Algebraic geometry

sequences. Similarly to the seventh and eighth book, the ninth book continues number theory. It explains perfect numbers and sums of geometric sequences. Book ten involves rational numbers. Books eleven through thirteen involve three-dimensional geometry. In the eleventh book, it explains parallelism and volumes of parallelepipeds. Parallelepipeds are three-dimensional parallelograms or six parallelograms in one. The twelfth book explains the

Why Beauty is truth: A History of Symmetry by Ian Stewart is in depth on how mathematicians came about symmetry. Instead of coming across symmetry by geometry as someone today might think, Stewart shows how it became an idea by algebra. Most of the book is told in chronological order from the early Egyptians and Babylonians discovery of the quadratic equation and leading up to the impossibility to solve the quintic equation. Through each chapter we see how mathematicians get one step closer to solving

At an early age, I was bad at math, yet I knew it would be my passion. Throughout elementary school, I gave into the idea that I lacked intelligence enough to pursue mathematics seriously in school, and later on in my life. Nonetheless, math found itself back into my life during my middle school years and solidified its presence within my life. I was the dumb kid in class, unable to add and subtract, unable to memorize the multiplication table. Before, I found joy in knowing. To this date I remember

Science” Contributions: * He is credited with the first use of deductive reasoning applied to geometry. * Discovery that a circle is bisected by its diameter, that the base angles of an isosceles triangle are equal and that vertical angles are equal. * Accredited with foundation of the Ionian school of Mathematics that was a centre of learning and research. * Thales theorems used in Geometry: 1. The pairs of opposite angles formed by two intersecting lines are equal. 2. The base

includes both measuring and calculating. Africa is also one of the places where both basic and advanced mathematics were originated. Much of the math that is used by human beings today was used a long time ago in Africa. Math such as algebra and geometry that are used by us today, were used by the Africans back then. African math was then transferred to other countries through migration out of Africa and invasions of Africa by Europe and Asia. Over 3,500 years have passed since the origination of

regent I knew I wasn’t ready for it. I doubted myself because I had absolutely no clue how to solve algebraic equations and trigonometric functions. The only reason I took the exam was that my teachers told me to try it. I like to go by the saying “You never know unless you try.” So I said to myself “why not” and then I went into the examination room and took the test. Even though I passed my geometry class, I still failed the exam, which made it challenging for me because I couldn't take over the

The transition to geometric language, more precisely to constructions realizable by ruler and compass, made it possible for the first time to give general proofs of certain algebraic identities. (p.16) Figure 3 is an example of ancient Greek geometric algebra that proves the identity 〖(a+b)〗^2=a^2+ b^2+2ab. Figure 3. The length of a and b are arbitrary, solve for the area of the rectangle. Conclusion Rome was not built in

Unlike geometry, algebra was not developed in Europe. Algebra was actually discovered (or developed) in the Arab countries along side geometry. Many mathematicians worked and developed the system of math to be known as the algebra of today. European countries did not obtain information on algebra until relatively later years of the 12th century. After algebra was discovered in Europe, mathematicians put the information to use in very remarkable ways. Also, algebraic and geometric ways of thinking

Before explaining the obtained results in details we start a summary on the intellectual merits and broader impact of the project. The PI initiates a new approach (in items 2,5, 6), using the precise large time asymptotic behavior of solutions of a parabolic equation to study the geometric property of K manifolds, and to solve the Poincar Lelong equation. The method is effective in proving sharp and optimal result. The method reminisces the celebrated ergodic theorem of Birkhoff which connects

The application of algebraic topology to data analysis is relatively new but promising. When confronted with large volumes of high dimensional data we would like to identify significant phenomena, and the persistence of topological features provides a new and potentially useful measure of significance. A key promise of this method is the ability to identify features without a model- truly unsupervised learning. Unlike traditional statistical methods of data analysis which are primarily concerned