In the master-equation formalism, a set of differential equations describe the time-evolution of the probability distribution of an ensemble of systems. This can be used, for example, to describe the varied mRNA copy numbers found in individual cells in a population.

The stochastic simulation algorithm (SSA, Kinetic Monte Carlo, Gillespie algorithm) produces an example trajectory for a particular member of a probabilistic ensemble by looping over the following steps. The current state of the system is used to determine the likelihood of each possible chemical reaction in relative comparison to the likelihoods for the other possible reactions, as well as to determine when the next reaction is expected. Pseudo-random numbers are drawn to "roll the dice" to determine exactly when the next reaction will proceed, and which kind of reaction it will happen to be.

In this video from DragonflyTV, Jai and Jonathan track, graph, and analyze the motion of basketball shots as they investigate what factors influence the accuracy of their game.

Look inside a resistor to see how it works. Increase the battery voltage to make more electrons flow though the resistor. Increase the resistance to block the flow of electrons. Watch the current and resistor temperature change.

Look inside a battery to see how it works. Select the battery voltage and little stick figures move charges from one end of the battery to the other. A voltmeter tells you the resulting battery voltage.

Look inside a battery to see how it works. Select the battery voltage and little stick figures move charges from one end of the battery to the other. A voltmeter tells you the resulting battery voltage.

This video segment describes how the Australopithecus afarensis skeleton known as Lucy could have been fossilized. Footage courtesy of NOVA: "In Search of Human Origins."

The PhET project at the University of Colorado creates "fun, interactive, research-based simulations of physical phenomena." This particular one deals with Beer's Law. "The thicker the glass, the darker the brew, the less the light that passes through." Make colorful concentrated and dilute solutions and explore how much light they absorb and transmit using a virtual spectrophotometer! The simulation is also paired with a teachers' guide and related resources from PhET. The simulation is also available in multiple languages.

This text introductory chemistry text is aimed for a single semester or quarter beginning experience to the field. The textmaps survey some of the basic topics of chemistry. This survey should give student enough knowledge to appreciate the impact of chemistry in everyday life and, if necessary, prepare student for additional instruction in chemistry.

This activity is a scientific investigation focusing on inquiry after using the Foss Water Kit. The students will pose a question, create a procedure and produce a poster showing their findings.

Watch beta decay occur for a collection of nuclei or for an individual nucleus.

Watch beta decay occur for a collection of nuclei or for an individual nucleus.

In this activity, students conduct an energy audit to determine how much carbon dioxide their family is releasing into the atmosphere and then make recommendations for minimizing their family's carbon footprint.

Biology is designed for multi-semester biology courses for science majors. It is grounded on an evolutionary basis and includes exciting features that highlight careers in the biological sciences and everyday applications of the concepts at hand. To meet the needs of today’s instructors and students, some content has been strategically condensed while maintaining the overall scope and coverage of traditional texts for this course. Instructors can customize the book, adapting it to the approach that works best in their classroom. Biology also includes an innovative art program that incorporates critical thinking and clicker questions to help students understand—and apply—key concepts.

Biology is designed for multi-semester biology courses for science majors. It is grounded on an evolutionary basis and includes exciting features that highlight careers in the biological sciences and everyday applications of the concepts at hand. To meet the needs of today’s instructors and students, some content has been strategically condensed while maintaining the overall scope and coverage of traditional texts for this course. Instructors can customize the book, adapting it to the approach that works best in their classroom. Biology also includes an innovative art program that incorporates critical thinking and clicker questions to help students understand—and apply—key concepts.

This ZOOM video segment shows how to create a self-contained environment and explores evaporation, condensation, and precipitation.

A free online textbook for biophysical chemistry. The book covers probability, statistics, thermodynamics, kinetics, Monte Carlo methods, biochemistry, diffusion, stochastic processes, and others.