Niels Henrik Abel’s manuscripts

Quelle tête celle du jeune Norvégien!

– Adrien-Marie Legendre (1752-1833)

Two of Abstract Algebra‘s most illustrious pioneers were Évariste Galois (1811–1832) and Niels Henrik Abel (1802-1829). There are many similarities between these two great thinkers: both Galois and Abel made important contributions at a very tender age, both died prematurely (Galois died in a duel at the age of 20, Abel died of tuberculosis at the age of 26), and neither Galois’ nor Abel’s work were fully appreciated until much after their tragic deaths. I will focus on Abel, Norway’s greatest mathematician.

[ Norwegian NK1483 stamp portraying Niels Henrik Abel ]

During his short life, Abel worked on various areas of Mathematics, such as functional equations, integral transforms, series, elliptic integrals, and the solution of algebraic equations. If you want to know more about Abel‘s work and contributions, I suggest you read Christian Houzel’s The Work of Niels Henrik Abel (PDF – 3.57 MB). Some of Niels Henrik Abel’s manuscripts are available at The Abel Prize:

• Recherches sur les fonctions elliptiques (PDF – 6.71 MB)

• Note sur quelques formules elliptiques (PDF – 1.47 MB)

• Recherches sur les fonctions elliptiques II (PDF – 4.52 MB)

If you are interested in the “Archaeology of Mathematics”, you might find the manuscripts quite interesting.

Applications of Algebraic Geometry

Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate.

– David Mumford (b. 1937)

The IMA Thematic Year on Applications of Algebraic Geometry was a series of events that took place at the University of Minnesota’s Institute for Mathematics and its Applications (IMA) from September 2006 to June 2007.

Some tutorials:

• Algebraic Geometric Methods in Engineering (Sept. 15-16, 2006)

• Algebraic Algorithms in Optimization (Jan. 12-13, 2007)

• What is Algebraic Geometry? (April 13-14, 2007)

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Some workshops:

• Algorithms in Algebraic Geometry (Sept. 18-22, 2006)

• Software for Algebraic Geometry (Oct. 23-27, 2006)

• Optimization and Control (Jan. 16-20, 2007)

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Prof. Sanjay Lall‘s lecture on Control Theory and Algebraic Geometry was particularly interesting.

Gilbert Strang’s lectures on Linear Algebra

Matrix theory is the arithmetic of higher mathematics.

–Richard Bellman (1920-1984)

Prof. Gilbert Strang‘s famous lectures on Linear Algebra are available for download here. You can also watch the 34 lectures on YouTube. More material can be found on the course’s OCW page. Highly recommended. Strang is an awesome teacher. His lectures are delightful.

Thanks to MIT OCW for making the lecture available online.

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Related:

• MIT leads elite colleges offering free resources (Dec. 2007)

• Online university courses big hit (Dec. 2007)