**Best Reference Books on Mathematics**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Mathematics Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Mathematics below.

## 1. Introductory Mathematics

1."Introductory Mathematics: Algebra and Analysis (Springer Undergraduate Mathematics Series)" by Geoffrey C Smith
“Introductory Mathematics: Algebra and Analysis (Springer Undergraduate Mathematics Series)” Book Review: This book is written for students studying mathematical sciences in college. It covers various topics like sets, functions, relations, complex numbers, vectors, matrices, and group theory. The book also includes chapters on epsilon-delta technology, continuity, and functions. It aims to bridge the gap between high school and university curricula. To help with understanding challenging concepts, the book provides numerous exercises for practice. It is a helpful resource for students looking for a comprehensive introduction to these mathematical topics.
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2."Introductory Real Analysis (Dover Books on Mathematics)" by A N Kolmogorov and S V Fomin
“Introductory Real Analysis (Dover Books on Mathematics)” Book Review: This revised book serves as an introduction to real and functional analysis, starting with the fundamental concepts and basic principles of set theory, metric spaces, topological spaces, and linear spaces. It then delves into a thorough explanation of topics such as linear operators, continuous linear functionals, conjugate space, weak topology and weak convergence, generalized functions, linear operators, inverse operators, and continuous operators. The final section of the book covers integration, differentiation, Lebesgue integral, Fubini’s theorem, and Stieltjes integral. It is a self-contained and reader-friendly text that includes multiple examples and problem sets.
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3."New Guided Mathematics Introductory Book" by Abhijit Mukherjea
“New Guided Mathematics Introductory Book” Book Review: This book links various mathematical concepts to real-world situations, introducing readers to the applications of mathematics. The chapters are well-structured, comprehensive, and easy-to-understand, with numerous examples, exercises, and questions provided throughout. Each chapter concludes with revision exercises for self-study and self-assessment. The book also introduces several new topics and emphasizes mental mathematics. It includes worksheets and comprehensive test papers, making it suitable from an examination point of view.
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4."Probability Theory: A Concise Course (Dover Books on Mathematics)" by Iu A Rozanov and Richard A Silverman
“Probability Theory: A Concise Course (Dover Books on Mathematics)” Book Review: This book aims to introduce readers to modern probability theory. It begins with a clear explanation of fundamental concepts of probability, including combination of events, dependent events, and random variables. The book then progresses to cover Bernoulli trials and the De Moivre-Laplace theorem, as well as three probability distributions: binomial, Poisson, and Gaussian. The final section focuses on limit theorems, Markov chains, and continuous Markov processes. In addition, the book includes chapters on information theory, game theory, branching processes, and problems of optimal control. To aid readers, the book offers several relevant problems along with hints and answers. This text will be useful for natural scientists and mathematicians alike.
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5."Introductory Mathematics for Engineering Applications" by Kuldip S Rattan and Nathan W Klingbeil
“Introductory Mathematics for Engineering Applications” Book Review: This book is a valuable resource for engineering students who are studying various aspects of mathematics. The chapters in this book are written with an engineering perspective and provide comprehensive explanations of topics such as straight lines, quadratic equations, trigonometry, two-dimensional vectors, complex numbers, sinusoids, derivatives, integrals, and differential equations. It is a well-written and self-contained work that clearly presents concepts and their applications. The book features numerous diagrams and figures to aid in understanding the material.
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6."Introductory Functional Analysis with Applications" by Erwin Kreyszig
“Introductory Functional Analysis with Applications” Book Review: This book aims to introduce practical applications of functional analysis. It explains the concepts, principles, methods, and major applications of functional analysis in a clear manner. The chapters cover important topics such as metric spaces, normal spaces, branched spaces, inner product spaces, Hilbert spaces, Banach fixed point theorem, approximation, spectral theory, and linear operations. The book effectively explains the content through various examples. The chapters on Hilbert space theory and Banach spaces include several worked problems. It will be beneficial for students and professionals in natural sciences and mathematics.
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7."Analysis for Applied Mathematics (Graduate Texts in Mathematics)" by Ward Cheney
“Analysis for Applied Mathematics (Graduate Texts in Mathematics)” Book Review: This book gives you the tools and knowledge you need for applied mathematics. It explains practical methods for solving problems like differential equations, boundary value problems, and integral equations. It also teaches you programmatic approaches to tackle difficult equations, such as the Galerkin method, the method of iteration, Newton’s method, projection techniques, and homotopy methods. With this book, you’ll learn how to solve challenging mathematical problems using different techniques and approaches.
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## 2. Advanced Mathematics

