This first course in the physics curriculum introduces classical mechanics. Historically, a set of core concepts—space, time, mass, force, momentum, torque, and angular momentum—were introduced in classical mechanics in order to solve the most famous physics problem, the motion of the planets.

The topic of this video module is how to classify animals based on how closely related they are. The main learning objective is that students will learn how to make phylogenetic trees based on both physical characteristics and on DNA sequence. Students will also learn why the objective and quantitative nature of DNA sequencing is preferable when it come to classifying animals based on how closely related they are. Knowledge prerequisites to this lesson include that students have some understanding of what DNA is and that they have a familiarity with the base-pairing rules and with writing a DNA sequence.

This course analyzes combinatorial problems and methods for their solution. Topics include: enumeration, generating functions, recurrence relations, construction of bijections, introduction to graph theory, network algorithms, and extremal combinatorics.

Thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems. 18.310 helpful but not required.

Content varies from year to year. An introduction to some of the major topics of present day combinatorics, in particular enumeration, partially ordered sets, and generating functions. This is a graduate-level course in combinatorial theory. The content varies year to year, according to the interests of the instructor and the students. The topic of this course is hyperplane arrangements, including background material from the theory of posets and matroids.

Content varies from year to year. An introduction to some of the major topics of present day combinatorics, in particular enumeration, partially ordered sets, and generating functions. This course serves as an introduction to major topics of modern enumerative and algebraic combinatorics with emphasis on partition identities, young tableaux bijections, spanning trees in graphs, and random generation of combinatorial objects. There is some discussion of various applications and connections to other fields.

In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.

This course covers the analytical, graphical, and numerical methods supporting the analysis and design of integrated biological systems. Topics include modularity and abstraction in biological systems, mathematical encoding of detailed physical problems, numerical methods for solving the dynamics of continuous and discrete chemical systems, statistics and probability in dynamic systems, applied local and global optimization, simple feedback and control analysis, statistics and probability in pattern recognition.

Welcome to 2.007! This course is a first subject in engineering design. With your help, this course will be a great learning experience exposing you to interesting material, challenging you to think deeply, and providing skills useful in professional practice. A major element of the course is design of a robot to participate in a challenge that changes from year to year. This year, the theme is cleaning up the planet as inspired by the movie Wall-E.

This course covers the design, construction, and testing of field robotic systems, through team projects with each student responsible for a specific subsystem. Projects focus on electronics, instrumentation, and machine elements. Design for operation in uncertain conditions is a focus point, with ocean waves and marine structures as a central theme. Topics include basic statistics, linear systems, Fourier transforms, random processes, spectra, ethics in engineering practice, and extreme events with applications in design.

This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions for elliptic; hyperbolic and parabolic differential operators; method of characteristics; review of Lebesgue integration; distributions; fourier transform; homogeneous distributions; asymptotic methods.

In this course, we study elliptic Partial Differential Equations (PDEs) with variable coefficients building up to the minimal surface equation. Then we study Fourier and harmonic analysis, emphasizing applications of Fourier analysis. We will see some applications in combinatorics / number theory, like the Gauss circle problem, but mostly focus on applications in PDE, like the Calderon-Zygmund inequality for the Laplacian, and the Strichartz inequality for the Schrodinger equation. In the last part of the course, we study solutions to the linear and the non-linear Schrodinger equation. All through the course, we work on the craft of proving estimates.

This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature.

In this video module, students learn how scientists use genetic information from dogs to find out which gene (out of all 20,000 dog genes) is associated with any specific trait or disease of interest. This method involves comparing hundreds of dogs with the trait to hundreds of dogs not displaying the trait, and examining which position on the dog DNA is correlated with the trait (i.e. has one DNA sequence in dogs with the trait but another DNA sequence in dogs not displaying the trait). Students will also learn something about the history of dog breeds and how this history helps us find genes.

Scientists who are working to discover new medicines often use robots to prepare samples of cells, allowing them to test chemicals to identify those that might be used to treat diseases. Students will meet a scientist who works to identify new medicines. She created free software that ''looks'' at images of cells and determines which images show cells that have responded to the potential medicines. Students will learn about how this technology is currently enabling research to identify new antibiotics to treat tuberculosis. Students will complete hands-on activities that demonstrate how new medicines can be discovered using robots and computer software, starring the student as ''the computer.'' In the process, the students learn about experimental design, including positive and negative controls.

Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems.

Seminar on a selected topic from Renaissance architecture. Requires original research and presentation of a report. The aim of this course is to highlight some technical aspects of the classical tradition in architecture that have so far received only sporadic attention. It is well known that quantification has always been an essential component of classical design: proportional systems in particular have been keenly investigated. But the actual technical tools whereby quantitative precision was conceived, represented, transmitted, and implemented in pre-modern architecture remain mostly unexplored. By showing that a dialectical relationship between architectural theory and data-processing technologies was as crucial in the past as it is today, this course hopes to promote a more historically aware understanding of the current computer-induced transformations in architectural design.

This class is a multidisciplinary introduction to pharmacology, neurotransmitters, drug mechanisms, and brain diseases from addiction to schizophrenia.

This lesson is about the flow of energy in ecosystems. The setting is Plimoth Plantation, a living history museum in Plymouth, Massachusetts, USA, where students will learn about the first Thanksgiving meal in America, celebrated in 1621 by early American settlers and Wampanoag Indians. By examining this meal and comparing it to a modern day Thanksgiving celebration, students will be able to explore the way in which food energy moves and is transformed in an ecosystem. The learning goals focus on the movement of energy from one feeding level to the next within a food web, the way in which energy changes form, and the inefficiency of energy transfer, which in turn affects the availability of food energy for organisms at the highest feeding level. The lesson is directed at high school level biology students. Students should be familiar already with food webs, food chains, and trophic (feeding) levels. They should also be familiar with the general equations for photosynthesis (CO2 + H2O => C6H12O6) and cell respiration (C6H12O6 => CO2 + H2O), and understand the basic purpose of these processes in nature. This lesson can be completed during one long classroom period, or can be divided over two or more class meetings. The duration of the lesson will depend on prior knowledge of the students and on the amount of time allotted for student discussion. There are no supplies required for this lesson other than the downloadable worksheets (accessed on this BLOSSOMS site), paper and some glue or tape.

The major goal of this lesson is to provide students with some of the tools they will need to analyze and solve the many complex problems they will face during their lifetimes. In the lesson, students learn to use Flow Charts and Feedback Diagrams to analyze a very complex problem of ecological sustainability. The lesson looks at a specific case study—from my home town in the Philippines—of the Live Reef Fish Trade now threatening survival of the Coral Reef Triangle of Southeast Asia. Live reef fish have long been traded around Southeast Asia as a luxury food item, but in recent decades trade in fish captured on coral reefs has expanded rapidly. Although the trade has provided communities with additional income, these benefits are unsustainable and have come at considerable cost to the environment. This lesson begins by having students analyze a familiar or personal problem, using Flow Charts and Feedback Diagrams, and then moves on to the application of those tools to a complex environmental problem. The lesson could be completed in a 50-minute class session, but using it over two class sessions would be preferable. Everything needed for the lesson is downloadable from the BLOSSOMS website, including blank Flow Charts and Feedback Diagrams, as well as articles on the Philippines case study from the World Wildlife Fund and the United States Agency for International Development.