Instructor(s):  Robert Jensen

Required text(s):  Title: Elementary Number Theory, Author: David Burton, Publication Date: February 4, 2010, ISBN-10: 0073383147, ISBN-13: 978-0073383149, Edition: 7.

Prerequisites:  None

Course description:  It is strongly recommended that students take Math 162 before taking Math 201. This course introduces students to the rigorous construction of "proofs" through the medium of Number Theory. The core of the course will cover Chapters 1 - 7 in Burton's book, "Elementary Number Theory". Additional topics will be covered as time permits.

Instructor(s):  Peter Tingley - MWF 10:25-11:15; Anthony Giaquinto - MWF 11:30-12:20

Required text(s):  Anton, Howard. Elementary Linear Algebra. 10th ed. Wiley, 2010. ISBN 978-0-470-45821-1.

Prerequisites:  MATH 132 or MATH 162

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

Instructor(s):  Marian Bocea (Section 1: MWF 12:35pm - 1:25pm)
John G. Del Greco (Section 2: TuTh 2:30pm - 3:45pm)

Required text(s):  Nagle, R. Kent, Edward B. Saff, and Arthur David Snider. Fundamentals of Differential Equations. 8th ed. Boston: Pearson, 2011. Print.

Prerequisites:  Math 263

Course description:  This course will be a rigorous treatment of ordinary differential equations and their applications. Topics will include first- and second-order linear differential equations and methods for their solution: separable and exact equations, integrating factors, substitutions and transformations, method of undetermined coefficients, variation of parameters, Laplace transformations, series solutions, systems of differential equations, and phase-plane analysis.

Instructor(s):  John G. Del Greco

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

Prerequisites:  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.

Instructor(s):  Anne Hupert

Required text(s):  Abstract Algebra, a First Course by Dan Saracino (2nd edition) ISBN 1-57766-536-8, 978-1-57766-536-8

Prerequisites:  Math 201, 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.

Instructor(s):  Joseph Mayne

Required text(s):  Fraleigh, John B. A First Course in Abstract Algebra. Seventh Edition. New York: Addison Wesley, 2003. Print

Prerequisites:  Math 313

Course description:  This course is a continuation of Math 313. We will study rings with an emphasis on integral domains, rings of polynomials, and then more general non-commutative rings. Following this we will examine fields, both characteristic 0 and p; finite and infinite. Topics here will include extension fields, splitting field and algebraic closure. The course concludes with the study of Galois theory.

Instructor(s):  Dr. A. Lauve

Required text(s):  Miklós Bóna, A Walk Through Combinatorics: an Introduction to Enumeration and Graph Theory, 2nd Edition (Paperback), World Scientific (2006). ISBN: 9812-56885-9.

Prerequisites:  MATH 162

Course description:  Combinatorial problems from enumeration and graph theory and methods for their solution. Prior experience with abstraction and proofs is helpful, but not necessary. Graduate students will complete more advanced exercises than the undergraduate students and will present some supplemental topics from independent reading.

Syllabus: 
Topics: Permutations, binomial theorem, compositions, partitions, Stirling numbers, Catalan numbers, graphs, trees, Eulerian walks, Hamiltionian cycles, electrical networks, graph colorings, chromatic polynomials, combinatorial algorithms, optimization, among others. Techniques: Pigeon-hole principle, mathematical induction, inclusion-exclusion principle, recurrence relations, generating functions, matrix-tree theorem, Polya theory, Ramsey theory, pattern avoidance, probabilistic methods, partial orders, combinatorial algorithms, among others.

Instructor(s):  Curtis Tuckey

Required text(s):  Enderton, Herbert. A Mathematical Introduction to Logic. 2nd ed. San Diago: Academic Press, 2001. Print.

