OER Textbooks | Mathematics

One of the most common complaints from faculty about using OER materials is that they don’t know how to find materials.  I’ve started to link resources and created a list of OER Textbooks organized by academic discipline.


Beginning Algebra

This textbook is housed on the oddly named Lardbucket.org and was developed by a professional publishing company.


Beginning Statistics

This textbook is housed on the oddly named Lardbucket.org and was developed by a professional publishing company.


Advanced Algebra

This textbook is housed on the oddly named Lardbucket.org and was developed by a professional publishing company.


A First Course in Linear Algebra

A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite.  Housed on the  University of Minnesota Center for Open Education site.



A Computational Introduction to Number Theory and Algebra

This text is an introduction to number theory and abstract algebra; based on its presentation, it appears appropriate for students coming from computer science.  It is available as a PDF file, and is housed at the  University of Minnesota Center for Open Education site.


A First Course in Linear Algebra

Ken Kuttler, Brigham Young University

The book is sufficiently comprehensive for its purpose as a first course in the subject. The row reduced echelon form and its many consequences and applications are covered well in the first several chapters.   Available as a PDF file from the  University of Minnesota Center for Open Education site.


A Gentle Introduction to the Art of Mathematics

Joseph Fields, Southern Connecticut State University

This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction.  Available as a PDF file from the  University of Minnesota Center for Open Education site.


Abstract Algebra: Theory and Applications

Thomas W. Judson, Stephen F. Austin State University

This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Available as a PDF file from the  University of Minnesota Center for Open Education site.


Active Calculus 2.0

David Austin, Grand Valley State University
Matt Boelkins, Grand Valley State University
Steve Schlicker, Grand Valley State University

Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF.  Available as a PDF file from the  University of Minnesota Center for Open Education site.


Active Calculus Multivariable

Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format.  Available as a PDF file from the  University of Minnesota Center for Open Education site.


Advanced High School Statistics First Edition

Christopher Barr, Varadero Capital
David Diez, Google/YouTube
Mine Çetinkaya-Rundel, Duke University

Advanced High School Statistics is ready for use with the AP® Statistics Course.  Available as a PDF file from the  University of Minnesota Center for Open Education site.


Algebra and Trigonometry

Multiple Authors, Openstax College

Algebra and Trigonometry provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra & Trigonometry course.  Available in PDF and HTML versions.


APEX Calculus

Brian Heinold, Mount St. Mary’s University
Dimplekumar Chalishajar, Virginia Military Institute
Gregory Hartman, Virginia Military Institute
Troy Siemers, Virginia Military Institute

APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).  available in PDF and print formats.


Applied Combinatorics

Mitchel T. Keller, Washington and Lee University
William T. Trotter, Georgia Institute of Technology

Applied Combinatorics is an open-source textbook for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). There are also chapters introducing discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other nuggets of discrete mathematics.  Available in PDF, HTML, and Print formats.


Applied Discrete Structures

Alan Doerr, University of Massachusetts Lowell
Kenneth Levasseur, University of Massachusetts Lowell

The text is divided into lecture-length sections, facilitating the organization of an instructor’s presentation.Topics are presented in such a way that students’ understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words.  Available in HTML, PDF, and Print formats.


Applied Finite Mathematics

Rupinder Sekhon, De Anza College Cupertino, CA, United States

Applied Finite Mathematics covers topics including linear equations, matrices, linear programming, the mathematics of finance, sets and counting, probability, Markov chains, and game theory.


Applied Probability

Paul Pfeiffer, Rice University

In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user defined MATLAB procedures and functions (which we refer to as m-programs, or simply programs) to solve many important problems in basic probability. This should make the work useful as a stand alone exposition as well as a supplement to any of several current textbooks.  Available in PDF and EPUB formats.


Basic Analysis: Introduction to Real Analysis

Jirí Lebl, Oklahoma State University

This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course.  Available in PDF and Print formats.


Book of Proof

Dr. Richard Hammack, Virginia Commonwealth University

Book of Proof is an introduction to the language and methods of mathematical proofs. The text is meant to bridge the computational courses that students typically encounter in their first years of college (such as calculus or differential equations) to more theoretical, proof-based courses such as topology, analysis and abstract algebra. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.  Available in PDF and Print formats.


Calculus

Gilbert Strang, MIT

Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a straightforward introductory calculus textbook available free online to educators and self-learners alike. It is covers single variable and multivariable calculus, including applications.  Available in PDF and Print formats.


Calculus for the Life Sciences: A Modeling Approach Volume 1

James L. Cornette, Iowa State University
Ralph A. Ackerman, Iowa State University

This text is a product of a two-semester calculus course for life sciences students in which students gathered biological data in a laboratory setting that was used to motivate the concepts of calculus.  The book contains data from experiments, but does not require that students do laboratory experiments.  Available in PDF and EPUB formats.


Calculus for the Life Sciences: A Modeling Approach Volume 2

James L. Cornette, Iowa State University
Ralph A. Ackerman

This text is a product of a two-semester calculus course for life sciences students in which students gathered biological data in a laboratory setting that was used to motivate the concepts of calculus.  The book contains data from experiments, but does not require that students do laboratory experiments.


Calculus One

Multiple Authors, Mooculus

This text is based on David Guichard’s open-source calculus text which in turn is a modification and expansion of notes written by Neal Koblitz at the University of Washington.  Available in PDF format.


Calculus Volume 1

Edwin Herman, University of Wisconsin-Stevens Point
Gilbert Strang, MIT

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning.

Calculus Volume 2

Gilbert Strang, Massachusetts Institute of Technology

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them.

Calculus Volume 3

Gilbert Strang, Massachusetts Institute of Technology

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them.  This series is available in HTML and PDF formats.


Calculus: Early Transcendentals

David Guichard, Whitman College

Calculus: Early Transcendentals, originally by D. Guichard, has been redesigned by the Lyryx editorial team. Substantial portions of the content, examples, and diagrams have been redeveloped, with additional contributions provided by experienced and practicing instructors. This approachable text provides a comprehensive understanding of the necessary techniques and concepts of the typical Calculus course sequence, and is suitable for the standard Calculus I, II and III courses.  Available in PDF format.


Collaborative Statistics

Barbara Illowsky, De Anza College
Susan Dean, De Anza College

Collaborative Statistics was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it.


College Algebra

Dr. Carl Stitz, Lakeland Community College
Dr. Jeff Zeager, Lorain County Community College

College Algebra is an introductory text for a college algebra survey course.  The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as “Functions First,” believing introducing functions first will help students understand new concepts more completely.


College Algebra

Multiple Authors , Openstax College

College Algebra provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra course.  Available in HTML and PDF formats.


College Trigonometry

Carl Stitz, Lakeland Community College
Jeff Zeager, Lorain County Community College

Available in HTML and PDF formats.


Combinatorics Through Guided Discovery

Kenneth P. Bogart, Dartmouth College

This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Available in PDF format.


Discrete Mathematics: An Open Introduction

Oscar Levin, University of Northern Colorado

Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach.


Elementary Algebra

John Redden, College of the Sequoias

Elementary Algebra, is an introductory text that focuses on the study of algebra at the beginning stages.  It assumes no prior algebraic experience and is intended for any student who needs build a strong algebraic foundation.  The book presents real world applications, setting a foundation for students to translate problems described in words into mathematical equations. The book illustrates the steps required to solve equations and interpret the results through the use of exercise sets and practice problems. The book stresses both the importance to solve problems correctly, and to learn to communicate those solutions to others.  Available in HTML and PDF formats.


Elementary Algebra

Denny Burzynski, College of Southern Nevada
Wade Ellis, West Valley Community College

Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. Use of this book will help the student develop the insight and intuition necessary to master algebraic techniques and manipulative skills.  Available in PDF and EPUB formats.


Elementary Algebra

Lynn Marecek, Santa Ana College
MaryAnne Anthony-Smith, Santa Ana College

Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course.  Available in HTML and PDF formats.


Elementary College Geometry

Henry Africk, New York City College of Technology

This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra.


Elementary Differential Equations with Boundary Value Problems

William F. Trench, Trinity University

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.


Fundamentals of Mathematics

Denny Burzynski, College of Southern Nevada
Wade Ellis, West Valley Community College

Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra.


How We Got from There to Here: A Story of Real Analysis

Eugene Boman, The Pennsylvania State University
Robert Rogers, State University of New York

This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context.


Intermediate Algebra

John Redden, College of the Sequoias

Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Intermediate Algebra, is the second part. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study in applications found in most disciplines.


Intermediate Algebra

Lynn Marecek, Santa Ana College

Intermediate Algebra is designed to meet the scope and sequence requirements of a one-semester Intermediate algebra course.


Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students

Jason Lachniet, Wytheville Community College

This guide is heavy on linear algebra and makes a good supplement to a linear algebra textbook. But, it is assumed that any college student studying linear algebra will also be studying calculus and differential equations, maybe statistics. Therefore it makes sense to apply the Octave skills learned for linear algebra to these subjects as well. Chapters 3 and 5 have several applications to calculus, differential equations, and statistics. The overarching objective is to enhance our understanding of calculus and linear algebra using Octave as a tool for computations. For the most part, we will not address issues of accuracy and round-off error in machine arithmetic. For more details about numerical issues, refer to [1], which also contains many useful Octave examples.


Introduction to Mathematical Analysis I – Second Edition

Beatriz Lafferriere, Portland State University
Gerardo Lafferriere, Portland State University
Mau Nam Nguyen, Portland State University

Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.


Introduction to Probability

Charles M. Grinstead, Swarthmore College
J. Laurie Snell, Dartmouth College

This text is designed for an introductory probability course taken by sophomores, juniors, and seniors in mathematics, the physical and social sciences, engineering, and computer science. It presents a thorough treatment of probability ideas and techniques necessary for a firm understanding of the subject. The text can be used in a variety of course lengths, levels, and areas of emphasis.


Introduction to Real Analysis

William F. Trench, Trinity University

This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course.


Introduction to Statistics

David Lane, Rice University

Introduction to Statistics is a resource for learning and teaching introductory statistics.


Introductory Business Statistics

Thomas K. Tiemann, Elon University

The book “Introductory Business Statistics” by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions.


Introductory Business Statistics

Barbara Illowsky, De Anza College
Lex Holmes, University of Oklahoma
Susan Dean, De Anza College

Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors. Core statistical concepts and skills have been augmented with practical business examples, scenarios, and exercises. The result is a meaningful understanding of the discipline, which will serve students in their business careers and real-world experiences.


Introductory Business Statistics with Interactive Spreadsheets – 1st Canadian Edition

Mohammad Mahbobi, Thompson Rivers University
Thomas K. Tiemann, Elon University

Introductory Business Statistics with Interactive Spreadsheets – 1st Canadian Edition is an adaptation of Thomas K. Tiemann’s book, Introductory Business Statistics. This new edition also allows readers to learn the basic and most commonly applied statistical techniques in business in an interactive way — when using the web version — through interactive Excel spreadsheets. All information has been revised to reflect Canadian content.


Introductory Statistics

Douglas S. Shafer, University of North Carolina
Zhiyi Zhang, University of North Carolina

Shafer and Zhang wrote Introductory Statistics by using their vast teaching experience to present a complete look at introductory statistics topics while keeping in mind a realistic expectation with respect to course duration and students’ maturity level.


Introductory Statistics

Multiple Authors, Openstax College

Introductory Statistics follows the scope and sequence of a one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering.


Introductory Statistics with Randomization and Simulation First Edition

Christopher Barr, Varadero Capital
David Diez, Google/YouTube
Mine Çetinkaya-Rundel, Duke University

We hope readers will take away three ideas from this book in addition to forming a foundation
of statistical thinking and methods.


Learning Statistics with R: A tutorial for psychology students and other beginners

Dr Danielle Navarro, University of New South Wales

Learning Statistics with R covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software.


Linear Algebra

Jim Hefferon, Saint Michael’s College

This text covers the standard material for a US undergraduate first course: linear systems and Gauss’s Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications.


Linear Algebra

Andrew K. Waldon, UC Davis
David Cherney, UC Davis
Tom Denton, The Fields Institute and York University

This book is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors.


Linear Algebra with Applications

W. Keith Nicholson, University of Calgary

Overall, the aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work.


