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Math Books: Recommended books about mathematics Countless math books are published each year, however only a tiny percentage of these titles are destined to become the kind of classics that are loved the world over by students and mathematicians. Within this page, you’ll find an extensive list of math books that have sincerely earned the reputation that precedes them. For many of the most important branches of mathematics, we’ve provided what we consider to be the best math books for the subject at hand. We aimed for a list of titles that were either introductory in nature or that fall into the category of “must-have” math reference books. Naturally a universal consensus doesn’t exit, but the books below are as close as it gets to a wish list for any aspiring mathematician or person who’s interested in mathematics. We highly recommend each and every one of these titles, and hope that you’ll enjoy them, too. Please note, this list will constantly be updated so as to keep it current. Math Books Menu Abstract Algebra Algorithms Calculus Helpers Calculus I Calculus II Coffee Table Combinatorics Differential Equations Encyclopedias of Mathematics Foundations of Mathematics History of Mathematics Information Theory Linear Algebra and Geometry Mathematical Methods Numerical Analysis Number Theory Precalculus Probability Real and Complex Analysis Statistics (+)

Math Blog's Recommended Reading List

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Recommended reading list from quality site named Math Blog covers 182333-299192 chapters and includes wordlist.There topics also many markov chain and you can consider Your user name must contain at least 3 characters.Password: Required: Length 8-20 characters, must not match login name or email address, at least one upper and one lower case letter, one digit [0-9], and one non-alphanumeric character.Re-enter Password: Password Question: You will need to know your Password Answer to obtain a new password.Password Answer: First Name: Your privacy is important. Please rPlease remember.Recommended reading list from.

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Page 1: Math Blog's Recommended Reading List

Math Books: Recommended books about mathematics

Countless math books are published each year, howeveronly a tiny percentage of these titles are destined tobecome the kind of classics that are loved the world overby students and mathematicians. Within this page, you’llfind an extensive list of math books that have sincerelyearned the reputation that precedes them.

For many of the most important branches of mathematics,we’ve provided what we consider to be the best mathbooks for the subject at hand. We aimed for a list of titlesthat were either introductory in nature or that fall into thecategory of “must-have” math reference books. Naturally auniversal consensus doesn’t exit, but the books below areas close as it gets to a wish list for any aspiringmathematician or person who’s interested in mathematics.We highly recommend each and every one of these titles,and hope that you’ll enjoy them, too. Please note, this listwill constantly be updated so as to keep it current.

Math Books Menu

AbstractAlgebra

AlgorithmsCalculusHelpers

Calculus I

Calculus II Coffee Table CombinatoricsDifferentialEquations

EncyclopediasofMathematics

FoundationsofMathematics

History ofMathematics

InformationTheory

Linear Algebraand Geometry

MathematicalMethods

NumericalAnalysis

NumberTheory

Precalculus ProbabilityReal andComplexAnalysis

Statistics

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Topology

Abstract Algebra Books

Contemporary Abstract Algebra

by Joseph Gallian

Review: The seventh edition ofContemporary Abstract Algebra covers the basics ofabstract algebra with clarity and a rarely seen brightness.Opting for readability over the rigor many of itscontemporaries embrace, this textbook provides anexcellent starting point for any student looking to learn andunderstand the subject. Gallian’s writing is inviting andcomprehensive, the proofs are rock-solid, and his overallhandling of the topic and the reader is gentle – somethingbeginners will be grateful for. Abundantly filled withexercises, well chosen examples, and even biographies onnotable mathematicians, this book makes the perfectcompanion for both students and teachingassistants. More info.

Abstract Algebra

by David S. Dummit and Richard M. Foote

Review: Serious math learners will be (+)

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thrilled by the rigorous conciseness of this textbook. Densewith information on every page and presented in a relaxed,open manner, Dummit and Foote’s Abstract Algebraeffectively works to usher the reader into a realm ofsophisticated algebraic concepts and theories. Itseamlessly bridges any gap between graduate andundergraduate studies. The book is chock-full of clearexamples and succinct proofs, making it evident that theauthors have no intention of keeping the reader on aparticular topic any longer than is necessary. Withcountless exercises and examples, Abstract Algebra provesto be an invaluable tool that is undeniably worth the price.More info.

Algorithms Books

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Introduction to Algorithms, Third Edition

by Thomas H. Cormen, Charles E. Leiserson and Ronald L.Rivest

Review: Introduction to Algorithms is adistinctly theoretical but all-around comprehensive book.Its use is not only limited to those taking algorithmscourses but can also be utilized by anyone as an extensivereference source. Readers will learn quintessentialalgorithms as well as concepts such as what makes analgorithm efficient and why. Students will need a bit ofmathematical background to get from cover to cover,however those who are able to do so will be intrigued bythe content depth and wide spectrum of topics covered.These topics run the gamut from classical algorithms tocomputational geometry. More info.