Prerequisites:  Math 313

Course description:  This course is a mathematical study of the concepts of truth and proof and how they relate to each other. The three main topics are propositional logic, first-order predicate logic, and decidability. Propositional logic is the study of the expressive power of a language that uses only the Boolean connectives and, or, and not. Topics include truth tables, induction, and compactness. First-order logic builds on propositional logic and has more expressive power. It adds the ability to refer to properties of individuals through predicates, as well as existential and universal quantifiers. Most of the mathematics that you are familiar with can be expressed in first-order logic. We will study the language, theories, and models of first-order logic, looking to number theory and standard and non-standard models of arithmetic for examples. After establishing these foundations we will study the notion of decidability and Goedel's incompleteness theorems. Goedel's Incompleteness Theorem tells us that in any first-order theory strong enough to formalize arithmetic, and in which the axioms are decidable, there is a statement that is true but not provable.

Instructor(s):  Marian Bocea

Required text(s):  Arthur MATTUCK, Introduction to Analysis, 1st edition, latest printing; Publisher: Prentice-Hall (1999) ISBN-10: 0130811327; ISBN-13: 978-0130811325

Recommended text(s):  Tom M. APOSTOL, Mathematical Analysis, Second Edition; Publisher: Pearson (1974); ISBN-10: 0201002884; ISBN-13: 978-0201002881

Prerequisites:  MATH 201 Elementary Number Theory & MATH 212 Linear Algebra

Course description:  The course offers a rigorous treatment of properties and applications of real numbers and real-valued functions of a real variable. Topics include: sequences, limits, the Bolzano-Weierstrass theorem, compactness and the Heine-Borel theorem, connectedness, topology, continuity, uniform continuity, fixed-point theorems, derivatives.

Instructor(s):  Alan Saleski

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

Prerequisites:  Math 351

Course description:  In this continuation of Real Analysis I (Math 351), we explore the Riemann integral, improper integrals, and sequences and series of functions. The Lebesgue integral is introduced as well as basic point set topology.

Instructor(s):  W. Cary Huffman

Required text(s):  A Friendly Introduction to Number Theory, 4th Edition, by Joseph H. Silverman; ISBN-10: 0-321-81619-6; ISBN-13: 978-0-321-81619-1

Prerequisites:  Math 201

Course description:  Simply put, number theory is the study of the positive integers. At first glance, this may seem uninteresting and even boring. However, many people throughout the ages have been intrigued by many subtle and deep relationships between the integers. For example, by considering the simple concept of a square integer, one is quickly led to questions such as: If you add two squares, when do you get a square? If you add two squares, what positive integers do you get? How about adding three squares or four squares? Moving to higher powers, when is the sum of two n-th powers another n-th power? The latter question is Fermat’s Last Theorem, first posed in the seventeenth century but not solved until 1994. While considered a topic in pure mathematics, number theory has many practical applications to areas such as cryptography and coding theory. After beginning with a quick review of the number theory concepts from Math 201, we will look at several different topics in number theory. These topics will be chosen from Pythagorean triples, prime numbers, perfect numbers, primitive roots, quadratic residues, quadratic reciprocity, Pell’s equation, continued fractions, Fermat’s Last Theorem, and others. This course is a combined undergraduate/graduate course. The requirements of the course for the graduate students will be different from the requirements for the undergraduates.

Instructor(s):  E.N.Barron

Required text(s):  A Primer for Mathematics of Financial Engineering, 2nd Edition, by Dan Stefanica, FE Press, New York, ISBN 13 978-0-9797576-2-4.

Recommended text(s):  Derivatives Markets, MacDonald, Pearson Press, 3rd Edition; Options and Futures, Hull, Pearson Press, 8th Edition.

Additional notes:  Notes by R.Kohn at Courant Institute will be required.

Prerequisites:  Math 264 and Math 304. A class in elementary programming will be helpful.

Course description:  This class provides a rigorous introduction to modern mathematical finance. No knowledge of finance is assumed. We will cover the basics of the pricing of bonds, options, and futures. We will discuss in detail the Black-Scholes option pricing model, the binomial option pricing model, forward and futures contracts, and various other mathematical models arising in finance. Numerical methods and simulation will also be covered if time permits.

