Some Good Books for Math Undergrads

A Listmania! list by A Customer 2000
The list author says: "Here are some good books to checkout if you like Math at the Undergrad/Grad level (mostly undergrad).

I tried to pick books which were for the most part user-friendly (except for Rudin). I also only know of 1 differential equations book so I put it down (actually, there's one more I know of that Mathematicians think is good- which means it's not a good intro)."
A Mathematical Introduction to Logic, Second Edition
1.  A Mathematical Introduction to Logic, Second Edition by Herbert B. Enderton
The list author says:
  "Best book ever for mathematical logic.  The exposition is wonderful.   His basic recursion theory is the best out there.  He's a VERY rare combination, someone who teachs it well and knows what he is doing."
$90.40   Used & New from: $48.52
3.4 out of 5 stars  See all reviews (17 customer reviews)

Elements of Set Theory
2.  Elements of Set Theory by Herbert B. Enderton
The list author says:
  "Great book by a great guy.  He is the master of written mathematical exposition."
$49.54   Used & New from: $45.05
4.7 out of 5 stars  See all reviews (10 customer reviews)

Linear Algebra Done Right (Undergraduate Texts in Mathematics)
3.  Linear Algebra Done Right (Undergraduate Texts in Mathematics) by Sheldon Jay Axler
The list author says:
  "This is a great "determinant free" book for the most part.  It's on the theory side so maybe not for someone who hasn't had an intro. "computational" linear algebra course."
$38.04   Used & New from: $29.20
4.0 out of 5 stars  See all reviews (94 customer reviews)

Contemporary Abstract Algebra Fifth Edition
4.  Contemporary Abstract Algebra Fifth Edition by Joseph A. Gallian
The list author says:
  "Easy to understand.  Good start."
Used & New from: $6.00
4.2 out of 5 stars  See all reviews (10 customer reviews)

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Abstract Algebra, 3rd Edition
5.  Abstract Algebra, 3rd Edition by David S. Dummit
The list author says:
  "This is a comprehensive (if there is such a thing nowadays) and "easy-to-understand" basic algebra book for beginning grad and curious undergrads."
$113.04   Used & New from: $54.94
4.3 out of 5 stars  See all reviews (43 customer reviews)

Rings, Modules and Linear Algebra (Mathematics Series)
6.  Rings, Modules and Linear Algebra (Mathematics Series) by B. Hartley
The list author says:
  "I thought this book was out of print, but if this is what I am thinking of, it should be a great introduction to "Rings, Modules, and Linear Algebra."  Very easy to follow (especially on things such as Jordan canonical form)."
Used & New from: $19.97

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A First Course in Probability (8th Edition)
7.  A First Course in Probability (8th Edition) by Sheldon M. Ross
The list author says:
  "This book is great once you've had an intro. course.  It's good for people starting upper div. probability (and for people thinking about being actuaries and taking the P1 exam).  Ross has tons of examples of varying difficulty."
Used & New from: $44.97
3.1 out of 5 stars  See all reviews (38 customer reviews)

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Introduction to Abstract Algebra
8.  Introduction to Abstract Algebra by W. Keith Nicholson
The list author says:
  "Great for self-study.  Has a lot of answers."
$137.75   Used & New from: $19.95
4.2 out of 5 stars  See all reviews (4 customer reviews)

Algebra (2nd Edition) (Featured Titles for Abstract Algebra)
9.  Algebra (2nd Edition) (Featured Titles for Abstract Algebra) by Michael Artin
The list author says:
  "If you've had a solid course in linear algebra (or similar course in understanding proofs), this book is a great introduction to algebra.  It's a classic."
$153.33   Used & New from: $77.00
3.0 out of 5 stars  See all reviews (6 customer reviews)

Introduction to Analysis (Dover Books on Mathematics)
10.  Introduction to Analysis (Dover Books on Mathematics) by Maxwell Rosenlicht
The list author says:
  "Great exposition and CHEAP since it's Dover."
$9.12   Used & New from: $5.00
4.0 out of 5 stars  See all reviews (31 customer reviews)

Model Theory : An Introduction (Graduate Texts in Mathematics)
11.  Model Theory : An Introduction (Graduate Texts in Mathematics) by D. Marker
The list author says:
  "This is a good (modern) treatment of Modal Theory for beginning grad students or curious undergrads."
$50.52   Used & New from: $47.15
3.5 out of 5 stars  See all reviews (6 customer reviews)

Notes on Set Theory (Undergraduate Texts in Mathematics)
12.  Notes on Set Theory (Undergraduate Texts in Mathematics) by Yiannis N. Moschovakis
The list author says:
  "Great book to look at after Enderton's.  Moschovakis writes well."
$79.20   Used & New from: $61.26
3.4 out of 5 stars  See all reviews (5 customer reviews)

A Shorter Model Theory
13.  A Shorter Model Theory by Wilfrid Hodges
The list author says:
  "I like this book.  People seem to like the more modern book by Marker (which is superb).  I'm a bit old-fashioned and still like Chang and Kiesler as well."
$67.45   Used & New from: $44.40
4.6 out of 5 stars  See all reviews (5 customer reviews)

Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics)
14.  Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics) by Walter Rudin
The list author says:
  "I included this book because it's a classic.  But, I don't know how well you will learn from it.  The proofs are very slick. 

