Recommended Books and Textbooks

Personal Recommendations

Calculus of Several Variables (Serge Lang) – Written by a Yale professor, this is a well-written introductory multivariable calculus book for those just finishing calculus II or AP Calculus BC. This book takes a more pure math based approach of teaching and starts to expose the reader to proof-based concepts. Buy it now!

Linear Algebra Done Right (Sheldon Axler) – Being the perfect textbook for the second course of linear algebra, it is targeted towards undergraduate or graduate math majors in university or college. In a novel approach, this textbook helps the reader understand the structure of linear operators on finite-dimensional vector spaces which is the main goal of linear algebra. This San Francisco State University professor drives concepts and simplifies proof to the best of his abilities. Buy it now!

Challenge and Thrill of Pre-College Mathematics (V Krishnamurthy, C R Pranesachar) – The book does a very good job in allowing high school students to transition from school to college level mathematics seamlessly and building upon their understanding of different geometrical, trigonometric and algebraic concepts. What makes the book distinct is its detailed sections on geometry with some challenging problems. Employing distinct approaches to problems, the book is recommended for anyone wishing to explore fundamentals of geometry and related problems in depth. Buy it now!

Fundamentals of Differential Equations (R. Kent Nagle, Edward B. Saff, Arthur David S.) by Pearson – This book provides depth explanation from the introduction of differential to partial differential equations. It starts off by the basic theory, methodology, methods, and relevant applications of differential equations which are beneficial in the field of science and engineering. The perfect book for high school students learning to excel differentials at school. Buy it now!

How to Solve it (George Polya, New Foreword by John H. Conway) – Known as the father of problem solving, this Stanford professor researched complex mathematical physics and many other mathematical topics. His research includes number theory, numerical analysis, probability theory, combinatorics, geometry, and other complex analysis. His published papers of research and theory provides intense and deep results of the study of integral functions. Buy it now!

Advanced Calculus (Lynn Harold Loomis, Shlomo Sternberg) – Written by two professors from Harvard University who taught in the 1960s, Advanced Calculus remains a vital component of the Math 55 class taught at Harvard. Math 55 is known as one of the most rigorous undergraduate math courses in the United States and lasts two semesters. If interested in this textbook, it is recommended that the reader has knowledge about limit and continuity type arguments along with partial derivatives. Buy it now!

General Lists

List of Math Textbooks – Includes topics from basic algebra to topology, number theory, mathematical physics, and pretty much every other math topic.

Introduction to Probability by Charles Grinstead and J. Laurie Snell – This textbook teaches you about probability and and random variables. Before jumping into this book, you should already have a good understanding of multivariable calculus. In this book, you’ll learn about binomial, distribution functions, Poisson distribution, geometric, and hypergeometric. There’s problem sets available in the book for practice as well.