We bring the cylindrical tank, filled to a depth of 10 cm or so with water at a uniform temperature, up to solid-body rotation at a speed of 5 rpm, say. We sprinkle a few small crystals of potassium permanganate in to the tank. Note the Taylor columns. Now we reduce ...

It is straightforward to obtain a steady, axially-symmetric circulation driven by radial temperature gradients in our laboratory tank, which provides an ideal opportunity to study the thermal wind relation.

Here we illustrate the dynamical principles that underlie the abyssal circulation of the ocean, driven by the sinking of dense fluid formed by surface cooling at polar latitudes.

It is relatively straightforward to demonstrate the essential mechanism behind wind-driven ocean circulation in a laboratory experiment.

Description: This video lecture demonstrates how to manipulate the style, axes, and position of plots in MATLAB and how to create multiple subplots. Instructor: Yossi Farjoun

Description: This lecture covers depth-first search, including edge classification, and how DFS is used for cycle detection and topological sort. Instructor: Erik Demaine

Description: This lecture covers open addressing, which is another approach to dealing with collisions (hashing with chaining was covered in Lecture 8). Cryptographic hashing is also introduced. Instructor: Srini Devadas

Description: This lecture introduces dynamic programming, in which careful exhaustive search can be used to design polynomial-time algorithms. The Fibonacci and shortest paths problems are used to introduce guessing, memoization, and reusing solutions to subproblems. ...

Description: This lecture introduces weighted graphs and considers general approaches to the shortest paths problem. The lecture discusses single source shortest paths, negative-weight edges, and optimal substructure. Instructor: Srini Devadas

Description: This lecture starts with how to define useful subproblems for strings or sequences, and then looks at parenthesization, edit distance, and the knapsack problem. The lecture ends with a brief discussion of pseudopolynomial time. Instructor: Erik Demaine

Instructor: Dennis Freeman Description: Sampling produces a discrete-time (digital) signal from a continuous-time (physical) phenomenon. Anti-aliasing and reconstruction filters remove unnecessary frequencies while retaining enough information to reconstruct the ...

Description: In this lecture, the professor discussed Poisson process, distribution of number of arrivals, and distribution of interarrival times. Instructor: John Tsitsiklis

Description: In this lecture, the professor discussed principles of counting, permutations, combinations, partitions, and binomial probabilities. Instructor: John Tsitsiklis

Description: In this lecture, the professor discussed Bayes rule, Bayes variations, and derived distributions. Instructor: John Tsitsiklis

We can study convection in a laboratory setting. A stable stratification can be set up in a 50cm square tank by slowly filling it up with water whose temperature is slowly increased with time. This is done using (i) a mixer that mixes hot and cold water together and ...

We place a large tank on our rotating table and fill it with water to a depth of 10 cm or so. We then take a hollow metal cylinder, generously rub petroleum jelly around its lower rim, and place it in the center of the tank so that it protrudes slightly above the ...

Everyone is familiar with the swirl and gurgling sound of water flowing down a drain. In this laboratory experiment we explore this problem quantitatively, and draw out the strong parallels between it and the large scale flow in the atmosphere and ocean. We rotate a ...

Project Laboratory in Mathematics is a course designed to give students a sense of what it's like to do mathematical research.

Description: This lecture introduces the topics covered in the course and its motivation. Examples of applications are provided, along with types and charaterizations of geometric objects, foldability and design questions, and results. Select open problems are also ...