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Curated: The List of Clear Knowledge.

As the title says! recently, I become deep into special areas, and references became increasingly "dirty". So, here I'm setting the top-ranked and clear references. Classified by specialty.

  • The list contains resources written in non-English languages. You can figure it out by in LANG.
  • This list is not for school students! usually, these references need prerequisites to understand.
  • Don't consider the classification as a final fact, especially in mathematics.

[Copyrights] - [Contribution] - [Topics] - [Featured Authors] - [AR List]

22 / Jul / 2023: I uploaded some references here. Consider it as a backup.

14 / Aug / 2023: You can sponsor the project to maintain & continue gathering the resources from here.

Table of Content

Mathematics

Mathematician's Work & Career

  • Pólya, G. How to Solve It.
  • Tao, T. Solving Mathematical Problems. [Online]
  • Hamkins, J. D. Proof and the Art of Mathematics. [Online]
  • Hamkins, J. D. Lectures on the Philosophy of Mathematics. [Online]
  • Paper - Tao, T. What is Good Mathemtatics? [PDF]
  • Paper - Thurston, W. P. On Proof and Progress in Mathematics. [PDF]
  • Paper - Poincaré, H. Intuition and Logic in Mathematics. [Online]
  • Lang, S. The Beauty of Doing Mathematics. [Online]

Alan Beardon, has two books [1],[2] I think it's good, but I cannot officially list it, since I didn't read them yet.

Mathematical Logic

  • Smullyan, R. M. Gödel's Incompleteness Theorems. [Online]
  • Lakatos, I. Proofs and Refutations: The Logic of Mathematical Discovery. [Online][PDF]

Category Theory

  • Smith, P. Category Theory I: Notes Towards a Gentle Introduction. [Online]
  • Smith, P. Category Theory II: More Notes Towards a Gentle Introduction. [Online]
  • Leinster, T. Basic Category Theory. [Online]

Abstract Algebra

  • Fraleigh, John B. A First Course in Abstract Algebra.
  • Paper - In Arabic - AlYasry, A. The Concept of Equivalence and its Classes in Mathematics. [Online]
  • Lang, S. Undergraduate Algebra. [Online]

Number Theory

  • Serre, J. P. A Course in Arithmetic1. [Online]

Analytic Number Theory

  • Lang, S. Elliptic Functions. [Online]

Algebraic Number Theory

  • Lang, S. Algebraic Number Theory. [Online]

Geometric Number Theory

  • MIT Course. Introduction To Arithmetic Geometry. [Online]

Partition Theory

TODO

Ring Theory

  • Kleiner, I. From Numbers to Rings: The Early History of Ring Theory. [Online][PDF]

Mathematical Analysis

  • Ruden, W. Principles of Mathematical Analysis. [Online]
  • Ruden, W. Real and Complex Analysis.
  • Keisler, H. J. Elementary Calculus: An Infinitesimal Approach. [Online & PDF]
  • Lang, S. Undergraduate Analysis. [Online]
  • Lang, S. Real and Functional Analysis. [Online]

Real Analysis

  • Tao, T. Analysis I.
  • Tao, T. Analysis II.
  • Beardon, A. Limits: A New Approach to Real Analysis. [Online]
  • Paper - Tao, T. Compactness and Compactification. [PDF]
  • Paper - Raman-Sundstrom, M. A Pedagogical History of Compactness. [PDF]

Complex Analysis

  • Needham, T. Visual Complex Analysis.
  • Beautiful Paper - Velleman, D. The Fundamental Theorem of Algebra: A Visual Approach. [PDF]
  • Lang, S. Complex Analysis. [Online]

Fourier Analysis

TODO

Functional Analysis

  • Debnath, L. & Mikusinski, P. Introduction to Hilbert Spaces with Applications.
  • Ruden, W. Functional Analysis.

Harmonic Analysis

TODO

Spectral Theory

TODO

Measure Theory

  • Tao, T. An Introduction to Measure Theory. [Online]

Differential Equations

Ordinary Differential Equations (ODE)

TODO

Partial Differential Equations (PDE)

TODO

Geometry

Euclidean and Non-Euclidean Geometry

  • Beardon, A. Algebra and Geometry.

Differential Geometry

  • Abate, M. & Tovena, F. Curves and Surfaces.
  • Tu, W. L. Differential Geometry: Connections, Curvature, and Characteristic Classes. [PDF][Online]
  • Lang, S. Fundamentals of Differential Geometry. [Online]

Topological Geometry

  • Porteous, I. R. Topological Geometry. [Online] [PDF]

Topology

  • Munkres, J. R. Topology.
  • Hatcher, A. Notes on Introductory Point-Set Topology. [Online]
  • Khatchatourian I. MAT327 • TOPOLOGY. [Online]
  • AlYasry, A. Lectures in Advance Topology. [Online]
  • Paper - In Arabic - AlYasry, A. Simple Explanations in Topology and Ideas of High Dimensions. [Online]
  • Armstrong, M. A. Basic Topology. [Online]

Algebraic Topology

  • Hatcher, A. Algebraic Topology. [Online]
  • Paper - In Arabic - AlYasry, A. Homology. [Online]