Syllabus:  1. Introduction to Options and Arbitrage pricing. 2. Bonds, interest rate curves. 3. Black-Scholes formulas, greeks and hedging. 4. Portfolio Optimization.

Instructor(s):  Rafal Goebel

Required text(s):  none

Prerequisites:  Math 212: Linear Algebra and Math 264: Ordinary Differential Equations

Course description:  A majority of systems encountered in biology, chemistry, economics, engineering, etc. evolve over time and can be described and then studied using differential equations. Some of such systems can be controlled, for example by eliminating a number of predators in a predator-prey system or by firing rocket engines in a mechanical system involving a satellite. While some arising differential equations and control systems are linear, which means, for example, that doubling the voltage in a simple electrical circuit may double the current, a great variety of systems leads to nonlinear differential equations and nonlinear control systems. The nonlinearity is displayed, for example, when doubling the initial investment does not double the eventual profit, or when your car accelerates only so much no matter how hard you press on the gas pedal. This course will present the basic theory and several applications of nonlinear differential equations. Elements of control theory will be included. Linear differential equations, in 2 or more variables, will be studied to some extent and then used to approximate nonlinear differential equations. Asymptotic behavior of solutions to differential equations and control systems will be carefully analyzed, as motivated by the need to predict long-term behavior of economic systems or ensure stability of a mechanical system. To this end, Lyapunov functions, invariance principles, and other design tools used by control engineers, will be used. The lectures will be loosely based on the first several chapters of the textbook "Nonlinear Systems" by Hassan Khalil but other supplementary material will be used as well.

Instructor(s):  Dr. Martin Buntinas

Required text(s):  Dennis Wackerly, William Mendenhall, Richard L. Scheaffer, Mathematical Statistics with Applications, 7th edition (2007), Duxbury/Brooks/Cole/Thomson. ISBN-10: 0-495-11081-7 (ISBN-13:978-0-49-511081-1).

Prerequisites:  MATH/STAT 404

Course description:  A continuation of MATH/STAT 404. Limit theorems, point and interval estimation, hypothesis testing, maximum likelihood, Neyman-Pearson Lemma, likelihood ratio, nonparametric statistics. There will be two quizzes, a midterm exam and a final exam. Homework will be assigned every class, collected, and graded.

Instructor(s):  Dr. A. Lauve

Required text(s):  Miklós Bóna, A Walk Through Combinatorics: an Introduction to Enumeration and Graph Theory, 2nd Edition (Paperback), World Scientific (2006). ISBN: 9812-56885-9.

Prerequisites:  MATH 162

Course description:  Combinatorial problems from enumeration and graph theory and methods for their solution. Prior experience with abstraction and proofs is helpful, but not necessary. Graduate students will complete more advanced exercises than the undergraduate students and will present some supplemental topics from independent reading.

Syllabus: 
Topics: Permutations, binomial theorem, compositions, partitions, Stirling numbers, Catalan numbers, graphs, trees, Eulerian walks, Hamiltionian cycles, electrical networks, graph colorings, chromatic polynomials, combinatorial algorithms, optimization, among others. Techniques: Pigeon-hole principle, mathematical induction, inclusion-exclusion principle, recurrence relations, generating functions, matrix-tree theorem, Polya theory, Ramsey theory, pattern avoidance, probabilistic methods, partial orders, combinatorial algorithms, among others.

Instructor(s):  E.N.Barron

Required text(s):  A Primer for Mathematics of Financial Engineering, 2nd Edition, by Dan Stefanica, FE Press, New York, ISBN 13 978-0-9797576-2-4.

Recommended text(s):  Derivatives Markets, MacDonald, Pearson Press, 3rd Edition; Options and Futures, Hull, Pearson Press, 8th Edition.

Additional notes:  Notes by R.Kohn at Courant Institute will be required.

Prerequisites:  Math 264 and Math 304. A class in elementary programming will be helpful.

