MATH 100. Intermediate Algebra
Instructor(s): Staff
Required text(s): Ron Larson. Intermediate Algebra (WebAssign eBook) 5th ed.
Textbook notes: Students are required to have access to WebAssign for this course. Students buying used textbooks should arrange to purchase WebAssign separately
Prerequisites: None
Course description: Fundamentals of algebra. Graphs of linear equations, polynomials and factoring, first and second-degree equations and inequalities, radicals and exponents, and systems of equations. Word problems emphasized throughout the course.
Syllabus: Common
MATH 108. Real World Modeling
Instructor(s): Staff
Required text(s): Consortium for Mathematics and Its Applications (COMAP), S. Garfunkel, ed. For All Practical Purposes: Mathematical Literacy in Today's World. 9th ed. ISBN-13: 978-1429243162. New York: W. H. Freeman, 2011. Print.
Prerequisites: None
Course description: An introduction to mathematical modeling. Topics chosen from linear programming, probability theory, Markov chains, scheduling problems, coding theory, social choice, voting theory, geometric concepts, game theory, graph theory, combinatorics, networks. Emphasis placed upon demonstrating the usefulness of mathematical models in other disciplines, especially the social science and business.
Syllabus: Common
MATH 117. Precalculus I
Instructor(s): Staff
Required text(s): Carl Stitz and Jeff Zeager. Precalculus (WebAssign eBook), 3rd edition.
Stitz Zeager Open Source Mathematics, 4 July 2014. Web. http://www.stitz-zeager.com/.
Prerequisites: MATH 100 or Math Diagnostic Test
Course description: Inverse functions, quadratic functions, complex numbers. Detailed study of polynomial functions including zeros, factor theorem, and graphs. Rational functions, exponential and logarithmic functions and their applications. Systems of equations, inequalities, partial fractions, linear programming, sequences and series. Word problems are emphasized throughout the course.
Syllabus: Common
MATH 118. Precalculus II
Instructor(s): Staff
Required text(s): Carl Stitz and Jeff Zeager. Precalculus (WebAssign eBook), 3rd edition.
Stitz Zeager Open Source Mathematics, 4 July 2014. Web. http://www.stitz-zeager.com/.
Prerequisites: MATH 117 or Math Diagnostic Test
Course description: Functions and change with an emphasis on linear, quadratic, exponential, and logarithmic functions and their graphs. Specific geometric topics include concavity and how transformations affect graphs. Topics in trigonometry include radians, sinusoidal functions, identities, sum/difference formulas, double/half angle formulas, and trigonometric equations. Other topics include polar coordinates.
Syllabus: Common
MATH 131. Applied Calculus I
Instructor(s): Staff
Required text(s): Hughes-Hallett, Deborah, et al. Applied & Single Variable Calculus for Loyola University Chicago, Custom (WebAssign eBook). 4th ed.
Print text (optional): ISBN-13: 9781118747476. Hoboken, NJ: Wiley, 2013.
Prerequisites: MATH 118 or Math Diagnostic Test
Course description: An introduction to differential and integral calculus, with an emphasis on applications. This course is intended for students in the life and social sciences, computer science, and business. Topics include: modeling change using functions including exponential and trigonometric functions, the concept of the derivative, computing the derivative, applications of the derivative to business and life, social, and computer sciences, and an introduction to integration. This course is not a substitute for MATH 161.
MATH 132. Applied Calculus II
Instructor(s): Staff
Required text(s): Hughes-Hallett, Deborah, et al. Applied & Single Variable Calculus for Loyola University Chicago, Custom (WebAssign eBook). 4th ed.
Print text (optional): ISBN-13: 9781118747476. Hoboken, NJ: Wiley, 2013.
Prerequisites: MATH 131 or MATH 161
Course description: A continuation of MATH 131. Topics include: properties of the integral, techniques of integration, numerical methods, improper integrals, applications to geometry, physics, economics, and probability theory, introduction to differential equations and mathematical modeling, systems of differential equations, power series. This course is not a substitute for MATH 162.
Syllabus: Common
MATH 161. Calculus I
Instructor(s): Staff
Required text(s): Stewart, James. Calculus: Early Transcendentals (WebAssign eBook). 8th ed.
Print text (optional): ISBN-13: 978-1285741550. Boston: Centage Learning, 2015.
