How does a lens form an image? See how light rays are …
How does a lens form an image? See how light rays are refracted by a lens. Watch how the image changes when you adjust the focal length of the lens, move the object, move the lens, or move the screen.
This site teaches the Geometry of Circles to High Schoolers through a …
This site teaches the Geometry of Circles to High Schoolers through a series of 1084 questions and interactive activities aligned to 9 Common Core mathematics skills.
This site teaches High Schoolers how to express geometric properties with equations …
This site teaches High Schoolers how to express geometric properties with equations through a series of 1721 questions and interactive activities aligned to 12 Common Core mathematics skills.
This site teaches High Schoolers Geometric Measurement and Dimension through a series …
This site teaches High Schoolers Geometric Measurement and Dimension through a series of 82 questions and interactive activities aligned to 4 Common Core mathematics skills.
This site teaches High Schoolers how to Interpret Categorical and Quantitative Data …
This site teaches High Schoolers how to Interpret Categorical and Quantitative Data through a series of 45 questions and interactive activities aligned to 2 Common Core mathematics skills.
A rigorous introduction designed for mathematicians into perturbative quantum field theory, using …
A rigorous introduction designed for mathematicians into perturbative quantum field theory, using the language of functional integrals. Basics of classical field theory. Free quantum theories. Feynman diagrams. Renormalization theory. Local operators. Operator product expansion. Renormalization group equation. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and string theory.
This is a second-semester graduate course on the geometry of manifolds. The …
This is a second-semester graduate course on the geometry of manifolds. The main emphasis is on the geometry of symplectic manifolds, but the material also includes long digressions into complex geometry and the geometry of 4-manifolds, with special emphasis on topological considerations.
This resource contains a facilitation guide. Students practice data analysis and review …
This resource contains a facilitation guide. Students practice data analysis and review the point-slope form of a line. This activity primarily aligns with MATH 1332 Learning Outcome 5: Interpret and analyze various representations of data.
The Open Resource site is intended to facilitate discovery and use of …
The Open Resource site is intended to facilitate discovery and use of open resources starting with Open Educational Resources (OER). The Open Resource site will continue to develop and change depending on the needs of the community, and are outlined in the future developments section. Essentially it is a place to search for all the places to search for OER.
Studies how randomization can be used to make algorithms simpler and more …
Studies how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Models of randomized computation. Data structures: hash tables, and skip lists. Graph algorithms: minimum spanning trees, shortest paths, and minimum cuts. Geometric algorithms: convex hulls, linear programming in fixed or arbitrary dimension. Approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.
In this undergraduate level seminar series topics vary from year to year. …
In this undergraduate level seminar series topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry.
Seminar for mathematics majors. Students present and discuss the subject matter, taken …
Seminar for mathematics majors. Students present and discuss the subject matter, taken from current journals or books and write up exercises. Topic for spring 2003: Elementary topological properties of differentiable manifolds. Topics covered include Sard's theorem, the Thom transversality theorem, vector fields and the Poincare-Hopf theorem, and cohomolgy via differential forms. Prerequisites subject to negotiation with the instructor. Instruction and practice in oral communication provided. In this course, students take turns in giving lectures. For the most part, the lectures are based on Robert Osserman's classic book A Survey of Minimal Surfaces, Dover Phoenix Editions. New York: Dover Publications, May 1, 2002. ISBN: 0486495140.
This resource contains a transcript of lessons, a facilitation guide, and three …
This resource contains a transcript of lessons, a facilitation guide, and three activity handouts. Guides students’ understanding of inflation using the Consumer Price Index average price data. This activity primarily aligns with MATH 1332 Learning Outcome 3: Solve problems in mathematics of finance. It also algins with MATH 1332 Learning Outcomes 5 & 6.
This 10-minute video lesson shows that three points uniquely define a circle …
This 10-minute video lesson shows that three points uniquely define a circle and that the center of a circle is the circumcenter for any triangle that the circle is circumscribed about.
The main aims of this seminar will be to go over the …
The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.
Topics vary from year to year. Fall Term: Numerical properties and vanish …
Topics vary from year to year. Fall Term: Numerical properties and vanish theorems for ample, nef, and big line bundles and vector bundles; multiplier ideals and their applications
This is an introductory (i.e. first year graduate students are welcome and …
This is an introductory (i.e. first year graduate students are welcome and expected) course in generalized geometry, with a special emphasis on Dirac geometry, as developed by Courant, Weinstein, and Severa, as well as generalized complex geometry, as introduced by Hitchin. Dirac geometry is based on the idea of unifying the geometry of a Poisson structure with that of a closed 2-form, whereas generalized complex geometry unifies complex and symplectic geometry. For this reason, the latter is intimately related to the ideas of mirror symmetry.
" This course will focus on various aspects of mirror symmetry. It …
" This course will focus on various aspects of mirror symmetry. It is aimed at students who already have some basic knowledge in symplectic and complex geometry (18.966, or equivalent). The geometric concepts needed to formulate various mathematical versions of mirror symmetry will be introduced along the way, in variable levels of detail and rigor."
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