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 Arithmetic. [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
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
- 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. 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