**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: The book is basically for the under-graduating students of mathematical sciences. The topics like sets, functions and relations, induction and contradiction, complex numbers, vectors, matrices, and group theory are discussed in detail. The chapters based on epsilon-delta technology as well as continuity and functions are included in this text. It will act as a link between school and university curriculums. For better explanation of difficult and complex topics, the book consists of several exercises.
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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: The book is an updated and revised piece of work introducing real and functional analysis. It begins with the fundamental concepts and basic principles in set theory, metric spaces, topological spaces, and linear spaces. Moving on, the topics like linear operators, continuous linear functionals, conjugate space, weak topology and weak convergence, generalized functions, linear operators, inverse operators, and continuous operators are thoroughly explained. The final section of the book features integration, differentiation, Lebesque integral, Fubini’s theorem, and Stieltjes integral. The book is a self-contained and reader friendly text, enhanced with several examples and problem-sets.
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3."New Guided Mathematics Introductory Book" by Abhijit Mukherjea
“New Guided Mathematics Introductory Book” Book Review: The book explains various concepts of mathematics by linking them to real-world situations, and hence introduces the applications of mathematics. The chapters of this book are well-structured, comprehensive, and easy-to-understand. Several exercises, examples, and questions are mentioned thorough-out the chapter. Each chapter ends with revision exercises for self-study and self-assessment of the readers. The book introduces several new topics and lays an emphasis on mental mathematics. This textbook will be suitable from the examination point-of-view as it contains worksheets and comprehensive test papers.
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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: The book aims at introducing the concept of modern probability theory. The book begins with a clear explanation of fundamental concepts of probability along with a combination of events, dependent events, and random variables. Moving further to Bernoulli trials and the De Moivre-Laplace theorem, three probability distributions namely, binomial, Poisson, and Gaussian are discussed. The final section of this book presents limit theorems, Markov chains, and continuous Markov processes. The chapters based on information theory, game theory, branching processes, and problems of optimal control are also included. The book is supported with several relevant problems along with their hints and answers. It will be useful for natural scientists and mathematicians.
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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: The book will be an excellent resource for the engineering students dealing with various aspects of mathematics. The chapters of this book are written from the perspective of engineering courses and thoroughly explain topics like straight lines, quadratics equations, trigonometry, two-dimensional vectors, complex numbers, sinusoids, derivatives, integrals, and differential equations. The book is a well-written and self-contained piece of writing. The concepts featured in this book are explained with the help of their applications. The book is illustrated with several diagrams and figures.
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6."Introductory Functional Analysis with Applications" by Erwin Kreyszig
“Introductory Functional Analysis with Applications” Book Review: The book aims at introducing applications of functional analysis from a practical point-of-view. The concepts, principles, methods, and major applications of functional analysis are clearly mentioned. The chapters of this book cover all the major topics related to metric spaces, normal spaces, branched spaces, inner product spaces, Hilbert spaces, Banach fixed point theorem, approximation, spectral theory, and linear operations. The content of this book is explained efficiently thorough various examples. The chapters based on Hilbert space theory and Banach spaces contain several worked problems. The book will be beneficial for the students and professionals of 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 provides the analytical tools, concepts, and viewpoints required for modern applied mathematics. It explains different practical methods for solving problems such as differential equations, boundary value problems, and integral equations. The book also gives programmatic approaches to difficult equations including the Galerkin method, the method of iteration, Newton’s method, projection techniques, and homotopy methods.
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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 designed for the staff selection commission examination. The chapters which are covered in this book are indices & surds, linear equations in two variables, graphic representation of straight lines, coordinate geometry, polynomials etc.This book contains various chapterwise questions on advanced maths for ssc combined graduate level with solution. This book is also helpful for ssc cpo, delhi police, fci, mts, chsl and other ssc, bank examinations.
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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: It is designed for the students preparing for the examinations like JEE Main and Advanced. This book is divided into seven chapters covering essential mathematical tools, differentiation, functions, graphical transformations, limits, continuity & differentiability, dy/dx as a rate measurer & tangents, normals and monotonicity, maxima & minima. This book contains the single correct answers, multiple correct answers, multiple correct options, passage-based, matching types, assertion & reason, integer answer types – with complete solutions. Previous years questions from last six years examinations (2010-2015) have also been provided at the end of the book.
