Fast Track
This is a fast-track guide to essential mathematical subjects, providing key resources to accelerate your learning journey. The following books are highly recommended for a comprehensive understanding of each topic.
Calculus
Calculus, Volume 1 and 2 by Tom M. Apostol
(Essential)
A rigorous and comprehensive introduction to calculus and analysis.
Volume 1:
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Volume 2:
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Ordinary Differential Equations
Ordinary Differential Equations by Vladimir I. Arnold
(Essential)
A classic text offering deep insights into the theory of differential equations.
Linear Algebra
Linear Algebra Done Right by Sheldon Axler
(Essential)
An innovative approach to linear algebra focusing on vector spaces and linear maps.
Linear Algebra by Georgi E. Shilov
(Optional but Recommended)
A comprehensive treatment of linear algebra with a balance of theory and applications.
Complex Analysis
Complex Analysis by Lars Ahlfors
Topology and Groupoids
Topology and Groupoids by Ronald Brown
Topology by James Munkres
Algebra
Algebra by Michael Artin
(Essential)
A modern introduction to algebra with a strong emphasis on linear algebra and geometry.
Algebra by Serge Lang
(Optional but Recommended)
An extensive and rigorous text covering all aspects of algebra.
Concrete Mathematics
Concrete Mathematics by Ronald L. Graham, Donald E. Knuth, and Oren Patashnik
(Essential)
A blend of continuous and discrete mathematics focusing on problem-solving techniques.
Probability
A First Course in Probability by Sheldon Ross
Probability and Measure by Patrick Billingsley
Number Theory
Introduction to Number Theory by Richard E. Borcherds
(Essential)
A lecture series providing a comprehensive introduction to number theory.
Lecture 1:
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