# John Emerson

## Professor of Mathematics

jemerson@middlebury.edu

work802.443.5589

Warner Hall 312

**Degrees, Specializations & Interests:**

A.B., University of Rochester; M.S., Ph.D., Cornell University; (Statistical methods, Data Analysis, Biostatistics)

## Courses

Courses offered in the past four years.

▲ *indicates offered in the current term*

▹ *indicates offered in the upcoming term[s]*

##### MATH 0116 - Intro to Statistical Science

**Introduction to Statistical Science**

A practical introduction to statistical methods and the examination of data sets. Computer software will play a central role in analyzing a variety of real data sets from the natural and social sciences. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, correlation, regression, contingency tables, and analysis of variance. The course has no formal mathematics prerequisite, and is especially suited to students in the physical, social, environmental, and life sciences who seek an applied orientation to data analysis. (Credit is not given for MATH 0116 if the student has taken ECON 0210 or PSYC 0201 previously or concurrently.) 3 hrs. lect./1 hr. computer lab. **DED**

Fall 2012, Spring 2013, Spring 2015

##### MATH 0121 - Calculus I ▹

**Calculus I**

Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc. **DED**

Fall 2015

##### MATH 0122 - Calculus II

**Calculus II**

A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc. **DED**

Fall 2011, Spring 2012, Fall 2012, Spring 2013

##### MATH 0200 - Linear Algebra

**Linear Algebra**

Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc. **DED**

Fall 2013, Spring 2015

##### MATH 0310 - Probability ▹

**Probability**

An introduction to the concepts of probability and their applications, covering both discrete and continuous random variables. Probability spaces, elementary combinatorial analysis, densities and distributions, conditional probabilities, independence, expectation, variance, weak law of large numbers, central limit theorem, and numerous applications. (concurrent or prior MATH 0223 or by waiver) 3 hrs. lect./disc. **DED**

Fall 2011, Fall 2015

##### MATH 0311 - Statistics

**Statistics**

An introduction to the mathematical methods and applications of statistical inference. Topics will include: survey sampling, parametric and nonparametric problems, estimation, efficiency and the Neyman-Pearsons lemma. Classical tests within the normal theory such as F-test, t-test, and chi-square test will also be considered. Methods of linear least squares are used for the study of analysis of variance and regression. There will be some emphasis on applications to other disciplines. (MATH 0310) 3 hrs. lect./disc. **DED**

Spring 2012, Fall 2013

##### MATH 0500 - Advanced Study ▹

**Advanced Study**

Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Spring 2016

##### MATH 1139 / INTD 1139 - Statistics with Randomization

**Understanding Uncertainty: Exploring Data Using Randomization**

In this course we will use computer-intensive methods to explore the randomness inherent in a data set and to develop the scientific logic of statistical inference. We will introduce randomization methods as a basis for framing fundamental concepts of inference: estimates, confidence intervals, and hypothesis tests. The capabilities of computers to draw thousands of random samples and to simulate experiments will replace theoretical approximations grounded in mathematical statistics, especially the normal theory methods like t-tests and chi-squared analyses. Students will use the R programming language to implement the analyses. Much of the course development will proceed through independent and collaborative computer investigations by students using real data sets. No prior experience with statistics and with computer programming is necessary. **CW DED WTR**

Winter 2014

#### Recent Publications

Moses, L.E., Emerson, J.D., and Hosseini, H. "Analyzing Data from Ordered Categories." In J.C. Bailar III and D. Hoaglin, Eds., *Medical Uses of Statistics*,* 3rd Ed.,* Hoboken, NJ: Wiley. 2009, 311-323.

Agarwal, S., Colditz, G.A., and Emerson, J.D. "Use of Statistical Analysis in the New England Journal of Medicine." In J.C. Bailar III and D. Hoaglin, Eds., *Medical Uses of Statistics*, * 3rd Ed.,* Hoboken, NJ: Wiley. 2009, 41-49.

Emerson, J.D., Brooks, R.L., and McKenzie, E.C. "College Sports and Student Achievement: The Evidence at Small Colleges." In *Data-Driven Decision-Making in Intercollegiate Athletics. *New Directions in Institutional Research, edited by J.L. Hoffman, J.S. Antony, and D.D. Alfaro. San Francisco: Jossey-Bass, No. 144, 2009, 65-76.