Journey towards Algebraic Geometry and Number Theory

Chapter 3: Set Theory Module 5 & 6 Chapter 4: There does not exist square root of 2 in the domain of rational numbers

My strategy would be: To rigorously prove everything that you would use in the future(e.g, reals have the sup inf property) Make a comments column where you put down why you did that step. In the last write the general strategy you used for the proof(e.g, in the sup inf case make the bound shorter for the last values) If you are doing a study of a particular field say Analytic Number Theory then make a content sheet of pdf format preferably so that you could find whatever proof you want to have a look on.It should be an exhaustive list.

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.