1."Advance maths for General Competitions" by Rakesh Yadav
“Advance maths for General Competitions” Book Review: This book is made for the staff selection commission examination. It covers topics like indices & surds, linear equations in two variables, graphic representation of straight lines, coordinate geometry, polynomials, and more. It has many questions on advanced math for the SSC combined graduate level, along with solutions. This book is also useful for other exams like SSC CPO, Delhi Police, FCI, MTS, CHSL, and bank examinations. It provides comprehensive preparation material for various SSC exams and other related tests.
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2."Advanced Problems in Mathematics for JEE Main and Advanced" by Vikas Gupta | |

3."Skills In Mathematics - DIFFERENTIAL CALCULUS for JEE Main and Advanced" by Amit M Agarwal
“Skills In Mathematics – DIFFERENTIAL CALCULUS for JEE Main and Advanced” Book Review: This book is for students preparing for exams like JEE Main and Advanced. It is divided into seven chapters that cover important mathematical topics such as differentiation, functions, limits, graphical transformations, and more. The book includes various question types like single correct answers, multiple correct answers, matching types, and integer answer types, with complete solutions. It also includes previous years’ questions from exams held between 2010 and 2015. This book is a helpful resource for students aiming to excel in JEE exams by providing comprehensive coverage of key concepts and practice questions.
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4."Advances in Mathematics: Scientific Developments and Engineering Applications" by S Lakshmi and T Chandrakalarani | |

