Is algebraic geometry difficult?
1) Algebraic geometry is indeed vast and difficult. But don’t be discouraged: professors and experts only know parts of it and you would be surprised to discover how little they know outside of their narrow domain of expertise.
Should you learn algebra or geometry first?
If we are talking the bare minimum and basics, you should do algebra first so that when you transfer on to more advanced geometry such as right angle trig. You will have a much easier time learning how to organize equations and things such as that.
What should I study before algebraic geometry?
Prerequisites: Comfort with rings and modules. At the very least, a strong background from Math 120. Background in commutative algebra, number theory, complex analysis (in particular Riemann surfaces), differential geometry, and algebraic topology will help.
What is the difference between algebra and number theory?
Algebra includes the study of structures of solution-sets of algebraic equations, structure of permutations, combinations and transformations. Solution-sets of power-series equations also arise naturally in Algebraic Geometry. Number Theory is mainly the study of integers especially, prime numbers.
Is algebraic geometry useful for physics?
Algebraic geometry is the central aspect of geometry for the physicists now.” “In recent years algebraic geometry and mathematical physics have begun to interact very deeply mostly because of string theory and mirror symmetry,” said Migliorini.
Why do people find geometry hard?
Why is geometry difficult? Geometry is creative rather than analytical, and students often have trouble making the leap between Algebra and Geometry. They are required to use their spatial and logical skills instead of the analytical skills they were accustomed to using in Algebra.
Who invented commutative algebra?
mathematician David Hilbert
The foundation of commutative algebra lies in the work of 20th century German mathematician David Hilbert, whose work on invariant theory was motivated by questions in physics.
Is analytic number theory hard?
This is a rigorous but often terse book which I liked but many others on the course seemed to find difficult. The course was very interesting and contains a fascinating insight into the mathematics required to attack the Prime Number Theorem.
Is algebraic number countable?
The set of algebraic numbers is countable (enumerable), and therefore its Lebesgue measure as a subset of the complex numbers is 0 (essentially, the algebraic numbers take up no space in the complex numbers). That is to say, “almost all” real and complex numbers are transcendental.