OPEN PROBLEM SESSION FROM THE CONFERENCE
... discrete invariant, J-invariant, and motivic decomposition type—see, e.g., [Vis04], [Vis05], and [Vis10]—give information about various cycles on quadrics and orthogonal Grassmannians. What possible values can it take? For example, the Steenrod operations give some restrictions on the Jinvariant of ...
... discrete invariant, J-invariant, and motivic decomposition type—see, e.g., [Vis04], [Vis05], and [Vis10]—give information about various cycles on quadrics and orthogonal Grassmannians. What possible values can it take? For example, the Steenrod operations give some restrictions on the Jinvariant of ...
a ,b
... (0,1,0), and (0,0,1) under the rotation. Turn in the source code, the rotation quaternion, and the images. 3. Use the quaternion multiplication package in Mathematica to perform the same rotation described in 2. Turn in the Mathematica notebook. It should include the rotation quaternion used, the im ...
... (0,1,0), and (0,0,1) under the rotation. Turn in the source code, the rotation quaternion, and the images. 3. Use the quaternion multiplication package in Mathematica to perform the same rotation described in 2. Turn in the Mathematica notebook. It should include the rotation quaternion used, the im ...
Matrix operations
... example, the additive identity for real number addition (scalar addition) is 0, because x + 0 = x for any real number x. Matrices have something analogous – the zero matrix serves as an additive identity: A + 0 = A. It is a matrix whose elements are all zero, and whose dimensions are whatever you ne ...
... example, the additive identity for real number addition (scalar addition) is 0, because x + 0 = x for any real number x. Matrices have something analogous – the zero matrix serves as an additive identity: A + 0 = A. It is a matrix whose elements are all zero, and whose dimensions are whatever you ne ...
Classes
... 46. Write an equation describing the line that is parallel to the y-axis and that is 6 units to the right of the y-axis. 47. Write an equation describing the line that is perpendicular to the y-axis and that is 4 units below the x-axis. 48. Critical Thinking Is it possible for two linear functions w ...
... 46. Write an equation describing the line that is parallel to the y-axis and that is 6 units to the right of the y-axis. 47. Write an equation describing the line that is perpendicular to the y-axis and that is 4 units below the x-axis. 48. Critical Thinking Is it possible for two linear functions w ...
Week 1: Configuration spaces and their many guises September 14, 2015
... The subject of this course will be, loosely, to survey what algebraic topology can say about configuration, moduli, and function spaces, most particularly with an eye towards their use in algebraic geometry and geometric topology. Definition 1. Let X be a topological space, and n ∈ Z≥0 . Define the nth ...
... The subject of this course will be, loosely, to survey what algebraic topology can say about configuration, moduli, and function spaces, most particularly with an eye towards their use in algebraic geometry and geometric topology. Definition 1. Let X be a topological space, and n ∈ Z≥0 . Define the nth ...
ON DENSITY OF PRIMITIVE ELEMENTS FOR FIELD EXTENSIONS
... the density ρ(F; α1 , . . . , αn ) may be zero, so there is no primitive element among the linear combinations of the generators. For example, let F = F2 , and let α1 = γ1 + γ2 and α2 = γ2 + γ3 where γ1 , γ2 , γ3 ∈ F2 have degrees 3, 5, 7, respectively, over F2 . Note that F23·5·7 = F2 (α1 , α2 ), h ...
... the density ρ(F; α1 , . . . , αn ) may be zero, so there is no primitive element among the linear combinations of the generators. For example, let F = F2 , and let α1 = γ1 + γ2 and α2 = γ2 + γ3 where γ1 , γ2 , γ3 ∈ F2 have degrees 3, 5, 7, respectively, over F2 . Note that F23·5·7 = F2 (α1 , α2 ), h ...
Linear algebra
Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations.Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models.