Art of Computer Programming, The, Volumes1-3 Boxed Set

by Donald E. Knuth

Review: This 3 volume box set does amarvelous job of covering subjects in the vast field ofcomputer science. The writing is intact and brimming withmathematical rigor. Readers whose sole focus is learningcan easily skim over areas that are excessively detailed

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without losing grasp of the core concepts. All threevolumes are equally definitive and provide a cleantheoretical explanation of fundamentals of computerscience. The entire set is organized into six chapters: BasicConcepts, Information Structures, Random Numbers,Arithmetic, Sorting, and Searching. Additionally, eachchapter section comes with questions students can use togain better hands on experience. This is book is akin to thebible for computer scientists. A fourth volume is alsoavailable. More info.

Calculus Helpers Books

The Calculus Lifesaver: All the Tools You Needto Excel at Calculus

by Adrian Banner

Review: Lengthy yet vital, this resource bookis jam packed with straight-forward explanations and loadsof solved problems for students to easily learn from.Excelling many of its contemporaries by leaps and bounds,The Calculus Lifesaver truly lives up to its title. Studentswho are tired of dreary calculus textbooks that provide nomotivation behind the concepts will be gladly surprised bythe detailed and informal approach Banner uses to capturetheir attention. He fills all gaps and leaves readers feelingsatisfied and enlightened. This book dually holds thecharacteristics of both an instructive primary aid as well asthat of a supplementary read. More info.

Calculus Made Easy(+)

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by Silvanus P. Thompson

Review: Even those who are not particularlygifted or even proficient in mathematics will enjoy sittingdown and studying from Calculus Made Easy. Thompsoncreates a warm, inviting environment where students willlearn and grasp the true essence of calculus without anyadded fluff or overt technicality. Frustrated students whohave sought after a compatible calculus aid to no avail willagree that this is a professional tool that is presented tothe reader on the same wavelength. Thompson knows thatmath is hard. Rather than taking the standard approachthat many use to confound and further bewilder students,he breaks calculus down into a form that is a lot lessthreatening. More info.

Calculus I Books

Calculus, Vol. 1

by Tom M. Apostol

Review: The author strikes a perfect balancebetween theory and technique by explaining the “why” ofcalculus in addition to the “how”. He wanders off thestandard presentational path for a calculus course andthereby creates a more historically accurate and usefulbook. Those who are bound by the established method of (+)

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teaching calculus and are more interested in problems andexercises may not identify with Apostol’s method. But thisis a book that was written for the curious student with theintention of being read and understood, not practiced andblindly memorized. The result is that students will be readyto tackle calculus subjects and courses with a newfoundclarity. More info.

Calculus

by Michael Spivak

Review: Tenacious students in favor ofstimulating study will love this book. Spivak’s prose isalmost charming in the way that it thrusts readers into achallenge that advanced learners will be happy to take on.He forces them to rely on their own perspicacity andreason instead of a collection of random techniques andmechanics. Sophisticated readers will appreciate the stylehe uses to communicate and teach calculus while othersmay first want to opt for a more elementary text beforeattempting to penetrate the solidity of Spivak’s. This fourthedition includes additional problems and other minorchanges not included in the third. More info.

Calculus II/III Books

Calculus, Vol. 2

by Tom M. Apostol

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Review: In this follow-up to Volume I of hisseries, Apostol continues to lay the groundwork forcalculus students with precision and ease. Where volumeone helped establish the basics and form the reader’sunderstanding, volume two expands that knowledge in away that demands full immersion into the text. Unlikeother calculus books, this one is replete with substance.The author takes time to build and prove each theorem theway it ought to be done. Unlike many follow-up mathbooks, this one never mindlessly repeats the samematerial. Instead, it vigorously moves ahead into newterritory involving the use of multi-variables and advancedapplications. More info.

Calculus On Manifolds

by Michael Spivak

Review: This short and concise book onlyfocuses on what is essential and nothing else. It works toquickly develop the reader’s understanding of differentialand integral calculus. Spivak makes his writing on the mainobjective of the book – Stokes Theorem – painless and easyto grasp. Readers are encouraged to keep a pen and paperon hand to rewrite the proofs on their own. The book’schapters are as follows: Functions on Euclidean Spaces,Differentiation, Integration, Integration on chains, and (+)

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Integration on Manifolds. Spivak’s mathematical prowess isapparent by his ability to pack so much punch in only asmall amount of pages. If you enjoyed Calculus by Spivak,you’ll love Calculus On Manifolds. More info.

