Free Online Mathematics Textbooks

I was always fascinated by math. One of the few electives that I took in college was fourth semester Calculus. (Yes, I am a nerd. And, I'm darn proud of it.)

Anyway, learning mathematics is perhaps one of the many academic disciplines where the words an instructor uses to explain a concept can make all the difference whether or not you will grasp that concept. Since the Internet was not available when I was in college, I haunted used book and thrift stores for cast-off copies of calculus, statistics and other math textbooks that could provide me with one more explanation of more complicated concepts. Those extra textbooks saved my GPA more than a few times.

Today's students have a tremendous advantage - the Internet. My pile of 10, 20, 30 and even 40-year old worn out textbooks seems pathetic when compared to the wealth of mathematics-related materials online. Even if your instructor insists on using his or her favorite, and oh-so-expensive, text, the resources listed here will provide you with additional explanations, sample problems and practice exercises.

Math Refresher

Returning students have always faced the challenge of dredging up long-unused mathematical concepts. Now, the online degree or returning student only has to look to the web to find a multitude of textbooks, study guides and tutorials. No longer will they have to waste precious time and money on taking courses a second time, they can study at their own pace or study specific concepts as they encounter them in other courses.

Open Textbook Revolution

Sadly, mathematics is one of those fields where the core material does not change all that often but the textbook companies still are continually releasing "new editions". Would you believe that I found a pair of calculus textbooks from the same publisher but published decades apart that had virtually the same content? While I'm just a little speck in the whole that is the Internet, I hope my efforts in supporting the wonderful educators, who are fighting to end the madness that is textbook sales, will encourage them to offer more and more free, top-quality materials to math students.

 
 
Wallace C. Boyden, 1895. This algebra textbook explains concepts well and might make a good reference source. It has many great practice problems but without an answer key, this vintage math textbook might not be a good choice for self-study.

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Oliver E. Glenn, unknown but most likely early 1900s. From the preface, "The object of this book is, first, to present in a volume of medium size the fundamental principles and processes and a few of the multitudinous applications of invariant theory, with emphasis upon both the nonsymbolical and the symbolical method."

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Online abstract algebra textbook based upon the earlier works of Abstract Algebra by John A. Beachy and William D. Blair and Abstract Algebra II by John A. Beachy. This new text, offered by John A. Beachy, Professor Emeritus of Mathematical Sciences at Northern Illinois University, is offered for advanced undergraduate and graduate-level students. Chapter titles include: Integers, Functions, Groups, Polynomials, Rings, Fields, Structure of Groups, Galois Theory, Unique Factorization, Modules, Structure of Noncommutative Rings and Ideal Theory of Commutative Rings.

Last Verified: (Oct 12, 2011) Report Broken  Listing

 

 
Tom Judson, 2011. A full online abstract algebra text which includes a Chapter 0 that provides an overview of the prerequisite mathematical knowledge needed to successfully complete a course utilizing this text. The author has provided the solutions to the chapter exercises making this free online textbook useful for self-study as well as instructor led study on the subject of abstract algebra. This textbook has been continually updated and has enough material to be used across at least two semesters.

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Professors Leonard Soicher and Franco Vivaldi of the School of Mathematical Sciences at Queen Mary, University of London have written this web book for the corresponding course MAS202 Algorithmic Mathematics. Students should have some exposure to discrete mathematics but do not need computing experience. Students will be introduced to basic algorithms for computing exactly with integers, polynomials and vector spaces which will teach them how to think algorithmically and be able to design and analyze algorithms. This online mathematics textbook will also provide a constructive approach to abstract mathematics with a focus on algebra. In their introduction of the elements of ring and field theory, the authors will show how algorithms offer concrete tools, constructive proofs and a crisp environment where the benefits of rigor and abstraction become tangible.

Last Verified: (Oct 10, 2011) Report Broken  Listing

 
 
William Elwood Byerly, 1893. Another great vintage math textbook from Gutenberg. This math text is full of well-explained examples. Despite the age, this text uses plain language to explain terms and would probably make a great supplement to a more modern text on the same subject.

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This open source pre-calculus textbook has nine chapters on college algebra.

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George Cain, 2001. This textbook has been utilized at SUNY Binghamton, Clifornia State University Dominguez Hills, Drexel University as well as Georgia Tech where the author is a professor.

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Written by Ruslan Sharipov, this online differential geometry textbook is available in PDF, PostScript and other formats. Classified as a introductory course, the text covers topics such as curves in 3-D space, finding the length of curves, Frenet frames and torsion, vector and tensor notations and changed of coordinates.

Last Verified: (Oct 9, 2011) Report Broken  Listing

 
 
David E. Joyce, Professor of Mathematics and Computer Science at Clark University has written this online complex numbers textbook for a general audience. It assumes a basic knowledge of ordinary real numbers and algebra. The text covers nine topics: Quadratic and cubic equations; fundamental theorem of algebra; the number i; the complex plane, addition and subtraction; absolute value; multiplication; angles and polar coordinates; reciprocals, conjugation and division; and powers and roots.

Last Verified: (Oct 13, 2011) Report Broken  Listing