Prerequisites: MATH 118
Course description: A traditional introduction to differential and integral calculus. Functions, limits, continuity, differentiation, intermediate and mean-value theorems, curve sketching, optimization problems, related rates, definite and indefinite integrals, fundamental theorem of calculus, logarithmic and exponential functions. Applications to physics and other disciplines.
Syllabus: Common
MATH 162. Calculus II
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. Aaron Greicius
Required text(s): We will use a free, open source text for this course. The exact text is to be decided.
Prerequisites: MATH 161
Course description: This course serves as a bridge course from calculus to upper-level mathematics. Students will develop a collection of proof, computational, and problem-solving techniques that will serve as an invaluable toolkit throughout their mathematical career. They will also be introduced to a variety of new mathematical objects and theoretical frameworks that play a crucial role in higher mathematics.
Topics: Topics include: propositional and quantifier logic; sets, relations and functions; counting and combinatorial objects; elementary number theory; big-O and little-o notation; graph theory.
Assessment: Students should expect one or more in-class exams, frequent quizzes and homework sets, and a final.
MATH 212. Linear Algebra
Instructor(s): Dr. Joseph Mayne
Required text(s): Lay, David C., Lay Steven R., and McDonald, Judi J., "Linear Algebra and its Applications," 5th Edition. Packaged with MyMathLab access, Pearson, 2016. ISBN-13: 9780134022697
Prerequisites: MATH 132 or MATH 162
Course description: Linear algebra is widely used in mathematics, science, engineering, and the social sciences. For example, statisticians and economists often employ linear models when trying to analyze problems with many variables. And linear algebra is an important tool in many areas of mathematics itself. Much of functional analysis is devoted to the study of functions preserving linearity and field theory uses linear algebra in the proofs of many results. The course starts with the problem of solving simultaneous linear equations using the Gaussian elimination algorithm. The solution of this important practical problem motivates the definition of many linear algebra concepts: matrices, vectors and vector spaces, linear independence, dimension, and vector subspaces. The emphasis then shifts to general vector spaces and proofs using an axiom system. Most of the results will be for finite dimensional spaces and we will always attempt to visualize theorems in 2 or 3 dimensional Euclidean space. Topics to be covered include: linear transformations, change of basis, determinants, eigenvalues and eigenvectors, and diagonalization. Students will be encouraged to improve their skills at constructing mathematical proofs.
MATH 212. Linear Algebra
Instructor(s): Dr. Aaron Lauve
Required text(s): Beezer, Robert A. A First Course in Linear Algebra (Beta Version) Available at linear.ups.edu/fcla/ under GNU Free Documentation License v. 1.2. May, 2017. Web.
Textbook notes: Students may also wish to have on hand:
- Lipschutz, Seymour, and Lipson, Marc. Schaum's Outline of Linear Algebra. 5th ed. ISBN-13: 9780071794565. McGraw-Hill, 2012. Print.
- Hefferon, Jim. Linear Algebra. Available at joshua.smcvt.edu/linearalgebra/ under Creative Commons License BY-SA 2.5. December, 2013. Web.
Prerequisites: MATH 162 or MATH 132
Course description: Linear systems are ubiquitous in mathematics, science, engineering, and the social sciences. (For example, statisticians and economists often employ linear models to analyze otherwise intractable problems with many variables.) Evidently, a systematic approach for solving linear systems would be immensely valuable. The course begins by giving one approach, the algorithm of Gaussian Elimination, then continues by developing the axioms and theorems of the subject already present in this elegant algorithm. Motivating examples will frequently be illustrated using the open source computer algebra package Sage.
Syllabus: An introduction to linear algebra in abstract vector spaces with particular emphasis on finite dimensional Euclidean space. Topics: Gaussian elimination, matrix algebra, linear independence, span, basis, linear transformations, Gram-Schmidt, determinants, eigenvalues, eigenvectors, and diagonalization. Some of the basic theorems will be proved rigorously; other results will be demonstrated informally. Applications will be emphasized throughout. Assessments: bimonthly quizzes and online homework; two in-term exams; and a final exam.
MATH 263. Multivariate Calculus
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
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): Dr. Adam Spiegler
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.
Prerequisites: 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 first and second order differential equations and uses real models throughout the semester. We will analysis 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.
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: Math 263
Course description: The course is an introduction to linear algebra and differential equations, and is oriented toward students of engineering science.