5."Higher Mathematics in Problems and Exercises" by P E Danko | |

6."Methods in the Theory of Hereditarily Indecomposable Banach Spaces (Memoirs of the American Mathematical Society)" by Spiros Argyros and Andreas Tolias
“Methods in the Theory of Hereditarily Indecomposable Banach Spaces (Memoirs of the American Mathematical Society)” Book Review: This book is about creating special types of Banach spaces called hereditarily indecomposable Banach spaces. It covers important topics such as the conjugate operator of the quotient map, the weakly compact operator, and the space of bounded linear operators. The methods used to construct these spaces are explained in detail. This book is recommended for advanced mathematics students who want to explore these advanced concepts.
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7."Four Non-Linear Problems on Normed Spaces - Volume I" by Francisco Garcia Pacheco
“Four Non-Linear Problems on Normed Spaces – Volume I” Book Review: This book discusses 4 non-linear problems on normal spaces. The problems included are the lineability problem for functionals (Aron and Gurariy, 2004) and the nowhere density problem for functionals (Enflo, 2005). Other 2 problems mentioned are the minimum-norm problem for translations (Aizpuru and Garcia-Pacheco, 2003) and the banach-mazur conjecture for rotations (Banach and Mazur, 1932). All the problems are discussed in detail and proper manner. This book can be referred to by advanced applied mathematics students.
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8."Encyclopedia of Applied and Computational Mathematics" by Björn Engquist
“Encyclopedia of Applied and Computational Mathematics” Book Review: EACM is a comprehensive reference book that focuses on applied and computational mathematics. It highlights the growing significance of computational methods across various fields of application. EACM emphasizes the strong relationship between applied mathematics and important scientific fields like physics, chemistry, biology, and computer science. It also includes unique areas like ocean-atmospheric science. Additionally, EACM recognizes the valuable contributions of mathematics to modern engineering and technology.
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9."Introduction to Mathematical Logic" by E Mendelson
“Introduction to Mathematical Logic” Book Review: This book delves into important topics in mathematical logic, including propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. It also includes a section dedicated to non-standard models of number theory. The book extensively discusses significant results from renowned mathematicians such as Godel, Church, Kleene, Rosser, and Turing. It is recommended for students and professionals who already possess a foundational understanding of abstract mathematical thinking.
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10."Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics)" by Randall J LeVeque
“Finite Volume Methods for Hyperbolic Problems (Cambridge Texts in Applied Mathematics)” Book Review: This book provides a comprehensive survey of hyperbolic partial differential equations, covering key topics such as wave propagation, the mathematical theory of hyperbolic problems, Godunov’s method, and shock waves. The material is presented clearly with the aid of high-quality images, while numerous examples and practice problems are included to aid student learning. This resource is ideal for students of applied mathematics seeking to deepen their understanding of hyperbolic partial differential equations.
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11."Basic Training in Mathematics: A Fitness Program for Science Students" by R Shankar
“Basic Training in Mathematics: A Fitness Program for Science Students” Book Review: This is a helpful book for science students looking to enhance their mathematical skills. The book covers various chapters, including numbers and algebra, functions, trigonometry, calculus, vectors, and matrices. It presents mathematical concepts in a clear and concise manner, making it easy for readers to understand. The book provides numerous exercises and problems to practice, allowing students to reinforce their learning and improve their mathematical abilities. Overall, it is a valuable resource for science students aiming to strengthen their foundation in mathematics.
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12."Tensors, Differential Forms and Variational Principles (Dover Books on Mathematics)" by David Lovelock and Hanno Rund
“Tensors, Differential Forms and Variational Principles (Dover Books on Mathematics)” Book Review: This book provides a comprehensive overview of tensor analysis, the calculus of variations, and exterior differential forms. The text offers detailed explanations of the calculus of exterior differential forms and the calculus of variations, including a thorough exploration of the interaction between the two. Analytical techniques are emphasized throughout, with a variety of problems included to aid student understanding. These problems range from simple manipulative exercises to more technically challenging problems, offering a comprehensive preparation for a range of exercises. Overall, this resource is an excellent choice for students seeking to deepen their knowledge of these complex topics.
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13."Functions of One Complex Variable II (Graduate Texts in Mathematics)" by John B Conway
“Functions of One Complex Variable II (Graduate Texts in Mathematics)” Book Review: This book offers an extensive collection of problems related to the theory of functions of one complex variable. The text provides detailed explanations of several key topics, including geometric function theory, potential theory in a plane, conformal equivalence for simply connected and finitely connected regions. It also covers other important subjects such as analytic covering maps, de Branges’ proof of the Bieberbach conjecture, harmonic functions, Hardy spaces on the disk, and potential theory in the plane. Intended primarily for graduate students, this resource is an excellent choice for those seeking to deepen their understanding of complex analysis.
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14."Elements of Advanced Mathematical Analysis for Physics and Engineering" by Filippo Gazzola and Alberto Ferrero
“Elements of Advanced Mathematical Analysis for Physics and Engineering” Book Review: This book provides a comprehensive overview of the essential topics required to attain knowledge in advanced analysis. While many texts cover similar material, this book offers a unique advantage due to the diverse expertise of its three authors. Alberto Ferrero is a researcher in Mathematical Analysis at the Università del Piemonte Orientale, with a degree in Mathematics from 2000. Filippo Gazzola, a full professor in Mathematical Analysis at the Politecnico di Milano, earned his degree in Mathematics in 1987. Maurizio Zanotti, with a degree in Mechanical Engineering from 2004, is a structural and machine designer and lecturer professor in Mathematical Analysis at the Politecnico di Milano. The combination of their skills and expertise allowed the authors to create a valuable resource for those seeking to deepen their understanding of advanced analysis.
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15."The Steiner Tree Problem: A Tour through Graphs, Algorithms, and Complexity (Advanced Lectures in Mathematics)" by Angelika Steger and Hans Jürgen Prömel
“The Steiner Tree Problem: A Tour through Graphs, Algorithms, and Complexity (Advanced Lectures in Mathematics)” Book Review: This is an insightful book that explores the fascinating world of the Steiner Tree problem. The book delves into various topics, including graph theory, algorithms, and computational complexity. It offers a comprehensive understanding of the problem, its applications, and the mathematical techniques used to solve it. With clear explanations and illustrative examples, the authors guide readers through the intricacies of this challenging problem. This book is highly recommended for mathematics enthusiasts, researchers, and students interested in graph theory and algorithmic problem-solving.
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16."Tensor Analysis on Manifolds (Dover Books on Mathematics)" by Richard L Bishop
“Tensor Analysis on Manifolds (Dover Books on Mathematics)” Book Review: This book is specifically designed for advanced undergraduate and graduate students in engineering, physics, and applied mathematics. It delves into the general theory of relativity and its application to a broad spectrum of mathematical and physical problems. The book covers topics such as tensor analysis, notation conventions, index manipulation, advanced calculus, set theory, and topology. The latter half of the book concentrates on function theory, algebraic aspects, manifolds, and integration theory. Additionally, the book features numerous worked examples and exercises throughout the text to aid in comprehension.
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17."Mathematics for Physicists (Dover Books on Physics)" by Philippe Dennery and Andre Krzywicki
“Mathematics for Physicists (Dover Books on Physics)” Book Review: This book is for students studying advanced mathematics at the university level. It is also useful for students studying physics and engineering. The book covers important topics such as analytic functions, vector spaces, and linear operators. It also includes topics like Fourier series and transforms, distributions, differential equations, and special functions. The book uses graphs and diagrams to help explain the concepts. It also provides worked examples and exercises to practice the material. This book is a valuable resource for students looking to deepen their understanding of these mathematical subjects.
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18."Nonlinear Smoothing and Multiresolution Analysis (International Series of Numerical Mathematics)" by Carl Rohwer
“Nonlinear Smoothing and Multiresolution Analysis (International Series of Numerical Mathematics)” Book Review: This book is a valuable resource for anyone interested in nonlinear smoothing and multiresolution analysis. It is part of the International Series of Numerical Mathematics. The book covers important topics such as signal processing, image reconstruction, and data analysis. It explains various techniques for smoothing and analyzing data, including wavelet analysis and multiresolution methods. The chapters provide a comprehensive and detailed explanation of these topics, accompanied by helpful examples and illustrations. Whether you are a researcher or a student, this book will enhance your understanding of nonlinear smoothing and multiresolution analysis.
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