Coffee Table Math Books

Mathematicians: An Outer View of the InnerWorld

by Mariana Cook

Review: In this uniquely interesting book,photographer Mariana Cook offers readers high qualityblack and white photographs of 92 noteworthymathematicians. Cook’s unusual concept for this book hasraised several eyebrows. However it provides a muchneeded break from the rather austere climate that themath world is usually comprised of. Her selectedmathematicians come from diverse backgrounds and haveall reached their authoritative status in equally differentways. Each photograph is accompanied by a quick,informative and often enlightening essay by themathematician at hand, frequently revealing the passionand deep love for their discipline that each mathematicianpossesses. Cook does a wonderful job of capturing hersubjects in an honest and purely human light. As such, thistitle is the ideal coffee table book for math geeks. Moreinfo.

Sacred Mathematics: Japanese TempleGeometry

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by Fukagawa Hidetoshi and Tony Rothman

Review: In Sacred Mathematics, Hidetoshiand Rothman present a tantalizing and detailed history ofSangaku puzzles that will keep the reader engaged formany hours. For those who are unfamiliar with the subject,sangakus are Japanese geometrical puzzles that werecreated on wooden tablets and hung in sacred temples andshrines. Readers will discover how the Japanese cleverlyintertwined the mathematical, the spiritual, and the artisticto create their own cultural brand of geometry. Sangakuwas formulated during an era before western influencehad reached Japan. This makes it a unique and fascinatingart that has attracted many mathematicians. The authorsdo a beautiful job of introducing the reader to Japaneseculture and the mastery of the country’s sangakusmathematicians. This hardcover volume is rich ofillustrations and would be a nice coffee table book. Moreinfo.

Combinatorics Books

Principles and Techniques in Combinatorics

by Chen Chuan-Chong and Koh Khee-Meng

Review: Math undergrads will find Principlesand Techniques in Combinatorics to be a detailed but easy (+)

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to read book. This is a much needed textbook that can trulybe classified as introductory. The authors take carefulconsideration not to over-elaborate key concepts andthereby confuse those readers who are not as advanced inmathematics as others. Students will enjoy walking step bystep through precisely detailed combinatorial proofs aswell as reading the greatly in depth chapter on RecurrenceRelations (Chapter 6). An abundance of combinatorialproblems that are perfect for math competition trainersand participants can be found at the end of each chapter,adding even more value to this already low-priced gem.More info.

Combinatorics and Graph Theory (2nd edition)

by John Harris, Jeffry L. Hirst, and Michael Mossinghoff

Review: This second edition of Combinatoricsand Graph Theory presents all relevant concepts in a clearand straight to-the-point manner that students willundoubtedly favor. The authors waste no time and quicklyset out to teach readers in a brilliantly written and warmlyengaging manner. Within its 382 pages, students will findunambiguous explanations on a range of combinatorialand graph theory topics such as Ramsey numbers, Cayley’stree-count theorem, inclusion-exclusion, vertex coloring,and elementary combinations to just name a few. Thesecond edition also contains new material not previouslyincluded in the first, such as extended information onPolya theory, stable marriage problems, and Eulerian trails.More info.

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Differential Equations Books

Differential Equations and Their Applications

by Martin Braun

Review: This high-level text is clearlyunderstandable and widely engaging. Braun runs throughthe pages of his book in a light, expertly written mannerthat will keep readers hooked for hours. As highly technicalas this field is, he covers it fluidly spurring readers to digdeeper into other sources on the subject long after they’vefinished reading this one. Motivated students will findBraun’s discussion insightful, a result of his strive toimplement understanding. Anyone taking a course indifferential equations for the first time or as a refresherwill be greatly pleased by this book’s clear and invigoratingapproach. More info.

Encyclopedias of Mathematics Books

The Princeton Companion to Mathematics

by Timothy Gowers, June Barrow-Green and Imre Leader(Editors)

Review: This is an extraordinary book thatevery student and mathematician should absolutely have.

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The PCM carries the true signature of a math encyclopediain that it is versatile and capable of being all things to alllearners in every field of mathematics, and on all levelsalso. In light of its broad spectrum of topics, the editorshave managed to keep this book cohesive and well knittogether. The PCM includes specialized articles fromcontributors on a variety of math topics that even the mostadvanced pros can learn from. Non-mathematicians whoare curious about the trade can also learn a great deal ofinformation from the PCM due to its overall accessiblenature. This is the kind of book that will still be read ahundred years from now, and it truly is the nicest book Iown. More info.