Math 304. Math 304
Instructor(s): Robert Jensen
Required text(s): Basic Probability Theory (Dover Books on Mathematics) by Robert B. Ash Paperback: 352 pages; Publisher: Dover Publications (June 26, 2008); Language: English; ISBN-10: 0486466280; ISBN-13: 978-0486466286
Prerequisites: Math 263
Course description: An introduction to probability, including random variables, mean, variance, and basic theorems such as the Law of Large Numbers and the Central Limit Theorem.
MATH 305. [ STAT 305 ] Probability and Statistics II
Instructor(s): Gregory J. matthews
Required text(s): Wackerly, D., Mendenhall, W. and Scheaffer, R.L. Mathematical Statistics with Applications 7th Edition. ISBN-13: 978-0495110811
Recommended text(s): Casella, G. and Berger, R.L. Statistical Inference 2nd edition. 2008.
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): Dr. Anne Peters 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. Advanced Topics in Abstract Algebra
Instructor(s): Emily Peters
Required text(s): Algebra: Abstract and Concrete, by Frederick M. Goodman.
Textbook notes: The textbook is no longer in print, but is available as a PDF from http://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/download.htm
Prerequisites: Math 313
Course description: Study of commutative and non-commutative rings, integral domains, and fields. Selected topics may include Galois theory, group representations, modules, and advanced group theory.
Math 322. [ Math 422 ] Advanced Number Theory
Instructor(s): Dr. Anthony Giaquinto
Required text(s): Silverman, Joseph. Friendly Introduction to Number Theory. 4th Edition, Pearson, 2018.
Prerequisites: MATH 201
Course description:
Despite the title, this course will be an introduction to classic topics in number theory. We will explore the topics using a wealth of examples which will be analyzed for patterns and conjectures. Once conjectures are formed the theorems will be rigorously proved. Mathematical thinking will be promoted throughout the course. Topics will include Pythagorean triples, divisibility, fundamental theorem of arithmetic, congruences, Fermat's little theorm, Euler's formula, Chinese remainder theorem, RSA public key cryptosystem, quadratic reciprocity, Pell's equation, continued fractions and additional topics as time permits. Grading will be based on midterm and final exams as well as numerous homework assignments.
A note on the text: used copies of previous editions will be sufficient for this course.
MATH 328. [ COMP 328 COMP 428 MATH 428 ] Algebraic Coding Theory
Instructor(s): Dr. W. Cary Huffman
Required text(s):
Huffman, W. Cary, and Pless, Vera. 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. The recently ended Casini mission to Saturn returned over 100,000 photographs. The use of error-correcting codes allowed these stunning photographs to be transmitted to Earth, and remarkably, helped extend the mission to almost 20 years. 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 regular 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 345. [ MATH 445 ] Financial Math-Derivatives
Instructor(s): Dr. E.N. Barron
Required text(s): A Factor Model Approach to Derivative Pricing, James Primbs, CRC Press, ISBN: 978-1-4987-6332-5
Prerequisites: MATH 264, 304
Course description: This course is an introduction to determining the fair market price of financial instruments whose value is derived from underlying equity, interest rate, or bond assets. The course will cover the basics of stochastic modeling of prices using Brownian motion and stochastic calculus. Using the absence of arbitrage, we will derive Black-Scholes models of derivative prices for various types of instruments. We also consider hedging strategies. If you are planning to take the Financial Math Actuarial Exam, this course is a must for providing the tools needed for that exam.
Syllabus: 1. Brownian motion and Poisson processes. Ito's Lemma and stochastic differential equations. 2. Factor model approach to Arbitrage Pricing. 3. Black-Scholes Models for European Calls and Puts. 4. Interest rate and Credit Derivatives. 5. Hedging. 6. Computation, Binomial Trees. 7. Risk Neutral Pricing.
Math 351. Introduction to Analysis
Instructor(s): Alan Saleski
Required text(s): Arthur Mattuck, Introduction to Real Analysis, paperback, CreateSpace Independent Publishing Platform (2013)
Prerequisites: Math 201, Discrete Mathematics and Number Theory Math 263, Multivariable Calculus
Course description: An introductory course in real analysis is an opportunity to reexamine the calculus from a theoretical point of view. Topics include construction of the real numbers; order properties of the real numbers; sequences; limits and convergence; continuity; uniform continuity; absolute continuity; series; Taylor series; Fourier series; differentiation; Riemann integration; and possibly an introduction to the Lebesgue integral. Besides studying n-dimensional Euclidean space, general metric spaces will be introduced to offer a more general framework. There will be two or three tests, a final exam, weekly homework, and group presentations.