If you're looking for a read where you don't put effort in, then this is not the book for you."
$125.89   Used & New from: $30.00
4.2 out of 5 stars  See all reviews (139 customer reviews) | 2 customer discussions

Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds
15.  Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds by Theodore Shifrin
The list author says:
  "This book is great, but not necessarily a starting book (depends on what you like I guess).  Most people will prefer Stewart, Rogawski, Sallas, etc for standard multivariable calc.  After that and a little bit of linear algebra, this book would be fun."
$187.50   Used & New from: $149.99
4.2 out of 5 stars  See all reviews (4 customer reviews)

Applied Combinatorics, Second Edition
16.  Applied Combinatorics, Second Edition by Fred S. Roberts
The list author says:
  "Great text.  It covers a wide variety of topics and applications.  Easy to understand."
$96.86   Used & New from: $42.93
4.2 out of 5 stars  See all reviews (13 customer reviews)

A Course in Combinatorics
17.  A Course in Combinatorics by Jacobus Hendricus van Lint
The list author says:
  "From the CalTech course.  Good book.  Chapters are more or less individual lectures."
$63.37   Used & New from: $51.98
4.3 out of 5 stars  See all reviews (6 customer reviews)

Introduction to Topology: Second Edition (Dover Books on Mathematics)
18.  Introduction to Topology: Second Edition (Dover Books on Mathematics) by Theodore W. Gamelin
The list author says:
  "This book has good exercises (and answers).  It's exposition is clear and concise.  Greene is a great guy.  He always wants you to see the idea (not just the details).  Gamelin is excelent with mathematical prose for the non-mathematican (the mathematician as well)."
$10.59   Used & New from: $4.29
4.4 out of 5 stars  See all reviews (13 customer reviews)

Topology (2nd Edition)
19.  Topology (2nd Edition) by James R. Munkres
The list author says:
  "A classic.  Skip the first chapter and get straight to the topology.  More comprehensive than Gamelin and Greene."
$162.30   Used & New from: $74.00
4.4 out of 5 stars  See all reviews (47 customer reviews)

Complex Analysis (Undergraduate Texts in Mathematics)
20.  Complex Analysis (Undergraduate Texts in Mathematics) by Theodore W. Gamelin
The list author says:
  "Modern and clear.  There's also a solutions manual in progress (not by the author) somewhere on the web for public display.  I prefer this to Ahlfors (but then again some people would think I'm a moron for doing so)."
$55.71   Used & New from: $29.63
4.0 out of 5 stars  See all reviews (22 customer reviews)

Elementary Differential Equations and Boundary Value Problems
21.  Elementary Differential Equations and Boundary Value Problems by William E. Boyce
The list author says:
  "The only diffEQ I know."
$196.74   Used & New from: $24.99
2.8 out of 5 stars  See all reviews (51 customer reviews) | 1 customer discussion

Algebra (Graduate Texts in Mathematics)
22.  Algebra (Graduate Texts in Mathematics) by Serge Lang
The list author says:
  "Great reference text. Grad level."
$64.69   Used & New from: $41.00
4.0 out of 5 stars  See all reviews (19 customer reviews)

Basic Algebra (Cornerstones)
23.  Basic Algebra (Cornerstones) by Anthony W. Knapp
The list author says:
  "Another great reference text (grad level)."
$63.96   Used & New from: $49.73
4.5 out of 5 stars  See all reviews (2 customer reviews)

Introduction to Smooth Manifolds (Graduate Texts in Mathematics)
24.  Introduction to Smooth Manifolds (Graduate Texts in Mathematics) by John M. Lee
The list author says:
  "As far as grad books go, this is incredible."
Used & New from: $53.99
4.8 out of 5 stars  See all reviews (20 customer reviews)

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Introduction to Topological Manifolds (Graduate Texts in Mathematics)
25.  Introduction to Topological Manifolds (Graduate Texts in Mathematics) by John M. Lee
The list author says:
  "As far as grad books go, this book is king if you want to learn the material quickly.  I like this book much better than Hatcher, but, then again,  I never seriously used Hatcher (so maybe I'm wrong)."
Used & New from: $33.70
5.0 out of 5 stars  See all reviews (9 customer reviews)

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Naive Set Theory (Undergraduate Texts in Mathematics)
26.  Naive Set Theory (Undergraduate Texts in Mathematics) by P. R. Halmos
The list author says:
  "This is a very nice, well-written book by a great mathematics writer.  His linear algebra is also fantastic if you want a more "upper div." approach."
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4.0 out of 5 stars  See all reviews (27 customer reviews)

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Introduction to Topology: Third Edition (Dover Books on Mathematics) by Bert Mendelson

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Set Theory An Introduction To Independence Proofs (Studies in Logic and the Foundations of Mathematics)
27.  Set Theory An Introduction To Independence Proofs (Studies in Logic and the Foundations of Mathematics) by Kenneth Kunen
The list author says:
  "Great book for a grad level text.  Less dense than Jech."
$68.60   Used & New from: $55.49
4.2 out of 5 stars  See all reviews (4 customer reviews)

Introduction to Lie Algebras (Springer Undergraduate Mathematics Series)
28.  Introduction to Lie Algebras (Springer Undergraduate Mathematics Series) by Karin Erdmann
The list author says:
  "I've always liked the Springer undergrad series.  I guess at this level, it's more about how you say it.  Most grad books seem to take the approach of "it's what you say" not "how you convey it."  If only Springer had an undergrad version of its grad series."
$40.15   Used & New from: $28.92
4.7 out of 5 stars  See all reviews (3 customer reviews)

Real Analysis (4th Edition)
29.  Real Analysis (4th Edition) by H. L. Royden
The list author says:
  "I like this grad level book over Folland as an intro."
$149.47   Used & New from: $94.94
3.6 out of 5 stars  See all reviews (14 customer reviews)

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A Customer 2000
Qualifications: Like Math
Last updated: 9/11/10
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