Course description:  This class provides a rigorous introduction to modern mathematical finance. No knowledge of finance is assumed. We will cover the basics of the pricing of bonds, options, and futures. We will discuss in detail the Black-Scholes option pricing model, the binomial option pricing model, forward and futures contracts, and various other mathematical models arising in finance. Numerical methods and simulation will also be covered if time permits.

Syllabus:  1. Introduction to Options and Arbitrage pricing. 2. Bonds, interest rate curves. 3. Black-Scholes formulas, greeks and hedging. 4. Portfolio Optimization.

Instructor(s):  W. Cary Huffman

Required text(s):  A Friendly Introduction to Number Theory, 4th Edition, by Joseph H. Silverman; ISBN-10: 0-321-81619-6; ISBN-13: 978-0-321-81619-1

Prerequisites:  Math 201

Course description:  Simply put, number theory is the study of the positive integers. At first glance, this may seem uninteresting and even boring. However, many people throughout the ages have been intrigued by many subtle and deep relationships between the integers. For example, by considering the simple concept of a square integer, one is quickly led to questions such as: If you add two squares, when do you get a square? If you add two squares, what positive integers do you get? How about adding three squares or four squares? Moving to higher powers, when is the sum of two n-th powers another n-th power? The latter question is Fermat’s Last Theorem, first posed in the seventeenth century but not solved until 1994. While considered a topic in pure mathematics, number theory has many practical applications to areas such as cryptography and coding theory. After beginning with a quick review of the number theory concepts from Math 201, we will look at several different topics in number theory. These topics will be chosen from Pythagorean triples, prime numbers, perfect numbers, primitive roots, quadratic residues, quadratic reciprocity, Pell’s equation, continued fractions, Fermat’s Last Theorem, and others. This course is a combined undergraduate/graduate course. The requirements of the course for the graduate students will be different from the requirements for the undergraduates.

Instructor(s):  Rafal Goebel

Required text(s):  none

Prerequisites:  Math 212: Linear Algebra and Math 264: Ordinary Differential Equations

Course description:  A majority of systems encountered in biology, chemistry, economics, engineering, etc. evolve over time and can be described and then studied using differential equations. Some of such systems can be controlled, for example by eliminating a number of predators in a predator-prey system or by firing rocket engines in a mechanical system involving a satellite. While some arising differential equations and control systems are linear, which means, for example, that doubling the voltage in a simple electrical circuit may double the current, a great variety of systems leads to nonlinear differential equations and nonlinear control systems. The nonlinearity is displayed, for example, when doubling the initial investment does not double the eventual profit, or when your car accelerates only so much no matter how hard you press on the gas pedal. This course will present the basic theory and several applications of nonlinear differential equations. Elements of control theory will be included. Linear differential equations, in 2 or more variables, will be studied to some extent and then used to approximate nonlinear differential equations. Asymptotic behavior of solutions to differential equations and control systems will be carefully analyzed, as motivated by the need to predict long-term behavior of economic systems or ensure stability of a mechanical system. To this end, Lyapunov functions, invariance principles, and other design tools used by control engineers, will be used. The lectures will be loosely based on the first several chapters of the textbook "Nonlinear Systems" by Hassan Khalil but other supplementary material will be used as well.

Instructor(s):  Curtis Tuckey

Required text(s):  Enderton, Herbert. A Mathematical Introduction to Logic. 2nd ed. San Diago: Academic Press, 2001. Print.

Prerequisites:  Math 313

Course description:  This course is a mathematical study of the concepts of truth and proof and how they relate to each other. The three main topics are propositional logic, first-order predicate logic, and decidability. Propositional logic is the study of the expressive power of a language that uses only the Boolean connectives and, or, and not. Topics include truth tables, induction, and compactness. First-order logic builds on propositional logic and has more expressive power. It adds the ability to refer to properties of individuals through predicates, as well as existential and universal quantifiers. Most of the mathematics that you are familiar with can be expressed in first-order logic. We will study the language, theories, and models of first-order logic, looking to number theory and standard and non-standard models of arithmetic for examples. After establishing these foundations we will study the notion of decidability and Goedel's incompleteness theorems. Goedel's Incompleteness Theorem tells us that in any first-order theory strong enough to formalize arithmetic, and in which the axioms are decidable, there is a statement that is true but not provable.

