Awesome Math

English quick reference for the Russian awesome math list.

Russian version

Contents

• Math Links
  • Resources
  • Communities
  • VK Groups
  • Telegram Channels
  • Tools
  • Popular Mathematics
  • Lists of Lists
• Mathematics for Beginners
  • General Courses
  • Algebra
  • Geometry
  • Trigonometry
  • Introductory Calculus
• Core Mathematics
  • General Algebra
  • Linear Algebra
  • Mathematical Analysis
  • Differential Equations
  • Calculus of Variations
  • Topology
  • Logic
  • Functional Analysis
• Advanced Courses
  • Mathematical Analysis
  • Differential Equations
  • Category Theory
  • Differential Geometry
  • Algebraic Geometry
  • Topology
• Interesting Books
• History of Mathematics
• Physics
  • General Physics
  • Theoretical Physics

Math Links

Resources

• Library Genesis - Large online library with many books from this list.
• Kolxo3 Library - Electronic library focused on science literature.
• Kvant Library - Books from the physics and mathematics editorial office of Nauka.
• Mathprofi.net - Accessible higher mathematics through roughly the second university year.
• Math Stack Exchange - Mathematics Q&A.
• MathOverflow - Research-level mathematics discussion.
• Freely available books - Free books from MCCME.

Communities

• MSU Faculty of Mechanics and Mathematics Telegram chat - Discuss mathematics and suggestions for this list.
• Infernal Math Telegram chat - Discussion and problem solving.
• dxdy.ru - Scientific forum with a large mathematics community.
• /math/ - Mathematics board.

VK Groups

• Matematura: MCCME books
• Hedgehog in Analysis - Interesting stories and help with problems.

Telegram Channels

• MCCME
• Geometry Channel

Tools

• WolframAlpha - Problem solver for early university courses with many math examples.

Popular Mathematics

• Mathematical Etudes

Lists of Lists

• Math Textbook Recommendations
• The MAA Basic Library List
• How to Become a Pure Mathematician
• Chicago undergraduate mathematics bibliography
• NMU Literature
• HSE Faculty of Mathematics recommendations

Mathematics for Beginners

General Courses

• Courant and Robbins: What Is Mathematics?
• M. I. Skanavi: Elementary Mathematics.
• G. V. Dorofeev, M. K. Potapov, N. Kh. Rozov: mathematics for university entrance exams.
• Oleg Ivanov: Elementary Mathematics.
• Felix Klein: Elementary Mathematics from a Higher Standpoint.

Algebra

• I. M. Gelfand, A. Shen: Algebra.
• S. B. Gashkov: Modern Elementary Algebra.

Geometry

• A. D. Alexandrov, A. L. Werner, V. I. Ryzhik: Geometry for grades 10-11.
• Ya. P. Ponarin: Elementary Geometry, two volumes.
• A. Yu. Kalinin, D. A. Tereshin: Geometry, grades 10-11.
• D. Hilbert, S. Cohn-Vossen: Geometry and the Imagination.
• A. P. Kiselev: Geometry.

Trigonometry

• I. M. Gelfand, S. M. Lvovsky, A. L. Toom: Trigonometry.

Introductory Calculus

• B. M. Davidovich: Mathematical Analysis at School 57.
• L. S. Pontryagin: Introduction to Higher Mathematics, four books.
• Ya. B. Zeldovich: Higher Mathematics for Beginners and Its Applications to Physics.

Core Mathematics

General Algebra

• E. B. Vinberg: A Course in Algebra.
• A. I. Kostrikin: Introduction to Algebra.
• A. G. Kurosh: Higher Algebra, Lectures on General Algebra, Group Theory.
• M. Atiyah, I. Macdonald: Introduction to Commutative Algebra.
• A. L. Gorodentsev: Algebra.
• I. R. Shafarevich: Basic Notions of Algebra.
• E. Connell: Elements of Abstract and Linear Algebra.
• P. Grillet: Abstract Algebra.
• J. Rotman: Advanced Modern Algebra.
• M. Artin: Algebra.
• I. Herstein: Topics in Algebra.
• P. Aluffi: Algebra: Chapter 0.

