On matrix theory, graph theory, and finite geometry

... set of matrices that preserve some function, subset or a relation. If the studied maps are bijective by the assumption, then the characterization of the maps involved is often easier to obtain. In the case of certain preservers of binary relations it turns out that bijectivity can be deduced automat ...

... set of matrices that preserve some function, subset or a relation. If the studied maps are bijective by the assumption, then the characterization of the maps involved is often easier to obtain. In the case of certain preservers of binary relations it turns out that bijectivity can be deduced automat ...

Exam 2 Review 2.1-2.5, 3.1-3.4 2.1:Coordinate Geometry 2.2: Linear

... – A graph has y-axis symmetry if replacing x with -x results in an equivalent equation – A graph has x-axis symmetry if replacing y with -y results in an equivalent equation – A graph has origin symmetry if replacing both x with -x and y with -y results in an equivalent equation • Be familiar with c ...

... – A graph has y-axis symmetry if replacing x with -x results in an equivalent equation – A graph has x-axis symmetry if replacing y with -y results in an equivalent equation – A graph has origin symmetry if replacing both x with -x and y with -y results in an equivalent equation • Be familiar with c ...

Math 8301, Manifolds and Topology Homework 8 1. Show that S

... by gluing together S 2 and S 1 at a single point. 3. Suppose X and Y are path-connected spaces, p : Y → X is a covering map, and y ∈ Y . Let the image of π1 (Y, y) in the fundamental group G = π1 (X, p(y)) be the subgroup H. Let N H be the normalizer of H in G. Show that there is a bijection between ...

... by gluing together S 2 and S 1 at a single point. 3. Suppose X and Y are path-connected spaces, p : Y → X is a covering map, and y ∈ Y . Let the image of π1 (Y, y) in the fundamental group G = π1 (X, p(y)) be the subgroup H. Let N H be the normalizer of H in G. Show that there is a bijection between ...

CHAPTER 4: SOME OTHER FUNCTIONS 1. The Absolute Value 1.1

... the integers are separated from each other on the real line – i.e. they are a ‘discrete’ set – the graphs of such functions tend to have sudden discrete jumps. Functions like this arise naturally in the mathematics of electronic technology. Definition 2.1. (The ‘greatest integer function’ ): For any ...

... the integers are separated from each other on the real line – i.e. they are a ‘discrete’ set – the graphs of such functions tend to have sudden discrete jumps. Functions like this arise naturally in the mathematics of electronic technology. Definition 2.1. (The ‘greatest integer function’ ): For any ...

I.1 Connected Components

... Connectivity. In a simple graph, a path from u ∈ V to v ∈ V can be described by a sequence of vertices, u = u0 , u1 , u2 , . . . , uk = v, where we have an edge from ui to ui+1 for each 0 ≤ i ≤ k − 1. Vertices can repeat allowing the path to cross itself or fold onto itself. Definition A. A simple g ...

... Connectivity. In a simple graph, a path from u ∈ V to v ∈ V can be described by a sequence of vertices, u = u0 , u1 , u2 , . . . , uk = v, where we have an edge from ui to ui+1 for each 0 ≤ i ≤ k − 1. Vertices can repeat allowing the path to cross itself or fold onto itself. Definition A. A simple g ...

7th Grade Common Core Appendix to Math Curriculum

... Below, we have matched up the new Core Curriculum Standards with our own New York State math standards for reference. On the left are the Common Core Standards in the order that they have been p ...

... Below, we have matched up the new Core Curriculum Standards with our own New York State math standards for reference. On the left are the Common Core Standards in the order that they have been p ...

Year 9 Maths Assessment Criteria

... Calculate with standard form Use the form y = mx + c to A x 10n, where 1 ≤ A < 10 and identify parallel lines n is an integer ...

... Calculate with standard form Use the form y = mx + c to A x 10n, where 1 ≤ A < 10 and identify parallel lines n is an integer ...

step assignment 9 - March

... Euclid’s Proposition 5, which is proved in part (i) of the warm-up above, says that the base angles of an isosceles triangle are equal. Euclid’s proof was a bit harder than the one suggested in part (i) above, because he had not yet (i.e. in propositions 1 to 4) shown that two triangles with corresp ...

... Euclid’s Proposition 5, which is proved in part (i) of the warm-up above, says that the base angles of an isosceles triangle are equal. Euclid’s proof was a bit harder than the one suggested in part (i) above, because he had not yet (i.e. in propositions 1 to 4) shown that two triangles with corresp ...

A new class of graphs that satisfies the Chen

... graph induces a metric space on its vertex set, where the distance between two vertices u and v is defined as the length of a shortest path linking u and v. Such metric spaces are called graph metrics and are the subject of this paper. The best known lower bound on the number of lines in a graph met ...

... graph induces a metric space on its vertex set, where the distance between two vertices u and v is defined as the length of a shortest path linking u and v. Such metric spaces are called graph metrics and are the subject of this paper. The best known lower bound on the number of lines in a graph met ...

Italo Jose Dejter (Bahia Blanca, 1939) is an Argentine-born American mathematician of Bessarabian Jewish descent. He is a professor at the University of Puerto Rico (UPRRP) since 1984 and has conducted research in mathematics, particularly in areas that include algebraic topology, differential topology, graph theory, coding theory and design theory.He has an Erdos number of 2 since 1993.Dejter completed the Licentiate degree in Mathematics from University of Buenos Aires in 1967, and the Ph.D. degree in Mathematics from Rutgers University in 1975 under the supervision of Ted Petrie. He was a professor atFederal University of Santa Catarina, Brazil, from 1977 to 1984. Dejter has been a visiting scholar at a number of research institutions, including University of São Paulo,Instituto Nacional de Matemática Pura e Aplicada, Federal University of Rio Grande do Sul,University of Cambridge,National Autonomous University of Mexico, Simon Fraser University, University of Victoria, New York University, University of Illinois at Urbana–Champaign, McMaster University,DIMACS, Autonomous University of Barcelona, Technical University of Denmark, Auburn University, Polytechnic University of Catalonia, Technical University of Madrid, Charles University, Ottawa University, Simón Bolívar University, etc. The sections below describe the relevance of Dejter's work in the research areas mentioned in the first paragraph above, or in the box to the right.