Encyclopedia of Mathematics

by James Stuart Tanton

Review: This awesome reference givesmath lovers exactly what they want from a mathencyclopedia. Those who want to quickly search and learnabout a particular topic without unneeded rambling fromthe author or unsatisfactory terseness, will find atrustworthy companion in Tanton’s aptly named work. Thisbook is formatted in an A- Z structure. Tanton makes nodiversions in outlining or trying to draw connections otherthan what is necessary. He essentially gives readers theneeded facts and resources, and then keeps it moving. Thiswill prove to be wonderful for some while disappointing forothers. The book contains more than 800 entries as well asrelevant timelines following the entries. More info.

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Foundations of Mathematics Books

A Mathematical Introduction to Logic, SecondEdition

by Herbert Enderton

Review: This is one of the finest introductorytexts on logic that any student can read. Enderton iscohesive in his explanations and skillfully covers all theessential bases, from number theory to first and secondorder logic as well as several theorems, including Godel’s.While not a mandatory requirement, it is highlyrecommended that the reader has a slight understandingof math logic. This will make it easier to complete the manyexercises found throughout. Complete with manywell-chosen examples and a wider scope than most of itspeers, I’d suggest this book to anyone seeking to learn orbetter understand math logic. More info.

Classic Set Theory for Guided IndependentStudy

by Derek C. Goldrei

Review: This is a clearly written andexpertly arranged independent study guide designed tomake the topic of set theory comprehensible and easy to

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grasp for self-study students. Without a doubt, this booksmore than delivers. Readers can expect a smooth ridedevoid of complexity and assumed pre-exposure to thesubject. Goldrei’s book brings forth an abundance of bothsolved an unsolved exercises, illustrations and thoroughexplanations. Ideas, commentaries and recommendationsthat are resourcefully placed alongside the main textdelightfully height the learning experience. This is one ofthose unfortunately rare but wonderfully rigorousindependent study math books that many studentsstumble across and never seem to put down. More info.

Categories for the Working Mathematician

by Saunders Mac Lane

Review: The author of this work, Sunders MacLane, has concisely spread out all the vital category theoryinformation that students will probably ever need to know.Category theory is a tough topic for many and is noteffortlessly explained. However, Mac Lane approaches thetask with skill, dexterity and an orderly flow of writing – butthis isn’t surprising being that Mac Lane is the veryoriginator of category theory. Those with limitedexperience with graduate-level mathematics are cautionedto start with a more basic text before delving into this one.However, serious mathematicians looking to learn fromone of the masters in the trade will be thoroughly delightedwith Mac Lane’s exposition. More info.

History of Mathematics Books

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Mathematics: From the Birth of Numbers

by Jan Gullberg

Review: Gullberg’s takes an amazing dive intothe deep grounded roots of mathematics and its origins.The astounding part about all of it is that Jan Gullberg is adoctor and not a mathematician. Despite this, he hasmanaged to write a thorough book that captures the entirehistory of math along with answers to the “why” and “how”that students often ask. The enthusiasm he exhibitsthroughout will spread onto readers like wildfire. This workis clearly a labor of love, not self-exaltation. Readers willappreciate that Gullberg is simply a man who has fallen inlove with and holds an immense adoration for one of themost important components of human civilization. Moreinfo.

What Is Mathematics? An ElementaryApproach to Ideas and Methods

by Richard Courant and Herbert Robbins

Review: Math aficionados will profit greatlyfrom this book. Those interested in breezing through amath history text won’t however have much luck with thisone. That is because this book does more than just skim

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the surface. The authors prompt readers to actually thinkabout the ideas and methods mentioned rather thanblindly swallow them down for later use. They presentcaptivating discussions on many topics instead of dull factsand easy answers. The end result of reading this book is anappreciation that will develop from the thought processesreaders are required to use. The writing is classic andelucidating, accompanied by many engaging illustrationsand side notes. More info.

Mathematics and its History

by John Stillwell

Review: This book contains a treasure chest ofpriceless history and deep facts that even established proswill find themselves learning from. John Stillwell foregoesthe encyclopedic route and makes it his goal to help thereader understand the beauty behind mathematicsinstead. He brilliantly unifies mathematics into a cleardepiction that urges readers to rethink what they thoughtthey knew already. He effectively travels all pertinentground in this relatively short text, striking a clever balancebetween brevity and comprehensiveness. Readers lookingto truly understand the whole concept of mathematics andits disciplines will enjoy reading Stillwell’s Mathematics andits History. More info.