Linear Algebra

• V. A. Ilyin, E. G. Poznyak: Linear Algebra.
• D. V. Beklemishev: A Course in Analytic Geometry and Linear Algebra.
• I. M. Gelfand: Lectures on Linear Algebra.
• A. I. Maltsev: Foundations of Linear Algebra.
• A. I. Kostrikin, Yu. I. Manin: Linear Algebra and Geometry.
• S. Axler: Linear Algebra Done Right.
• S. Treil: Linear Algebra Done Wrong.
• G. Shilov: Linear Algebra.
• K. Hoffman, R. Kunze: Linear Algebra.
• P. Halmos: Finite-Dimensional Vector Spaces.
• P. Peterson: Linear Algebra.
• S. Roman: Advanced Linear Algebra.

Mathematical Analysis

• T. Tao: Real Analysis.
• C. Pugh: Real Mathematical Analysis.
• W. Rudin: Principles of Mathematical Analysis.
• V. A. Zorich: Mathematical Analysis.
• R. Courant: Differential and Integral Calculus.
• G. M. Fichtenholz: A Course of Differential and Integral Calculus.
• S. M. Lvovsky: Lectures on Mathematical Analysis.
• A. Ya. Khinchin: Eight Lectures on Mathematical Analysis.
• Hardy, Littlewood, Polya: Inequalities.
• N. N. Lebedev: Special Functions and Their Applications.
• G. P. Tolstov: Fourier Series.

Differential Equations

• V. I. Arnold: Ordinary Differential Equations.
• I. G. Petrovsky: Lectures on Ordinary Differential Equations.
• S. Farlow: Partial Differential Equations for Scientists and Engineers.

Calculus of Variations

• I. M. Gelfand, S. V. Fomin: Calculus of Variations.

Topology

• Yu. G. Borisovich, N. M. Bliznyakov, Ya. A. Izrailevich, T. N. Fomenko: Introduction to Topology.
• V. Runde: A Taste of Topology.
• J. Strom: Modern Classical Homotopy Theory.
• T. Dieck: Algebraic Topology.
• M. Crossley: Essential Topology.
• Milnor and Wallace: Differential Topology.

Logic

• S. C. Kleene: Introduction to Metamathematics, Mathematical Logic.
• R. Stoll: Sets, Logic, and Axiomatic Theories.

Functional Analysis

• A. A. Kirillov, A. D. Gvishiani: Theorems and Problems in Functional Analysis.
• A. N. Kolmogorov, S. V. Fomin: Elements of the Theory of Functions and Functional Analysis.

Advanced Courses

Advanced Mathematical Analysis

• A. I. Markushevich: Theory of Functions of a Complex Variable.
• S. Ramanan: Global Calculus.
• H. Amann, J. Escher: Analysis.
• W. Fischer, I. Lieb: A Course in Complex Analysis.

Advanced Differential Equations

• V. I. Arnold: advanced chapters on ordinary differential equations.

Category Theory

• S. Mac Lane: Categories for the Working Mathematician.
• R. Goldblatt: Topoi: The Categorial Analysis of Logic.

Differential Geometry

• B. A. Dubrovin, S. P. Novikov, A. T. Fomenko: Modern Geometry.
• M. Spivak: A Comprehensive Introduction to Differential Geometry.
• K. Nomizu: Foundations of Differential Geometry.
• J. Lee: Manifolds and Differential Geometry.
• L. Nicolaescu: Lectures on the Geometry of Manifolds.
• P. Michor: Topics in Differential Geometry.

