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Is algebraic number theory difficult?
The ‘next level’ of number theory, Algebraic number theory, involves upper level algebra and can be difficult at first glance, but if you have done any studying in field theory or a related subject you will recognize some stuff.
How difficult is algebraic geometry?
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.
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 can algebraic geometry be used for?
Algebraic geometry now finds applications in statistics, control theory, robotics, error-correcting codes, phylogenetics and geometric modelling. There are also connections to string theory, game theory, graph matchings, solitons and integer programming.
What is modern number theory?
Modern number theory is a broad subject that is classified into subheadings such as elementary number theory, algebraic number theory, analytic number theory, geometric number theory, and probabilistic number theory. These categories reflect the methods used to address problems concerning the integers.
Why is number theory important?
As it holds the foundational place in the discipline, Number theory is also called “The Queen of Mathematics”. Description: The number theory helps discover interesting relationships between different sorts of numbers and to prove that these are true .
Why is algebraic geometry so abstract?
The rapid development of abstract algebraic geometry was due to the recognition of the fact that it is possible, in the framework of the theory of schemes, to apply to the “abstract case” practically all of the known concepts of the classical complex case and, in particular, the homology theory of complex-analytic …
Where do I start with algebraic geometry?
Basic Algebraic Geometry by Shafarevich is probably the best introduction out there. Hartshorne is another classic book, but I would recommend learning from Shafarevich and referring to Hartshorne in case anything is unclear.
Is algebraic geometry useful?
Since in the end, any mathematical subject works within specified algebras, studying the geometry those algebras define is a useful tool and interesting endeavor in itself.