Journey towards Algebraic Geometry and Number Theory

Ravi Vakil's Foundations of Algebraic Geometry Robin Hartshorne's Algebraic Geometry Griffith and Harris's Principles of Algebraic Geometry

chap 7 infinite inf problem Chap 8 whole (Ex. 8.1.1 Ex. 8.1.9 Ex 8.1.10) Chap 9: heine-borel Theorem, f being convergent at xo equivalent statement problem supremum definition for functions exponentiation functions are continuous 9.5 question Finbonacci sequence a principle of strong induction (for fibonacci especiallly ) Example 9.8.4 Exercise 9.8.4 Exercise 9.8.5

1.Terence Tao Analysis I 2.Terence Tao Analysis II 3.Linear Algebra 4.Introduction to Topology 5.Complex Analysis (Elias Stein, Rami Shakarjee) 6.Analysis and Manifolds 7.Introduction to Analytic Number Theory 8.Hon's Differential Equations 9.Real Analysis (Rudin) 10.Algebra I 11.Algebra II 12.Differential Geometry 13.Introduction to Functional Analysis 14.Elliptic Curves 15.Introduction to Topology 16.Riemannian Geometry 17.Commutative Algebra 18.Algebraic Topology I 19.Partial Differential Equations 20.Elliptic Curves 21.Geometry of Manifolds 22.Algebraic Geometry I 23.Number Theory I 24.Introduction to Representation Theory 25.Geometry of Manifolds I 26.Algebraic Topology II 27.Algebraic Geometry II 28.Number Theory II 29.Gaps that i need to fill in to understand the proof of Perelman like (Ricci Flow) Publish some good papers & try to uncover the proofs of Perelman and Wiles's

I am now doing Terence Tao Analysis I but i want to quickly and swiftly go through the remaining chapters which are infinite sets, continuous functions, differentiation, Integration. I am now in Semester 3 of BS Mathematics at Nust. Following is my plan for this semester: Terence Tao Analysis I Terence Tao Analysis II Linear Algebra Done Right. (Axler Sheldon) Honors Differential Equations Algebra I Introduction to Topology Functions of a complex variable Analysis and Manifolds Analytic Number Theory (Tom .P. Apostol) I am excited to learn PNT and the generalized Stokes Theorem.