Instructor(s):  Molly Walsh

Required text(s):  Buntinas and Funk, Statistics for the Sciences, Thomson/Brooks/Cole, 2005, ISBN: 0-534-38774-8

Prerequisites:  Math 132 or Math 162

Course description:  Our society is increasingly dependent upon statistics. For example, decisions about the safety and effectiveness of drugs, changes in tax laws that affect the economy, and environmental regulations that strive to improve our lives all involve the use of statistics. In spite of this importance, there is widespread ignorance about the proper application of statistics. In this course we will look at examples of the use and misuse of statistics using methods of differential and integral calculus to justify results. We will study some standard statistical methods and learn how to determine when they should be used and how they should be applied. The goal is to understand how these methods work and how they can be applied correctly.

Instructor(s):  John G. Del Greco

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

Prerequisites:  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.

Instructor(s):  Changwon Lim

Required text(s):  Statistical Analysis of Designed Experiments Theory and Applications by Ajit C. Tamhane, John Wiley & Sons, Inc (2009). ISBN 978-0-471-75043-7.

Prerequisites:  STAT 203 or 335.

Course description:  Comparative experiments, analysis of variance, fixed and random effects models, randomized block designs, Latin square designs, incomplete block designs, and factorial designs. Use of packaged computer programs such as Minitab or SAS.

Instructor(s):  Dr. Molly K. Walsh

Required text(s):  D’Agostino, Sullivan & Beiser, Introductory Applied Biostatistics, Brooks/Cole, 2006. ISBN: 978-0-534-42399-5.

Prerequisites:  STAT 335 or with the permission of the instructor

Course description:  This course covers the basics of hypothesis testing, sample size and power calculations, categorical data techniques, experimental design and ANOVA, repeated measures ANOVA, simple and multiple linear regression, analysis of covariance (ANCOVA), generalized linear models, maximum likelihood estimation, logistic regression, survival analysis, and if time allows, relative potency and drug synergy. 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.

Instructor(s):  Liping Tong

Required text(s):  Biological Sequence Analysis -- Probabilistic Models of Proteins and Nucleic Acids, R. Durbin, S. Eddy, A. Krogh and G. Mitchison, 2007 (12th version), Cambridge. ISBN 978-0-521-62041-3 (hardback) or 978-0-521-62971-3 (paperback)

Recommended text(s):  Introduction to Mathematical methods in Bioinformatics, Alexander Isaev, 2006, Springer. ISBN # 3-540-21973-0.

Prerequisites:  STAT 203 or STAT 335. Students must know basic discrete probability distributions and feel comfortable with calculus and algebra. Experience in at least one basic computer programming language, such as c, c++, fortran, etc, is not required, but would be a big plus, for this class. This course assumes little or no background in biology.

Course description:  The term bioinformatics is often used to describe applications of computer technology, mathematics, and statistics to acquire, store, organize, archive, and analyze or visualize biological structure and function. Research in this field includes DNA and amino acid sequence alignment, models of evolution, phlyogenetics, gene identification, prediction of gene expression, etc. The aim is go give an introduction to some of the probability theory, statistics, stochastic process theory, and dynamic computational algorithms appropriate to computational biology and bioinformatics.

Instructor(s):  Michael Perry

Required text(s):  ACTEX Study Manual SOA Exam P CAS Exam 1, 2005 ed Samuel A. Broverman, Ph.D., ASA.

Prerequisites:  STAT 304

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

Instructor(s):  Dr. Martin Buntinas

Required text(s):  Dennis Wackerly, William Mendenhall, Richard L. Scheaffer, Mathematical Statistics with Applications, 7th edition (2007), Duxbury/Brooks/Cole/Thomson. ISBN-10: 0-495-11081-7 (ISBN-13:978-0-49-511081-1).

