MATHEMATICS AND MATHEMATICAL PHYSICS TUTORIALS AND REVIEW ARTICLES

MATHEMATICS AND MATHEMATICAL PHYSICS

(UNDER CONSTRUCTION)

General: REFERENCE: Eric's Treasure Trove (Dictionary of Mathematics);

General: GATEWAYS: Rusin's Mathematical Atlas;

MIT Open Courseware
At the Sign of the Wooden Spoon A large collection of pre-1925 but still valuable mathematics and physical-science problem sets.
Archive of This Week's Finds in Mathematical Physics, 1--50 by John C. Baez [1993-1995] 242 pp.
Mathematical methods of theoretical physics by Karl Svozil [2012/03] 222 pp.
Cut the Knot: Interactive Mathematics Miscellany and Puzzles by A. Bogomolny [2017]
Tunneling Through the Math Barrier: The Fledgling Physics Student's Field Guide to Essential Mathematics by William J. Meese [2018/05] 187 pp. For students entering university.
Elements of Mathematics in Problems: From Olympiads and Mathematical Circles to Profession edited by A. Skopenkov et al. [2018] Problem collection. 592 pp. In Russian.

MATHEMATICS EDUCATION:

On the Study and Difficulties of Mathematics by Augustus De Morgan [Chicago: Open Court, 1898]
Mathematical education by W. P. Thurston [1990/09]
Reforms of the [Chinese] university mathematics education for non-mathematical specialties by S. Xiao [1995]
From art to geometry: Æsthetic and beauty in the learning process by N. Pastena et al. [2015/01]
Mathematics education in Russia and mathematics circles by D. G. Bartolomé [2015/12]
From Mathematics and Education, to Mathematics Education by F. Furinghetti et al. [2016/02]
History of mathematics education: Italy by M. Menghini [2016/03]
Cut the Knot: Interactive Mathematics Miscellany and Puzzles by A. Bogomolny [2017]
Kolmogorov reform of mathematical education, 1970--1980 by Yu. A. Neretin [2019/11]
On teaching mathematics to gifted students by A. Shukla [2019/10]
The human brain and mathematics: Recent research and educational questions by G. E. Davis and M. A. McGowen [2021/09]
Mathematics and mathematics education in the 21st century by A. Borovik et al. [2022/01]

WRITING:

A Primer of Mathematical Writing by Steven G. Krantz [2016/12]
How to write a contemporary scientific article by V. M. Krasnov [2022/03]

Algebra
Algebraic Geometry
Analysis
Complexity
Computation
Cosmology
Discrete Mathematics;
Field Theory (General)
Foundations of Physics
General Relativity
Functional Analysis
Geometry and Topology
Group Theory and Abstract Algebra
Knots and Braids
Non-Standard Analysis
Special Functions
Statistical Mechanics and Thermodynamics
Supersymmetry and String Theory

Aspects: FOUNDATIONS OF ARITHMETIC:

Gödel for Goldilocks: A Rigorous, Streamlined Proof of Gödel's First Incompleteness Theorem, Requiring Minimal Background by Dan Gusfield [2014/09]
Current research on Gödel's incompleteness theorems by Y. Cheng [2020/09]
Goedel's incompleteness theorem by S. Batzoglou [2021/12]
Sixty-three years of the MacDowell--Specker theorem by R. Kossak [2022/08]
Independence of the Continuum Hypothesis: An Intuitive Introduction by S. Batzoglou [2022/08]
An introduction to mathematical logic by A. Freund [2023/10] Short textbook.

Aspects: PROOF THEORY:

Developments in Formal Proofs by Thomas C. Hales [2014/06]

Aspects: SEQUENCES AND SERIES:

Convergence of sequences: A survey by B. Franci and S. Grammatico [2021/11]

Re: COMPUTER METHODS:

A Survey on Retrieval of Mathematical Knowledge by Ferruccio Guidi and C. Sacerdoti Coen [2015/05]

To contribute to this page, write Norman Redington, redingtn@mit.edu

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