“One of the symptoms of an approaching nervous breakdown is the belief that one’s work is terribly important.” ― Bertrand Russell
Real Analysis (2021)
References:[1]Real analysis: modern techniques and their applications, Gerald B. Folland [2]Real analysis:measure theory, integration and Hilbert spaces, Elias M. Stein, Rami Shakarchi [3]Real and Complex Analysis, Rudin [4]Measure Theory, Cohn
Ⅰ.Lebesgue Measure: Properties, Integration Theory, and Differentiation Theory
Ⅱ.Abstract Measure: Properties, Integration Theory, and Differentiation Theory
Ⅲ.Radon Measure: Representation, Reguarity, Duality, and Product measure
Ⅳ.Hausdorff Measure: Properties and Self-similarity
Ⅴ.Haar Measure on LCH topological groups
Complex Analysis (2021)
References:[1]Complex analysis, Elias M. Stein, Rami Shakarchi [2]Invitation to Complex Analysis, Ralph P. Boas [3]Complex analysis, Ahlfors L.[4]Real and Complex Analysis,Rudin
Ⅶ.Linear Fractional Transformations
Ⅸ.Fourier Transformations in Complex Domain
Differential Manifolds (2021)
In fact, most manifolds in my notes are SMOOTH.
Reference:[1]Manifolds, Ed Segal [2]Introduction to Manifolds, Loring W. Tu
Ordinary Differential Equations (2022)
Reference:[1]常微分方程教程,丁同仁; 李承治(primary)[2]Ordinary Differential Equations and Dynamical Systems, Gerald Teschl
Ⅴ.Parameters and Initial Value in High Order Equations
General Topology (2021)
I will “refresh” the note which’s totally a DISASTER because it’s my first time to make a note.
References:[1]Topology, James R. Munkres(primary) [2]Lectures on Basic Topology, Chengye You
Set Theory and General Topology
Advanced Algebra (2021)
I will “refresh” the note which’s totally a DISASTER because it’s my first time to make a note.
References:[1]Algebra, Thomas W. Hungerford(primary) [2]Abstract algebra, David S. Dummit, Richard M. Foote
Ⅰ.Groups and Preliminary Category Theory