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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 includes general methods of producing hereditarily indecomposable banach spaces. Important chapters included are conjugate operator of the quotient map, weakly compact operator and the space of bounded linear operators. All the methods are discussed in detail. This book is suitable for advanced mathematics students.
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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 systematic reference work covering the broad field of applied and computational mathematics. It represents the present and ever-increasing importance of computational methods in all fields of application. EACM emphasizes the close connection between applied mathematics and major fields of science, such as physics, chemistry, biology, and computer science, as well as unique fields such as ocean-atmospheric science. Also, mathematical input into modern engineering and technology is another main component of EACM.
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9."Introduction to Mathematical Logic" by E Mendelson
“Introduction to Mathematical Logic” Book Review: This book explores the principal topics of mathematical logic – propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. A separate section covers all the basic ideas and results about non-standard models of number theory. Besides these, the major results of Godel, Church, Kleene, Rosser, and Turing are also discussed in great detail. This book is suitable for students and professionals who have prerequisite knowledge on 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 is an overview of hyperbolic partial differential equations. The main chapters included are wave propagation, the mathematical theory of hyperbolic problems, Godunov’s method and shock waves. High resolution images are given for clear explanation. Plenty of examples and problems are provided for student’s practice. This book can be used by students studying applied mathematics.
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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 book bridges the gap between the mathematics needed for upper-level courses in the physical sciences and the knowledge of incoming students. It provides a good opportunity for students to strengthen their mathematical skills by solving various problems in differential calculus. It is written in a simple and student-friendly manner.
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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 explains tensor analysis and calculus of variations and exterior differential forms thoroughly. It provides a detailed account of the calculus of exterior differential forms as well as the calculus of variations. The book also demonstrates in-depth interaction between the calculus of variations and the concept of invariance. It highlights analytical techniques and contains a set of problems for better understanding of concepts. The book covers problems ranging from simple manipulative problems to technically more difficult to prepare students for different kinds of exercises.
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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 addresses a large number of problems on the subject of theory of functions of one complex variable. Several topics like geometric function theory, potential theory in a plane, conformal equivalence for simply connected regions, conformal equivalence for finitely connected regions explained in detail. It also covers topics like analytic covering maps, de Branges’ proof of the Bieberbach conjecture, harmonic functions, Hardy spaces on the disk, potential theory in the plane etc are covered extensively in the book. It is mainly written for graduate students.
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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 aims to deal with the main topics that are necessary to achieve such knowledge. Still, this is the goal of many other texts in advanced analysis; and then, what would be a good reason to read or to consult this book? In order to answer this question, let us introduce the three Authors. Alberto Ferrero got his degree in Mathematics in 2000 and presently he is researcher in Mathematical Analysis at the Università del Piemonte Orientale. Filippo Gazzola got his degree in Mathematics in 1987 and he is now full professor in Mathematical Analysis at the Politecnico di Milano. Maurizio Zanotti got his degree in Mechanical Engineering in 2004 and presently he is structural and machine designer and lecturer professor in Mathematical Analysis at the Politecnico di Milano. The three Authors, for the variety of their skills, decided to join their expertises to write this book.
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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: In recent years, algorithmic graph theory has become increasingly important as a link between discrete mathematics and theoretical computer science. This textbook introduces students of mathematics and computer science to the interrelated fields of graphs theory, algorithms and complexity.
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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 designed for engineers, physicists. And also for applied mathematicians at advanced undergraduate and graduate levels. This book covers the general theory of relativity and its adaptability to a wide range of mathematical and physical problems. It includes tensor analysis, an emphasis on notation, and the manipulation of indices. It also includes advanced calculus, notation and explains various topics in set theory and topology. Later, it focuses on function-theoretical and algebraic aspects, manifolds, and integration theory. The book contains Worked examples and exercises that appear throughout the text.
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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 designed for advanced undergraduate and graduate mathematics students. Also for students of physics, and engineering. The required chapters starting from the theory of analytic functions, linear vector spaces, and linear operators. It includes orthogonal expansions (including Fourier series and transforms), the theory of distributions. Later it focuses on ordinary and partial differential equations and special functions: series solutions, Green’s functions, eigenvalue problems, integral representations. The book contains a large number of graphs and diagrams for better understanding. The book contains Worked examples and exercises that appear throughout the text.
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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 discusses theory for analysis, comparison and design of nonlinear smoothers. The book has a part of mathematical morphology. It has additional specific structures and properties. The book targets mathematicians, scientists and engineers.
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