Information Theory Books

Computational Science and Engineering

by Gilbert Strang(+)

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Review: Gilbert Strang has a reputation forwriting ample, pragmatic, and insightful books. During thecourse of reading this one, it will become blatantly clear tothe reader that the author has created this work out ofpassion and a genuine love for the subject. Every engineercan benefit deeply from reading this. Strang’s writing styleand his instructive approach are unrivaled. He covers allaspects of computational science and engineering withexperience and authority. The topics discussed includeapplied linear algebra and fast solvers, differentialequations with finite differences and finite elements, andFourier analysis and optimization. Strang has taught thismaterial to thousands of students. With this book manymore will be added to that number. More info.

Information Science

by David G. Luenberger

Review: This book has what many of its peersdon’t: the skill and finesse to clearly explain complexconcepts in a manner that appeals to readers, but neverloses integrity. The book contains interesting historicalfacts and insightful examples. Luenberger forms thestructure of his book around 5 main parts: entropy,economics, encryption, extraction, and emission, otherwiseknown as the 5 Es. He encompasses several points of viewand thereby creates a well-rounded text that readers willadmire. He details how each of the above parts provide (+)

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function for modern info products and services.Luenberger is a talented teacher that readers will enjoylearning from. More info.

Introduction to Coding and Information Theory

by Steve Roman

Review: Undergraduate math and computerscience students will be thrilled to learn information theoryand coding theory from Steve Roman’s book. Readers willgain a profound understanding of the types of codes andtheir efficiency. Roman starts his exposition off with anintroductory section containing brief preliminaries and anintroduction to codes that preps the reader and makes iteasier for them to process the remaining material. Hefollows that with two chapters containing a preciseteaching on information theory, and a final sectioncontaining four chapters devoted to coding theory. Hefinishes this pleasing journey into information and codingtheory with a brief introduction to cyclic codes. More info.

Linear Algebra and Geometry Books

Linear Algebra Done Right

by Sheldon Axler

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Review: This is an exemplary bookrequiring a small level of mathematical maturity. Axlertakes a thoughtful and theoretical approach to the work.He skillfully takes the focus off from matrices and shifts thereader’s attention more towards linear mappings. Thismakes his proofs elegant, simple, and pleasing. Consciousof the reader’s possible unfamiliarity as well as time frame,Axler does a fine job of preparing and developing readers’understanding rather than fully detailing applicationmethods and formulas. He leaves the reader with unsolvedexercises which many will find to be thought-provoking andstimulating. An understanding of working with matrices isrequired. This book works great as a supplementary orsecond course introduction to linear algebra. More info.

The Four Pillars of Geometry

by John Stillwell

Review: This is a beautifully written book thatwill help students connect the dots between four differingviewpoints in geometry. These four “pillars”, as Stillwellrefers to them, are: straightedge and compassconstructions, linear algebra, projective geometry andtransformation groups. This book will help the readerdevelop a stronger appreciation for geometry and itsunique ability to be approached at different angles – an (+)

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exciting trait which ultimately enables students tostrengthen their overall knowledge of the subject.Undergraduate students and professors alike will enjoy thebrevity of Stillwell’s writing and his ability to rapidlyexamine each of these topics of geometry rather thanemphasize just one. More info.

Mathematical Methods Books

Mathematical Methods: For Students ofPhysics and Related Fields

by Sadri Hassani

Review: This book gives readers anenhanced view of complex mathematics and theirapplications than most standard courses don’t do. It isrecommended that only those with some existingknowledge of linear and complex algebra, differentialequations, and even complex analysis and algebra only usethis book. Physics and engineering students beyond theirintroductory courses are the intended audience and willbenefit the most. The material can be used as bothrefresher reading and as a primary study guide. Hassani iswell-versed and hispresentation is expertly organized. He also effectivelybegins each chapter with a short preamble that helpsfurther instill understanding of the main concepts. Moreinfo.

Mathematical Methods in the Physical Sciences

by Mary L. Boas(+)

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Review: Boas continues her tradition ofconciseness and wholly satisfies physical science studentswith her third edition of Mathematical Methods in thePhysical Sciences. Mathematics majors need to be awarethat this book is intended for the fields of science andengineering, therefore the author’s focus is not on proofsor mathematical rigor. She even makes a point to stressthis in the preface. Boas has done students a tremendousservice by combining essential math concepts into oneeasy to use reference guide. It contains vital pieces and bitsof all the major topics including Complex numbers, linearalgebra, PDEs, ODEs, calculus, analysis and probability andstatistics. Every physics student should certainly own thisone. More info.

