th Edition by Sheldon Ross (Author). Students may substitute a more recent edition of this text.
Prerequisites: MATH 263
Course description: 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.
STAT 307. [ STAT 407 ] Statistical Design & Analysis of Experiments
Instructor(s): Dr. Timothy E. O'Brien
Required text(s): Montgomery, Douglas C. (2013), Design and Analysis of Experiments, 8th Edition, Wiley, ISBN: 9781118146927
Prerequisites: STAT 203 or STAT 335 or equivalent, or permission of the instructor.
Course description: As no subject is more central to the development of statistical methods, this course provides students with a thorough introduction to statistical experimental design and to the statistical methods used to analyze the resulting data. The concepts of comparative experiments, analysis of variance (ANOVA) and mean separation procedures will be reviewed; blocking (complete and incomplete) will be discussed, as will be factorial designs, fractional factorial designs, and confounding. The course will focus on biometric applications such as clinical trials, HIV studies, and environmental and agricultural research, but industrial and other examples will occasionally be provided to show the breadth of application of experimental design ideas. Students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. Grading is based on participation, homework assignments, a project/paper, exam(s) and a final.
STAT 308. Applied Regression Analysis
Instructor(s): Dr. Earvin Balderama
Required text(s): Faraway, Julian J. Linear Models with R. Second Edition. ISBN-13: 978-1439887332. Taylor & Francis Group/CRC Press. 2015.
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. [ BIOL 335 ] Introduction to Biostatistics
Instructor(s): Dr. Molly K. Walsh
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. Timothy E. O'Brien
Required text(s): Vittinghoff, Glidden, Shiboski & McCulloch (2012), Regression Methods in Biostatistics: Linear, Logistic, Survival, and Repeated Measures Models, 2nd Edition, Springer, ISBN: 9781461413523.
Additional notes: Extensive additional Lecture Notes and Computer Code/Programs will be distributed in class.
Prerequisites: STAT 203 or STAT 335 or equivalent.
Course description: This course covers experimental design (interaction, analysis of covariance, crossover designs, etc.) and the analysis of designed studies, simple and multiple linear regression, generalized linear and nonlinear regression, bioassay, relative potency and drug synergy, repeated measures designs and analysis (longitudinal data analysis), and survival analysis of censored data (Cox proportional odds model, log-rank tests, Kaplan-Meier estimation). The emphasis of the course is on applications instead of statistical theory, and students are required to analyze real-life datasets using the Minitab, SAS and R statistical packages, although no previous programming experience is assumed. Grading will be based on homework assignments, a course project/paper, quiz(zes)/exam(s) and a final.
STAT 388. [ STAT 488 ] Applied Multivariate Statistical Analysis
Instructor(s): Dr. Adriano Zanin Zambom
Required text(s): Applied Multivariate Statistical Analysis (6th Edition), by Richard A. Johnson (Author), Dean W. Wichern (Author)
Prerequisites: -
Course description: This course will cover the basic principles of multivariate statistical analysis including: multivariate Normal distribution, inferences about mean vectors, comparisons of several multivariate means, multivariate linear regression, principal components, factor analysis, discrimination and classification, clustering and others.
STAT 407. [ STAT 307 ] Statistical Design & Analysis of Experiments
Instructor(s): Dr. Timothy E. O'Brien
Required text(s): Montgomery, Douglas C. (2013), Design and Analysis of Experiments, 8th Edition, Wiley, ISBN: 9781118146927
Prerequisites: STAT 203 or STAT 335 or equivalent, or permission of the instructor.
Course description: As no subject is more central to the development of statistical methods, this course provides students with a thorough introduction to statistical experimental design and to the statistical methods used to analyze the resulting data. The concepts of comparative experiments, analysis of variance (ANOVA) and mean separation procedures will be reviewed; blocking (complete and incomplete) will be discussed, as will be factorial designs, fractional factorial designs, and confounding. The course will focus on biometric applications such as clinical trials, HIV studies, and environmental and agricultural research, but industrial and other examples will occasionally be provided to show the breadth of application of experimental design ideas. Students will develop expertise using the SAS and R computer packages, although no previous programming experience will be assumed. Grading is based on participation, homework assignments, a project/paper, exam(s) and a final.
STAT 408. Applied Regression Analysis
Instructor(s): Dr. Earvin Balderama
Required text(s): Faraway, Julian J. Linear Models with R. Second Edition. ISBN-13: 978-1439887332. Taylor & Francis Group/CRC Press. 2015.
Prerequisites: Some background in basic statistical methods or biostatistics, or permission of instructor.
Course description: This course provides students with a thorough introduction to applied regression methodology. The concept of simple linear regression will be reviewed and discussed using matrices, and multiple linear regression, transformations, diagnostics, polynomial regression, indicator variables, model building and multicollinearity will be discussed, as will be nonlinear and generalized linear regression. The course will focus on applications such as those from biometry and biostatistics (clinical trials, HIV studies, etc.), sports, engineering, agriculture and environmental science.
STAT 488. [ STAT 388 ] Applied Multivariate Statistical Analysis
Instructor(s): Dr. Adriano Zanin Zambom
Required text(s): Applied Multivariate Statistical Analysis (6th Edition), by Richard A. Johnson (Author), Dean W. Wichern (Author)
Prerequisites: -
Course description: This course will cover the basic principles of multivariate statistical analysis including: multivariate Normal distribution, inferences about mean vectors, comparisons of several multivariate means, multivariate linear regression, principal components, factor analysis, discrimination and classification, clustering and others.
STAT 488. Statistical Consulting
Instructor(s): Dr. Gregory J. Matthews
Required text(s): None
Prerequisites: STAT 408
Course description: This course serves as a program capstone course for the MS program in Applied Statistics; as such it synthesizes the course material in the context of actual statistical consulting sessions. Students are required to assist in analyzing real-life data sets using SAS and R statistical packages. Students also learn to sharpen their verbal, written and non-verbal communication skills. Grading is based on in-class presentations and consulting sessions and practicum, quizzes and a course project.