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Algebraic Geometry, Spring 2009
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" This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry."

Subject:
Algebra
Geometry
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Kedlaya, Kiran
Date Added:
01/01/2009
Calculus III, Fall 2010
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CC BY-NC-SA
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This course is an introduction to the calculus of functions of several variables. It begins with studying the basic objects of multidimensional geometry: vectors and vector operations, lines, planes, cylinders, quadric surfaces, and various coordinate systems. It continues with the elementary differential geometry of vector functions and space curves. After this, it extends the basic tools of differential calculus - limits, continuity, derivatives, linearization, and optimization - to multidimensional problems. The course will conclude with a study of integration in higher dimensions, culminating in a multidimensional version of the substitution rule.

Subject:
Calculus
Geometry
Material Type:
Full Course
Homework/Assignment
Syllabus
Provider:
UMass Boston
Provider Set:
UMass Boston OpenCourseWare
Author:
Catalin Zara
Ph.D.
Date Added:
08/13/2020
Computational Geometry, Spring 2003
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Topics in surface modeling: b-splines, non-uniform rational b-splines, physically based deformable surfaces, sweeps and generalized cylinders, offsets, blending and filleting surfaces. Non-linear solvers and intersection problems. Solid modeling: constructive solid geometry, boundary representation, non-manifold and mixed-dimension boundary representation models, octrees. Robustness of geometric computations. Interval methods. Finite and boundary element discretization methods for continuum mechanics problems. Scientific visualization. Variational geometry. Tolerances. Inspection methods. Feature representation and recognition. Shape interrogation for design, analysis, and manufacturing. Involves analytical and programming assignments.

Subject:
Environmental Engineering
Geometry
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Patrikalakis, Nicholas
Date Added:
01/01/2003
Differential Geometry, Fall 2008
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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.

Subject:
Geometry
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Seidel, Paul
Date Added:
01/01/2008
Distance from a point to a line using trigonometry
Read the Fine Print
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An interactive applet and associated web page that demonstrate how to find the perpendicular distance between a point and a line using trigonometry, given the coordinates of the point and the slope/intercept of the line. The applet has a line with sliders that adjust its slope and intercept, and a draggable point. As the line is altered or the point dragged, the distance is recalculated. The grid and coordinates can be turned on and off. The distance calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of the concepts, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Subject:
Geometry
Trigonometry
Material Type:
Reading
Simulation
Provider:
Math Open Reference
Author:
John Page
Date Added:
06/03/2021
Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics, Fall 2009
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" 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."

Subject:
Algebra
Geometry
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Etingof, Pavel
Date Added:
01/01/2009
Drawings & Numbers: Five Centuries of Digital Design, Fall 2002
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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.

Subject:
Creative and Applied Arts
Architecture and Design
Geometry
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Carpo, Mario
Date Added:
01/01/2002
Elementary College Geometry
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CC BY-NC-SA
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This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra.

The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem-proving or formal methods of reasoning. However the topics are ordered so that they may be taught deductively.

The problems are arranged in pairs so that just the odd-numbered or just the even-numbered can be assigned. For assistance, the student may refer to a large number of completely worked-out examples. Most problems are presented in diagram form so that the difficulty of translating words into pictures is avoided. Many problems require the solution of algebraic equations in a geometric context. These are included to reinforce the student's algebraic and numerical skills, A few of the exercises involve the application of geometry to simple practical problems. These serve primarily to convince the student that what he or she is studying is useful. Historical notes are added where appropriate to give the student a greater appreciation of the subject.

This book is suitable for a course of about 45 semester hours. A shorter course may be devised by skipping proofs, avoiding the more complicated problems and omitting less crucial topics.

Subject:
Geometry
Material Type:
Textbook
Provider:
CUNY Academic Works
Provider Set:
New York City College of Technology
Author:
Henry Africk
Date Added:
01/01/2013
Euclidean plane and its relatives
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CC BY-SA
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This book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalistic.

Subject:
Geometry
Material Type:
Textbook
Author:
Anton Petrunin
Date Added:
08/13/2018
Geometric Disciplines and Architecture Skills: Reciprocal Methodologies, Fall 2012
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CC BY-NC-SA
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This course is an intensive introduction to architectural design tools and process, and is taught through a series of short exercises. The conceptual basis of each exercise is in the interrogation of the geometric principles that lie at the core of each skill. Skills covered in this course range from techniques of hand drafting, to generation of 3D computer models, physical model-building, sketching, and diagramming. Weekly lectures and pin-ups address the conventions associated with modes of architectural representation and their capacity to convey ideas. This course is tailored and offered only to first-year M.Arch students.

Subject:
Architecture and Design
Geometry
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Brandon Clifford
Date Added:
01/01/2012
Geometry: Expressing Geometric Properties with Equations
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CC BY-NC-SA
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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.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Interactive
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
08/13/2020
Geometry: Geometric Measurement and Dimension
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CC BY-NC-SA
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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.

Subject:
Mathematics
Geometry
Material Type:
Activity/Lab
Interactive
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
08/13/2020
Geometry: Inscribed Angles
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This geometry lesson shows that that an inscribed angle is half of a central angle that subtends the same arc. [Geometry playlist: Lesson 24 of 31]

Subject:
Geometry
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
02/20/2011