Linear Algebra, Theory And Applications

Kenneth Kuttler, Bringham Young University

This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however.


Linear Regression Using R: An Introduction to Data Modeling

David J. Lilja, University of Minnesota

Linear Regression Using R: An Introduction to Data Modeling presents one of the fundamental data modeling techniques in an informal tutorial style.


Math in Society

David Lippman, Pierce College

Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors.


Mathematical Reasoning: Writing and Proof, Version 2.1

Ted Sundstrom, Grand Valley State University

Mathematical Reasoning: Writing and Proof is designed to be a text for the ?rst course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics.


My Math GPS: Elementary Algebra Guided Problem Solving (2016 Edition)

Jonathan Cornick, Queensborough Community College
Karan Puri
Michael Guy, Queensborough Community College

My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE).


Notes on Diffy Qs: Differential Equations for Engineers

Jirí Lebl, Oklahoma State University

A one semester first course on differential equations, aimed at engineering students.


Open Logic Project

Andrew Arana, University of Paris
Audrey Yap, University of Victoria
Gillian Russell, University of North Carolina
Jeremy Avigad, Carnegie Mellon University
Nicole Wyatt, University of Calgary
Richard Zach, University of Calgary
Walter Dean, University of Warwick

The Open Logic Project is a collection of teaching materials on mathematical logic aimed at a non-mathematical audience, intended for use in advanced logic courses as taught in many philosophy departments.


OpenIntro Statistics

Christopher D. Barr, Harvard School of Public Health
David M. Diez, Harvard School of Public Health
Mine Cetinkaya-Rundel, Duke University

OpenIntro Statistics 3rd Edition strives to be a complete introductory textbook of the highest caliber. Its core derives from the classic notions of statistics education and is extended by recent innovations. The textbook meets high quality standards and has been used at Princeton, Vanderbilt, UMass Amherst, and many other schools. We look forward to expanding the reach of the project and working with teachers from all colleges and schools.


Ordinary Differential Equations

Stephen Wiggins, University of Bristol

This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take.


Prealgebra

Multiple Authors, Openstax College

Prealgebra is a textbook for a one-semester course that serves as a bridge between arithmetic and algebra. It can be used in courses named “Basic Mathematics,” “Introductory Algebra,” “Fundamentals of Algebra,” and so on. The organization makes it easy to adapt the book to suit a variety of course syllabi.


Precalculus

Carl Stitz, Lakeland Community College
Jeff Zeager, Lorain County Community College

A casual glance through the Table of Contents of most of the major publishers’ College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled “Functions First.” To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic “equations first, then the Cartesian Plane and THEN functions” approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class.


Precalculus

Multiple Authors, Openstax College

Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course.


Precalculus

Holly Carley, NYC College of Technology
Thomas Tradler, NYC College of Technology

These are notes for a course in precalculus, as it is taught at New York City College of Technology – CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems.


Precalculus: An Investigation of Functions

David Lippman, Pierce College
Melonie Rasmussen, Pierce College

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry.


Principles of Business Statistics

This textbook provides a brief introduction to the field of statistics, including examples of how these topics shows up in a variety of real-life examples.


Proofs and Concepts: The Fundamentals of Abstract Mathematics

Dave Witte Morris, University of Lethbridge
Joy Morris, University of Lethbridge

This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics.


Single Variable Calculus I: Early Transcendentals

David Guichard, Whitman College

The original version of the text was written by David Guichard. The single variable material is a modification and expansion of notes written by Neal Koblitz at the University of Washington, who generously gave permission to use, modify, and distribute his work. New material has been added, and old material has been modified, so some portions now bear little resemblance to the original.


Statistical Inference For Everyone

Brian Blais, Bryant University

This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic.


Trigonometry

Steven Schlicker, Grand Valley State University
Ted Sundstrom, Grand Valley State University

This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them.


Vector Calculus

Michael Corral, Schoolcraft College

 This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.


Whitman Calculus

Dr David Guichard, Whitman College

An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available.


Yet Another Calculus Text

Dan Sloughter, Furman University

This book is an introduction to calculus based on the hyperreal number system.


 

 

Last Modified:  07/29/2018

 

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.