This unit extends the ideas introduced in the unit on first-order differential equations to a particular type of second-order differential equations which has a variety of applications. The unit assumes that you have previously had a basic grounding in calculus, know something about first-order differential equations and some familiarity with complex numbers.

This case is based on an actual news release reporting on research about the effects of eating Lake Ontario fish contaminated with PCBs. Developed to teach students about statistical analysis and experimental design, the case has been used in a senior-level biostatistics course as well as part of a one-week survey of statistics for a biological methods course. It could also be used in an ecology or environmental science course or as a component of a course examining how the media reports science.

This is a "clicker" adaptation of another case in our collection, "Eating PCBs from Lake Ontario: Is There an Effect or Not?" (2001), written by the same author. It encourages students to examine how scientific results get presented and interpreted for the public as well as how experiments are planned, carried out, and analyzed. Students read three different news reports about the same scientific study, then sort through the different accounts to determine for themselves what happened in these studies and what the findings were. The case illustrates the complexities of scientific reporting and challenges students to figure out the original research design and data. It was designed for an introductory biology course for majors that uses personal response systems, or "clickers." The story is presented in class using a PowerPoint (~1MB) presentation punctuated by multiple-choice questions that students answer using their clickers.

In this unit, students use online pan balances to study equality, order of operations, numerical and variable expressions, and other key algebraic concepts. Lessons focus on balancing shapes to study equality and equivalence; balancing algebraic understanding, to explore simplifying expressions; and balancing algebra, to determine if algebraic expressions are equal.

This case is based on a research paper about the lignin content of genetically modified corn published in the American Journal of Botany. Students are asked to analyze and discuss the paper, focusing on questions related to experimental design and interpretation and a critique of the statistical data presented. Developed for use in an upper-level undergraduate course in plant ecology and a graduate biostatistics course, the case could also be used in courses in plant anatomy, plant physiology, soil ecology, agriculture, or genetics.

Junior Lab consists of two undergraduate courses in experimental physics. The courses are offered by the MIT Physics Department, and are usually taken by Juniors (hence the name). Officially, the courses are called Experimental Physics I and II and are numbered 8.13 for the first half, given in the fall semester, and 8.14 for the second half, given in the spring.The purposes of Junior Lab are to give students hands-on experience with some of the experimental basis of modern physics and, in the process, to deepen their understanding of the relations between experiment and theory, mostly in atomic and nuclear physics. Each term, students choose 5 different experiments from a list of 21 total labs.

This Unit will introduce you to a number of ways of representing data graphically and of summarising data numerically. You will learn the uses for pie charts, bar charts, histograms and scatterplots. You will also be introduced to various ways of summarising data and methods for assessing location and dispersion.

This unit will help you to identify and use information in maths and statistics, whether for your work, study or personal purposes. Experiment with some of the key resources in this subject area, and learn about the skills which will enable you to plan searches for information, so you can find what you are looking for more easily. Discover the meaning of information quality, and learn how to evaluate the information you come across. You will also be introduced to the many different ways of organising your own information, and learn how to reference it properly in your work. Finally, discover how to keep up to date with the latest developments in your area of interest by using tools such as RSS and mailing lists.

By considering real-world, hands-on activities, students develop their understanding of time and distance. Students reconsider their concept of time by finding their speeds for walking 100 feet. The idea of distance as compared to time comes from a second activity: marking the distance each can travel in 8 seconds. Finally, students plot the data they have collected. Teaching instructions are clear and well thought out.

This learning video presents an introduction to the Flaws of Averages using three exciting examples: the ''crossing of the river'' example, the ''cookie'' example, and the ''dance class'' example. Averages are often worthwhile representations of a set of data by a single descriptive number. The objective of this module, however, is to simply point out a few pitfalls that could arise if one is not attentive to details when calculating and interpreting averages. The essential prerequisite knowledge for this video lesson is the ability to calculate an average from a set of numbers. During this video lesson, students will learn about three flaws of averages: (1) The average is not always a good description of the actual situation, (2) The function of the average is not always the same as the average of the function, and (3) The average depends on your perspective. To convey these concepts, the students are presented with the three real world examples mentioned above.

Subject assesses the relationships between sequence, structure, and function in complex biological networks as well as progress in realistic modeling of quantitative, comprehensive functional-genomics analyses. Topics include: algorithmic, statistical, database, and simulation approaches; and practical applications to biotechnology, drug discovery, and genetic engineering. Future opportunities and current limitations critically assessed. Problem sets and project emphasize creative, hands-on analyses using these concepts. From the course home page: In addition to the regular lecture sessions, supplementary sections are scheduled to address issues related to Perl, Mathematica and biology.

Handling statistical data is an essential part of psychological research. However, many people find the idea of using statistics, and especially statistical software packages, extremely daunting. This unit takes a step-by-step approach to statistics softw

In this math lesson, learners read the book "How Big Is a Foot?" by Rolf Myller to explore the need for a standard unit of measure. Students then create non-standard units (using their own footprints) and use the footprints to make "beds." This lesson guide includes a student activity sheet, questions for learners, assessment options, extensions, and reflection questions.

Monika Wahi describes how to install packages in R for both Windows and Mac. Check out her other Research Tips at http://www.dethwench.com/?cat=26

This 2-lesson unit focuses on combinations, a subject related to probability. Students develop strategies for discovering all the possible combinations in two given situations. They learn to collect and organize data and then use the results to generalize methods for determining possible combinations. They discuss how the number of possible outcomes is affected by decisions about the order of choices, or whether choices may be repeated. The unit includes student activity sheets, questions and extensions for students, and a link to an interactive applet.

This unit is concerned with two main topics. In Section 1, you will learn about another kind of graphical display, the boxplot. A boxplot is a fairly simple graphic, which displays certain summary statistics of a set of data. Boxplots are particularly useful for assessing quickly the location, dispersion, and symmetry or skewness of a set of data, and for making comparisons of these features in two or more data sets. Boxplots can also be useful for drawing attention to possible outliers in a data set. The other topic, which is covered in Sections 2 and 3, is that of dealing with data presented in tabular form. You are, no doubt, familiar with such tables: they are common in the media and in reports and other documents. Yet it is not always straightforward to see at first glance just what information a table of data is providing, and it often helps to carry out certain calculations and/or to draw appropriate graphs to make this clearer. In this unit, some other kinds of data tables and some different approaches are covered.

This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB in particular.

This unit looks at complex numbers. You will learn how they are defined, examine their geometric representation and then move on to looking at the methods for finding the nth roots of complex numbers and the solutions to simple polynominal equations.

This course covers descriptive statistics, the foundation of statistics, probability and random distributions, and the relationships between various characteristics of data. Upon successful completion of the course, the student will be able to: Define the meaning of descriptive statistics and statistical inference; Distinguish between a population and a sample; Explain the purpose of measures of location, variability, and skewness; Calculate probabilities; Explain the difference between how probabilities are computed for discrete and continuous random variables; Recognize and understand discrete probability distribution functions, in general; Identify confidence intervals for means and proportions; Explain how the central limit theorem applies in inference; Calculate and interpret confidence intervals for one population average and one population proportion; Differentiate between Type I and Type II errors; Conduct and interpret hypothesis tests; Compute regression equations for data; Use regression equations to make predictions; Conduct and interpret ANOVA (Analysis of Variance). (Mathematics 121; See also: Biology 104, Computer Science 106, Economics 104, Psychology 201)

Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs.