Post by Cynicus Rex on Apr 27, 2019 6:55:45 GMT
I always argue that there is no better way to learn a topic than from its masters, provided that they are excellent educators. It turns out that Leonhard Euler, (probably) the greatest mathematician who ever lived, wrote a book aimed at beginners. Below, an excerpt from the preface of Elements of Algebra:
"The object of the celebrated author was to compose an Elementary Treatise, by which a beginner, without any other assistance, might make himself complete master of algebra. The loss of sight had suggested the idea to him, and his activity of mind did not suffer him to defer the execution of it. For this purpose M. Euler pitched on a young man whom he had engaged as a servant on his departure from Berlin, sufficiently master of arithmetic, but in other respects without the least knowledge of mathematics. He had learned the trade of a tailor; and, with regard to this capacity, was not above mediocrity. This young man, however, has not only retained what his illustrious master taught and dictated to him, but in a short time was able to perform the most difficult algebraic calculations and to resolve with readiness whatever analytical questions were proposed to him.
This fact alone must be a strong recommendation of the manner in which this work is composed, as the young man who wrote it down, who performed the calculations, and whose proficiency was so striking, received no instructions whatever but from his master, a superior one indeed, but deprived of sight.
Independently of so great an advantage, men of science will perceive with pleasure and admiration the manner in which the doctrine of logarithms is explained, and its connection with other branches of calculus pointed out, as well as the methods which are given for resolving equations of the third and fourth degrees.
Lastly, those who are fond of Diophantine problems will be pleased to find in the last Section of the Second Part, all these problems reduced to a system, and all the processes of calculation, which are necessary for the solution of them, fully explained."
This fact alone must be a strong recommendation of the manner in which this work is composed, as the young man who wrote it down, who performed the calculations, and whose proficiency was so striking, received no instructions whatever but from his master, a superior one indeed, but deprived of sight.
Independently of so great an advantage, men of science will perceive with pleasure and admiration the manner in which the doctrine of logarithms is explained, and its connection with other branches of calculus pointed out, as well as the methods which are given for resolving equations of the third and fourth degrees.
Lastly, those who are fond of Diophantine problems will be pleased to find in the last Section of the Second Part, all these problems reduced to a system, and all the processes of calculation, which are necessary for the solution of them, fully explained."
I am now working through this book, which I already most highly recommend. However, I do advise simultaneously reading (or following it up by) Algebra by I.M. Gelfand, because its proofs it asks you to do are more rigorous. Elements of Algebra 'just' takes √a*√b = √ab as 'evident', Gelfand makes you prove it.
PS Euclid's Elements is next on my list.
"His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century."