Elements of Algebra
Encyclopedia
Elements of Algebra is a mathematics textbook by mathematician Leonhard Euler
, originally published circa 1765. His Elements of Algebra is one of the first books to set out algebra in the modern form we would recognize today. However, it is sufficiently different from most modern approaches to the subject to be interesting for contemporary readers. Indeed, the choices made for setting out the curriculum, and the details of the techniques Euler employs, may surprise even experts. It is also the only mathematical work of Euler which is genuinely accessible to all. The work opens with a discussion of the nature of numbers and the signs + and -, before systematically developing algebra to a point at which polynomial equations of the fourth degree can be solved, first by an exact formula and then approximately. The Elements of Algebra contains many important early results in mathematical analysis
; for example, it contains Euler's original proof of Fermat's Last Theorem
for the special case of n = 3.
The original German name is: Vollständige Anleitung zur Algebra, which literally means: Complete Instruction to Algebra.
In 1771, Joseph Lagrange
published a follow-up volume entitled Additions to Euler's Elements of algebra, which featured a number of important mathematical results.
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
, originally published circa 1765. His Elements of Algebra is one of the first books to set out algebra in the modern form we would recognize today. However, it is sufficiently different from most modern approaches to the subject to be interesting for contemporary readers. Indeed, the choices made for setting out the curriculum, and the details of the techniques Euler employs, may surprise even experts. It is also the only mathematical work of Euler which is genuinely accessible to all. The work opens with a discussion of the nature of numbers and the signs + and -, before systematically developing algebra to a point at which polynomial equations of the fourth degree can be solved, first by an exact formula and then approximately. The Elements of Algebra contains many important early results in mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
; for example, it contains Euler's original proof of Fermat's Last Theorem
Fermat's Last Theorem
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
for the special case of n = 3.
The original German name is: Vollständige Anleitung zur Algebra, which literally means: Complete Instruction to Algebra.
In 1771, Joseph Lagrange
Joseph Lagrange
Count Joseph Lagrange was a French soldier who rose through the ranks and gained promotion to the rank of general officer during the French Revolutionary Wars, subsequently pursuing a successful career during the Napoleonic Wars and winning promotion to the top military rank of General of Division....
published a follow-up volume entitled Additions to Euler's Elements of algebra, which featured a number of important mathematical results.