Note that books listed below are not necessarily the books currently in use for each course. This website lists free/open textbooks that could be used for each course, but this does not mean they have necessarily been adopted by the instructor. Please check your textbook lists for the most accurate information.
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Math courses for which we do not currently have an open textbook to recommend: Math 4310, Math 4500, Math 4505.
Introductory Statistics (OpenStax), by Illowsky and Dean
Statistical Inference
Open Intro Statistics, by Diez et al.
The OpenIntro Statistics book doesn't have a straightforward PDF download link. The link above takes you to a "purchase" page, but it's pay-what-you-want. For free access, set the slider to $0.
Introduction to Calculus: covers precalculus and basic differential calculus
The textbooks above are in PDF format, and haven't been recently updated. Additional resources, including some books in HTML format, can be found in the Precalculus Section.
Elementary Linear Algebra: vector geometry, systems of equations, matrices, matrix transformations, determinants, and eigenvalues and eigenvectors.
There are a couple of different open textbooks available for Math 1410. Which one is used varies from one term to the next, depending on who is teaching the course. One book is by Kenneth Kuttler, and provided provided by Lyryx Learning.
Lyryx also provides the textbook Linear Algebra with Applications, by Keith Nicholson. This text has sufficient content for both Math 1410 and Math 3410.
A First Course in Linear Algebra, by Kenneth Kuttler
Linear Algebra with Applications, by Keith Nicholson
There is also a textbook available in PDF, created by Sean Fitzpatrick. This book is based on the text Matrix Algebra, by Greg Hartman, using content from APEX Calculus. Both books can be found on the APEX Calculus website.
This book is available in both colour (for use as an e-book) and black and white (for printing).
Calculus for Management and Life Sciences
We are pleased to be able to host a copy of the textbook Business Calculus with Excel, by Mike May and Anneke Bart, of Saint Louis University. The book is available in both PDF and HTML formats.
A short introduction to the calculus offerings below. Everything is based on the APEX Calculus textbook by Greg Hartman. This is a free, high-quality calculus textbook, similar in format to a lot of the commercial books. It was originally written in the LaTeX typesetting language, as is commmon for math books.
A recent (and ongoing) project aims to convert the book to a new language called PreTeXt. The advantage of PreTeXt is that we can produce both HTML and PDF versions of the books. The HTML has better accessibility features, it works well even on phones, and it contains features like embedded videos.
Below you will find several options for each calculus book:
The HTML version.
A PDF version, based on PreTeXt source, both a colour e-book and a black and white print book.
A classic version, in PDF, based on the original LaTeX source.
Calculus I: limits, derivatives, curve sketching, related rates, optimization, differentials, Taylor polynomials, Riemann integration, Fundamental Theorem of Calculus.
Calculus II: techniques of integration, applications of integration, differential equations, parametric curves, and polar coordinates.
Calculus III: sequences and series, vectors, vector-valued functions, velocity and acceleration, introduction to functions of several variables, and partial derivatives.
Calculus IV: partial derivatives, multivariable chain rule, gradients and directional derivatives, local and global extrema, double and triple integrals, change of variables, vector calculus.
The material for the Accelerated Calculus stream is essentially the same as that for the regular Calculus stream. The primary difference is that the book is divided into three parts, instead of four, and there is some rearrangement of sections.
Also, the book for Accelerated Calculus does not include embedded videos. However, students who want to access this content can still find it on YouTube.
Note: Math 2575 is a newly created course, and it is not being offered in Fall 2020, due to insufficient enrolment, so we haven't yet created PDF textbooks for the course.
Calculus I: limits, derivatives, curve sketching, applications of derivatives, L'Hosptial's rule, Taylor polynomials, hyperbolic functions, Riemann integration, Fundamental Theorem of Calculus, numerical integration.
Calculus II: techniques of integration, applications of integration, differential equations, sequences and series, parametric curves, polar coordinates, introduction to functions of several variables.
Calculus III: vector geometry, vector-valued functions, differential and integral calculus of functions of several variables, vector geometry.
Mathematical Concepts (Introduction to Proofs): logic, sets, relations, functions, proof techniques, cardinality, congruence and modular arithmetic.
Professors Dave and Joy Morris have written a textbook called Proofs and Concepts for Math 2000. This book is provided below, along with links to two external open textbooks that have been used for the course.