Number Theory Books

Elementary Number Theory

by Gareth A. Jones and Josephine M. Jones

Review: Undergraduate math majors will findthis book to be easily approachable but containing muchdepth. Jones and Jones form a powerful duo and expertlytake students through a painless and surprisingly enjoyablelearning experience. They seem aware that many readersprefer readability over a more pedantic style. They brieflytouch base on advanced topics such as Fermat’s Last

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Theorem and its history while still remainingunderstandable. This book rightfully puts emphasis on thebeauty of number theory and the authors accompany eachexercise with complete solutions – something students willcertainly enjoy. This book can work excellently as bothintroductory course literature or supplementary study andreference material. More info.

An Invitation to Modern Number Theory

by Steven J. Miller and Ramin Takloo-Bighash

Review: Advanced undergrads interested ininformation on modern number theory will find it hard toput this book down. The authors have created anexposition that is innovative and keeps the readers mindfocused on its current occupation. The subject of modernnumber theory is complex and therefore this book isintended for the more experienced student. However, theauthors tackle the subject in a well-paced yet rigorous stylethat is more than commendable. Each page exudesbrilliance, birthing an underlying deeper awareness of thetopic. As described in the title this book really is aninvitation – and curious readers would be wise to accept it.More info.

An Introduction to the Theory of Numbers

by G. H. Hardy, Edward M. Wright and Andrew Wiles

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Review: This is a book that is commonly usedin number theory courses and has become a classic stapleof the subject. Beautifully written, An Introduction to theTheory of Numbers gives elementary number theorystudents one of the greatest introductions they could wishfor. Led by mathematical giant G. H Hardy, readers willjourney through numerous number theoretic ideas andexercises. Hardy’s writing brims with a knowledge andelegance that subtly displays the razor sharp expertise hepossessed. This book will not only guide number theorystudents through their current studies but will also preparethem for more advanced courses should they pursue themin the future. An absolute classic that belongs to thebookshelf on any math lover. More info.

Numerical Analysis Books

Numerical Analysis with CD-ROM

by Timothy Sauer

Review: Sauer has created a book that ismore than suitable for first course studies in numericalanalysis. He highlights the five critical areas of the subjectwhich are: Convergence, Complexity, Conditioning,Compression, and Orthogonality, and makes well-plannedconnections to each throughout the book. The proofs areexacting but not too intricate and will firmly satisfy

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students. Each chapter is laden with insight, and not justanalysis. Sauer attentively infuses his book with numerousproblems, some to be completed by hand and othersthrough the use of the Matlab numerical computingpackage. Complete with Matlab code in the back of thebook and an accompanying CD-ROM, students will findNumerical Analysis a pleasure to own. More info.

Numerical Recipes 3rd Edition: The Art ofScientific Computing

by William H. Press, Saul A. Teukolsky, William T. Vetterlingand Brian P. Flannery

Review: This third edition of a widelyesteemed favorite has been upgraded to include the latestmodern scientific computing methods as well as twocompletely new chapters. The book is still written andpresented in the same practical an easy to read style thatthe previous versions were known for. The authorsdiligently treat the old familiar methods with passion whiletactfully intertwining them with newer and equallyimportant more contemporary ones. The exceptionallywritten C++ code will help readers incorporate and test thealgorithmic solutions in their own environments for furtherlearning. However there are strict licensing rules to payattention to. More info.

Precalculus Books

Precalculus Mathematics in a Nutshell:Geometry, Algebra, Trigonometry

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by George F. Simmons

Review: George Simmons takes newbies andout of practice scholars alike, through a refreshing crashcourse in three basic mathematical practices (Geometry,Algebra and Trigonometry) in their simple but often hatedform. High school graduates and others on the way to theirfirst college calculus course will be thoroughly prepared totake on the intimidating realm of college levelmathematics. Simmons shows readers just howuncomplicated and enjoyable mathematics can be – all in atransparent and fluid tone. He goes into adequate depthwhile still maintaining enough brevity to encourage thereader to think on their own. He cuts to the chase andafterwards leaves readers feeling capableand well-equipped. More info.

Basic Mathematics

by Serge Lang

Review: The late Serge Lang’s BasicMathematics will help students properly commence theirventure into college calculus. The book is divided into foursections: Algebra, Intuitive Geometry, CoordinateGeometry, and Miscellaneous. Each section offersnumerous exercises for readers to practice and fine-tune

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their abilities on. Lang carefully uses his groundedexpertise to construct a sturdy foundation for the reader tobuild their future mathematical knowledge on. Basic mathconcepts are his sole focus and he comfortably takesreaders through the material with an advanced but stressfree tone. The principles Lang brings to the forefront areabsolutely vital for anyone wishing to move forward incalculus, college algebra, and other areas of mathematics.More info.