Algebraic Geometry

• I. R. Shafarevich: Basic Algebraic Geometry.
• D. Mumford: The Red Book of Varieties and Schemes.
• V. V. Ostrik, M. A. Tsfasman: algebraic geometry and number theory.
• V. I. Arnold: Real Algebraic Geometry.
• Yu. I. Manin: introduction to schemes and quantum groups.
• R. Vakil: Foundations of Algebraic Geometry.
• S. Bosch: Algebraic Geometry and Commutative Algebra.
• U. Gortz, T. Wedhorn: Algebraic Geometry.
• E. Harris: The Geometry of Schemes.

Advanced Topology

• A. T. Fomenko, D. B. Fuks: A Course in Homotopic Topology.
• A. Hatcher: Algebraic Topology.
• J. Munkres: Topology.

Interesting Books

• Manga Guide to… series.
• N. A. Vavilov: Concrete Group Theory I: Basic Concepts.
• P. S. Alexandrov: Introduction to Group Theory.
• V. B. Alekseev: Abel’s Theorem in Problems and Solutions.
• N. Ya. Vilenkin: Stories About Sets.
• M. M. Postnikov: Fermat’s Theorem: Introduction to Algebraic Number Theory.
• N. Steenrod: The Topology of Fibre Bundles.
• A. Ya. Khinchin: Three Pearls of Number Theory.
• O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov: Elementary Topology.
• Ya. P. Ponarin: Algebra of Complex Numbers in Geometric Problems.
• A. A. Zaslavsky: Geometric Transformations.
• V. Akopyan, A. A. Zaslavsky: geometric properties of conic sections.
• V. I. Arnold: geometry of complex numbers, quaternions, and spins.
• V. V. Prasolov: Lobachevsky Geometry.
• D. V. Anosov: differential equations and visual methods.
• V. V. Prasolov: Intuitive Topology.
• D. V. Anosov: From Newton to Kepler.
• G. Polya: Mathematical Discovery.
• L. Carroll: The Game of Logic.
• G. Polya: How to Solve It.
• O. Ya. Viro, D. B. Fuks: introduction to homotopy theory, homology, and cohomology.
• S. M. Gusein-Zade: The Selective Bride.
• A. Ostermann, G. Wanner: Geometry by Its History.
• T. Sundstrom: Mathematical Reasoning: Writing and Proof.
• D. Dummit, R. Foote: Abstract Algebra.

History of Mathematics

• M. Kline: Mathematics: The Search for Truth, Mathematics: The Loss of Certainty.
• A. N. Kolmogorov: Mathematics in Its Historical Development.
• I. K. Shtokalo: History of Russian Mathematics.
• B. L. van der Waerden: Science Awakening.

Physics

General Physics

• Introductory course: The Feynman Lectures on Physics; Landsberg’s Elementary Textbook of Physics.
• Advanced course: D. V. Sivukhin, Berkeley Physics Course, I. V. Savelyev, A. N. Matveev.
• Electricity: I. E. Tamm, Fundamentals of the Theory of Electricity.

Theoretical Physics

• General reference: Landau and Lifshitz, all volumes; George Joos and Ira Freeman, Theoretical Physics.
• Classical mechanics: V. I. Arnold, Mathematical Methods of Classical Mechanics; Lanczos, The Variational Principles of Mechanics.
• Electrodynamics: Landau and Lifshitz, volume 2; Jackson, Classical Electrodynamics.
• Quantum mechanics: Dirac, The Principles of Quantum Mechanics; Feynman and Hibbs, Quantum Mechanics and Path Integrals; Landau and Lifshitz, volume 3.
• Quantum field theory: Bogoliubov and Shirkov, Peskin and Schroeder, Weinberg.
• Statistical physics: Fermi, Thermodynamics; Landau and Lifshitz, volume 5; Huang.
• Solid-state physics: Ashcroft and Mermin; Kittel.
• Hydrodynamics: L. G. Loitsyansky; Landau and Lifshitz, volume 6.