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 an excursion to Lebesque integrability; infinite series of numbers and functions; the fixed point theorem and the implicit function theorem; and elements of convex analysis, dealing with convex sets and functions. Students enrolled in Math 452 will see the same material but will face tougher problems and higher standards.
MATH 405. [ STAT 405 ] Probability and Statistics II
Instructor(s): Swarnali Banerjee
Required text(s): Mathematical Statistics by Wackerly, Mendenhall and Scheaffer, (7th edition)
Recommended text(s): Statistical Inference by Casella and Berger (2nd edition)
Prerequisites: MATH/STAT 404
Course description: In continuation of MATH/STAT 404, MATH/STAT 405 explores the statistical analyses based on the distribution models. Topics to be covered include Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests).
Math 422. [ Math 322 ] Advanced Number Theory
Instructor(s): Dr. Anthony Giaquinto
Required text(s): Silverman, Joseph. Friendly Introduction to Number Theory. 4th Edition, Pearson, 2018.
Prerequisites: MATH 201
Course description:
Despite the title, this course will be an introduction to classic topics in number theory. We will explore the topics using a wealth of examples which will be analyzed for patterns and conjectures. Once conjectures are formed the theorems will be rigorously proved. Mathematical thinking will be promoted throughout the course. Topics will include Pythagorean triples, divisibility, fundamental theorem of arithmetic, congruences, Fermat's little theorm, Euler's formula, Chinese remainder theorem, RSA public key cryptosystem, quadratic reciprocity, Pell's equation, continued fractions and additional topics as time permits. Grading will be based on midterm and final exams as well as numerous homework assignments.
A note on the text: used copies of previous editions will be sufficient for this course.
MATH 428. [ COMP 328 COMP 428 MATH 328 ] Algebraic Coding Theory
Instructor(s): Dr. W. Cary Huffman
Required text(s):
Huffman, W. Cary, and Pless, Vera. 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. The recently ended Casini mission to Saturn returned over 100,000 photographs. The use of error-correcting codes allowed these stunning photographs to be transmitted to Earth, and remarkably, helped extend the mission to almost 20 years. 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 regular 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 445. [ MATH 345 ] Financial Math-Derivatives
Instructor(s): Dr. E.N. Barron
Required text(s): A Factor Model Approach to Derivative Pricing, James Primbs, CRC Press, ISBN: 978-1-4987-6332-5
Prerequisites: MATH 264, 304
Course description: This course is an introduction to determining the fair market price of financial instruments whose value is derived from underlying equity, interest rate, or bond assets. The course will cover the basics of stochastic modeling of prices using Brownian motion and stochastic calculus. Using the absence of arbitrage, we will derive Black-Scholes models of derivative prices for various types of instruments. We also consider hedging strategies. If you are planning to take the Financial Math Actuarial Exam, this course is a must for providing the tools needed for that exam.
Syllabus: 1. Brownian motion and Poisson processes. Ito's Lemma and stochastic differential equations. 2. Factor model approach to Arbitrage Pricing. 3. Black-Scholes Models for European Calls and Puts. 4. Interest rate and Credit Derivatives. 5. Hedging. 6. Computation, Binomial Trees. 7. Risk Neutral Pricing.
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 an excursion to Lebesque integrability; infinite series of numbers and functions; the fixed point theorem and the implicit function theorem; and elements of convex analysis, dealing with convex sets and functions. Students enrolled in Math 452 will see the same material but will face tougher problems and higher standards.
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): Dr. Adriano Zanin Zambom
Required text(s): Walpole, Myers, Myers and Ye. Essentials of Probability and Statistics for Engineers and Scientists. Pearson.
Prerequisites: Math 162 or 132 with a minimum grade of “C”
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.
STAT 305. [ MATH 305 ] Probability and Statistics II
Instructor(s): Gregory J. matthews
Required text(s): Wackerly, D., Mendenhall, W. and Scheaffer, R.L. Mathematical Statistics with Applications 7th Edition. ISBN-13: 978-0495110811
Recommended text(s): Casella, G. and Berger, R.L. Statistical Inference 2nd edition. 2008.
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. Earvin Balderama
Required text(s): Agresti, A. (2007). An Introduction to Categorical Data Analysis, Second Edition. John Wiley & Sons, Inc. ISBN 978-0-471-22618-5
Prerequisites: STAT 203 or STAT 335, or instructor consent. STAT 308 is recommended.
