" This course provides an introduction to the language of schemes, properties …
" 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."
This resource contains a student activity handout, a facilitation guide, example solutions, …
This resource contains a student activity handout, a facilitation guide, example solutions, and class notes. Students work together to discover one-to-one correspondences between various infinite sets of numbers and the set of natural numbers. At the end of this activity the compiled results of their group work form a list of infinite sets that all have the same cardinality as the set of natural numbers. Instructors may take this lesson further by discussion countably infinite versus uncountably infinite sets. This activity aligns with MATH 1332 Learning Outcome 1: Apply the language and notation of sets.
This course is an introduction to the calculus of functions of several …
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.
This resource contains a facilitation guide, class notes, and an activity handout. Students …
This resource contains a facilitation guide, class notes, and an activity handout. Students play the game “Let’s Make a Deal” to explore the underlying probability that guides the optimal strategy for contestants. This activity aligns with MATH 1332 Learning Outcome 4: Demonstrate fundamental probability/counting techniques and apply those techniques to solve problems.
This resource contains a slide deck and a facilitation guide. Students are …
This resource contains a slide deck and a facilitation guide. Students are guided to consider how mathematics can help us understand the phenomenon of a pandemic and inform our responses. Students work in groups using the NCTM’s browser pandemic app to manipulate four factors that influence the spread of a virus to see the how changing these variables creates different outcomes. They learn and explore how a log curve is used in this model. This activity aligns with MATH 1332 Learning Outcome 6: Demonstrate the ability to choose and analyze mathematical models to solve problems from real-world settings, including, but not limited to, personal finance, health literacy, and civic engagement
This resource contains a student activity handout, class notes, and a facilitation …
This resource contains a student activity handout, class notes, and a facilitation guide. Students work together to discover one-to-one correspondences between various infinite sets of numbers and the set of natural numbers. At the end of this activity the compiled results of their group work form a list of infinite sets that all have the same cardinality as the set of natural numbers. Instructors may take this lesson further by discussion countably infinite versus uncountably infinite sets. This activity aligns with MATH 1332 Learning Outcome 1: Apply the language and notation of sets
This course is an introduction to differential geometry. The course itself is …
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.
An interactive applet and associated web page that demonstrate how to find …
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.
" Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their …
" 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 …
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 text is intended for a brief introductory course in plane geometry. …
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.
This course is an intensive introduction to architectural design tools and process, …
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.
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