Probability Books

Introduction to Probability Models, TenthEdition

by Sheldon M. Ross

Review: Introduction to Probability Modelsdiffers from many probability books in that it covers avariety of disciplines. It has been widely used by a numberof professors as the main text for many first courses. Thiselementary introduction provides ample instruction onprobability theory and stochastic processes, and insightinto its application in a broad range of fields. Ross has filledeach chapter with loads of exercises and clear examples.He also takes his time in explaining the thinking andintuition behind many of the theorems and proofs. Eventhose who don’t specialize in the field will find it a joy toread this book. More info.

An Introduction to Probability Theory and ItsApplications

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by William Feller

Review: In this first volume, William Fellerpaints a clear picture of probability theory and several ofits interesting applications from the discrete viewpoint. Thematerial is a bit advanced and is only recommended forstudents going into their third or fourth years. His writingbrims with examples that help establish an accurateconception of discrete probability, and it includes soundinsight into the history and development of probabilitytheory. Readers will walk away with an intuitiveunderstanding and sharper awareness of the subject. It is amust read item for any intermediate to advanced studentwho is working in the field of probability theory. More info.

Probability Theory: The Logic of Science

by E.T Jaynes

Review: Jaynes writes a fantastic prose thatviews probability theory beyond the usual context. Theideas found within this book are innovative and the authortakes a welcomed path away from the conventional.Readers will enjoy the intellectual journey into thefundamentals of probability theory coupled with the book’srelaxed and informal tonality. It is strangely akin toreceiving a one-on-one lesson from the author himself.

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Jaynes should be praised for taking a huge step away frommainstream probability theory and into this fresherapproach. The only disappointment to this masterpiece isthat, sadly, Jaynes died before completely finishing it,causing the editor to step in and thinly inject the missingpieces. More info.

Fifty Challenging Problems in Probability withSolutions

by Frederick Monsteller

Review: This small entertaining book presentsa remarkable assortment of probability problems andpuzzles that will keep readers stimulated for hours.Monsteller narrates parts of his book with a sense ofhumor which creates an easy-going and comfortablelearning environment. The problems the author hasselected put emphasis on, and will help readers learn,invaluable techniques. Detailed solutions to each problemare also included so as not to leave the reader bewilderedor uncertain. The book ranges in scope from basicprobability puzzlers to very difficult and intricate ones forthe highly advanced student. This book easily doubles assupplementary study material or as a source ofrecreational math enjoyment. More info.

Real and Complex Analysis Books

Principles of Mathematical Analysis, ThirdEdition

by Walter Rudin(+)

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Review: Rudin has written an exquisite bookon analysis. Before approaching, students should have amodest understanding of mapping, set theory, linearalgebra and other basic topics. Rudin’s problem setsappear tough, but once figured out students will be morethan grateful for his rigor. For readers, the key to reallybenefiting from this book is not only in reading it but incompleting Rudin’s exercises and proofs on their own. Thechallenge will train them to think intuitively and effectively.This book is also known as “baby rudin” and it’s a realclassic. More info.

Real Analysis

by N.L Carothers

Review: There are many math books that goby the same straightforward title, however not many ofthem exude the same amount of mastery and reverencefor the subject as Carothers’ does. The book is infused withenlightening historical commentary which keeps the readerengaged and helps break the stereotype of “boring mathbooks”. The author also has an interesting custom ofinserting a parenthesized “why” whenever he purposelybypasses a detail by forcing readers to figure it outthemselves. While some will find this frustrating, motivatedand determined students will take it as an opportunity to (+)

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probe deeper and explore real analysis further than theynormally might. More info.

Real and Complex Analysis

by Walter Rudin

Review: Rudin provides a solid handling ofgraduate level real and complex analysis. He encompassesall basic and advanced topics such as differentiation,Banach and Hilbert Spaces, Fourier analysis, etc. Readerswho are familiar with Rudin can expect to see his usualwriting style – elegant and concise. He goes through astandard but thorough teaching on measure theory in thefirst half of the book and then progresses onto aninnovative study of complex analysis. He starts basic butfluidly moves towards a level that requires persistence onthe reader’s part. This book (aka “big rudin” or “paparudin”) is a masterpiece for students who are looking for aclassic read on real and complex analysis. More info.