Prerequisites:  MATH/STAT 404

Course description:  A continuation of MATH/STAT 404. Limit theorems, point and interval estimation, hypothesis testing, maximum likelihood, Neyman-Pearson Lemma, likelihood ratio, nonparametric statistics. There will be two quizzes, a midterm exam and a final exam. Homework will be assigned every class, collected, and graded.

Instructor(s):  Changwon Lim

Required text(s):  Statistical Analysis of Designed Experiments Theory and Applications by Ajit C. Tamhane, John Wiley & Sons, Inc (2009). ISBN 978-0-471-75043-7.

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

Course description:  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, 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.

Instructor(s):  Dr. Molly K. Walsh

Required text(s):  An Introduction to Categorical Data Analysis, 2nd Ed, by Alan Agresti (2007), John Wiley & Sons, Inc., ISBN: 978-0-471-22618-5.

Prerequisites:  For graduate students only (or with instructor permission)

Course description:  Normally distributed response variables lead statistical practitioners to use simple linear models procedures such as simple and multiple regression or one- or two-way ANOVA, but other types of data cannot be analyzed in the same ways. Thus, these simple (regression) techniques have been generalized to handle nominal, ordinal, count and binary data under the general heading of categorical data analysis. Contingency table analyses, generalized linear models, logistic regression and log-linear modeling are the focus of this course. This course also addresses the fundamental questions encountered with regression and ANOVA for count data. Specialized methods for ordinal data, small samples, multi-category data, matched pairs, marginal models and random effects models will also be discussed. The focus throughout this course will be on applications and real-life data sets; as such, theorems and proofs will not be emphasized.

Instructor(s):  Dr. Tim O'Brien

Required text(s):  None. Course notes will be provided in class.

Prerequisites:  Some background in applied statistics such as introductory statistics, experimental design, and/or regression.

Course description:  Basic courses in statistics and biostatistics prepare individuals to perform the simplest statistical analyses such as simple linear regression or correlation, paired or two-sample t-tests, one- or two-way ANOVA, and analysis of covariance. However, practitioners are often faced with more sophisticated datasets for which these methods are invalid. Fortunately, basic statistical techniques have been adapted and generalized to categorical data techniques, generalized and nonlinear regression, repeated-measures and survival analysis methods, and these latter techniques are the focus of this course. Each of these methods is motivated in this course using real-life examples. As such, the focus throughout this course is on applications; mathematical theory and derivations will not be emphasized. This course covers the basics of experimental design and analysis, simple and multiple linear regression, generalized linear and nonlinear regression, statistical bioassay and drug synergy, repeated measures, and censored data analysis and survival statistics methods (e.g., Cox proportional odds, log-rank tests, Kaplan-Meier estimation). Students will be required to analyze real-life data sets using the Minitab, R and SAS statistical packages. Grading will be based on participation, homework assignments, quizzes and exams.

Instructor(s):  Liping Tong

Required text(s):  Biological Sequence Analysis -- Probabilistic Models of Proteins and Nucleic Acids, R. Durbin, S. Eddy, A. Krogh and G. Mitchison, 2007 (12th version), Cambridge. ISBN 978-0-521-62041-3 (hardback) or 978-0-521-62971-3 (paperback)

Recommended text(s):  Introduction to Mathematical methods in Bioinformatics, Alexander Isaev, 2006, Springer. ISBN # 3-540-21973-0.

Prerequisites:  STAT 203 or STAT 335. Students must know basic discrete probability distributions and feel comfortable with calculus and algebra. Experience in at least one basic computer programming language, such as c, c++, fortran, etc, is not required, but would be a big plus, for this class. This course assumes little or no background in biology.

Course description:  The term bioinformatics is often used to describe applications of computer technology, mathematics, and statistics to acquire, store, organize, archive, and analyze or visualize biological structure and function. Research in this field includes DNA and amino acid sequence alignment, models of evolution, phlyogenetics, gene identification, prediction of gene expression, etc. The aim is go give an introduction to some of the probability theory, statistics, stochastic process theory, and dynamic computational algorithms appropriate to computational biology and bioinformatics.