Written by Dan Sloughter, this real analysis online textbook has no formal prerequisites does suggest students have a strong foundation in calculus and other high mathematics.

# Free Mathematics Textbooks

There were two subjects where having a small collection of thrift store used textbooks aided in my success – high school biology and college calculus. I don’t know how I would have gotten through 4th semester calculus without those extra books.

Today’s math students are luckier. Many courses are now being taught from freely available online materials and free online mathematics textbooks. Even if you are not using an online mathematics textbook, the many included here on The Free Textbook list should provide extra help, should you need it.

## Math Refresher

Returning students have the added challenge of trying to remember material they may not have seen in years. In year’s past, that usually created the need to retake a course or pay for private tutoring. Now, the returning student or anyone needing a little extra practice can find numerous materials to learn from online. They can study at their own pace or pick and choose the topics they need to review.

I’ve included the table of contents for each of the free math textbooks featured on The Free Textbook List. Hopefully, that will make it easier to zero in on specific topics you may need to review.

## Open Textbook Revolution

Let’s face it, most mathematics topics are not being significantly changed by new theories or discoveries. For decades, publishers and educators force students to purchase new textbooks when they simply re-edited the same material. One of my assigned texts actually was a very close match for a text published decades earlier by the same publisher.

Some of the authors featured here on The Free Textbook List are finally living the dream of writing their own textbook. All of the authors are apparently embracing the Open Textbook Revolution. They are generously offering an ever-growing library of free learning materials to math students.

## About Mathematical Symbols

Mathematics, by it’s very nature uses many symbols. I’ve debated on using them or not within the tables of contents. Do I use “pi” or the symbol we all know as pi? And, how would that affect the search feature. For now, I’ve opted to primarily stick to straight text to make searching this site a bit easier. So, for example, x^{2} becomes x2 and you should search for pi rather than it’s symbol.

## Subcategories

## List of Free Mathematics Textbooks

### Algorithmic Mathematics

A mathematics textbook with a constructive approach to abstract mathematics with a focus on algebra. It also includes the elements of ring and field theory.

### An Elementary Treatise on Fourier’s Series and Spherical, Cylindrical, and Ellipsoidal Harmonics With Applications to Problems in Mathematical Physics

A vintage text on Gutenberg.org by Harvard University Professor William Elwood Byerly on Fourier’s Series and Harmonics.

### Arithmetic for College Readiness

Before students can begin their studies of calculus, the physical sciences, accounting or any other subject which requires advanced mathematics; they first must know basic arithmetic. This workbook was prepared by the department of Mathematics at Scottsdale Community College to help students prepare for university-level mathematics courses. The development team for the first edition, published […]

### Elementary Number Theory

Textbook on prime numbers, congruences, public-key cryptography, quadratic reciprocity, continued fractions, elliptic curves and number theory algorithms.

### Lie Algebras

A math professor from Harvard University, Shlomo Sternberg is offering his textbook on Lie Algebras in PDF form.

### Math In Society

Math in Society is a free online textbook that is designed for non-science and math majors. It covers a variety of topics, mostly in a non-algebraic way.

### Mathematical Reasoning: Writing and Proof

Mathematical Reasoning, a free online textbook on writing proofs with a study guide, answer key and even videos to aid learning.

### Mathematics for Business and Social Sciences

Post-algebra college-level mathematics textbook for business and social science majors that introduces concepts from finite mathematics, linear algebra, statistics, pre-calculus and other college topics in mathematics.

### The MacTutor History of Mathematics Archive

The School of Mathematics and Statistics at the University of St Andrews, has created a virtual history of mathematics with bios of famous mathematicians.