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This guide is a collection of Open Educational Resources across disciplines relevant to the Touro College community. A work-in-progress!

- Science ForwardFrom the site: "Science Forward is a new type of undergraduate science seminar, helping students to see science as a lens on the world, a way of approaching questions and challenges.

The course focuses on the critical thinking skills in use across the scientific disciplines, which we have summarized as the “science senses.” Starting with critical issues in the contemporary world, from climate change to the social and economic implications of artificial intelligence, the course encourages active learning and inquiry-based instruction." - Virtual Lab and Science Resource DirectoryFrom the site: "The BCcampus Open Education Virtual Lab and Science Resource Directory lists free science resources designed to support remote science education. This directory is updated as new resources are identified. Note that, while all resources in this directory are free, not all are open. Resources that carry Creative Commons or otherwise open licences are clearly labelled."

The peer-reviewed textbook below also provide ancillary resources such as PowerPoint slides, test banks, sample syllabus, etc.

Click on the book cover or the book title to access multiple formats of the textbook.

https://openstax.org/details/books/anatomy-and-physiology

Anatomy and Physiology is a dynamic textbook for the two-semester human anatomy and physiology course for life science and allied health majors. The book is organized by body system and covers standard scope and sequence requirements. Its lucid text, strategically constructed art, career features, and links to external learning tools address the critical teaching and learning challenges in the course. The web-based version of Anatomy and Physiology also features links to surgical videos, histology, and interactive diagrams.

- Human Anatomy and Physiology Preparatory Courseby Carlos Liachovitzky, Bronx Community College

The overall purpose of this preparatory course textbook is to help students familiarize with some terms and some basic concepts they will find later in the Human Anatomy and Physiology I course.The organization and functioning of the human organism generally is discussed in terms of different levels of increasing complexity, from the smallest building blocks to the entire body. This Anatomy and Physiology preparatory course covers the foundations on the chemical level, and a basic introduction to cellular level, organ level, and organ system levels. There is also an introduction to homeostasis at the beginning. - Introduction to Human OsteologyThis text was designed for use in the human osteology laboratory classroom. Bones are described to aid in identification of skeletonized remains in either an archaeological or forensic anthropology setting. Basic techniques for siding, aging, sexing, and stature estimation are described. Both images of bone and drawings are included which may be used for study purposes outside of the classroom. The text represents work that has been developed over more than 30 years by its various authors and is meant to present students with the basic analytical tools for the study of human osteology.
- UGA Anatomy and Physiology 1 Lab Manual, 2nd EditionThis lab manual was created for Anatomy and Physiology I at the University of Georgia. The manual contains the following labs:
- UGA Anatomy and Physiology 2 Lab Manual, 2nd EditionThis lab manual was created for Anatomy and Physiology II at the University of Georgia. The manual contains the following labs:
- Georgia Highlands Anatomy Video SeriesThis anatomy video series is released under a Creative Commons license, which allows its reuse.
- Anatomy and Physiology I & II (Open Course)This Open Course is an adaptation of OpenStax Anatomy and Physiology. The course includes quizzes, study guides, slide decks, recorded lectures and transcriptions, and a list of videos related to each module.

- Biology 2eBiology is designed to cover the scope and sequence requirements of a typical two-semester biology course for science majors. The text provides comprehensive coverage of foundational research and core biology concepts through an evolutionary lens. Biology includes rich features that engage students in scientific inquiry, highlight careers in the biological sciences, and offer everyday applications.
- MicrobiologyMicrobiology covers the scope and sequence requirements for a single-semester microbiology course for non-majors. The book presents the core concepts of microbiology with a focus on applications for careers in allied health. The pedagogical features of the text make the material interesting and accessible while maintaining the career-application focus and scientific rigor inherent in the subject matter.
- Concepts of BiologyConcepts of Biology is designed for the introductory biology course for nonmajors taught at most two- and four-year colleges. The scope, sequence, and level of the program are designed to match typical course syllabi in the market. Concepts of Biology includes interesting applications, features a rich art program, and conveys the major themes of biology.
- Biology II Laboratory ManualThis set of Biology II lab assignments ensures students have the opportunity to apply the concepts and information they learn as they work through Biology II course content.
- Biology I Laboratory ManualThese lab materials were developed by faculty at College of the Redwoods and Tidewater Community College
- Laboratory Exercises in Microbiology: Discovering the Unseen World Through Hands-On Investigationby Susan McLaughlin & Joan Petersen, Queensborough Community College

The exercises in this laboratory manual are designed to engage students in hand-on activities that reinforce their understanding of the microbial world. Topics covered include: staining and microscopy, metabolic testing, physical and chemical control of microorganisms, and immunology. The target audience is primarily students preparing for a career in the health sciences, however many of the topics would be appropriate for a general microbiology course as well. - Microbiology: A Laboratory Experienceby Holly Ahern

As a group of organisms that are too small to see and best known for being agents of disease and death, microbes are not always appreciated for the numerous supportive and positive contributions they make to the living world. Designed to support a course in microbiology, Microbiology: A Laboratory Experience permits a glimpse into both the good and the bad in the microscopic world. The laboratory experiences are designed to engage and support student interest in microbiology as a topic, field of study, and career. - General Biology 1 Lab Manual (BIO1101L)Material created by Jeremy Seto, CUNY New York City College of Technology
- Microbiology laboratory exercises, 3rd ed.NameKeddis, Ramaydalis (author); Rauschenbach, Ines (author)

Date Created 2020 - Microbiology for Allied Health Studentsby Molly Smith & Sara Selby

Microbiology for Allied Health Students is designed to cover the scope and sequence requirements for the single semester Microbiology course for non-majors and allied health students. The book presents the core concepts of microbiology with a focus on applications for careers in allied health. The pedagogical features of Microbiology for Allied Health Students make the material interesting and accessible to students while maintaining the career-application focus and scientific rigor inherent in the subject matter. - Basic Cell and Molecular Biology 3e: What We Know & How We Found Outby Gerald Bergtrom, University of Wisconsin, Milwaukee

A grasp of the logic and practice of science is essential to understand the rest of the world around us. To that end, the CMB3e iText (like earlier editions) remains focused on experimental support for what we know about cell and molecular biology, and on showing students the relationship of cell structure and function. Rather than trying to be a comprehensive reference book, CMB3e selectively details investigative questions, methods and experiments that lead to our understanding of cell biology. - Biofundamentals 2.0by Michael Klymkowsky, University of Colorado and Melanie Cooper, Michigan State University

Our goal is to present the key observations and unifying concepts upon which modern biology is based; it is not a survey of all biology! Once understood, these foundational observations and concepts should enable you to approach any biological process, from disease to kindness, from a scientific perspective. - Cells: Molecules and Mechanismsby Eric Wong

Yet another cell and molecular biology book? At the very least, you would think that if I was going to write a textbook, I should write one in an area that really needs one instead of a subject that already has multiple excellent and definitive books. So, why write this book, then? First, it's a course that I have enjoyed teaching for many years, so I am very familiar with what a student really needs to take away from this class within the time constraints of a semester. Second, because it is a course that many students take, there is a greater opportunity to make an impact on more students' pocketbooks than if I were to start off writing a book for a highly specialized upper- level course. And finally, it was fun to research and write, and can be revised easily for inclusion as part of our next textbook, High School Biology. - Environmental Biologyby Matthew Fisher

This open textbook covers the most salient environmental issues, from a biological perspective. The text is designed for an introductory-level college science course. Topics include the fundamentals of ecology, biodiversity, pollution, climate change, food production, and human population growth. - Laboratory Exercises in Microbiology: Discovering the Unseen World Through Hands-On Investigationby Susan McLaughlin & Joan Petersen, Queensborough Community College

The exercises in this laboratory manual are designed to engage students in hand-on activities that reinforce their understanding of the microbial world. Topics covered include: staining and microscopy, metabolic testing, physical and chemical control of microorganisms, and immunology. The target audience is primarily students preparing for a career in the health sciences, however many of the topics would be appropriate for a general microbiology course as well. - Designing Computational Biology Workflows with Perl - Part 1 & 2This manual guides the instructor to combine the partial files of the virtual machine image and construct sequencer.ova file. It is accompanied by the partial files of the virtual machine image.
- Fundamentals of Biology Research ProjectExercise created by Ana Lucia Fuentes and Maria Entezari, from CUNY LaGuardia Community College
- Biology: Inquiry-Based Learning AssignmentStudents perform a literature review on a biology topic, choose 2-3 papers published in scientific journals to discuss in their assignment, provide a final opinion on the topic, and some voluntarily present on their selected topic.

- Chemistry (OpenStax)Chemistry 2e is designed to meet the scope and sequence requirements of the two-semester general chemistry course. The textbook provides an important opportunity for students to learn the core concepts of chemistry and understand how those concepts apply to their lives and the world around them. The book also includes a number of innovative features, including interactive exercises and real-world applications, designed to enhance student learning.
- Chemistry: Atoms FirstChemistry: Atoms First 2e is a peer-reviewed, openly licensed introductory textbook produced through a collaborative publishing partnership between OpenStax and the University of Connecticut and UConn Undergraduate Student Government Association.

This text is an atoms-first adaptation of OpenStax Chemistry 2e. The intention of “atoms-first” involves a few basic principles: first, it introduces atomic and molecular structure much earlier than the traditional approach, and it threads these themes through subsequent chapters. - Organic Chemistry with a Biological Emphasis Volume ITim Soderberg, University of Minnesota, Morris

The traditional approach to teaching Organic Chemistry, taken by most of the textbooks that are currently available, is to focus primarily on the reactions of laboratory synthesis, with much less discussion - in the central chapters, at least - of biological molecules and reactions. This is despite the fact that, in many classrooms, a majority of students are majoring in Biology or Health Sciences rather than in Chemistry, and are presumably taking the course in order to learn about the chemistry that takes place in living things. - Organic Chemistry with a Biological Emphasis Volume IITim Soderberg, University of Minnesota, Morris
- Organic Chemistry Laboratory TechniquesIn this resource you will find theory and procedures on the main organic lab techniques (chromatography, crystallization, extraction, distillation) as well as general concepts on how to set up and heat apparatuses (see the Table of Contents tab for a more complete listing of topics).
- The Basics of General, Organic, and Biological ChemistryDavid Ball, Cleveland State University

John Hill, University of Wisconsin

Rhonda Scott, Southern Adventist University

The Basics of General, Organic, and Biological Chemistry by David W. Ball, John W. Hill, and Rhonda J. Scott is for the one-semester General, Organic and Biological Chemistry course. The authors designed this textbook from the ground up to meet the needs of a one-semester course. It is 20 chapters in length and approximately 350-400 pages; just the right breadth and depth for instructors to teach and students to grasp. - Analytical Chemistry 2.1David Harvey, DePauw University

As currently taught in the United States, introductory courses in analytical chemistry emphasize quantitative (and sometimes qualitative) methods of analysis along with a heavy dose of equilibrium chemistry. Analytical chemistry, however, is much more than a collection of analytical methods and an understanding of equilibrium chemistry; it is an approach to solving chemical problems. Although equilibrium chemistry and analytical methods are important, their coverage should not come at the expense of other equally important topics. - Chemistry of CookingSorangel Rodriguez-Velazquez, American University

People around the world are fascinated about the preparation of food for eating. There are countless cooking books, TV shows, celebrity chefs and kitchen gadgets that make cooking an enjoyable activity for everyone. The chemistry of cooking course seeks to understand the science behind our most popular meals by studying the behavior of atoms and molecules present in food. This book is intended to give students a basic understanding of the chemistry involved in cooking such as caramelization, Maillard reaction, acid-base reactions, catalysis, and fermentation. Students will be able to use chemistry language to describe the process of cooking, apply chemistry knowledge to solve questions related to food, and ultimately create their own recipes. - General Chemistry: Principles, Patterns, and ApplicationsBruce Averill, Strategic Energy Security Solutions

Patricia Eldredge, R.H. Hand, LLC

The overall goal of the authors with General Chemistry: Principles, Patterns, and Applications was to produce a text that introduces the students to the relevance and excitement of chemistry. - Introductory ChemistryDavid W. Ball of Cleveland State University brings his new survey of general chemistry text, Introductory Chemistry, to the market with a fresh theme that will be sure to hold student interest: "Chemistry is Everywhere." Introductory Chemistry is intended for a one-semester introductory or preparatory chemistry course. Throughout the chapters, David presents two features that reinforce the theme of the textbook, that chemistry is everywhere.
- CLUE: Chemistry, Life, The Universe & EverythingChemistry, Life the Universe and Everything (CLUE) is a transformed general chemistry curriculum, developed by an interdisciplinary team of a chemist and a molecular biologist, that aims to bring about evidence based change in general chemistry. The materials developed include a text (supplied free to students), lecture support materials, workshop/recitation activities, video mini-lectures, and formative and summative assessment materials.

- College PhysicsMultiple Authors, Openstax College

This introductory, algebra-based, two-semester college physics book is grounded with real-world examples, illustrations, and explanations to help students grasp key, fundamental physics concepts. This online, fully editable and customizable title includes learning objectives, concept questions, links to labs and simulations, and ample practice opportunities to solve traditional physics application problems. - University Physics Volume 1Jeff Sanny & Samuel Ling

University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result. - University Physics Volume 2Jeff Sanny & Samuel Ling

University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result. - Light and MatterBenjamin Crowell, Fullerton College

This is an introductory text intended for a one-year introductory course of the type typically taken by biology majors, or for AP Physics B. Algebra and trig are used, and there are optional calculus-based sections. - Mechanics and RelativityTimon Idema

In Mechanics and Relativity, the reader is taken on a tour through time and space. Starting from the basic axioms formulated by Newton and Einstein, the theory of motion at both the everyday and the highly relativistic level is developed without the need of prior knowledge. The relevant mathematics is provided in an appendix. The text contains various worked examples and a large number of original problems to help the reader develop an intuition for the physics. Applications covered in the book span a wide range of physical phenomena, including rocket motion, spinning tennis rackets and high-energy particle collisions. - Variational Principles in Classical Mechanics - Second EditionDouglas Cline, University of Rochester

Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th – 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering. - The Adventure of Physics - Vol. I: Fall, Flow, and HeatChristoph Schiller

This book is written for anybody who is curious about nature and motion. Curiosity about how people, animals, things, images and space move leads to many adventures. This volume presents the best of them in the domain of everyday life. - The Adventure of Physics - Vol. II: RelativityChristoph Schiller

This book is written for anybody who is curious about nature and motion. Curiosity about how people, animals, things, images and empty space move leads to many adven- tures. This volume presents the best of them in the domains of relativity and cosmology. In the study of motion – physics – special and general relativity form two important building blocks. - The Adventure of Physics - Vol. III: Light, Charges, and BrainsChristoph Schiller

This book is written for anybody who is curious about nature and motion. Curiosity about how people, animals, things, images and space move leads to many adventures. This volume presents the adventures one encounters when exploring everything electric. The story ranges from the weighing of electric current to the use of magnetic fields to heal bone fractures and up to the understanding of the human brain.

The American Institute of Mathematics (AIM) seeks to encourage the adoption of open source and open access mathematics textbooks. The AIM Editorial Board has developed evaluation criteria to identify the books that are suitable for use in traditional university courses. The Editorial Board maintains a list of Approved Textbooks which have been judged to meet these criteria.

All of the books below, organized by course title, have been judged to meet the evaluation criteria set by the AIM editorial board.

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. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable.

It is written in an informal, conversational style with a large number of interesting examples and exercises, so that a student learns to write proofs while working on engaging problems.

Algebra and Trigonometry (OpenStax)

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book meets the needs of a variety of courses.

*Algebra: Abstract and Concrete, by Frederick Goodman, *provides a thorough introduction to "modern'' or "abstract'' algebra at a level suitable for upper-level undergraduates and beginning graduate students. The book addresses the conventional topics: groups, rings, fields, and linear algebra, with symmetry as a unifying theme.

Important note: the author reserves all rights to this work. However, individual readers, classes or study groups may copy, store and print the work, in whole or in part, for their personal use. Any copy of this work, or any part of it, must include the title page with the author’s name and this copyright notice. No use or reproduction of this work for commercial purposes is permitted without the written permission of the author. This work may not be adapted or altered without the author’s written consent.

The content of this book is traditional for a first course in abstract algebra at the junior or senior level. It may be used for either one or two semesters. The exercises include both computational and theoretical and there are a number of applications. Hints or short answers are given to most problems but not fully written solutions.

Versión en español disponible aquí.

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. Due to the comprehensive nature of the material, this book is offered in three volumes for flexibility and efficiency.

Click on the volume number to see each textbook and its ancillary resources.

Volume 1 covers functions, limits, derivatives, and integration.

Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.

Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.

The book covers the standard material in a calculus course for science and engineering. The size of the book is such that an instructor does not have to skip sections in order to fit the material into the typical course schedule. The single variable material is contained in eleven chapters beginning with analytic geometry and ending with sequences and series. The multivariable material consists of five chapters and includes with the vector calculus of in two and three dimensions through the divergence theorem. The book ends with a final chapter on differential equations.

License: Creative Commons Attribution-NonCommercial-ShareAlike

Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore. Following key activities or examples, the presentation normally includes some overall perspective and a brief synopsis of general trends or properties, followed by formal statements of rules or theorems. While we often offer a plausibility argument for such results, rarely do we include formal proofs.

The peer-reviewed textbooks below also provide ancillary resources such as PowerPoint slides, test banks, sample syllabus, etc.

Click on the book cover to access multiple formats of the textbook.

Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives and includes worked examples that demonstrate problem-solving approaches in an accessible way.

Applied Combinatorics, by Mitchel T. Keller and William T. Trotter

*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 Instructor resources are available upon request.

A First Course in Complex Analysis

Matthias Beck, Gerald Marchesi, Dennis Pixton, and Lucas Sabalka

For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and this book reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated from scratch, which has the (maybe disadvantageous) consequence that power series are introduced late in the course. The goal our book works toward is the Residue Theorem, including some nontraditional applications from both continuous and discrete mathematics.

Important license note: Copyright 2002-2017 by the authors. All rights reserved. This book may be freely reproduced and distributed, provided that it is reproduced in its entirety from the most recent version. This book may not be altered in any way, except for changes in format required for printing or other distribution, without the permission of the authors.

A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence. This free online book (e-book in webspeak) should be usable as a stand-alone textbook or as a companion to a course using another book such as Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling or Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (section correspondence to these two is given).

License: This work is dual licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License and Creative Commons Attribution-Share Alike 4.0 License.

These texts are appropriate for a first course in differential equations for one or two semesters. There are more than 2000 exercises, and the student manual has solutions for most of the even numbered ones.

License: Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

This textbook contains the content of a two semester course in discrete structures, which is typically a second-year course for students in computer science or mathematics, but it does not have a calculus prerequisite. The material for the first semester is in chapters 1-10 and includes logic, set theory, functions, relations, recursion, graphs, trees, and elementary combinatorics. The second semester material in chapters 11-16 deals with algebraic structures: binary operations, groups, matrix algebra, Boolean algebra, monoids and automata, rings and fields.

This open source textbook is being used at the University of Northern Colorado in a discrete mathematics course taken primarily by math majors, many of whom plan to become secondary teachers. This text can also be used in a bridge course or introduction to proofs. The major topics are introduced with Investigate! activities designed to get students more actively involved and which are suitable for inquiry based learning.

*Discrete Mathematics: An Open Introduction* by Oscar Levin is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

From the preface:

Geometry with an Introduction to Cosmic Topology offers an introduction to non-Euclidean geometry through the lens of questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have an edge? Is it infinitely big? This text is intended for undergraduate mathematics and physics majors who have completed a multivariable calculus course and are ready for a course that practices the habits of thought needed in advanced courses of the undergraduate mathematics curriculum. The text is also particularly suited to independent study, with essays and other discussions complementing the mathematical content in several sections.

License: Copyright by author: all rights reserved; you can print copies for personal use.

Ted Sundstrom

Mathematical Reasoning: Writing and Proof is designed to be a text for the ﬁrst 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.

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Math in Society, by David Lippman

This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level quantitative literacy topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation.

This work is licensed under a Creative Commons Attribution-Share Alike 3.0 United States License.

Andrew M. Bruckner, Brian S. Thomson, Judith B. Bruckner

This is a book about mathematics appreciation via discovery, rather than about practical mathematics. It considers several problems that don't appear to be amenable to ordinary arithmetic, algebraic or geometric techniques. It then guides the reader through the process of discovering the solution to each problem, using creative methods and simple techniques that arise naturally. It also indicates how each solution leads to new questions, provides a bit of history of the problem, and discusses a few related problems of current interest that have not yet been solved.

From the American Institute of Mathematics:

This book is a well-organized text with carefully constructed examples, a full quota of exercises with solutions, and an emphasis that is algebraic rather than geometric. The book is Sage-enabled with approximately 90 examples of Sage code spread throughout. The book sections can be loaded into Sage as worksheets so that the code can be evaluated immediately; however, it is not necessary to use Sage in order to make use of this textbook.

License: Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the appendix entitled GNU Free Documentation License.

From the American Institute of Mathematics: "This book has the standard content of a course for science, math, and engineering students that follows calculus. A semester of calculus is the explicit prerequisite, but most students would have three semesters of calculus and for them some of the beginning sections of the book can be skipped. Each chapter ends with three or four applications of that chapter’s subject."

License: This book is licensed under both the GNU Free Documentation License and the Creative Commons Attribution-ShareAlike 2.5 License,

Sergei Treil

From the American Institute of Mathematics: "Brown University has two introductory linear algebra courses. This text is used in the honors course that emphasizes proofs. The book’s title suggests that it is not the typical approach to linear algebra even among those books that are more theoretical. For example, the concept of a basis is treated as more fundamental than the concept of linear independence, and linear transformations are introduced before solving systems of linear equations. Especially noteworthy is the motivation and development of determinants."

License: This book is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

A Friendly Introduction to Mathematical Logic, by Christopher C. Leary and Lars Kristiansen

At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary’s user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition’s treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel’s First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.

Print copies available on Lulu.com, IndiBound.com, and Amazon.com.

- Sage for Undergraduates, by Gregory Bard"This textbook serves admirably as an introduction for newcomers to Sage as well as a reference for those with some experience. It is written in an engaging and informal style and does an excellent job in explaining how Sage works. The book can be used profitably as an auxiliary text in any undergraduate mathematics class with a computational component, and it can be used in the mathematical software courses that are becoming more common, especially for math majors."

"This book was developed as the text for a first course in numerical analysis at Southern Connecticut State University as an open source alternative to a classic text such as Burden and Faires. The first five chapters make up the content of a semester course. The style is engaging and conversational. As the author writes in the preface: “Much of the material will be presented as if it were being told to a student during tea time at University, but with the benefit of careful planning.” The exercises are plentiful and well-designed, and many of them have extensive solutions."

- A Computational Introduction to Number Theory and Algebra"This books does not presuppose any previous background in number theory or algebra, but it quickly moves into material beyond the usual courses in math departments because of the emphasis on algorithms and computation. The chapter titles give an idea of the unusual flavor of this book, which has a number of topics that would be suitable for a senior level “advanced topics” course following a more traditional algebra or number theory course. The author writes that the book could “be used as a textbook in a graduate or upper-division undergraduate course on (computational) number theory and algebra, perhaps geared towards computer science students.”

Although this book is published commercially by Cambridge University Press, who has the exclusive right to distribute it in print form, the publisher has granted access to a free PDF version that individuals can download, use, and print." - Introduction to Probability, by Charles M. Grinstead and J. Laurie SnellThis book of about 500 pages has become a classic because of its engaging style, interesting examples, historical notes, pedagogical use of computer simulations, and more than 600 exercises. Thanks to the American Mathematical Society the book is freely available, although many readers will want to buy the hardcover edition from the AMS.

From the American Institute of Mathematics:

- The book is quite new but has already been used by a number of other faculty at other institutions who say that they recommend the book and would use it again. This book originated as lecture notes for the undergraduate analysis course at the University of Illinois in 2009, and so it follows the syllabus for that course based on the text of Bartle and Sherbert.

Using a clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. This book is intended for those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.

License: This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

From the author website:

- This award-winning text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material.

- How We Got from There to Here: A Story of Real AnalysisThis text for a semester course portrays real analysis in the context of its historical development. It is written in a direct style aimed at students and not instructors. A student using the book is guided to understand and prove much of the actual mathematical content through the more than 200 problems that are embedded within the narrative and not placed at the end of sections as in most textbooks. For a course taught in the inquiry based learning mode this book should work better than standard texts. On the other hand, with the instructor offering more guidance it should also work well with a more traditional classroom style.
- A ProblemText in Advanced CalculusThis text is designed for a year long real analysis course at the advanced undergraduate level. It is both a textbook and a well-structured problem set. It is carefully laid out so that nothing has to be relearned in the transition from real valued functions to vector valued functions. It can be used for self-study by an independent student or for review, and it provides an excellent background for the traditional graduate course in real analysis.
- Online Statistics Education: A Multimedia Course of StudyOnline Statistics: An Interactive Multimedia Course of Study is a resource for learning and teaching introductory statistics. It contains material presented in textbook format and as video presentations. This resource features interactive demonstrations and simulations, case studies, and an analysis lab.
- OpenIntro StatisticsOpenIntro Statistics offers a traditional introduction to statistics at the college level. This textbook is widely used at the college level and offers an exceptional and accessible introduction for students from community colleges to the Ivy League. The textbook has been thoroughly vetted with an estimated 20,000 students using it annually.
- SticiGuiThis is a highly engaging “textbook” that makes extensive use of the capability for interactive instruction with current software, computers, and the Internet. Although it requires an internet connection, the students need only an up-to-date browser (Firefox recommended) and so there is no need to buy or install any other software. The author has been developing the course material for more than 15 years, and it is both stable and reliable. It resides on a server in the Statistics Department at UC Berkeley and will be there for the foreseeable future.
- Applied Math and Science Education RepositoryAMSER is a portal of educational resources and services built specifically for use by those in Community and Technical Colleges but free for anyone to use. AMSER is funded by the National Science Foundation as part of the National Science Digital Library, and is being created by a team of project partners led by Internet Scout.

- Climate Toolkit: A Resource Manual for Science and ActionFrom the site: "The Climate Toolkit is a resource manual designed to help the reader navigate the complex and perplexing issue of climate change by providing tools and strategies to explore the underlying science. As such it contains a collection of activities that make use of readily available on-line resources developed by research groups and public agencies. These include web-based climate models, climate data archives, interactive atlases, policy papers, and “solution” catalogs. Unlike a standard textbook, it is designed to help readers do their own climate research and devise their own perspective rather than providing them with a script to assimilate and repeat."

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