Course description: Normally distributed response variables lead statistical practitioners to use linear modeling 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 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. Exams, projects and take-home assignments will be used to determine the final grade in the course. The R statistical software will be used throughout the course, although no previous programming experience is necessary.
STAT 321. [ STAT 421 ] Statistical Computation and Simulation
Instructor(s): Gregory J. Matthews
Required text(s): Jones, O., Maillardet, R, and Robinson, A. Introduction to Scientific Programming and Simulation Using R<\i>. CRC Press. Taylor and Francis Group. 2009. ISBN 13-978-1-4200-6872-6
Prerequisites: STAT 308
Course description: This course will use the R language to solve statistical problems through simulation techniques. Topics covered will include random number generation, bootstrapping, permutation testing, monte carlo approaches, markov chain monte carlo (MCMC) algorithms, and parallel computing.
STAT 337. Quantitative Methods in 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 388. [ STAT 488 ] Intro Nonparametric Statistics
Instructor(s): Dr. Adriano Zanin Zambom
Required text(s): -
Recommended text(s): “Text Book”: Hollander, M; Wolfe, D.A., and Chicken E. “Nonparametric Statistical Methods”, 3rd Edition. - “Text Book 2”: Gibbons, J. D. and Chakraborti, S. “Nonparametric Statistical Inference”, Fourth Edition, Marcel Dekker, New York. - Eubank, R. L. “Nonparametric Regression and Spline Smoothing”, Second Edition, Marcel Dekker, New York. - Wasserman, L. “All of Nonparametric Statistics”, Springer.
Prerequisites: -
Course description: This course will cover the basic principles of nonparametric methods in statistics including: one, two and K sample location methods; tests of randomness; tests of goodness of fit; nonlinear correlation; histogram; density estimation; nonparametric regression.
STAT 405. [ MATH 405 ] Probability and Statistics II
Instructor(s): Swarnali Banerjee
Required text(s): Mathematical Statistics by Wackerly, Mendenhall and Scheaffer, (7th edition)
Recommended text(s): Statistical Inference by Casella and Berger (2nd edition)
Prerequisites: MATH/STAT 404
Course description: In continuation of MATH/STAT 404, MATH/STAT 405 explores the statistical analyses based on the distribution models. Topics to be covered include Limit theorems, point and interval estimation (including maximum likelihood estimates), hypothesis testing (including, uniformly most powerful tests, likelihood ratio tests, and nonparametric tests).
STAT 410. [ STAT 310 ] Categorical Data Analysis
Instructor(s): Dr. Earvin Balderama
Required text(s): Agresti, A. (2007). An Introduction to Categorical Data Analysis, Second Edition. John Wiley & Sons, Inc. ISBN 978-0-471-22618-5
Prerequisites: STAT 203 or STAT 335, or instructor consent. STAT 308 is recommended.
Course description: Normally distributed response variables lead statistical practitioners to use linear modeling 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 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. Exams, projects and take-home assignments will be used to determine the final grade in the course. The R statistical software will be used throughout the course, although no previous programming experience is necessary.
STAT 421. [ STAT 321 ] Statistical Computation and Simulation
Instructor(s): Gregory J. Matthews
Required text(s): Jones, O., Maillardet, R, and Robinson, A. Introduction to Scientific Programming and Simulation Using R<\i>. CRC Press. Taylor and Francis Group. 2009. ISBN 13-978-1-4200-6872-6
Prerequisites: STAT 308
Course description: This course will use the R language to solve statistical problems through simulation techniques. Topics covered will include random number generation, bootstrapping, permutation testing, monte carlo approaches, markov chain monte carlo (MCMC) algorithms, and parallel computing.
STAT 488. [ STAT 388 ] Intro Nonparametric Statistics
Instructor(s): Dr. Adriano Zanin Zambom
Required text(s): -
Recommended text(s): “Text Book”: Hollander, M; Wolfe, D.A., and Chicken E. “Nonparametric Statistical Methods”, 3rd Edition. - “Text Book 2”: Gibbons, J. D. and Chakraborti, S. “Nonparametric Statistical Inference”, Fourth Edition, Marcel Dekker, New York. - Eubank, R. L. “Nonparametric Regression and Spline Smoothing”, Second Edition, Marcel Dekker, New York. - Wasserman, L. “All of Nonparametric Statistics”, Springer.
Prerequisites: -
Course description: This course will cover the basic principles of nonparametric methods in statistics including: one, two and K sample location methods; tests of randomness; tests of goodness of fit; nonlinear correlation; histogram; density estimation; nonparametric regression.