A First Course in Complex Analysis WithApplications

by Dennis Zill and Patrick Shanahan

Review: This book gives students an (+)

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accessible introduction to the world of complex analysisand how its methods are used. A First Course in ComplexAnalysis is reader-friendly to the newcomer and thereforeis ideal for use by both undergrads as well as graduates.For undergrads, the authors refrain from abstractness andmaintain an appreciated level of transparency. While forgraduates, they effortlessly fill in the gaps that manystandard course texts tend to leave wide open. Eachchapter is followed by a section detailing the applicationsof the previously discussed topic. Additionally a quickreview quiz for further verification and cultivation of skillsis also included with each chapter. More info.

Visual Complex Analysis

by Tristan Needham

Review: Author Tristan Needham reveals theoften unrealized beauty of complex analysis through agraphical perspective. He takes an elegant approach tocomplex analysis that will cause the reader to turn eachpage in awe of the insightful prose and intricate visuals.This book momentarily takes the math student’s mind offof the abstractness and conciseness that it has been raisedon and transfers it to a place full of innovative approaches,but without sacrificing rigor. Readers will understandsolutions through their own intuition, not memorization.Rich in math history and lively from the start, this bookwould make excellent study and recreational reading forthe serious student. More info.

Statistics Books(+)

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Statistics in Plain English, Third Edition

by Timothy C. Urdan

Review: Just as the title implies, the author has submittedan unequivocal and palpable exposition on statistics.Statistics in Plain English is regarded by many as the mostappropriate statistics primer for undergraduates. Urdanhas managed to compress everything one needs to knowabout statistics into a compact 250 page book that doesn’tfeel hurried or unfulfilling. The text is general enough to beused in a variety of mathematical areas yet retains itscomprehensiveness and accuracy. Urdan masterfullymoves through essential concepts without losing thereader the way many professors would. Students harboringapprehension towards statistics will tremendously enjoythis book. More info.

Introductory Statistics

by Neil A. Weiss

Review: Introductory Statistics will greatlyincrease readers’ understanding of statistics and thereasoning behind the subject. Weiss has structured thesubject matter carefully and formulates his writing in alucid and enjoyable style. He thoughtfully steers away fromadvanced topics as they would only serve to confusereaders who are in this elementary stage. The focus is kepton detailed explanations of the basics in a clear languagethat will appeal to many beginners. Some of the chapterscovered include: The Nature of Statistics, Organizing Data,Descriptive Measures, Discrete Random Variables, (+)

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Inferential Methods in Regression and Correlation, andAnalysis of Variance (ANOVA). More info.

Statistics, 4th Edition

by David Freedman, Robert Pisani and Roger Purves

Review: This is an excellent, non-technicaland simple introduction to statistics. The book is intendedfor lower-level students who wish to know the standardtopics and methods that are included in most first statisticscourses. Math students will find it easy to understand theideas presented, while teachers and tutors will discover anengaging and highly effective way to teach statisticsmaterial. The authors provide real-life examples such asclinical trials and observational studies to help readersgrasp the subject matter even better. All that is needed tolearn from this book is a basic understanding of numbersand simple algebra. More info.

Topology Books

Introduction to Topology and Modern Analysis

by George F. Simmons

Review: The author of this book has divided itinto three sections: topology, operators, and algebras of (+)

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operators. He contrives a fantastic and classicalintroduction to topology that targets continuity andlinearity, the dominating themes. In the preface Simmonsstates that the goal is to illuminate these words’ meaningand their relation to each other, which is exactly what hedoes in the remaining pages. Self-study students will findSimmons to be a phenomenal communicator and will haveno problem at all going through chapter after chapter ofhis writings. He clarifies deep concepts in a manner thatboasts his mathematical capacity and skill while neverleaving the reader behind. More info.

Introduction to Topology: Third Edition

by Bert Mendelson

Review: Undergraduates will enjoy thisintroduction to the fundamentals of topology. Despite itsrelatively short length, this book thoroughly encompassesthe basic material students are required to know. Engagingexercises and problems urge the reader’s mind to fullycomprehend and absorb the material. In the first chapter,Mendelson explains set theory in an unmitigated mannerwhich primes readers for the following chapters. Self-studyenthusiasts will fall in love with the clarity and simpleprogress of the writing. However, despite its simplicity thisbook holds much contextual depth and gravity. AfterMendelson’s initial introduction to topology, students willhave no need for another. More info.

Feel free to get in touch if you think the list is really missingout by not listing a specific book. If you are a publisher and (+)

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feel that we’re missing a great book of yours, drop us aline. Please understand that we recommend only what weconsider to be the best books on the market today. Noexceptions.

Disclaimer: Here at Math-Blog.com we believe in fulldisclosure. The links to Amazon.com, have our referral idwhich earns us a tiny commission every time you buy fromthese links. Think of it as a tip that won’t cost you a cent, toreward us for our time investment. We appreciate yoursupport.

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