Extension Theory Grassmann Pdf 17

Extension Theory Grassmann Pdf 17 --->>> __https://cinurl.com/2tuX3e__

Extension Theory: A Mathematical Legacy of Hermann Grassmann

Extension theory, also known as Ausdehnungslehre, is a branch of mathematics that was developed by Hermann Grassmann (1809-1877), a German schoolteacher and polymath. Grassmann introduced the concept of a vector space and the operations of exterior and interior products, which are generalizations of the dot and cross products of vectors. He also applied his theory to various fields of mathematics and physics, such as geometry, algebra, differential equations, mechanics, optics, and electromagnetism.

Grassmann published his first book on extension theory in 1844, titled Lineale Ausdehnungslehre (Linear Extension Theory), which was largely ignored by his contemporaries due to its abstract and unconventional style. He revised and expanded his work in 1862, publishing a second book called Die Ausdehnungslehre (The Extension Theory), which was also met with little recognition during his lifetime. However, in the late 19th and early 20th centuries, Grassmann's ideas began to attract more attention and appreciation from mathematicians such as Arthur Cayley, William Clifford, Giuseppe Peano, David Hilbert, Hermann Weyl, and Albert Einstein. They recognized the power and elegance of Grassmann's approach and its relevance to modern mathematics and physics.

Today, extension theory is regarded as one of the foundations of linear algebra, multilinear algebra, exterior algebra, differential geometry, tensor analysis, and quantum mechanics. It has also inspired other mathematical developments such as Clifford algebras, Lie algebras, Grassmann algebras, and geometric algebra. Grassmann's work is considered to be a remarkable example of mathematical creativity and originality that was ahead of its time.

Grassmann's life was not only devoted to mathematics, but also to many other pursuits. He was interested in linguistics and studied several languages, such as Sanskrit, Latin, Greek, Hebrew, and Persian. He wrote a grammar of the German language and a dictionary of the dialect of his native region of Pomerania. He also translated various works from Sanskrit and Persian into German, such as the Rigveda and the Shahnameh. He was an editor and publisher of several journals and books on topics ranging from mathematics and physics to theology and philosophy. He was also a musician and composed songs and hymns for his family and friends.

Grassmann faced many difficulties and disappointments in his academic career. He was not well recognized or appreciated by his colleagues and the mathematical community during his lifetime. He applied several times for university positions, but was always rejected. He also submitted his works to various journals and societies, but often received negative or indifferent responses. He was awarded an honorary doctorate by the University of TÃbingen in 1876, but this was too late to change his situation. He died in 1877 in Stettin, the same city where he was born and spent most of his life.

Grassmann's legacy is now widely acknowledged and celebrated by mathematicians and historians of mathematics. His extension theory is seen as a visionary and innovative contribution to mathematics that anticipated many modern concepts and methods. His work has influenced many branches of mathematics and physics, such as linear algebra, multilinear algebra, exterior algebra, differential geometry, tensor analysis, quantum mechanics, relativity theory, and geometric algebra. He is regarded as one of the greatest mathematicians of the 19th century and one of the most original thinkers in the history of mathematics. ec8f644aee