Proofs and Concepts, by Dave and Joy Morris.
Mathematical Reasoning: Writing and Proof, by Ted Sundstrom.
Book of Proof, by Richard Hammack.
This is a course intended primarily for students in Education (or planning to enter Education) who are interested in elementary school teaching, and who would not otherwise take a mathematics course. The course explores numbers and arithmetic in a number of different contexts, including number systems from other cultures throughout history, modern algebraic axioms, fractions, congruence, and modular arithmetic.
We do not have our own book for this course, but there is a very good open resource: Mathematics for Elementary Teachers, by Michelle Manes.
Geometry: Introduction to classical geometry from the axiomatic point of view. Lines and affine planes. Separation, order, similarity, congruence. Isometries and their classification. Groups of symmetries. Projective, hyperbolic and inversive geometries.
This course was taught for a long time by Dennis Connolly, who has since retired. His notes are provided here as a resource, but are usually no longer used for the course. More recently, we have used the book The Four Pillars of Geometry, by John Stillwell. This is a Springer book. It's not an open resource, but it can be downloaded for free by U of L students, since it's included in our SpringerLink subscription. Students who are on the U of L campus network can get the book from link.springer.com.
Group and Ring Theory: Groups, abelian groups, subgroups, quotient groups. Homomorphism. Isomorphism theorems. Lagrange's theorem. Permutation groups. Sylow theorems. Commutative rings, subrings, ideals. Quotient rings and ideals. Polynomial rings.
Field Theory: Polynomial rings. Fields and field extensions, construction problems. Finite fields. Galois Theory. Fundamental Theorem of Algebra.
Linear Algebra: vector spaces, basis and dimention, linear transformations, orthogonality, eigenvalues and diagonalization, canonical forms.
Sean Fitzpatrick has written a set of lecture notes for Math 3410 in PreTeXt. These notes feature embedded code cells that allow students to perform computations using Python code. (Code provided: no programming experience necessary!) These notes are based in part on the textbook by Keith Nicholson.
Lecture Notes for Math 3410, by Sean Fitzpatrick.
Linear Algebra, with Applications, by Keith Nicholson.
Elementary Number Theory: Division algorithm. Fundamental Theorem of Arithmetic. Euclidean Algorithm. Linear Diophantine equations. Congruences. Chinese Remainder Theorem. Quadratic reciprocity. Additional topics such as Pythagorean triples, Gaussian integers, sums of squares, continued fractions, arithmetic functions, or cryptography.
Number Theory: In Context and Interactive, by Karl-Dieter Crisman.
Rigorous treatment of the notions of calculus of a single variable, emphasizing epsilon-delta proofs. Completeness of the real numbers. Upper and lower limits. Continuity. Differentiability. Riemann integrability.
Basic Analysis: Introduction to Real Analysis, by Jiří Lebl.
Complex variables: Complex number system and complex plane. Analytic functions. Complex integration. Power series. Calculus of residues.
This textbook does not (yet) appear to cover calculus of residues, but it is free, online, and it has plenty of nice visual and interactive content. Complex Analysis: A Visual and Interactive Introduction, by Juan Carlos Ponce Campuzano.
A more traditional complex variables textbook, A First Course in Complex Analysis, by Beck, Marchesi, Pixton, and Sabalka, is available for free as a PDF.
Differential Equations I: First order ordinary differential equations. Second and higher order ordinary differential equations. Linear systems of ordinary differential equations. Qualitative theory of ordinary differential equations. Applications. Series solutions. Singular point expansions. Elementary linear difference equations.
Differential Equations II: Adjoints. Oscillation theory. Matrix methods. Matrix exponential functions. Sturm-Liouville theory. Orthonormal systems and Fourier series. Eigenfunction expansions. Laplace, Fourier and Mellin transforms. Convolutions. Convergence theory. Plancherel and Parseval formulae. Distributions. Solving PDEs using integral transforms. Fundamental solutions. Separation of variables. Heat, wave and Poisson equations. Harmonic functions.
There are two open, online textbooks on differential equations. The book Notes on Diffy Q's, by Jiří Lebl, covers most of the content in both differential equations courses. The Differential Equations Project, by Thomas Judson, covers most of the topics in Math 3600.
Joy Morris has written her own textbook on combinatorics, which is available for use in this course.
Page maintained by Sean Fitzpatrick. .