Knot Theory

  • AlYasry, A. Knot Theory. [Online]

Manifolds

  • Thurston, W. P. Geometry and Topology of Three-manifolds. [Online]
  • Thurston, W. P. How to See 3-Manifolds. [PDF]
  • Paper - Tao, T. Ricci flow. [PDF]
  • Knopf, D. & Chow, B. The Ricci Flow: An Introduction. [PDF][Online]
  • Various Authors. The Ricci Flow: Techniques and Applications: Part I: Geometric Aspects. [PDF][Online]
  • Various Authors. The Ricci Flow: Techniques and Applications: Part II: Analytic Aspects. [PDF][Online]
  • Various Authors. The Ricci Flow: Techniques and Applications: Part III: Geometric-Analytic Aspects. [PDF][Online]
  • Tu, W. L. An Introduction to Manifolds. [PDF][Online]

Riemann Surfaces

  • Beardon, A. A Primer on Riemann Surfaces. [Online]

Graph Theory

  • Wilson, R. J. Introduction to Graph Theory. [Online][PDF]

Theory of Expander Graphs

Surveys
  • Goldreich, O. Basic Facts about Expander Graphs. [Online]
  • Hoory, S. & Linial, N. & Wigderson, A. Expander Graphs and Their Applications. [PDF]

Theory of Hypergraph

TODO

Combinatorics

TODO

Game Theory

TODO

Computer Science

Theoretical Computer Science

  • Sipser, M. Introduction to The Theory of Computation.
  • Arora, S. & Barak, B. Computational Complexity: A Modern Approach. [Online]
  • Barak, B. Introduction to Theoretical Computer Science. [Online]
  • Wigderson, A. Mathematics and Computation: A Theory Revolutionizing Technology and Science. [Online]
  • Hopcroft, J. Introduction to Automata Theory, Languages, and Computation. [Online]
  • Papadimitriou, C. Computational Complexity. [Online]
  • Lewis, C. & Papadimitriou, C. Elements of the Theory of Computation. [Online]
  • Essential Paper - Shannon, C. E. A Mathematical Theory of Communication. [PDF]
  • Essential Paper - Cook, S. A. The Complexity of Theorem-Proving Procedures. [Online][PDF Old][PDF Modern]
  • Essential Paper - Turing, A. On Computable Numbers, with an Application to the Entscheidungs problem. [Online]
  • Paper - Valiant, L. G. Three Problems in Computer Science. [Online]

Randomness and Pseudo-Randomness

Surveys

  • Various Authors. On the works of Avi Wigderson. [Online][PDF]
  • Aaronson, S. P =? NP. [PDF]
  • Vadhan, S. The Unified Theory of Pseudorandomness. [Online][PDF]

Cryptography

  • Goldreich, O. Foundations of Cryptography: A Primer. [Online]
  • Goldreich, O. The Foundations of Cryptography. [Online]
  • Paper - Kleppmann, M. Implementing Curve25519/X25519: A Tutorial on Elliptic Curve Cryptography. [PDF]

Artificial Intelligence

  • Russell, S. & Norving, P. Artificial Intelligence: A Modern Approach. [Online]
  • Paper - Valiant, L. G. A Theory of The Learnable. [PDF]

Algorithms and Data Structures

  • Knuth, D. The Art of Computer Programming. No one completes it, either Donald himself!!

Programming Languages

Erlang Programming Language

  • Armstrong, J. A History of Erlang. [Online]

C Programming Language

  • Kernighan, B. W. & Ritchie, D. M. The C Programming Language.

C++ Programming Language

  • Stroustrup, B. The C++ Programming Language. [Online]

Go Programming Language

  • Donovan, A. & Kernighan, B. The Go Programming Language. [Online]

Compilers

  • Essential Paper - Thompson, K. Reflections on Trusting Trust. [PDF]

Operating Systems

Linux Environment

  • LSB Workgroup, The Linux Foundation. Filesystem Hierarchy Standard. [Online]

Networks

TODO

Security

DISCLAIMER: All resources are listed for learning and white-use purposes. We carry no responsibility regarding any abuse.

  • Erickson, J. Hacking: The Art of Exploitation.

Software Engineering

Design Patterns

  • Gamma, E. & Helm, R. & Johnson, R. & Vlissides, J. 2 Design Patterns: Elements of Reusable Object-Oriented Software. [Online]

Statistics

Causal Inference

  • Pearl, J. Causal Inference in Statistics: A Primer. [Online]
  • Pearl, J. CAUSALITY. [Online]

Medicine

Surgery

  • Schwartz, S. I. Principles of Surgery. [Online]

Gastroenterology

  • Yamada, T. Textbook of Gastroenterology. [Online]

Cardiology

TODO

Interventional Cardiology

TODO

Oncology

TODO

Orthopaedics

TODO

Ophthalmology

TODO

Pediatrics

TODO

Dermatology

TODO

Psychology

Neurophysiology

  • Carpenter, R. & Reddi, B. Neurophysiology: A Conceptual Approach. [Online]

Translations

Mathematical Subjects

Footnotes

  1. The book isn't that easy. Here are some annotations for it [1],[2]. ↩

  2. Also known as "Big Four" or "Gang of Four". ↩