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Homology Theories Homologies are one of the basic notions of the algebraic topology. The homology theory provides a possibility to construct an algebraic object such as a group or a ring that is a topological variant of space.
A closed line on a surface is homologous to nought, if a surface breaks up into parts while the scission of a High school math paper.
For example, on a sphere any closed line is as such, but on a torus, though there exist the closed lines that are homologous to nought, the section along a meridian or a parallel will not lead to the separation of a surface part.
The topics that deal with Homology Theories are the following: K — Theories Basic group and Structure Operations 2. Unary and Binary Operations Research paper topics pertaining to Geometry: Geometry — methodology, terminologies and types: Euclidean Geometry Euclidean or elementary geometry is a geometric theory based on the system of axioms that was first stated by Euclid in the 3rd century BC.
This is a geometry that is generally defined by a group of displacements and a group of similarities. But the content of the elementary geometry is not formed by the mentioned transformations, it includes also the inversion transformation, the problems of spherical geometry, the elements of geometric constructions, the theory of the measurement of geometric magnitudes etc.
Stereometry Stereometry is a branch of geometry that deals with the solid figures in space. When the main figures in space there are a point, a line and a plane, in the stereometry there appears a new kind of the relationship of lines, that is the skew lines.
This is one of the few considerable differences of stereometry from planimetry, as in many cases the stereometric problems are solved by the consideration of different planes where the planimetric laws are satisfied.
Computational Geometry Computational Geometry is a branch of the discrete mathematics that deals with the algorithms for the solving of the geometric problems. It deals with such problems as triangulation, construction of a convex hull, the defining of the belonging of one object to another one, the search of their intersection etc.
It operates with such geometric objects as a point, a segment, a polygon and a circle. The computational geometry is used in the image recognition, computer graphics, engineering design etc. Geometry algorithms Research paper topics on Calculus: Foundation and history of Calculus Calculus is a branch of mathematics that deals with the research of functions and their generalization by the methods of the differential and integral calculus.
Calculus has the resources for solving such problems for which only algebra is insufficient and has application in various spheres pf science.
The history of calculus springs from the Ancient Greece, but many of the important ideas were developed in the 17th century, and the most prominent step in the development of calculus was made in the studies of Isaac Newton and Gottfried Leibniz who nowadays are considered to be the founders of calculus.
Vector Spaces A vector space is a structure formed by vectors. Vector spaces are used in mathematical analysis, generally as the infinite-dimensional spaces where vectors are functions, however, this still create a number of analytical problems.
In addition, vector spaces are applied in various spheres of science and engineering. Multivariate Calculus Multivariate calculus is differentiated and integrated calculus involving multiple variables.
Construction of real numbers The real numbers are constructed basing on the predetermined rational numbers. The rational numbers are taken as a basis, and the new objects are constructed, that are called the irrational numbers. As a result of their addition to the set of rational numbers, there is a set of real numbers.
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You are always welcome to order a Mathematics Research paper or any other written assignment in our company. Research paper topics on Mathematical Logic:The American High School Mathematics Examination (AHSME) was the first exam in the series of exams used to challenge bright students, grades 12 and below, on the path toward choosing the team that represents the United States at the International Mathematics Olympiad (IMO).
Puxi High School Examinations Semester 1, – IB Mathematics (HL) Year 1 Paper 1 Wednesday, December 16th, pm – pm Time: 1 hour 15 minutes. Advanced High-School Mathematics David B. Surowski Shanghai American School Singapore American School January 29, i Preface/Acknowledgment The present expanded set of notes initially grew out of an attempt to esh out the International Baccalaureate (IB) mathematics \Further.
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These math worksheets and math problems are for high school and secondary school math teachers and students. This is a free database of high school worksheets that are printable directly from your browser for classroom or homework use or for creating lesson plans.